Modeling Satellite District Heating and Cooling Networks by David Rulff A thesis submitted in conformity with the requirements for the degree of Masters of Applied Science Civil Engineering University of Toronto © Copyright by David Rulff 2011
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Modeling Satellite District Heating and Cooling Networks
by
David Rulff
A thesis submitted in conformity with the requirements
for the degree of Masters of Applied Science
Civil Engineering
University of Toronto
© Copyright by David Rulff 2011
ii
Modeling Satellite District Heating and Cooling Networks
David Rulff
Masters of Applied Science
Civil Engineering
University of Toronto
2011
Abstract
Satellite District Heating and Cooling (DHC) systems offer an alternative structure to
conventional, centralized DHC networks. Both use a piping network carrying steam or water to
connect disparate building heating and cooling loads together, providing a platform for
improving energy efficiency, reducing emissions, and incorporating alternative means of energy
generation. However, satellite DHC networks incorporate thermal production units that are
distributed amongst the buildings nodes, which offers greater operational flexibility and reduced
capital cost savings for applications using existing building stock. This study was focused on the
development of the methodology behind a comprehensive energy model that can assess the
practical and financial viability of satellite DHC network scenarios. A detailed scenario
application of the model demonstrated significant energy savings and investment potential.
Additionally, environmental assessment methods and alternative generation technology were
explored in supplementary studies of Deep Lake Water Cooling (DLWC) and building-scale
Combined Heat and Power (CHP).
iii
Acknowledgements
I would like to thank Enwave Energy Corporation for their support not only financially, but
through their contributions of knowledge, experience and time. In particular, I would like to
thank Graham Harding for all of the words of wisdom and useful direction he provided over the
course of the project.
I would also like to express my deep gratitude towards my supervisor, Professor Christopher
Kennedy, who was willing to take me on as a graduate student so soon before a new school
term, and who with great patience offered continual guidance and very pertinent advice through
every stage of my time spent at the University of Toronto - from preparing lecture notes, to
participating in conferences, to trying to wrap up a MASc thesis. Thank you Chris.
iv
Table of Contents
Abstract ................................................................................................................................................................ ii
Acknowledgements .............................................................................................................................................. iii
Table of Contents ................................................................................................................................................. iv
List of Tables ...................................................................................................................................................... viii
List of Figures ....................................................................................................................................................... ix
1. Introduction .................................................................................................................................................. 1
1.1 Background .......................................................................................................................................... 1
1.2 Motivation for an Alternative Approach to DHC .................................................................................... 3
1.3 Study Objectives ................................................................................................................................... 7
1.4 Model/Implementation ........................................................................................................................ 8
1.5 Literature Review ............................................................................................................................... 10
1.6 Structure of Study ............................................................................................................................... 17
2. LCA of DLWC ................................................................................................................................................ 20
2.1 Abstract .............................................................................................................................................. 20
2.2 Application to Satellite DHC System Study........................................................................................... 21
3. Satellite DHC Model - Components .............................................................................................................. 22
3.1 Introduction ....................................................................................................................................... 22
3.2 Demand/Load Profiles ........................................................................................................................ 22
3.2.1 Background .................................................................................................................................... 22
3.2.2 Approaches to Simulating Space Heating and Cooling Demands ...................................................... 23
3.2.3 Comprehensive simulation methods ............................................................................................... 24
3.2.4 Satellite Model Approach ............................................................................................................... 25
3.2.5 Demand Profile Characteristics ....................................................................................................... 26
3.2.6 Load profile aggregation & Load Diversity ....................................................................................... 30
3.3 Boiler/Chiller Performance modeling .................................................................................................. 33
3.3.1 Boiler Specifications ....................................................................................................................... 33
3.3.3 Chiller Specifications....................................................................................................................... 33
3.3.4 Basic Performance metrics ............................................................................................................. 36
3.3.5 Annual Performance Measures ....................................................................................................... 37
3.3.6 Establishing characteristic equations .............................................................................................. 40
3.3.7 Validation ....................................................................................................................................... 44
v
3.3.8 Implementation Parameters ........................................................................................................... 44
3.3.9 Special case handling ...................................................................................................................... 45
4. Satellite DHC Model - Operations Optimization ............................................................................................ 48
4.1 Introduction ....................................................................................................................................... 48
4.1.1 Defining the Optimization Problem ................................................................................................. 48
4.1.2 Literature Review ........................................................................................................................... 51
4.1.3 Heuristic Approach used in this study ............................................................................................. 52
4.2 Load Dispatch ..................................................................................................................................... 56
4.2.1 Performance Curves Revisited ........................................................................................................ 56
4.2.2 Optimization .................................................................................................................................. 60
4.3 Unit commitment ............................................................................................................................... 67
4.3.1 Introduction ................................................................................................................................... 67
4.3.2 The main stages of the unit commitment heuristic method............................................................. 69
4.3.3 Characterizing production equipment performance ........................................................................ 69
4.3.4 1-unit case...................................................................................................................................... 72
4.3.5 Generate independent m-unit solution sets .................................................................................... 73
4.3.6 Combine independent m-unit solution sets into a superset ............................................................. 75
4.3.7 Establish and then iteratively refine transition points between cases as superseded cases are
removed ...................................................................................................................................................... 76
4.3.8 Boiler version ................................................................................................................................. 78
4.4 Conclusions ........................................................................................................................................ 80
5. Satellite DHC Model - Network Analysis ....................................................................................................... 81
5.1 Introduction ....................................................................................................................................... 81
5.1.2 Savings Potential ............................................................................................................................ 81
5.1.2 Building Cluster .............................................................................................................................. 83
5.2 Thermal Energy Analysis ..................................................................................................................... 83
5.2.1 Thermodynamic Energy Balance ..................................................................................................... 83
5.2.2 Thermal Components ..................................................................................................................... 85
5.3 Hydraulic Energy Analysis ................................................................................................................... 89
5.3.1 Hydraulic Modeling ........................................................................................................................ 89
5.3.2 Layout ............................................................................................................................................ 89
5.3.3 Conservation Laws.......................................................................................................................... 91
5.3.4 Network Design Flows .................................................................................................................... 93
5.3.5 Pressure Losses .............................................................................................................................. 94
5.3.6 Pipe-sizing tool ............................................................................................................................... 95
vi
5.3.7 Pumping Requirements .................................................................................................................. 96
5.4 Thermal and Hydraulic Method Summary ........................................................................................... 98
5.5 Aggregate Energy Analysis .................................................................................................................. 99
5.6 Financial Analysis .............................................................................................................................. 101
5.6.1 Introduction ................................................................................................................................. 101
5.6.2 Initial Costs ................................................................................................................................... 102
5.6.3 Cash Flow Analysis ........................................................................................................................ 105
5.6.4 Financial Metrics .......................................................................................................................... 107
6. Scenario Analysis Results ........................................................................................................................... 111
6.1 Building Parameters.......................................................................................................................... 112
6.1.1 Basic Information ......................................................................................................................... 112
6.1.2 Building Demands......................................................................................................................... 113
6.1.3 Production Equipment .................................................................................................................. 116
6.2 Combined Operations Optimization .................................................................................................. 117
6.2.1 Production Schedules ................................................................................................................... 117
6.2.2 Production Performance (4-building case) .................................................................................... 119
6.3 Energy Analysis ................................................................................................................................. 121
6.3.1 Production Savings Details (4-building case).................................................................................. 121
6.3.2 Network Results (4-building case) ................................................................................................. 122
6.4 Financial Results ............................................................................................................................... 123
6.4.1 Cash Flow Analysis ........................................................................................................................ 123
6.5 Summary .......................................................................................................................................... 125
6.5.1 Heating ........................................................................................................................................ 125
6.5.2 Cooling ......................................................................................................................................... 127
6.5.3 Combined Satellite DHC Configuration .......................................................................................... 128
6.6 Conclusions ...................................................................................................................................... 130
7. Building-scale CHP Application ................................................................................................................... 131
7.1 Introduction ..................................................................................................................................... 131
7.2 First-Year Analysis............................................................................................................................. 131
7.2.1 Operating Costs and Potential Savings of the CHP System ............................................................. 131
7.2.2 Operating Procedure for the CHP System ...................................................................................... 133
7.2.3 Viability analysis of CHP systems (assessment of a specific scenario) ............................................. 135
7.2.4 High Level Parameters and Assumptions ....................................................................................... 137
7.3 Application to Scenarios (life-cycle analysis) ...................................................................................... 139
7.3.1 Impact of prices and escalation rates on year-to-year savings potential ........................................ 139
vii
7.3.2 Scenario Results ........................................................................................................................... 142
7.4 Conclusions ...................................................................................................................................... 146
7.5 Future Work ..................................................................................................................................... 147
8. Conclusions and Directions for Future Work............................................................................................... 148
8.1 Conclusions ...................................................................................................................................... 148
8.2 Directions for Future Work ............................................................................................................... 151
8.2.1 Conditions for Energy Savings ....................................................................................................... 151
8.2.2 Model Development ..................................................................................................................... 155
8.2.3 Satellite Systems in the Larger Context of Urban Energy Systems .................................................. 156
References ........................................................................................................................................................ 157
Appendix Material ............................................................................................................................................. 160
Appendix A .................................................................................................................................................... 161
Appendix B .................................................................................................................................................... 162
Appendix C .................................................................................................................................................... 163
Appendix D .................................................................................................................................................... 164
Appendix E .................................................................................................................................................... 165
Appendix F .................................................................................................................................................... 166
Appendix G.................................................................................................................................................... 167
Appendix H .................................................................................................................................................... 171
Appendix I ..................................................................................................................................................... 172
Appendix J ..................................................................................................................................................... 173
Appendix K .................................................................................................................................................... 175
viii
List of Tables
Table 1: Type assessment of available energy simulation tools (adapted from (Connolly, 2009)) .......................... 10
Table 2: Common chiller types and their typical capacities ................................................................................... 34
Table 3: ARI 550/590-98 standard testing conditions for determining IPLV (AHRI, 2003) ...................................... 39
Table 4: Default regression coefficients for production equipment functions (LBNL, 2009) ................................... 43
Table 5: Total number of possible combinations for sample of n-unit cases .......................................................... 50
Table 6: Production unit cost estimation coefficients (NRCan, 2011) .................................................................. 102
Table 7: Pump and motor cost estimate parameters .......................................................................................... 103
Table 8: ETS cost estimate parameters .............................................................................................................. 103
Table 9: Piping cost estimate parameters (NRC, 2002) ....................................................................................... 105
Table 10: Building and equipment information for scenario analysis .................................................................. 112
Table 11: Profile characteristics of independent buildings .................................................................................. 114
Table 12: The effective operating efficiencies of the independent buildings, base-case scenario ........................ 117
Table 13: Profile characteristics of the connected 4-building configuration ........................................................ 120
Table 14: Heating energy savings results of each independent building connected to the network, and the system
as a whole ......................................................................................................................................................... 121
Table 15: Cooling energy savings results of each independent building connected to the network, and the system
as a whole ......................................................................................................................................................... 121
Table 16: Heating network flows, line losses and piping characteristics .............................................................. 122
Table 17: Cooling network flows, line losses and piping characteristics .............................................................. 122
Table 18: Financial parameters .......................................................................................................................... 123
Table 19: Capital costs and first-year annual savings for 4-building scenarios ..................................................... 124
Table 20: Financial analysis results of 4-building scenarios over project life ........................................................ 125
Table 21: Heating scenario results summary and comparison for independent buildings, 2, 3, and 4-building cases
......................................................................................................................................................................... 125
Table 22: Cooling scenario results summary and comparison for independent buildings, 2, 3, and 4-building cases
......................................................................................................................................................................... 127
Table 23: Single-building scenario results for incorporating a selection of CHP units........................................... 145
ix
List of Figures
Figure 1: General effects on load profile of connecting two building systems together ........................................... 2
Figure 2: Illustrative comparison of conventional central DHC and satellite DHC configurations ............................. 4
Figure 3: A possible configuration for a distributed multi-generation (DMG) building node (adapted from (Chicco,
2007)) ................................................................................................................................................................... 6
Figure 4: Satellite DHC model method overview .................................................................................................. 18
Figure 5: Load Duration Curves representing the annual heating demands of 3 sample building archetypes ......... 27
Figure 6: Cooling load profiles for 3 building archetypes showing hourly loads with time for a 9 day period in
August 2010 ........................................................................................................................................................ 29
Figure 7: Random sample of hourly cooling loads vs. temperature (random sample from annual load profile data
for an example residential building) ..................................................................................................................... 30
Figure 8: Power curve for a constant speed drive chiller compared against equivalent VSD chillers with and
without condenser reset ..................................................................................................................................... 36
Figure 9: Boiler power curve adjustments taking into account low-load cycling strategies .................................... 47
Figure 10: A sample chiller power curve, highlighting Marginal Power and Performance measures ...................... 56
Figure 11: General unit commitment procedure .................................................................................................. 69
Figure 12: Example 1-unit chiller performance schedule ...................................................................................... 73
Figure 13: Operations optimization and production scheduling method breakdown ............................................ 80
Figure 14: Sample cumulative cooling demand bins for an independent 4-building case, along with corresponding
chiller COP .......................................................................................................................................................... 82
Figure 15: Sample cumulative cooling demand bins for an connected 4-building case, along with corresponding
chiller COP .......................................................................................................................................................... 82
Figure 16: Temperature profiles for either side of a counter-flow HX ................................................................... 86
Figure 17: Simplified Building node schematics showing different operating regimes ........................................... 90
Figure 18: General representation of an example satellite network ...................................................................... 91
Figure 19: High-level breakdown of the methods involved in analyzing the distribution network .......................... 98
Figure 20: High-level overview of the methods for aggregating energy results from hourly analyses .................... 99
Figure 21: High-level overview of methods for converting scenario energy results into cost estimates and financial
analysis ............................................................................................................................................................. 101
Figure 22: Basic site plan for scenario analysis ................................................................................................... 112
Figure 23: Load duration curves for heating demands of scenario buildings ....................................................... 113
Figure 24: Load duration curves for cooling demands of scenario buildings ........................................................ 113
Figure 25: The characteristic power and equivalent performance curves for the constituent boilers .................. 116
x
Figure 26: The characteristic power and equivalent performance curves for the constituent chillers .................. 116
Figure 27: Boiler schedules generated for the 2, 3, and 4-building combined scenarios ...................................... 117
Figure 28: Chiller schedules generated for the 2, 3, and 4-building combined scenarios ..................................... 118
Figure 29: The system heating load bins for the combined 4-building configuration, along with the corresponding
5-boiler schedule performance curve ................................................................................................................ 119
Figure 30: The system cooling load bins for the combined 4-building configuration, along with the corresponding
5-chiller schedule performance curve ................................................................................................................ 119
Figure 31: Cash flow diagram for 4-building heating scenario ............................................................................. 124
Figure 32: Cash flow diagram for 4-building cooling scenario ............................................................................. 124
Figure 33: Capital cost breakdown of 4-building heating, cooling and combined configurations ......................... 129
Figure 34: Boundary loading conditions for profitable operations of the 1000 kW CHP unit over base project life
......................................................................................................................................................................... 136
Figure 35: A detailed breakdown of the savings potential of a CHP application over the project life ................... 141
Figure 36: Load duration curves for 3 building archetypes compared to capacities of selected CHP units............ 142
Figure 37: Single-building 1000kW CHP scenarios - comparison of savings potential and building load bins ........ 143
Figure 38: Energy consumption breakdown for 1000 kW CHP scenarios ............................................................. 144
Figure 39: Individual building heating energy savings resulting from satellite DHC connection............................ 152
Figure 40: Individual building cooling energy savings resulting from satellite DHC connection ............................ 153
Figure 41: Changes in energy savings and performance resulting from consecutive addition of identical buildings
to a satellite DHC scenario ................................................................................................................................. 153
Figure 42: Impact of changes in fuel escalation rates on financial viability of example satellite DHC scenarios .... 154
Figure 43: Building savings associated with connecting to a satellite DH network, measured against initial
performance ..................................................................................................................................................... 155
Figure 44: Comparison of chiller power curves from different sources ............................................................... 162
1
Chapter 1 Introduction
1. Introduction
1.1 Background
District Heating and Cooling (DHC) refers to a strategy for supplying the space heating and
cooling requirements of a group of buildings by connecting their individual systems in a
combined configuration. The conventional application of this idea is to generate the thermal
energy potential at a central plant and distribute the energy amongst the buildings using a piping
network carrying water or steam.
Having a group of buildings with sufficient combined load density (high consumption and in
close to proximity to one another) and a diversity of load profiles (demands rise and fall with
time, and the individual patterns differ from one building to another) enables DHC
development. This is because the system load profile is formed from the combination of the
individual demands, and the conditions mentioned above result in smaller deviation from
average loading, a relative decrease in peak loading effects, and a relative improvement for low
loading conditions.
These effects are illustrated in Figure 1, which compares a pair of independent load profiles to
the combined profile of their equivalent connected configuration. It can be observed that the
combined peak is lower than the sum of the peaks (because they are not coincident). In fact, a
combined profile is in essence an “average” of the individual profiles with time, resulting in a
“smoothing” of peaks and troughs: a reduction in deviation from the mean.
2
Figure 1: General effects on load profile of connecting two building systems together
3
The energy savings potential of conventional DHC systems is largely framed around the
centralization of production capacity – allowing returns to scale on performance investments.
DH systems typically reduce fuel consumption by 10-20%, and DC systems tended to improve
system performance by 2-3 times over an equivalent cluster of independent buildings (Harvey,
2010). Conventional DHC projects involve constructing a central plant to supply the energy
potential to the distribution network. This allows production equipment to be selected to
especially suit to the expected system loads.
There are over 130 DHC installations across Canada, most of which are operated for clusters of
hospitals or on campuses, amounting to 27 million m2 of floor-space. In total, this accounts for
1.3% of all institutional, commercial, or residential floor-space in Canada (CDEA, 2009). This
can be contrasted against a major adopter of DH technology, Denmark, where heating provision
by such systems accounts for 50% of the potential market (the majority of which produce
electricity as a by-product)(CDEA, 2009). There is significant potential for further adoption of
DHC systems in Canada, particularly as the improvements in energy efficiency become more
attractive as fuel prices increase and concerns over greenhouse gas (GHG) emissions grow.
However, conventional systems are constrained by a number of factors.
1.2 Motivation for an Alternative Approach to DHC
Satellite DHC systems
The initial premise for this study was conceived with consideration of a problem identified by
the District Energy provider Enwave Energy (Harding, 2009). Cost-effective network growth is
vital to expanding the business of established DHC providers. However, there are often physical
constraints that limit the financial feasibility of adding new customers to the main network.
These include:
Distance: clusters of buildings with sufficient energy demand, density, and load
diversity may exist outside of the feasible reach of the existing distribution system;
4
Capacity: the current plant production capacity may be already fully utilized – potential
customers offering insufficient incentive to justify purchasing new capacity;
Compatibility: the distribution system may be unable to accommodate the specific
hydraulic and building system needs of the potential customers.
As the network grows and the most promising customers are absorbed into the system, these
factors cause a dampening effect on efforts for continued expansion, resulting in diminishing
returns that slow development.
There is potential here for an alternative, less conventional approach to system growth; one that
could be implemented to realize the load sharing potential of new customers while reducing
upfront capital requirements.
Essentially, the approach involves planting a small-scale seed network, independent of
established distribution lines; a “satellite” system that directly taps into the existing production
capacity in the buildings; a system that can be used as a hub for future development (Figure 2).
Figure 2: Illustrative comparison of conventional central DHC and satellite DHC configurations
5
Operating this system would involve coordinating the distributed generation potential of the
individual building plants to effectively supply a local piping network, satisfying the cumulative
demand of the connected customers. Future integration of alternative energy supplies, additional
capacity, or eventual connection to other networks (including integration into the main
centralized system) are all possible due to the distributed arrangement and reduction of sunk
costs that characterize the approach.
While such an approach may not be ideal for a new build (where centralizing production offers
increasing returns to scale, among other benefits), the goal of this approach is to realize the
energy savings potential of connecting the customers while avoiding the large capital
expenditures associated with distant connections and new production equipment.
Implications beyond an alternative growth strategy
Beyond economic considerations and growth potential for existing networks, investigation into
the concept of satellite DHC networks has the potential to contribute to a better understanding of
the principles and conditions underlying DHC energy savings at a more fundamental level.
By eliminating one confounding factor associated with the energy savings of DHC (new, large-
scale, high-performance production capacity), the other characteristics of DHC networks that
contribute to energy savings can be examined.
For existing building clusters, satellite network configurations offer the production savings
associated with combining demands and optimally allocating load to available production
equipment (at least as effectively as the base case, since the original equipment is still present on
site), without additional capital cost for constructing a central plant with new production
equipment.
Furthermore, satellite DHC networks offer benefits beyond direct energy savings. Combining
loads contributes to a more stable, less variable system dynamic that lends itself to adaptation of
alternative storage, production and distribution technology.
6
Satellite DHC configurations can also be considered among the even larger context of multi-
domain energy systems. “Distributed multi-generation” (DMG) offers a conceptual framework
for integrated energy systems (Chicco, 2007), where every building is a node in a larger energy
network, potentially able to produce, consume, store, or convert a variety of energy flows. An
adapted version of such a node is shown in Figure 3.
Figure 3: A possible configuration for a distributed multi-generation (DMG) building node (adapted from (Chicco, 2007))
Combined Heat and Power (CHP) or “cogeneration” is a concept that ties electricity production
together with the production of useful heat. It is commonly associated with large-scale DH
systems; however, small CHP units are becoming more economically viable (Harvey, 2006).
The application of the individual building model developed in this study to an investigation of
CHP potential was intended to highlight this connection (Section 7).
The distributed operations regime of satellite configurations make them particularly well-suited
for incorporating thermal energy storage, and distributed, alternative generation technology
7
(low-temperature or otherwise). This opens up the possibility for planning comprehensive future
adaptations to the existing system, or restructuring the network in case of changes in energy
markets. Therefore, incorporating CHP (among other alternative technologies) is a logical next
step from this work.
A final potential benefit of satellite networks is system robustness. The distributed structure of
the hydraulic and thermal energy components allows tighter control over sections of the
network. In case of catastrophic events (such as structural failure of a supply pipe or breakdown
of a primary production unit), the problem areas can be isolated, and the remaining nodes and
connections can operate within smaller island networks (or even independently).
Examination of system robustness or versatility could be accomplished using some form of
failure-mode analysis, but this is beyond the scope of the current study.
In summary, satellite DHC configurations have the potential to be:
less costly up front than conventional approaches, but not incompatible,
specifically suited for fitting in with existing building stock,
more resilient from an operational perspective [isolation, scheduling, islands, new gens,
etc.]
more readily adaptable to evolving technology and changing fuel markets
1.3 Study Objectives
The motivation behind this study is to create a framework for analyzing satellite DHC systems.
Rather than narrowing in on a specialized system configuration, this involves removing some of
the constraints on conventional modeling approaches – creating a more generalized framework,
for which a centralized configuration would be a subset.
Primary study objective:
To apply thorough research into DHC modeling approaches and rigorous engineering
analysis to develop a comprehensive energy and financial model capable of accurately
8
comparing satellite DHC configurations to their equivalent base cases of unconnected
buildings.
1.4 Model/Implementation
“A really good model should introduce the minimum amount of complexity while capturing the
essence of the relevant physics” -G.I. Taylor (referenced in Karney et. al., 2006)
There is a fundamental tension between accuracy and detail in energy modeling. This study
attempts to find balance by drawing on existing literature and introducing complexity only when
it would either reveal some aspect important to fulfilling the objectives, or when the reliability
of the results depends on it.
Drawn from the primary objective of this study, the specific needs of the model can be
ascertained:
The model must accurately assess the mechanisms of useful energy consumption,
production and loss that differentiate the base case (a group of independent buildings)
from the connected configuration (an equivalent satellite configuration, using the
existing production equipment).
This highlights the need for an accurate estimation of the production savings resulting from
optimized operation as a DHC system. It also implies that the effects of auxiliary systems are a
lower priority if the changes between cases are relatively small or based on extraneous
variables. For these components, assumptions that simplify computation are often used.
This is supplemented by additional modeling considerations based on availability of an Enwave
database of actual customer profile data.
It is these modeling needs and constraints that help establish the scope of the model, and the
level of detail required for each component. Additionally, they represent a set of metrics which
can be used to assess existing tools and methods for their potential applicability.
9
In a model of this scope, a large number of assumptions are necessary and it is vital to the
accuracy and usefulness of the results that these assumptions are reliable. Discussion of major
assumptions will be a component of each section in the following study.
One approach to mitigating some of the error introduced by the large number of assumptions is
to allow custom values to be used for most parameters, as more case-specific information
becomes available.
The level of discretization used in this model was selected to capture the diurnal variations in
demands (changes within a day, including peak daily loads and specific occupancy
irregularities), while simplifying the operational considerations associated with the propagation
of temperature and pressure changes through the network. A one hour discretization effectively
allows thermal and hydraulic variations to be modeled at a steady-state, which should not
compromise the overall energy analysis (Bøhm, 2002).
The model application was largely developed as research into the methods and concepts
progressed. The initial version of the model was a simplified 2-building, 2-unit case. The simple
model was later transformed into a 1-building, 2-unit version for use in generating individual
building node information in the expanded multi-building version. Implementation in this
context favoured low-level versatility and ease of adaptation, which is why the current version
of the model uses Microsoft Excel as a platform (with some Visual Basic for Applications
programming when necessary).
The scope of the current study suited this approach; however, the model structure was
deliberately designed with modular, class-oriented methods that could be implemented in an
environment more conducive to high-level flexibility (for defining and relating the method
modules), computational efficiency (particularly useful for batch processing used in sensitivity
and statistical analysis), and mathematical robustness (particularly for handling large, multi-
dimensional matrix algebra).
10
1.5 Literature Review
To examine the state of the art in energy simulation, and determine the applicability of available
tools, three industry organizations (the International District Energy Association (IDEA), the
Canadian District Energy Association (CDEA) and the International Energy Agency (IEA))
were consulted at the 2011 IDEA conference in Toronto (IDEA, 2011). The general response
from industry was that an extensive array of field-specific tools were used in practice (both
freely available and proprietary), and that the complexity of the design and operations problems
inherent in the multidisciplinary analysis meant that research in the area was still very dynamic
and diverse. Essentially, there was no consensus on the best approach to any specific aspect of
DHC modeling, let alone on a comprehensive tool that encompassed them all.
”A review of computer tools for analysing the integration of renewable energy into various
energy systems” examined many of the software applications potentially suitable for this study
(Connolly, 2009). It also contained assessment metrics that proved useful when considering
other programs not included in the study. While the focus of the study was towards high-level
implementation of general renewable energy projects, Table 1 shows a selection of some of the
most viable tools, indicating their fulfillment of a set of metrics, adapted and expanded upon
from those discussed by Connolly.
Table 1: Type assessment of available energy simulation tools (adapted from (Connolly, 2009))
Tool Type Adaptable Includes
Simulation Scenario Bottom-
up
Op.
optimiz.
Inv.
optimiz.
to external
data
dist. DHC
methods
EnergyPLAN Yes Yes Yes Yes Yes - Yes
energyPRO Yes Yes - Yes Yes Partly -
LEAP Yes Yes Yes - - - -
RETScreen - Yes Yes - Yes - -
TRNSYS16 Yes Yes Yes Yes Yes Yes Yes
TERMIS Yes Yes Yes Yes Partly - Yes
Simulink Yes Yes Yes Yes - Yes Partly
11
The types of energy tools referred to in Table 1 are:
Simulation tools provide operational simulation analysis of the an energy system (for
example, given hourly time-step loads).
Scenario tools assess and/or compare long-term scenarios, typically combining a series
of annual results.
Bottom-up tools examine specific technology and implementations, determining the
impact of low-level changes to the simulation
Operational optimization tools determine the optimal configurations and procedures
related to operating an energy system, with the goal of minimizing energy requirements
(often related to simulation tools).
Investment optimization tools determine the optimal selection, coordination and
configuration of components in energy projects, with the goal of minimizing costs and
maximizing financial returns (often related to scenario tools).
Two metrics left out from the study were for equilibrium and top-down types, because
they both relate to larger macroeconomic interactions and forecasts that are not directly
relevant to the current study.
Many of these comprehensive, self-contained tools offered components or methods that would
be useful for modeling district energy systems; however, they may be limited in other key
aspects specifically related to the objectives of this study. To reflect this, two further metrics
were included in Table 1, against which each tool was roughly measured:
Some of the tools were not designed to specifically handle district energy systems, and
lacked necessary methods or system components. Therefore, one additional metric was
“Includes distributed DHC methods”, which must also entail the ability to model
distributed (versus centralized) production.
Furthermore, the objective of this study depends on the ability to incorporate detailed
scenario information together with load-based performance functions, to accurately
determine the energy savings attributable to production sharing in a satellite DHC
system. The metric associated with this was labelled “Adaptability to external data”.
12
Discussion
Both RETScreen and LEAP offer high-level tools for analyzing a diverse array of energy
projects, however, they did not provide adequately detailed simulation capabilities for this study
(Connolly, 2009). RETScreen is a “Clean Energy Project Analysis” decision support tool
managed by Natural Resources Canada. It is freely available and accompanied by a large body
of supporting material which would prove useful for generating assumptions related to scenario
development (NRCan, 2011).
EnergyPLAN is an academic-based modeling tool for regional energy planning of all types
(hourly simulations, but with a focus on changes in prices and demands), developed since 1999
by the Sustainable Energy Planning Research Group at Aalborg University (Lund, 2011). The
production modeling simplifications inherent in the model (such as flat efficiency rates for
production equipment) make it inadequate for this study; however, it is also accompanied by a
significant body of freely available supporting material.
energyPRO, TERMIS, Simulink are proprietary simulation packages used in industry to model
DHC systems (Connolly, 2009). energyPRO is developed by EMD International as a
companion to their popular windPRO software. It is particularly suited for comprehensive
modeling of centralized co and tri-generation DHC projects. TERMIS is developed by 7T
Technologies, which operates out of Denmark and the UK. It focuses on comprehensive real-
time simulations of DHC systems, including operations optimization procedures. Simulink is a
multi-purpose, multi-domain simulation platform developed alongside Matlab by Mathworks. It
is more commonly used in other fields (signals, controls, etc.), but can be applied to DHC
network as well. The accessibility constraints on these tools prevented their use in this study.
TRNSYS is a “transient systems simulation program” that has been commercially available
since 1975 (TRNSYS, 2011). It has an open modular structure and open source code, which
permits the use of custom-built modules that can represent components of a novel network
design or unique performance characteristics. However, the focus on detailed, bottom-up
modeling makes it more suited for detailed analysis of specific case-studies, rather than general
13
concepts (such as “satellite DHC networks”). It also has accessibility constraints, though
information from individual modules can be used to validate methods used in this study.
Other tools included in the paper by Connolly were excluded if they were difficult to gain access
to (proprietary and/or limited-distribution), or did not seem to adequately assess the heating and
cooling sector.
Some of the programs provide means to enter in custom profile and performance data, or to
interface with other software. This leads to another possible model structure, which is to
integrate a selection of specialized tools into a high-level organization. Some particularly
relevant specialized areas are:
Buildings simulation tools could be used to generate demand profiles or simulate
independent buildings (eQuest, DOE-2.2, and PowerDOE, EnergyPlus, ESP-r,
HOT3000). Supporting material and open-source software could aid in development of
equipment performance functions.
Hydraulic simulation of piping networks is a vital component of the overall model,
and there are a number of specialized programs for this need (EPAnet, System
RORNET).
Stand-alone operations control and optimization tools are commonly part of custom-
designed proprietary software packages that would be difficult to gain access to (IDEA,
2011). Academic research in this area will be further discussed in Section 4 of this study.
However, the interfaces between software could often be cumbersome (if not incompatible), the
specialized tools might be too dependent on field-specific details irrelevant to the overall study,
and the overall organization could become unwieldy. Instead, it was determined that a modular
approach was best, and specialized tools should only be directly integrated when method
separation can be maintained. For many of the procedures, methods and routines that make up
the model super-structure, general approaches might be premised on field-specific programs and
research, but full development would draw from a variety of sources and be designed with the
objectives of the current study in mind.
14
DHC modeling approaches in literature
It is clear that many of the packaged tools lack either the functionality, the versatility or the
focus needed to answer the central modeling objectives of this study. However, there is also a
healthy body of research related to fundamental methods and custom modeling approaches
present in the field. While most do not consider distributed generation, they can be drawn upon
to help develop the model used in this study.
Comprehensive DHC modeling/IEA
The IEA organizes a District Heating and Cooling research programme every 3 years, collecting
contributions towards a particular objective or centered on a particular topic (IEA, 2011). There
have been 8 completed programmes (Annex I through VIII) since 1983, as well as Annex IX
(ongoing as of 2011) and Annex X (in the early stages as of 2011). Together, they offer a huge
body of information on and research into DHC and CHP.
An IEA Annex VI study “Simple Models for Operational Optimisation”, conducted by Benny
Bøhm et. al. (Bøhm, 2002), included a “state of the art” review of past work in high-level DHC
modeling (particularly related to the network optimization problem), and elaborated on a
particular dynamic modeling approach for forecasting the state of a DHC network based on
current conditions. Dynamic modeling involves determining system loads and corresponding
operating schemes. Dynamic models are typically used to help make operations decisions to
achieve the appropriate dynamic system response needed to accommodate changing conditions
in the network (loads, temperatures, equipment failure events, etc.).
The availability of full-year load profiles from Enwave databases meant that the model
developed for this study would not have to incorporate predictive methods linking consecutive
states to one another. As well, the focus on cumulative energy analysis meant that dynamic
response issues would not be necessary to the central modeling focus. Essentially, this allows
the system to be modeled in a quasi-steady state approach, ignoring the dynamic impacts of
hydraulic and temperature changes as they propagate throughout the system.
15
At a 1 hour discretization (suggested by Bøhm for non-predictive operational modeling
approaches) this study applies a “pseudo-dynamic” approach that assumes quasi-steady state
analysis for hydraulic modeling (Bøhm, 2002).
As further highlighted by Bøhm et al, a number of assumptions derive from this approach:
The supply temperature (Ts) is predetermined
The hydraulic regime of the DHC network is controlled by the critical point method
The dynamics of the network are disregarded
The task is to determined the start and stop of different heat production units and load
distribution among them
A paper conducted by Woods et al (Woods, 1999) for Annex V applies Simulink building
simulation and System RORNET network modeling software to investigate changes on system
performance due to changes in supply temperature, and financial implications for 3 different
locations (Toronto, London and Helsinki). The study simulated large, centralized districts using
a set of 16 “typical days” rather than hour-by-hour analysis. The generalizations for the plant
operations and operational modeling were not applicable for this current study; however the
paper found that even a 10°C variation in return temperature for DH systems led to less than 3%
deviation in energy results, implying that an assumption of all building plant operations being
roughly equivalent is reasonable for DH modeling.
A number of studies were designed to gather together industry knowledge and information
centered on specific aspects of DHC systems, such as hydraulic, operational, thermal
performance, cost and financial. Some particularly applicable works includes the Annex VI
“District Heating and Cooling Building Handbook” (Skagestad, 2002), the “District Cooling
Best Practice Guide” published with the IDEA (IDEA, 2008), and “The New District Energy:
Building Blocks for Sustainable Community Development” published by the CDEA (CDEA,
2008).
Analysis of and operating parameters specifically relating to chiller performance were the focus
of an Annex VIII collaboration with the IDEA (Thornton 2008) and a paper published with the
16
ASHRAE Journal (Hydeman, 2007). These were drawn upon for much of the performance
analysis and validation used in this study.
A paper by Söderman (Söderman, 2005) considered distributed generation in a heating network.
However, it sought to balance electricity and heating plant arrangements (developing a tool
called “DENSYS”), resolving the overall MILP optimization problem into periods of 1.5
months.
More relevant to this study was a pair of papers by Curti et al, titled “An environomic approach
for modeling and optimization of a district heating network based on centralized and
decentralized heat pumps, cogeneration and/or gas furnace” in two parts (“Methodology” and
“Application”)(Curti et al, 2000). The study includes a useful breakdown of the fundamental
optimization problem and discusses the benefits and drawbacks of decentralized (versus
centralized) heat pumps. However, the focus of the study is on incorporating environmental
penalty factors into the overall single-objective optimization problem (of designing a heating
network), while greatly simplifying the performance characteristics of the equipment.
The work by Curti was further built upon by Céline Weber for her PhD Thesis at the Swiss
Federal Institute of Technology Lausanne (Weber, 2008). For her work “Multi-objective design
and optimization of district energy systems including polygeneration energy conversion
technologies”, Weber develops a comprehensive DHC modeling tool called DESDOP. The tool
is implemented using the GAMS framework, applying its built-in Mized Integer Linear
Programming (MILP) optimiser.
The information contained in the thesis by Weber, and a follow-up application study (Weber &
Shaw, 2011), were very useful for the development of the model used in the current study.
However, the approach taken by DESDOP focuses on comparing different centralized layouts
and technology at a high-level, often simplifying performance functions that are vital for the
analysis in the model used for satellite configurations.
17
Application to the current study
The results of the literature review process provided a plethora of information and resources
applicable to modeling DHC networks, but very few considered distributed generation
technology in coordination with network connections. Those that did included it in a
supplementary role, with simplified analysis for more generalized scenario analyses.
In a practically sense, the final model structure of this study is analogous to the form of a
satellite DHC system itself, in that the information (process) flows of the various methods
(building node energy production and demand) interact only through an indirect exchange of
their specific inputs and outputs (indirect HX), allowing the larger model (network) to remain
modular and adaptable.
The details of the methodology, implementation and application of the model (the design and
operation of the flow conditions, control valves, thermodynamic processes, and other constituent
components of the system) comprise the focus of the following sections.
1.6 Structure of Study
LCA of DLWC
Before delving directly into the modeling approach for satellite DHC networks, a
complementary study was included that examines the life-cycle energy requirements and
environmental impacts (LCA) of the Deep Lake Water Cooling (DLWC) system in Toronto,
operated by Enwave Energy Corporation. The LCA study utilizes an hourly discretized analysis
method similar to that used in the satellite model, while also providing a comprehensive
assessment of the environmental impacts of the specific District Cooling implementation. The
novel characteristics of the energy production mechanisms, as well as the environmental
considerations are aspects that complement the satellite DHC study, and should be considered
for incorporation with further development of the model.
18
Model Approach (Chapters 3-5)
The satellite DHC model developed for this study is premised on the objectives and design
considerations discussed earlier in the Introduction. The modular structure of the methods and
sub-methods is reflected in the structure of this report (Figure 4).
Figure 4: Satellite DHC model method overview
Defining the Building Cluster: building load profiles (Chapter 3.2) and component
production equipment (Chapter 3.3) are selected and energy requirements of independent
systems are calculated on an hourly and annual basis
Production Scheduling: using the aggregate building information, an optimal
production schedule is generated for the connected satellite configuration, which can be
used to determine energy requirements for given combined system loads (Chapter 4)
Distribution Network Design: the network is laid out with appropriately sized pipelines
based on the relationships between the thermal and hydraulic elements (Chapter 5.2 and
5.3)
19
Energy Analysis: the production schedule and distribution network methods are applied
towards an hour-by-hour analysis of the building cluster, over the course of one year
(Chapter 5.4)
Financial Analysis: The energy results are converted into corresponding energy costs,
which are analyzed along with system design capital costs (associated with the network
design) to provide financial results for the scenario (Chapter 5.5)
Operations Optimization Method (Chapter 4)
A specific component of the larger satellite DHC model, the operations optimization problem
(involving production unit scheduling and operations optimization) is a particularly complex
and active field of research. The methods developed in this study draw from a diverse body of
academic literature, standard industry procedures, and from the fundamental mathematical
characteristics of the performance functions used in the model. The result is a novel heuristic
approach that provides effective solutions for the model, and could be used as a foundation for
further work on the problem.
Scenario Analysis (Chapter 6)
A representative building cluster was analyzed using the satellite DHC model, and the results
are used as an illustrative foundation for discussion of the factors and conditions that influence
energy savings potential and financial viability.
CHP Study (Chapter 7)
An application of the single-building version of the model developed for this study, the CHP
study was conducted as an exploratory extension of the idea of satellite DHC configurations
being part of larger, multi-domain energy systems.
20
Chapter 2 LCA of DLWC
2. LCA of DLWC
The LCA of DLWC was a report conducted in part for Enwave Energy Corporation, providing
valuable information on the environmental impact of their system using rigorous LCA methods.
The study involves hourly analysis of a centralized DC system that employs a novel method of
drawing cooling potential from the cold water of Lake Ontario for use in downtown Toronto,
Ontario. Detailed operations data for the DC system, a related boiler plant, and grid information
informed an exhaustive examination of the energy and corresponding environmental impacts of
the system, including inventory of local pollutants, GHG emissions, and possible thermal
degradation of the lake water.
The LCA of DLWC is attached as a self-contained report in Appendix K; however, the abstract
has been included below.
2.1 Abstract
Enwave Energy Corporation maintains a district Deep Lake Water Cooling (DLWC) system for
the downtown Toronto core. While it is generally accepted that DLWC requires significantly
less energy to operate than an equivalent conventional configuration, more segmented analysis
of operation modes and process flows in the system would yield more specific results. This
study involved the development of a comprehensive life cycle inventory (LCI) of the DLWC
system that includes emissions, wastes, and resource use. To address concerns unique to the
DLWC system, heat gain effects on the lake and on the local atmosphere were also included.
The data collected on operations and utilities were in disaggregated daily and hourly bases,
facilitating the analysis of differing operational modes for different loads. This is vital to
understanding air-conditioning systems, as cooling load profiles are characterized by huge
spikes in demand at intermittent periods, which in turn affects marginal electricity generation
and system robustness. A conventional configuration of individual building systems was used a
21
baseline for comparison. DLWC was found to provide a reduction in plant electrical
requirements of approximately 81%, as well as a 74% reduction in GHG emissions from the
conventional configuration. However, under mode 1 plant operation (where no chillers are
scheduled), an even greater reduction of 86% from the baseline GHG emissions is possible.
Overall, the DLWC system discharges 38% less thermal energy as waste than the equivalent
conventional configuration. The water-borne component of this thermal discharge from the
DLWC system was 4.7 times greater than that of the conventional baseline, which expels most
of its heat to the atmosphere; however, this discharge is largely mitigated by then having to pass
through the potable water system.
2.2 Application to Satellite DHC System Study
Environmental analysis was not included in the study of satellite DHC networks. For this
reason, future study could draw upon the techniques used in the LCA report to augment the
satellite DHC model.
In particular, the rigorous methodology applied in the LCA has proven useful to Enwave
(Enwave, 2010), and is compatible with the hour-by-hour approach used in the current study.
The grid emissions analysis, thermal considerations, water treatment chemical leakage
inventory, and operations data could all be transferrable to a future version of the satellite DHC
model. This process is important if the full impact of these systems is to be understood, both as a
general concept and in specific applications.
As the relationship between energy infrastructure and environmental impacts becomes better
recognized, such metrics will play a vital part in evaluating the role of DHC, alternative
generation, and energy conservation – all of which are concepts tied to satellite DHC systems.
22
Chapter 3 Satellite DHC Model - Components
3. Satellite DHC Model - Components
3.1 Introduction
The load profiles and production data form the foundation of the scenarios evaluated using the
model. Additionally, their characteristics and structure informed the development of the other
methods. Therefore, their formulation (and the assumptions inherent therein) will have a
profound influence over the accuracy and validity of the study as a whole. These are discussed
in detail in the following sections.
3.2 Demand/Load Profiles
3.2.1 Background
Heat energy in built environments is needed for space heating (occupant comfort), hot water
demands and industrial processes (such as equipment sterilization, chemical processes like
absorption cooling, etc.). Cooling energy is required for space cooling, dehumidification and
certain industrial processes (such as cooling for equipment like computer servers). (ASHRAE
2005)
“Demand” typically refers to the energy required measured across the consumption processes,
where-as “load” refers to the energy production charging the system, measured across the
production equipment. Hence, the load on the production systems must be sufficient to satisfy
the demand. It should be noted that in the context of the study, the values associated with either
term often refer to equivalent quantities.
In practice, designing an HVAC system to satisfy the space heating and cooling demands of a
building involves taking into account the peak or “design” loads that will have to be handled
over the course of a year. Equipment capacity will typically be selected to accommodate the
23
peak load condition in a given year, with additional over-sizing factors for safety and future
expansion considerations (Hutcheon, 1983).
In building simulation, the changes in loads over the course of the year, due to changes in
weather conditions and internal heat sources, must also be taken into account to determine the
cumulative energy demands of the system.
3.2.2 Approaches to Simulating Space Heating and Cooling Demands
Simple methods of building energy simulation involve generalized assumptions about the
relationship between weather conditions and demand, and often characterize the building
demand using condensed or aggregate metrics. This set includes degree-day procedures and the
bin method. Such methods can be particularly useful in rough feasibility studies, project
assessments and sensitivity analyses.
The degree-day method relates the energy requirements to the summation of the difference
between the outdoor temperature and some baseline reference temperature (a set-point for
turning on the system, often assumed to be 18°C for heating systems). By breaking down a
period (τ) into hour-long segments (t), and calculating an average temperature (Tav) of the
number of hours (t) that were above the threshold (Tth), a useful measure of HDD per period can
be found (McQuiston, 2005).
(3.1)
It therefore requires comprehensive temperature information, and involves simplified
assumptions about the operational efficiencies of the production equipment. It is also much less
reliable for cooling system analysis, due to the impact of solar radiation effects not accounted
for in the ambient temperature (McQuiston, 2005).
24
The bin method is premised on the idea that energy performance during different periods will
be similar if the temperature conditions are similar. Essentially, an annual load profile can be
reduced to a set of “bins”, each showing the total operation time within a definite range of
temperature conditions. To determine the energy requirements of the system, each bin can be
multiplied by a corresponding estimate for average production performance (ASHRAE 2005).
3.2.3 Comprehensive simulation methods
There is also a diverse set of energy modeling tools that incorporate more rigorous load
simulation and energy analysis methods. Such programs may take into account detailed climate
conditions and solar exposure, as well as elements of the building envelope, HVAC systems and
changes in internal loads.
This category includes packaged building simulation software such as those mentioned in the
Literature Review. A large number of generalized energy simulation software systems have also
been developed, that can be used in building load simulation, including Fortran-based TRNSYS,
or Simulink by Mathworks (Connolly, 2009).
Many of these tools are proprietary, and for the purposes of this study, availability of Enwave
customer data made them unnecessary. However, the model was designed to be compatible with
any hour-by-hour demand profile data, ensuring that profiles could be gathered or generated
from a wide variety of sources and methods.
Energy modeling of district energy systems can draw many parallels with building simulation.
However, the important distinction is that many of the metrics and methods used in packaged
software were intended for self-contained building simulation, and are therefore not flexible
enough to be applied to district systems.
While the simplified approaches may not be particularly appropriate for a comprehensive
district energy analysis model, supplementing the model with some examination of the
relationships between various aggregate loading metrics and energy consumption may yield
25
some interesting results. An integral part of the development of the model in this study was to
provide output that could be used for assessment of the relationship between aggregate metrics
and energy analysis results, with the eventual goal of identifying key high-level conditions that
signal potential for satellite district energy systems.
3.2.4 Satellite Model Approach
Flow rates and energy consumption data are recorded at each of the customer sites using a flow-
meter and digital data-logger, resolved into minute-by-minute time-steps. This data is collected,
validated and archived in databases on Enwave servers.
This study was framed around energy analysis of scenarios comprised of combinations of the
load profiles drawn from Enwave databases. These scenarios would aid in the development,
refinement and validation of the model. The profiles were representative of actual system
demands over coincident periods, thus incorporating realistic operations behaviour, while
avoiding the complications and assumptions inherent in simulating them directly.
The availability of high-resolution profile data provided an opportunity to develop a model
based on direct time-step analysis, similar to the comprehensive building simulation methods
discussed above. An hour-long time-step was selected for the level of discretization based on
experience with computation constraints in the LCA study (Chapter 2), and compatibility with
the majority of profile generating software (Connolly, 2009).
The use of time-step analyses is common for comprehensive simulation methods employed by
many building simulation software packages, as well as those used in other studies of district
energy systems (Bøhm, 2002). By breaking the load profiles into discrete time-steps, the study
can more easily incorporate aspects of energy and equipment performance analyses dependent
on variable operating conditions (such as thermal line losses, hydraulic flow calculations, heat
exchange processes, production performance, etc.).
26
Profile Handling Method
To facilitate the integration of the profiles into the district energy model, a tool for managing
demand data was developed. The tool provides a method for calling a profile from the database,
[trimming/truncating/pruning] it down within a selected start and end date, shifting it by a
specified interval, normalizing and then scaling it to an appropriate peak or cumulative demand
set-point.
The tool also provides methods to analyze the selected profiles, measuring peaks, cumulative
demand, variability, demand bins, etc. This information is output as tables and visualizations
(for example, load duration curves, and sample weekly load profiles)
Finally, the profile management tool can also provide comparative analyses on pairs of profiles,
assessing load diversity, coincident peaks, variability measures, and other metrics.
3.2.5 Demand Profile Characteristics
The profiles were manually filtered for discrepancies (potentially caused by site interference),
outliers (often the result of equipment failure or operations errors), and gaps in data (caused by
meter failure). For this study, the profile data of 24 buildings was extracted for the one year
period beginning 0:00 September 1, 2009 and ending 23:00 August 31, 2010. The data was
aggregated from 60 second resolution to the 1 hour resolution used in the model. The profiles
are therefore discrete time-series representations of load as a function of time (L(t)).
27
Figure 5: Load Duration Curves representing the annual heating demands of 3 sample building archetypes
The demand of a building will vary with outdoor weather conditions, occupancy and type of
use. A given demand profile can be characterized by the pattern of loading that occurs in
response to these factors over the course of a day (diurnal variation), over the course of a week
and over the course of a year (annual variation).
Two common ways to display profile data are temporal (load vs. time) and load duration curves
(or load utilization curves). A set of example load duration curves for heating systems are shown
in Figure 5. Figure 6 provides an example for the cooling demand profiles of 3 buildings as they
vary with time over the course of a week.
The summation of hourly demands provides a measure of the cumulative demand, over a given
period. As shown in Figure 5, Integration over a period of the load duration curve provides the
cumulative load for that period. More commonly, this involves a summation of discrete load
conditions over the period.
(3.2)
28
The ratio between the demand and the capacity of a given heating or cooling system is known as
the load condition or the part-load-ratio (PLR). As well, each period will have a maximum
load condition, known as the peak load (Lpeak).
(3.3)
(3.4)
It is important to consider the variations and patterns in heating and cooling demand typical of
different building categories or archetypes. (diurnal/daily, weekly, seasonally) For example,
peak cooling loads in an office building typically occur in anticipation of the morning arrival of
workers during the summer months, with a consistent base-load for server rooms that may last
year-round. Some example archetype categories include residential buildings, commercial-retail
spaces, office towers, hospitals, etc. Figures 5 and 6 show the load duration curves for 3
building archetypes, using different visualizations. The residential building exhibits erratic
fluctuation, likely due to operating practices, and the public building has a significant load
through the night of the first weekend, which might signify an event or some public function, or
even operating procedures during high loads (Harding, 2009).
29
Figure 6: Cooling load profiles for 3 building archetypes showing hourly loads with time for a 9 day period in August 2010
Drawing on the derivation of cumulative demand [equation 3.2], it can be seen that a region
with a steep slope implies less energy demand during the corresponding loading conditions
(Figure 5). Conversely, a gradual descent implies a larger portion of the cumulative demand
occurs during the corresponding loading conditions.
A near-level slope followed by a sharp drop off (as in the hospital case in Figure 5) implies a
consistent “base-load”: a narrow band of loads that account for a significant portion of all
operating hours, and may be present as a “base” year-round.
More specifically, base-loads are part of a class of load that are temperature-independent.
Loads related to maintaining comfortable space conditions are temperature-dependent. The
change-point temperature is a measured point for outdoor temperatures above which the
heating load becomes independent of temperature (or vice versa for cooling) (Hutcheon, 1983).
Appendix A provides a method for calculating the change-point temperature; however, the
general concept can be seen on the sample plot for building load measured against temperature
shown in Figure 7.
Daily Peak Loads
30
Figure 7: Random sample of hourly cooling loads vs. temperature (random sample from annual load profile data for an example residential building)
3.2.6 Load profile aggregation & Load Diversity
The basic metrics used to characterize the individual load profiles can also be applied to the
cumulative load profile of a connected system as follows:
(3.5)
(3.6)
(3.7)
31
An important class of metrics in the analysis and comparison of district energy configurations is
load diversity. In general terms, “load diversity” encompasses any discrepancy from exact
temporal symmetry between the load profiles of group of buildings. Diurnal and annual patterns
may not precisely coincide (or may even deviate significantly depending on archetypical use
and operational strategies), as shown in Figure 6. These differences help inform how a
connected configuration might behave differently from the sum of the parts.
Despite its paramount importance, there is no consensus on which metric best represents “load
diversity” (IDEA, 2009).
The simplest approach is to use a general correction factor based on historical precedence. An
example is the alleviation factor often used to roughly correspond with the effect implementing
a district system would have on energy savings, from the base case (sources have suggested 0.7-
0.9 for heating systems (GEF, 1996)).
A second group of diversity measures involve context-specific analysis. In general, individual
peak loads of different buildings are unlikely to exactly coincide, hence the sum of individual
peaks will always be greater than or equal to the equivalent combined system peak [Equation
3.7]. The coincidence factor, described by is a ratio comparing these two values (Skagestad,
2002).
(3.8)
(3.9)
A third group consists of deriving metrics analogous to statistical properties, for the profile data.
One example is load variance,
32
(3.10)
(3.11)
In real terms, a more applicable metric is the related measure variation from mean (σ), which
is similar to standard deviation, and represents the average difference in load from the mean
across the operating period:
(3.12)
These metrics represent the variability of the load profile function. Applying them to the base
case and connected configurations, the difference corresponds to a reduction in load variability,
which can benefit operations scheduling and equipment loading.
A number of context-specific extensions of these properties can also be applied. In general, low
loads tend to account for worse system performance, and hence they tend to offer the greatest
potential for energy savings in a connected configuration. Because of this, differentiation
between low-load deviation and high-load deviation is sometimes made. Offline periods - or
periods of zero demand - also uniquely affect combined system performance; therefore, they can
also be considered in load diversity analysis.
33
3.3 Boiler/Chiller Performance modeling
3.3.1 Boiler Specifications
Hot water (at 75-90°C or 167-194 F) was selected for the heat transmission medium. This
conforms with the prevalence of hydronic systems in medium to large-scale building
installations (Durkin, 2006). Hot water (rather than steam) networks are also used in the
majority of new district heating projects, which is attributed to the reduced line losses, and the
flexibility of heat generation technology and operating temperature (Harvey, 2010).
Conventional, non-condensing natural gas-fired hot-water boilers were selected as the default
equipment type for heat production in this study. They are the most common system used in
hydronic heating systems and have a nominal efficiency of 80 to 88% (Durkin, 2006).
Condensing boilers are an alternative type of these boilers that can improve the overall
efficiency of a unit in operation, reaching peak efficiencies of 88 to 95%;however, this benefit
depends on favourable proper operations and an adequately low return water temperature
(Durkin, 2006).
The model is compatible with a variety of heat-production performance functions (including
those for heat pump exchange with geothermal or solar-thermal systems, waste-heat utilization,
or alternative boiler technology such as the aforementioned condensing units); however, these
have not been included in the current model version.
3.3.3 Chiller Specifications
This study focuses on buildings of sufficient size to warrant consideration of a district energy
connection. A study by the IEA in 2008 indicated a minimum cooling load of 200 tons (700
kW) could be used as a benchmark for this metric, which further implies the use of certain types
of production equipment (Skagestad, 2002). In particular, this study examines the performance
of centrifugal compression water chillers, which are the most common type of system used for
these capacities do to larger capacity and relatively high performance for their cost (Skagestad,
2002).
34
Table 2: Common chiller types and their typical capacities
Centrifugal chillers operate using a vapour-compression cycle involving four stages (acting on
a closed loop refrigerant): compression, evaporator heat exchange, expansion, and condenser
heat exchange. The chiller generates a flow of thermal energy from the evaporator to the
condenser, driven by electrical energy input into the compressor. The chilled water leaving the
evaporator supplies the space cooling demands of the building before returning to the chiller as
warmer return water.
The heated water of the condenser loop, leaving the chiller condenser, is pumped to a thermal
sink to release the excess heat. In larger buildings, this typically involves a cooling tower on the
roof discharging heat to the local atmosphere. An important implication of this dependence on
ambient weather conditions is that the effectiveness of the heat exchange improves when the
outside air is colder (correlating with low cooling demands), leading to lower entering
condenser water temperatures (TECW), and vice versa.
The difference between the leaving chilled water temperature (TLCHW - leaving the chiller to
supply cooling potential to the building spaces) and the entering TECW is known as the “lift” of
the chiller. A lower lift typically corresponds to a better efficiency for the chiller.
(3.13)
Two main types of centrifugal chillers were considered for this study, distinguished by their
compressor drive system.
35
Constant-speed driven chillers are traditionally the most commonly implemented type of
centrifugal chiller, having a much longer history and lower capital cost; however, variable-
speed drives (VSD) began to be used in the 1970‟s as a means to enable higher operating
efficiencies in certain applications. They use modulated controls on the compressor drive,
relying more on mechanical adjustment of the flow vanes - adapted for low lift (low TECW and/or
high TLCHW) - to perform up to three times better than their constant speed counterparts within
the 30-50% loading range.
VSD centrifugal chillers tend to perform better at lower loads (typically peaking in performance
at loads of around 50-80%) than their constant-speed counterparts (Shepard, 1995); however,
the relative superiority of VSD chillers is contingent on low lift conditions (particularly a TECW
that declines with load). This is known as a “condenser relief” assumption. It is a common
assumption in operations energy analysis, made due to the correlation between outdoor
temperature and cooling loads, though it is not always appropriate (Shepard, 1995). Without low
lift conditions, the capacity control falls entirely onto the inlet vanes and drive losses can make
VSD chillers even less efficient than their constant-drive equivalents (LBNL, 2009). Regardless,
both systems experience a precipitous decline in efficiency as loading conditions drop below
40% (Skagestad, 2002). Figure 8 demonstrates the influence of condenser relief on the DOE-2.2
curve assumptions.
36
Figure 8: Power curve for a constant speed drive chiller compared against equivalent VSD chillers with and without condenser reset
Alternative chilled water production technology was not included in the model (including
chillers with multi-stage compression cycles, absorption chillers, or air and water-source heat
pumps); however, the modular structure of the model leaves the possibility open for future
versions by allowing a custom performance functions to be used alongside the default versions.
3.3.4 Basic Performance metrics
Efficiency (η) and Coefficient of Performance (COP): a dimensionless ratio between energy
output (chilled water production) and energy input (electricity supplied to the compressor). This
metric is comparable to traditional system efficiency metrics; however, it should be noted that
typical centrifugal chillers will operate with a COP between 5.0 and 7.5 (Harvey, 2010), which
represents more cooling energy supply than energy input (greater than “100% efficiency”). This
is because the process involves facilitating an energy exchange with an external heat sink
(usually a cooling tower discharging heat to the air). Nominal non-condensing boiler
efficiencies will vary from 80% to 88% (Durkin, 2006).
37
(3.14a) (3.14b) (3.14c)
Energy Performance (ρ) (kW/ton): the amount of electrical energy required to produce one
ton of cooling potential. This metric is proportional to the inverse of the COP, multiplied by a
conversion factor (3.516 kW/ton).
(3.15)
Energy Input Ratio (EIR) and Heat Input Ratio (HIR): dimensionless ratio of the energy
input requirements over the capacity of the unit. The EIR is also commonly referred to as
“Electrical Input Ratio” as it is primarily used for electrical equipment (e.g. pumps or chillers).
For gas-fired boilers, the HIR specifically refers to the heat inputs required from combustion of
fuel, and therefore, the useful heat content of the fuel. This ratio is the inverse of COP or
efficiency.
(3.16a)(3.16b)
3.3.5 Annual Performance Measures
Nominal (or “nameplate”) performance provided by a manufacturer represents the performance
at full-load conditions. However, nominal performance does not reflect efficiency at part-
loading conditions, nor does it account for potential variations in temperature at the evaporator
and condenser of a chiller. Also, the common practice of over-sizing production capacity
38
beyond actual peak loads further reduces its usefulness. Therefore, nominal metrics are not be
used for anticipating the actual performance of the system over the course of operations. Instead,
some measure or approximation of actual efficiency during operations is required (often referred
to as “seasonal efficiency”, “operational efficiency”, or “effective efficiency”).
Boilers
In the 2004 ASHRAE Handbook—HVAC Systems and Equipment, the different measures of
efficiency are defined as follows (ASHRAE, 2005):
Combustion efficiency: “Input minus stack (flue gas outlet) loss divided by input.” This
measure roughly corresponds to the nominal efficiency provided by manufacturers, under peak
conditions (the standard boiler rating procedure is defined by ANSI Z21.13-2000 operation at
steady-state, fully loaded, with 80°F (27°C) entering water temperature)
Overall efficiency: “Gross energy output divided by input…. Overall efficiency is lower than
combustion efficiency by the heat loss from the outside surface of the boiler (radiation or jacket
losses) and by off-cycle energy losses where boilers cycle off and on…”
Seasonal efficiency: “Actual operating efficiency that the boiler will achieve during the heating
season at various loads…”
Chillers
The Air-conditioning and Refrigeration Institute (ARI) establishes standard measures for
chillers that take into account full and part-load conditions (AHRI, 2003). ARI Standard
550/590 pertains to the following set of measures, with their associated testing parameters:
Integrated Part-Load Value (IPLV)
Full-load performance under the following conditions:
44°F (6.7°C) chilled water supply temperature (TLCHW)
85°F (29.4°C) entering condenser water temperature (TECW) for water-cooled systems
2.4 gpm per ton (0.043 lps per ton) evaporator flow
3.0 gpm per ton (0.054 lps per ton) condenser flow
39
0.0001 sqft-°F-hr/Btu (0.000018 m2-°C-/W) fouling factor
IPLV is a weighted average of the part-load performances based on a “typical season”,
accounting for the parameters listed above and in Table 3.
Table 3: ARI 550/590-98 standard testing conditions for determining IPLV (AHRI, 2003)
Table 3 shows that the condenser relief assumption is inherent in the standard. Additionally, the
weighting factor is intended to represent “average” conditions across the United States, for
comparison purposes (Skagestad, 2002).
(3.17)
Non-standard Part-Load Value (NPLV)
The NPLV is found using an equivalent method as for IPLV, except the ECWT values at part-
load conditions are based on the specific case, rather than the ARI standard (to localize the
measure).
Other Measures
EER/SEER is a similar standard used more commonly for smaller air-conditioning units.
ESEER is a European standard that is virtually equivalent to the IPLV. ASHRAE 90.1 provides
performance and operations guidelines for centrifugal chillers and auxiliary equipment based on
NPLV measures (Skagestad, 2002)
40
3.3.6 Establishing characteristic equations
Central to the goal of this study is the examination of the relationship between district network
connections, production loading and energy savings potential. This entails incorporating some
representative model of the production equipment performance as a function of loading
conditions, which in turn could add complexity as unit performance depends on:
Type (VSD, constant speed, etc.)
components (constant or variable compressors, hermetic or open containment, cooling
tower, fans, condenser fluid, condenser pumps, etc.)
condenser temperatures and supply/return temperatures, which in turn depend on
weather conditions (and also relate to demand profiles)
The fundamental relationships underpinning the operation of the production equipment are
multidimensional and nonlinear, and representative performance curves are very difficult to
assemble either experimentally from operations measurements or theoretically from component
equations.
Similar studies have either largely eschewed the complexity inherent in this area of analysis in
favour of more generalized approaches (often assuming constant seasonal efficiency across all
loads, or taken advantage of third-party software to provide detailed performance simulation
(Bøhm, 2002).
The specific needs of the current study demand a rigour in production modeling missing from
the aforementioned generalized studies. However, they also necessitate a flexibility of
implementation: an ability to incorporate the functions or methods directly into the higher-level
model procedures, to readily evaluate a large number of diverse scenarios. This functionality is
largely missing from the latter examples, which often rely on incompatible external simulation
software requiring case-by-case construction of scenarios.
The performance modeling must:
1. be sufficiently robust and adaptable, for integration within the overall model framework
41
2. provide accurate and consistent estimates of the energy requirements at part-loads (and
other case-specific conditions)
These two criteria clearly have conflicting implications (relating back to the central modeling
tension described in the Introduction), and thus a compromise would have to be made between
flexibility and accuracy. What is needed is something detailed and flexible enough to account
for benefits due to hourly loading differences across buildings (demand and condenser
conditions), as well as differences in equipment (type and performance), while also quick and
robust enough to incorporate it directly into an operations scheduling optimization program.
Constructing the functions from first-principles (or by regression based directly on operations
data) was rejected as a viable approach due to the time constraints and a lack of access to
reliable data to validate the result. It was more prudent to examine the literature for an
appropriate solution.
The first criteria could be satisfied by finding an explicit, parametric set of functions that could
be directly coded into the model processes. The model would need to access the function (and
revise its result) a large number of times (for each hour and each production unit, depending on
various conditions, as well as during the optimization stages and sensitivity analysis), which
supports using an approach that does not rely iterative, numerical approximation methods. The
development of the optimization heuristics would also be aided by limiting their complexity to a
well-defined form; for example, second order polynomials having specific global optima, and
constant values for the second derivative.
Satisfying the second criteria meant finding a set of functions from a well-established source,
with proven reliability and accuracy. The needs represented by the two criteria converge on the
formalized methods associated with comprehensive, well-established building energy simulation
software. Such methods are developed for computational simplicity, and robust application.
The DOE-2 family of building energy simulation software is a well-established platform
(McQuiston, 2005). With ongoing primary development by the Simulation Research Group at
42
the Lawrence Berekely National Laboratory, the family includes applications such as eQuest,
DOE-2.2, and PowerDOE (LBNL, 2009). The applications are free, and there exists a vast
reservoir of supplemental resources, documentation and support.
The DOE-2.2 routines use characteristic sets of bi-quadratic equations to find the power
requirements of a specific production unit for a given loading condition.
The set of methods and equations were gathered from supporting documentation (LBNL, 2009)
and the default regression coefficients were extracted directly from the eQuest raw data files.
The functions could then be directly incorporated into the various methods of the satellite
district energy model. A discussion of the specific equations and their implementation is
contained in section follows.
Boilers
The DOE-2.2 equations for gas-fired boiler performance provide the Heat Input Ratio (HIR) as a
quadratic function of the Part-Load Ratio (PLR):
(3.18)
(3.18a)
where,
(3.18b)
Table 4 shows the default coefficients used.
43
Table 4: Default regression coefficients for production equipment functions (LBNL, 2009)
Chillers
The DOE-2.2 equations for chiller performance provide the Energy Input Ratio (EIR) as a
function of the Part-Load Ratio (PLR), condenser temperature (Tcws), supply temperature (Tchws),
and the associated life (dT). The set is comprised of 3 bi-quadratic equations that collectively
translate the temperature conditions and load into adjustment factors that can be multiplied by
reference condition EIR to determine the specific part-load EIR.
(3.19)
(3.19a)(3.19b)(3.19c)
where,
(3.19d)
Table 4 shows the default coefficients used, depending on the type of chiller being modeled.
The temperatures used with these coefficients must be converted into Fahrenheit; however,
power can be input in any unit since EIR/HIR is unitless.
44
It can be seen that the revised DOE-2.2 equations for VSD chillers include explicit temperature
dependent terms, making them compatible with adjustments to the condenser-relief
assumptions. Figure 8 in Chapter 3.3.3 showed the impact of assuming condenser relief (ARI
Standard 550/590) and constant condenser temperature on the performance curves of otherwise
equivalent chillers using these functions (AHRI, 2003).
3.3.7 Validation
The default coefficients were determined using extensive regression analysis of the performance
tests for a large number of equipment (LBNL, 2009). The DOE-2 model for chiller performance
has been shown to be quite accurate for all types of chillers over most conditions, with
exceptions for variable speed driven chillers operating under part load and a variety of
temperature conditions (LBNL, 2009). The DOE-2.2 model addressed this by revising the
EIRf(PLR) equation to account for condenser and evaporator temperature differences.
Given a set of production units with equal performance and capacity, an assumption of constant
performance would calculate exactly equal cumulative energy requirements for a cluster of
independent buildings compared with its satellite DHC equivalent. This is because the same
production units are used in either configuration, and the production sharing benefits are not
realized.
For the chillers, additional comparisons were made to methods from other sources and software
packages and a general comparison is shown in Appendix B.
3.3.8 Implementation Parameters
Estimating condenser temperature is a complex problem, as it needs to take into account
equipment specifications, weather conditions, and system loads. For consistency, this model
estimates the condenser temperature based on the cumulative PLR of the whole system (for each
hour), based around the ARI Standard 550/590 assumptions (AHRI, 2003). As with Tcws, PLR is
45
typically correlated with ambient outdoor temperature; therefore, it was selected as a stand-in
for weather conditions.
Demand profile data would have corresponding weather information included, however, when
aggregated into DHC clusters, discrepancies in weather data would have to be removed. This
would imply that condenser temperatures would not be consistent between the pre-connection,
independent base-case chillers, and the post-connection, optimally scheduled configurations.
This would compromise the precision of the central comparison. Therefore consistency was
chosen over specificity, and a “global average” weather condition (and corresponding condenser
temperature) was established for each hour based on the overall average system PLR, to be used
by all units operating during that hour, regardless of configuration.
For implementation, a step-wise function was established by linear interpolation of the standard
conditions:
(3.20)
The default supply temperature for chilled water was assumed to be 4.4°C (40 F), which is
slightly lower than the typical of assumption of 6.7°C (44 F) (IDEA, 2008). This value was
selected to correspond with Enwave‟s DLWC system, from which most of the customer load
data was drawn (Harding, 2009). However, a different supply temperature can be manually
altered for specific cases. The hot water supply temperature can similarly be input on a case-by-
case basis; however, the default value was set alternatively to 75°C (167 F) for assessment of
“low-temperature” systems, and 90°C (194 F) for “high temperature” systems (Harvey, 2010).
3.3.9 Special case handling
Further provision had to be made for the physical constraints on the loading of the production
units. Both chillers and boilers have hard constraints at maximum loading capacity and absolute
minimum loading (near-zero).
46
In addition, a transition point (or soft constraint) in operations at a nominal “low-loading
minimum” (typically at 15-30% of full load) can also affect the formulation of the equations
(Durkin, 2006). Below this set-point, the units must be operated under a different control
scheme that often significantly degrades performance. The DOE-2.2 equations accounted for
low-loading conditions in their formulation (LBNL, 2009); however, this model provided an
alternative approach that more adequately represented a common practice for handling low
loads: cycling.
Cycling is a method of handling low loads that involves operating the unit at “minimum load”
(Lmin), but for only a portion of the loading period sufficient to satisfy that period‟s total demand
(e.g. 30 minutes of the 1 hour demand period). For the remainder of the time it operates in a
low-energy standby mode (Shepard, 1995). Combined, these assumptions result in a linear
function for energy demand below Lmin, connecting the energy at minimum loading to the full-
hour stand-by energy requirements as it approaches zero-loading (therefore adding another
discontinuity into the function at minimum load). (Figure 9)
With cycling, an extra conditional statement is included to handle the low load range of a given
production unit. This adds a second-order discontinuity at , below which the standard
power function is replaced by a linear approach:
(3.21)
47
Figure 9: Boiler power curve adjustments taking into account low-load cycling strategies
48
Chapter 4 Satellite DHC Model – Operations Optimization
4. Satellite DHC Model - Operations Optimization
4.1 Introduction
Central to the energy savings potential of a district energy network is the ability to allocate the
aggregate system load to any number of the available production units, in whatever arrangement
provides the optimal performance - determining which units should be brought online, and how
they should be loaded. This operations optimization or “production scheduling” problem can
be highly complex, with a long history of research and development (Weber, 2008). To ensure
that an appropriate method was taken, the first step involved classification of the optimization
problem.
4.1.1 Defining the Optimization Problem
In this study, the thermodynamic elements in the model are fundamentally non-linear (for
example, the production units are modeled by quadratic equations). This is necessary because
linear approximation would misrepresent the central focus on loading effects that distinguishes
district configurations from distributed, independent buildings (particularly for satellite
configurations that use the same production equipment as in the base case).
Additionally, discrete integer variables are also necessary. In particular, identifying which
specific units should be part of the optimal operating configuration for the given time requires a
binary distinction: whether it should be online or offline. This results in a discontinuity at zero-
loading (at which point power requirements drop from stand-by levels to zero) that prohibits a
continuous representation.
Therefore, the equipment scheduling problem belongs to the Mixed Integer Non Linear
Programming class of optimization problems (MINLP). Specifically, the problem involves
minimizing the cost associated with operating a particular configuration:
49
(4.1)
(and ρ is a function of Load, equipment specifications (and for chillers, temperature conditions))
The first simplification made was to consider the heating and cooling components separately
(since they are independent systems in these scenarios), forming two independent minimization
problems. Additionally, the auxiliary equipment was not included in the optimization process.
This reduction simplifies the problem without a significant cost to accuracy (Bøhm, 2002).
Also, for the current model and optimization process, cost values (c) are assumed to remain
constant within a given year; therefore, the optimization problem can solved independently of
the cost parameters.
The optimization problem therefore becomes:
(4.2)
subject to,
For t = 1, 2, 3, .... τ
(4.2a)
and,
For all t and all n
(4.2b)
50
The complexity of this problem is largely related to the scale of the potential solution space. The
total number of combinations of n production units can be determined using equation 4.3. Table
5 provides some cases under this relationship.
(4.3)
Table 5: Total number of possible combinations for sample of n-unit cases
n-units K combinations
3 7
5 31
10 1,023
20 1,048,575
This is an example of exponential growth, which puts a limit on the effectiveness of exhaustive
search techniques for determining the optimal configuration for every possible load. This
solution space is simply the binary component of the larger optimization problem, which must
take into account load allocation and equipment performance, as well as capacity constraints.
These conditions suggest that the overall problem space may be sparsely populated by regions
or islands of feasible solutions (for example, a large load cannot be satisfied by a single unit
beyond its capacity, even though the performance curve may mathematically extend that far).
Essentially, a 2-dimensional problem space (2 production units), will be constrained to a linear
feasible-solution space (all possible load allocations for a given total load), which is further
constrained by the minimum and maximum loading capacities of the production units (4
constraints). The extension of this into a 3-dimensional problem (adding a third production unit)
results in a planar feasible-solution space, subject to 6 load constraints. Therefore, an n-
dimensional problem will result in a (n-1)-dimensional solution space, subject to 2n inequality
load constraints - the implication being that there may be some more efficient method by which
the overall solution space can be reduced, making the problem more tractable.
51
4.1.2 Literature Review
Methods for solution
The papers by Bøhm and Weber both provide useful breakdowns of the optimization problem
and potential solution methods, which are discussed in the following section (Bøhm,
2002)(Weber, 2008).
Bøhm highlights that the complexity of the overall DHC optimization problem is largely
centered on the production optimization sub-problem, and that the problem is effectively
intractable (unless conditions are applied that simplify the problem).
Deterministic methods involve structured optimization procedures that take the same route to
finding an optimum solution on each run. Independent runs of a given deterministic procedure
will always converge on the same solution for a given problem space.
Stochastic methods use random elements in their search strategies to identify and refine
potential solutions to an optimization problem. This randomness can facilitate efficient
exploration of the problem space; however, different runs of the same procedure for the same
problem can result in different solutions
Both have advantages, but no single method has been developed that can guarantee optimality
for the generalized n-unit production scheduling optimization problem.
Deterministic
A large number of deterministic methods exist that could be applied to the n-unit production
scheduling problem (branch and bound, simplex, Newton-Raphson, etc.). The most basic of
which would be an exhaustive search of problem space. This would work for smaller problems,
but it becomes intractable for larger problems.
Weber also discusses the relevance of mathematical and hierarchical decomposition strategies,
that can break the larger problem into more manageable component problems.
52
For part of his method, Bøhm uses German stepwise-solving software called BoFiT in his
method that “is based on a decomposition co-ordination principle, called resource allocation
which involves mixed integer linear programming.”
Stochastic
Monte Carlo simulations involve random sampling of the problem space. In the context of this
model, that would imply attempting random combinations of production units, which faces the
issue that the problem space is very large, and sparsely populated by viable solutions (let alone
optimums).
In fact, the problem extends to many of the stochastic methods. These methods include
evolutionary algorithms, simulated annealing, neural networks, employed by Weber, Bøhm, and
others for variations of the operation optimization problem.
In his work, Bøhm applies neural network optimization of the hydraulic and thermal elements,
but at a predictor level not relevant for this study.
Methods that iteratively refine towards a potential solution using a systematic approach (such as
a modified gradient descent method) might provide a better fit with the performance functions
used in this study; however, a more fundamental approach was adopted for this study, with the
objective of establishing consistent, reliable schedules for the model, rather than attempting to
reach full optimization.
4.1.3 Heuristic Approach used in this study
The tension between convergence on a “good” solution and computation time stressed by Bøhm
is an important consideration discussed in this study as well (Bøhm, 2002):
the method must resolve quickly, as it is a sub-process of a larger application, with a
focus on generating energy and financial analysis results for a variety of scenarios
53
the solution set does not need to be the optimum, but it must be prove consistently equal
or better than standard practices
it must be practically implementable (neither too many transitions nor too many
configurations)
A “heuristic” method implies a systematic algorithm-like procedure related to the deterministic
approaches; however, it does not guarantee full optimization (which a true algorithm does). This
fits with the intractable nature of the problem, and the criteria discussed above.
A common approach to hierarchical decomposition for this class of production scheduling
optimization with electrical power generation was to divide the central problem into two sub-
problems: “unit commitment” and “load dispatch” (Weber, 2008). Unit commitment methods
involve determining which of the available production units (of various type, performance, and
capacity) should be brought online to satisfy the load. Load dispatch methods involve the
allocation of load across the selected units. Both have objectives of minimizing energy
consumption (or maximizing efficiency).
Both unit commitment and load dispatch methods are needed to define the overall, optimal
production schedule based on the production units available (a set of procedures outlining the
loading thresholds associated with different unit configurations). Once the schedule is set, it can
be used to determine which units are online or offline for a given load, which means the unit
commitment method is not called during the hourly analysis procedure. However, the load
dispatch method is still required to determine the optimal load allocation amongst the scheduled
units for each hourly load. This further justifies the hierarchical decomposition.
This division of work has the potential to reduce the load dispatch problem to a more
manageable non-linear programming (NLP) class; or more specifically, transforming it into a
constrained quadratic programming (QP) problem that enables use of more manageable and
well-established methods of optimization (due to the nature of the quadratic performance curves
for boilers and chillers).
54
To realize this potential, much of the uncertainty and complexity inherent in the overall problem
had to be isolated in the unit commitment procedures. In particular, the discontinuity in
performance at zero-loading had to be managed independently of the load dispatch sub-problem.
To ensure this, a strict condition must be met for any given scheduled configuration:
unit commitment condition A [UCC-A]: the m-unit solution set, selected by the unit
commitment method for a specified load range, must contain no optimal loading
configuration such that any of the m units would approach zero-load for any load
condition within the specified range
This condition (and much of the inherent complexity of the unit commitment problem) were in
turn handled using structured assumptions and heuristic methods of refinement, as devised in
development of this model.
Regardless of the separation of work, the two methods are intimately related to one another, and
a method of complete optimization would require either comprehensive consideration of both in
parallel, or iterative refinement and comparison of solutions. However, considering that this
problem is effectively intractable, this was not the goal in this study.
Instead, an approach was taken to attempt to incorporate the context-specific information,
standard industry practices, and a priori knowledge of the form of the performance curves to
effectively reduce the problem space to a set of feasible, “good” solutions.
The unit commitment sub-problem was further broken down into primary/secondary/tertiary
methods and sub-methods (roughly structured on the unit commitment and load dispatch
differentiation) that would incorporate the heuristic knowledge mentioned above.
The overall goal was to develop a method that was at least as good as basic industry practices
(Harding, 2009), some examples of which include:
scheduling based on unit capacities
operating best performers first, at optimal conditions
55
always favour schedules using a fewer number of units
approach full capacity of one unit before bringing next unit online to next (boilers)
always split loads equally (chillers)
The approach taken in this study uses the above procedures as a foundation, and new heuristic
conditions must guarantee equivalent or improved energy efficiency over the basic schedule.
Development and refinement of the heuristic conditions will be premised on an understanding of
the performance curves and optimization literature, but this bottom-up approach differs from
most literature.
The heuristic method developed for this model does not guarantee perfect optimality; however,
it guarantees a “good” solution that fits closely with common operating procedures, while
potentially reducing computation time relative to more high-level, non-deterministic
approaches.
Implementation note
Load dispatch is an independent method that can be called from other methods to provide the
performance/power requirements for a given configuration and load. It provides a specific value
for a single operating point, and will be called directly in the main analysis procedure for each
hour. It is also used in the assessment processes of the unit allocation method (in fact, the closest
to a full characterization of the load dispatch curve occurs in the unit allocation stage where
interpolation and intersections are found).
56
4.2 Load Dispatch
4.2.1 Performance Curves Revisited
Before directly engaging the load dispatch optimization problem, some further discussion of the
mathematical characteristics underpinning the production performance equations is necessary.
Chillers
The equation for determining chiller power requirements is a quadratic function, bounded such
that it is always positive, with positive curvature. The positive curvature is a characteristic of its
convexity, which has a number of implications for simplifying the optimization problem - in a
large part because convex functions guarantee a single, global optimal solution in minimization
problems. For a continuous differentiable function to be strictly convex, the function must lie
above all of its tangents (shown in Appendix C, and demonstrated in Figure 10).
Figure 10: A sample chiller power curve, highlighting Marginal Power and Performance measures
57
Marginal Power
To simplify further analysis of the curves, performance function shown in equation 19 can be
represented by the following 2nd
order polynomial:
(4.4)
where,
(4.4a)(4.4b)(4.4c)
The first derivative of the power curve (with respect to load) represents the marginal power
( ) requirements for increasing the load by a single unit (Figure 10). This value is
independent of the fixed energy requirements.
(4.5)
The performance of the chiller at a given operating point is equal to the power divided by the
load, which would be equivalent to the slope of a vector starting at the origin and ending at the
operating point (Figure 10). This takes into account fixed energy consumption requirements that
are independent of the load. Therefore, a steeper slope implies a poorer performance.
(4.6)
58
For convex power functions, this implies that the peak performance occurs at the loading point
for which the performance vector is tangent to the curve (where equals performance). This
formula has Load as a dependent variable, therefore it defines the load corresponding to peak
performance (Lpeak) for a given power curve or configuration.
(4.7)
(only the positive L is a possible solution)
Shifting the load allocation away from the optimum point will result in power requirements that
grow proportionally greater relative to the amount of additional load energy. Essentially, there is
a penalty for loading away from the optimum that grows more severe the greater the difference
in load.
Boilers
Similarly, the boiler power curves are also quadratic functions, bounded such that they are
always positive and always positively sloped; however, they have negative curvature, implying
that they are not convex. Mathematically, this can be traced to the negative c3 regression
coefficient.
Because the boiler curves are not convex, the stationary point for an equivalent formulation with
boiler power curves would correspond to a maximum (poor performance), which prevents use of
a direct optimization process equivalent to the chiller version.
The combination of guaranteed positive slope and non-convexity arises out of the method of
regression and the specific context of the problem (loading cannot rise above some fixed
capacity). This is a convenient property that can be exploited for optimization.
59
Assuming the scheduled configuration adheres to the UCC-A condition from Section 4.1.3, the
load dispatch process involves balancing the load across the committed boilers. Beginning from
an initial guess, shifting the load from one boiler to another would result in a change in power
requirements corresponding to the change in load represented by a secant line, starting from
some initial reference operating point:
From equation 3.18,
therefore,
(4.8)
For equal, consecutive steps in load (ΔL), and the relative change in power (Δ ) relates only to
changes in the corresponding power curve. Because the power curves are always positive and
non-convex, consecutive increases of equal loading steps must correspond with diminishing
additional power requirements. Therefore, if it makes sense to load a step of ΔL1 on boiler A
over boiler B (because Δ A1< Δ
B1), then it follows that an additional ΔL should again be loaded
on boiler A over boiler B (because Δ A2< Δ
A1< Δ B1), until boiler A reaches full capacity.
This condition could be called the “full-loading condition”. It is only possible because c is
negative, so each consecutive step of ΔL (towards higher load) will cause Δ to increase by a
fixed amount (the b term) less the changing amount (the c term). This condition is proven
mathematically in Appendix D.
60
The end result of these characteristics is that optimal n-boiler scheduling typically involves
loading the most suitable n-1 boilers fully, with the nth boiler handling what load remains.
4.2.2 Optimization
2-boiler case
As discussed earlier, the For the 2-unit problem, an examination of all possible allocation cases
is a feasible approach. The case breakdown is as follows:
let,
resulting in the following 2-unit Boiler cases:
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m-boiler optimization
The general n-boiler load dispatch problem can be seen as an extension of the 2-boiler case.
Because of the UCC-A condition, each configuration has pre-established which m boilers of the
full n set will be online (handling non-zero loads), and what remains is determining which single
unit of the m boilers will be at part load.
This is achieved by directly assessing each case and selecting the configuration that minimizes
overall energy requirements. There are m cases (m ≤ n), with each case having a different one of
the committed boilers handling the part-load (with the rest at full load). An “initial guess” is
arbitrarily selected, and each consecutive case is compared to the previous “best guess” using
equation 4.8. If it provides improved performance, it becomes the new “best guess”. When the
set of m cases is exhausted, the remaining “best guess” is chosen for handling the part-load.
Let,
(4.9)
and,
(4.10)
The boiler with the largest savings will be selected as the part-loaded boiler (m tests),
(4.11)
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where (using equation 4.8 again),
(4.12)
Therefore the optimal load dispatch would result in,
(4.13)
with loading,
(4.14)
This method is computable in linear time, and it also guarantees optimality for a given subset of
m boilers, as per the full-loading condition.
2-chiller case
The cumulative power function is simply a summation of the individual power functions,
(4.15)
The 2-unit optimization problem involves a 2-dimensional problem space with a single optimum
load allocation path (typically with a balance of part-loads between online chillers), reducing the
optimization problem to a directly solvable form:
(4.16)
Therefore (substituting equation 4.16 into 4.15),
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which can be solved directly,
(4.17)
Individual building application
The 2-unit models were applied in the energy analysis of the independent building systems
(each building was assumed to have up to two on-site production units for heating and cooling),
which was aggregated into the base case results for comparison against the equivalent satellite
DHC configuration. The 2-unit heating model was also used in the analysis of CHP potential for
individual buildings (Chapter 7)
This 2-unit models guarantee optimality; however, they do not readily scale up with the
inclusion of additional production units. Therefore generalized n-unit procedures had to be
developed, drawing on the analysis of the simplified models.
m-chiller optimization
The 2-chiller optimization problem could be solved directly, since it involved only 2 unknowns
(L1 and L2) and 2 equations (loading constraint and power function). Expanding the problem to
n-chillers introduces new loading variables with no additional equations, which necessitates the
inclusion of additional information for it to be solvable.
64
This can be drawn from a necessary condition of convexity: the secant line from some loading
point La to a larger Lb will always be greater than the tangent. This implies that any increase in
load on a unit from the following stationary point will result in a secant of greater slope than the
tangent. The corresponding decrease in load on the other units will have secants of lesser slope
than the tangent. Therefore, the cumulative effect would be an increase in power requirements
(and a less-optimal solution).
Therefore, optimal load allocation must occur when the marginal power curves are equal
(Equation 4.5)(The mathematical proof is included in Appendix E).
For all
(4.18)
Therefore Equation 4.5 becomes,
For all
(4.19)
Substituting Equation 4.19 into the load equality constraint (Equation 4.2a), this becomes,
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(4.20)
Substituting back into equation 4.19 yields specific load allocations for each chiller k as per the
following equation:
(4.21)
A further conditional element is necessary to account for the inequality capacity constraints: if
Lk is larger than a unit‟s capacity, it should be set to Lcap, and the remaining system load (Lsys –
Lcap) must be re-allocated to the remaining units according to Equations 4.20 and 4.21 again.
The power curves of the VSD chillers are similar in form, but are scaled depending on capacity
and nominal performance. Together with the necessary condition of equivalent M , this implies
that load will be allocated to the VSD chillers at roughly equivalent part-loading ratios (PLR)
(which is reinforced by the preliminary results of the 2-chiller optimization case). Constant
chillers have an optimal performance well outside of operating conditions, and thus tend to be
loaded more heavily in a particular configuration.
The results from the 2-chiller optimization suggested that the balancing point tended towards
balanced loading of all VSD chillers, proportional to their capacity and peak performance load.
Hence, each chillers in a subset of m units, selected according to UCC-A, would be loaded
roughly according to the Equations 4.21.
Assuming,
66
then initial loading conditions would be:
(4.22)
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4.3 Unit commitment
4.3.1 Introduction
The super-structure: the equipment scheduling aspect (determining which pieces of equipment
are online) is made of a combination these integer values.
The problem space is vast, [sparsely populated by regions of feasible solutions]. Equation 4.3
can be expanded using:
To become,
(4.23)
Each term represents an “m-unit” sub-problem (combinations involving m units from the n unit
superset; m Є n). This demonstrates that each n-unit scenario is comprised of a sum of the
component m-unit cases – each of which corresponds to the mth binomial coefficient. By first
separating the problem into these independent m-unit cases, there is potential to heuristically
reduce the problem space by initially handling each sub-problem with information specific to it.
Table 5 can be expanded by breaking down the overall combinations into components, which
helps highlight the m-unit cases with the largest solution spaces. For any given load:
3 units
5 units
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10 units
20 units
The initial case involves selecting from n combinations (1-unit) and the final case involves only
one choice (all units operating), which together define the extents of the range of loading
conditions for the scenario. The unit commitment problem involves selecting the series of
configurations offering optimal performance to fill in this range, and it is clear that the largest
number of combinations corresponds with these intermediate cases as they approach the n/2-
case.
The unit commitment problem also involves more than unit selection, since unique
configurations must be assessed and compared against one another - necessitating use of the
load dispatch methods.
The unit commitment problem involves identifying a series of consecutive optimal
configurations for the cumulative loading range of the units (from zero-load to loading
equivalent to the summation of all unit capacity (Lmax). The result is a production schedule that
establishes operating parameters for when units should be brought online, during which load
conditions.
Altogether, this problem is intractable, which has led many previous studies to directly apply
non-deterministic approaches (as shown in the Literature Review). However, there are many
opportunities to first apply heuristics to systematically and significantly reduce the scale of the
problem space.
69
4.3.2 The main stages of the unit commitment heuristic method
The overall optimal schedule for the n-unit problem (S) will be comprised of a subset of the total
K combinations. Similarly, each m-unit sub-problem will have its own optimized schedule (sm).
Therefore, the overall schedule S will eventually be comprised of an aggregation of the sub-
schedules s1 to sn. Figure 11 illustrates the staged procedures discussed in this section.
Figure 11: General unit commitment procedure
4.3.3 Characterizing production equipment performance
Information on the capacity and performance functions of each production unit is gathered into a
set, and a series of assessment procedures are applied to compare and sort the units. The result
of this analysis are a set of matrices that characterize the units. All sorting is achieved using a
insertion sort method, which is simple and robust, but computationally intensive, and therefore
only called in a few specific instances.
The insertion sort method works by starting with an empty set, and incrementally adding a new
unit to the set in its appropriate place. It accomplishes this by comparing the new unit to each
current unit in the set in turn, starting from the minimum. When it reaches a unit whose
parameter is greater than its own, its location is marked and the unit is inserted in its place, thus
growing the overall set.
Generate independent m-
unit solution sets (sm)
Combine solutions and
iteratively refine super-set
Refine transition points and
generate final schedule (S)
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The n-units are initially sorted (and numbered 1 to n) by their peak performance load (Lp_i),
which represents the operating point at which that unit is best suited for operation.
The first comparison involves identifying the operating points at which each unit supersedes,
and is superseded by, every other unit, based on performance at equivalent loads [equation
4.24]. This essentially involves superimposing the curves onto common axes and identifying the
points at which they intersect (as shown in Figure 12, later in this section). This can be found
using Equation 4.4 from Section 4.2.1.
(4.24)
These intersection points comprise the elements of the overall intersection matrix Lint.
(4.25)
Having been sorted by peak performance location, the element Lint_ij represents the load at which
chiller j surpasses chiller i in performance. Each chiller will therefore share two intersection
points, dividing the relationship into 3 regions. Towards the negative extent of the domain, as L
-> -∞, the larger chiller (A), having less curvature, will typically (and theoretically) be more
efficient than the smaller chiller (a). At the first intersection point (Lint_Aa, in the lower triangle
of the matrix), the smaller chiller will become the superior performer, which will last until the
second intersection point (Lint_aA, in the upper triangle of the matrix), at which point the larger
chiller takes over again. Special cases that must be handled include the presence of identical
71
chillers (with identical performance functions over the entire domain) and cases where one
chiller is superior to another over the entire domain (no intersection points).
Two further indicators are:
(4.26a)
(4.26b)
Where element minij is the lowest intersection point of chiller i relative to all chillers of order j
or larger (across the row – indicating the earliest point at which the unit is superseded by any
larger unit – the end of its optimal range); and:
(4.27a)
(4.27b)
Where element maxij is the highest intersection point of chiller j relative to all chillers of order i
or larger (down the column – indicating the earliest point at which the unit surpasses all other
units – the beginning of its optimal range).
A final matrix is populated using these indicators, where element ordij simply indicates whether
chiller j is preceded by chiller i (if not, the element is left empty). The sum of these elements
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(ordij) for a given chiller (j) provides an indicator for how many units will precede it in an
operation schedule.
(4.28a)
(4.28b)
(4.28c)
4.3.4 1-unit case
The 1-unit case is essentially a distillation of the exhaustive comparison matrices discussed in
Section 4.3.3. The pertinent data set need only contain the best performing chiller for operations
at any given load, up to the maximum capacity of the largest chiller.
This involves using the comparison matrices to identify which chiller is optimal for the lowest
loads, and determining the order and load for each consecutive succession by another chiller, by
searching for the next performance curve intersection.
This starting chiller in the 1-unit schedule (s11) is the smallest unit without a larger unit
superseding it at the origin (L=0). This is found by examining the min and max matrices such
that,
(4.29)
Each consecutive unit (s1(i+1)) in the 1-unit schedule is selected by finding the unit
corresponding to the loading point at which the previous scheduled unit (s1i) is superseded. This
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implies matching the value from the min matrix for s1i to the corresponding unit from the
intersection matrix, as shown:
(4.30)
while,
Figure 12 provides the 1-unit commitment solution for an example problem.
Figure 12: Example 1-unit chiller performance schedule
The 1-unit case involves only straightforward, direct assessment of the chillers, which makes it a
special case independent of the generalized m-unit procedure. It is, however, a vital component
in the overall unit commitment method, as information from each m-unit level cascades to the
following (m+1)-unit level.
Additionally, the procedure of determining single unit succession order within a subset of n-
units (drawing back from the exhaustive comparison matrices), is something that will be called
at each level of the overall unit commitment method.
4.3.5 Generate independent m-unit solution sets
The preliminary breakdown of the n-unit problem into independent m-unit cases, means that
solutions to each case will be generated and evaluated independently of the later cases.
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Essentially, what was needed was a rough estimate for the loading point at which the
configuration will peak, and what potential performance it can achieve, relative to the other
configurations. The information needed only be accurate enough for a rough ranking of
configurations. The explicit solution method was therefore replaced by a less computationally
intensive and more flexible approach. The simplified approach took advantage of the general
finding that load is approximately evenly distributed across the units, to assume that the
cumulative peak performance occurs at a load roughly equivalent to the sum of the individual
peak performance loads.
The process of solving the m-unit sub-schedule problem involves using the results of the
previous (m-1)-unit sub-schedule as a basis for iteratively generating new configurations until
the maximum combined capacity of m-units is reached (Lmax_m).
Each element of the (m-1)-unit schedule will correspond to (m-1) active units, with (n-(m-1))
units remaining offline. These remaining units can be sorted into the equivalent of a 1-unit
remainder-schedule; however, only the remaining unit with first precedence is needed (ξA),
which can be found using Equation 4.31.
(4.31)
The initial configuration (sm1) is determined by taking the first configuration from the previous
case (s(m-1)1) and adding in the first unit of its associated 1-unit remainder-schedule (held by a
temporary array ξA).
Let,
s(m-1)1 becomes the “current configuration base”, with ξA recalculated to also exclude the
previously selected unit. Now, loading conditions for the two combinations can be calculated:
75
(4.32a)(4.32b)
The two combinations are compared, using the following conditional process:
while s(m-1)(j+1) exists,
(Everything else stays the same)
else
iterate i = i + 1
Each consecutive configuration (smi) is found by comparing the combined peak load of the “old
configuration base” and the next unit in the corresponding remainder-schedule, to the equivalent
combined peak load of the “new configuration base” (the next combination in the s(m-1) set) and
the first unit of its remainder-schedule (ξB). If the new configuration peaks earlier, it is selected,
and becomes the “current configuration base”.
This process follows the standard industry procedures, but improves upon them (and has
potential to be improved further). Within these constraints however, it ensures no combination
with even the potential to be the best for a given range is overlooked – while eliminating cases
involving units that will definitely underperform relative to another case for all loads.
4.3.6 Combine independent m-unit solution sets into a superset
Each optimized m-unit case will then be compared with the overlapping portions of the other
cases to identify the optimal configuration among them.
76
Initially, each configuration from every set is combined into a single array, sorted by peak load.
Further heuristic reduction of the solution set can be applied based on industry standards or
specific operating needs (such as favouring fewer unit configurations when sets overlap, or
eliminating the worse performing configuration if peak loads coincide within some pre-defined
threshold).
(4.33)
This overall schedule contains a set of all configurations being considered and an estimate for
their peak load; however, many of the configurations may be redundant or sub-optimal, and it
does not identify the loading boundaries that characterize the transition from one configuration
to another.
4.3.7 Establish and then iteratively refine transition points between cases
as superseded cases are removed
The solution set (S) must be further refined by comparing neighbouring configurations against
one another and approximating intersection points. This is an iterative process as transition
points are identified by interpolation, and superseded configurations are removed.
A set of loading conditions is generated for each configuration:
The first step involves using the load dispatch method to determine the specific energy
requirements of each configuration under 2 separate loading conditions: those generated from its
own parameters, and those generated by its immediate neighbour (of lesser capacity).
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(4.34a)(4.34b)
Aside from two special cases (the configuration handling the lowest loads, and the final
configuration comprised of all units online), the transition point (Ltr_i) between two
configurations can be found by first localizing the search to a particular load range, using direct
comparison:
The transition point can then be approximated as the intersection of linear interpolations
between the two configurations in the specified load range using the following:
Let,
(4.35)
This procedure is applied to for each configuration in turn, reducing the set of candidates and
storing the information on transition points. Because the procedure involved only direct
comparison of neighbours, it must be iteratively applied to each new solution set until no further
eliminations are made, resulting in a final, optimal schedule (S) (the VBA code for this process
is provided in Appendix J).
The final set of transition points (Ltr) is established using a similar method as in previous
iterations; however, a finite difference Newton-Raphson method can be applied to produce more
refined approximations.
78
Together, the sets of unit configurations (S) and transition points (Ltr) make up the solution to
the unit commitment problem. The schedule can also be represented by a binary unit array (uij),
where i is corresponds with the scheduled configuration (Si), and corresponds with the
production unit j. Each element is either 1 if the unit is online during that schedule, or 0 if it is
not.
4.3.8 Boiler version
Due to the “full-loading condition”, and the performance function characteristics of the boilers,
the unit commitment optimization problem for the heating system requires a different approach
that aligns more closely with the original baseline standard operating procedures.
A particular assumption is made based on the characteristics of the boiler curves, that if one
boiler is superior in performance to another boiler, at the peak capacity of the second boiler, it
will be superior for all physically feasible loads (―assumption of precedence‖). Therefore, two
configurations can be compared using equation 4.8, where the load on the larger unit (B) is LB =
LcapA. If the larger unit performs better at this part load, it will take priority over the other unit in
any configuration for which both are available. If the larger unit is superior at its peak load, then
it takes precedence for all loads up to its capacity. This method of comparison will be referred to
as the “priority method”.
The basic heuristic process is similar to that used for the cooling version, in which the larger n-
unit problem is broken up into m-unit sub-problems. The first step involves sorting the boilers
by size and performance (ref chiller?).
1-unit case
The creation of the 1-unit can be drawn directly from the sorted list due to the full-loading
constraint – each successive boiler is loaded to its peak capacity, and then the next-best boiler,
with sufficient capacity, becomes the next unit in the schedule.
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Also similar to the cooling version, the basic 1-unit list will be re-established using the
remaining boilers at each m-unit stage.
m-unit cases
The approach for the heating version diverges somewhat from the cooling approach in the
development of the m-unit sets.
Rather than generating each m-unit schedule in turn (before moving to the next (m+1)-unit
case), a complete set of the best combinations for each m-unit case is generated in the
beginning. These have significance in that no configuration of (m+1)-units can possibly be
selected as optimal for any load less than the capacity of the m-unit “best” configuration
Using these configurations as a base, each potential m-unit alternative is also examined. These
are systematically generated by starting with the capacity of the smallest member of the “best”
set as a base, generating a 1-unit schedule of the remaining boilers and essentially
supplementing the base load with the optimal remaining single unit (similar to with the chillers).
This process alone narrows down the possible combinations to at set containing at most:
However, it may eliminate potentially optimal configurations. This is acceptable, because the
procedure of loading the best-performing boilers as a base is standard practice.
Due to the assumption of precedence, each configuration need only be compared to its
immediate superior, using the priority method.
However, if the capacity of the current m-unit configuration is greater than that of the m-unit
“best” set configuration, it is set aside temporarily while the process is continued for all m-unit
cases, creating an initial superset schedule. The leftover sets are inserted at their appropriate
capacities beginning with the largest. If they prove superior to the configuration that
80
immediately succeeds it, using the priority method, they are included in the final schedule; if
not, they are eliminated.
Each potential configuration is tested in turn by this method, gradually processing (in
consecutive reverse order) each of the m-unit sub-problems.
Final superset
The end result is an overall schedule (S) that does not need to be iteratively refined, and for
which the transition points (Ltr) are simply the sum of the capacities of each consecutive
configuration. The binary unit representation of the schedule (uij) can also be applied here.
4.4 Conclusions
Figure 13 provides a high-level representation of the different methods involved in the larger
operations optimization procedure. The methods contained in this study do not guarantee full
optimization; however, they approach the problem from a different direction than that of most of
the literature reviewed. Starting with the standard industry operating procedures, the heuristic
methods presented here provide a foundation for systematically generating reliable, improved
production schedules. These are a necessary component in the overall model for generating
consistent results and satisfying the objectives of the study.
Figure 13: Operations optimization and production scheduling method breakdown
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Chapter 5 Satellite DHC Model – Network Analysis
5. Satellite DHC Model - Network Analysis
5.1 Introduction
5.1.2 Savings Potential
A collection of independent buildings will satisfy their loading requirements using their
independent production units. By combining information collected for performance curves and
demand profiles - and incorporating an understanding of the optimization procedure for
operating a connected configuration - it becomes possible to explicitly determine production
savings potential for satellite DHC scenarios.
A simplified base-case with 4 buildings is shown in Figure 14. Each building has either a single
constant or VSD chiller with the performance curves shown. The cumulative demand
requirements can be determined by summation of similar hourly loads into bins for all buildings
regardless of incident time (using Equation 5.1 below). Multiplication of the cumulative hourly
loads of each bin by the characteristic power requirements for that bin‟s load range provides an
estimate of the energy requirements.
An equivalent connected system (using the same building load profiles and production units)
will have an overall system load profile that reduces the variability from the mean (as discussed
in Chapter 3.2.6, Equation 3.12). The bin representation of the cumulative system‟s hourly loads
is shown in Figure 15. The chillers can be operated together, and their optimal sequence results
in the combined performance curve shown. Following the same procedure as used for the
independent buildings, the energy requirements can be found.
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Figure 14: Sample cumulative cooling demand bins for an independent 4-building case, along with corresponding chiller COP
Figure 15: Sample cumulative cooling demand bins for an connected 4-building case, along with corresponding chiller COP
The energy savings potential is therefore derived from the capability of combining the load
profiles and loading the chillers at their more optimal conditions. This potential for energy
savings is the initial premise motivating an examination of satellite district energy systems. It
forms the basis of the modeling analysis conducted in this study, where it will be balanced
against the costs and energy losses associated with installing and operating the networks.
83
5.1.2 Building Cluster
The cumulative system load is simply the summation of the individual loads of all buildings,
over the same period of time [Equation 5.1]. Thermal energy losses throughout the network are
taken into account as part of the effective load on the system, using simplified assumptions that
will be discussed in the following section.
(5.1)
5.2 Thermal Energy Analysis
The fundamental relationship between flow and the corresponding thermal energy load it carries
can be found by taking into account the transfer of thermal energy from the process flow to the
building nodes. It is therefore dependent on the heat capacity property of the water (cp) and the
change in temperature associated with the process (ΔT = Ts - Tr).
5.2.1 Thermodynamic Energy Balance
A thermal energy balance can be derived from the first law of thermodynamics to be:
Where change in pressure and volume due to change in enthalpy is considered negligible (PdV ≈
0), all of the net incoming heat energy must be transformed into a change in internal thermal
energy (temperature):
(5.2)
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This expresses that a change in the thermal internal energy (d ) will be
approximately equal to the heat added to the system (∂L). Since the friction head losses and
minor losses represent a dissipation of kinetic energy, they must also be transferred to thermal
energy, which can be found by setting the work term in equation 1 equal to the energy
dissipated:
Heat conducted through the walls of the piping can be calculated using the following:
Where Up is the thermal conductance of the pipe (in SI units of W/m2K), LMTD is a measure of
the average difference between the ambient temperature surrounding the pipe and the
temperature of the water over the length of the pipe (l) (discussed more fully in the Appendix F),
and dAw is a section of surface area along the pipe being examined.
The overall losses are a summation of the individual losses, whose cumulative effect can in turn
be represented by simplified line losses factors (for both independent building nodes, and the
system as a whole):
(5.3)
substituting back into equation 5.1,
(5.4)
It is clear that the efficient operation of a DHC system is tied to both the hydraulic and thermal
conditions of the flow, based on the relationship shown in Equation 5.2. System energy loads
are expressed by equation 5.4, which in turn relates to both flow rate and heat transfer rate of the
HX. Within most of the distribution system, temperature changes will be caused by friction
losses, leaks, thermal discharge from auxiliary equipment and conductive heat transfer through
85
the pipe walls; however only the latter is modeled in this study, while the others are considered
negligible. The resulting direct changes in fluid characteristics will also likely be negligible
(making the Bernoulli principle applicable).
The basis of this relationship between temperature and flow rate is centred on the ETS, or more
specifically, the HX. In a sense, the production and consumption equipment tie the two, largely
independent, energy flows together.
5.2.2 Thermal Components
Liquid water is the heat transfer medium assumed for this model, for both heating and cooling
systems (as discussed in Chapter 3).
Each building node interacts with the distribution network by means of an Energy Transfer
Station (ETS), which contains an indirect HX, adequate secondary distribution pumping
equipment and the necessary valves and fittings. The indirect HX process keeps the internal
building hydronic system hydraulically separate from the distribution network process flow.
Energy Transfer Station (ETS)
The most common type of recuperator typically used in a customer‟s ETS is a counter-flow
plate HX with gaskets (the low temperature conditions would make the alternative concurrent-
flow systems prohibitively long, and the gaskets allow the HX to be opened up and cleaned)
(Skagestad, 2002). A plate HX consists of a series of thin chambers through which the two
streams flow in alternating sequence. They are separated by a thin, highly conductive surface
that facilitates heat transfer but prevents mixing. The two flows run in opposite directions,
transferring heat and changing temperature as shown in Figure 16.
86
Figure 16: Temperature profiles for either side of a counter-flow HX
Provided the heat capacity of the water (cp) and an energy demand (L), the temperature
difference for either stream (ΔT) can be used to determine the flow rate needed using Equation
5.2:
(5.5)
This required flow rate is important to determining the optimal size for the HX. The above
equation also shows importance of maintaining a high ΔT: if the energy demand remains
constant, but the return temperature drops then the flow rate must increase, which increases the
load on the distribution pumps.
Design considerations of the HX related to the “Log Mean Temperature Difference” (LMTD)
are discussed in Appendix F.
Supply Temperature
Corresponding to the equipment assumptions laid out in Section 3, the supply temperature for
the hot water network (Ts_h) is assumed to be a fixed input parameter, with a default value of 75
87
to 90°C (167 to 194 F), which was supported by a variety of sources. Similarly, the chilled
water supply temperature (Ts_ch) can be input for a given scenario, with a default assumed value
of 4.4°C (40 F).
Line Losses
The impact of thermal line losses is assumed to be relatively small, on the order of 2-5% of
transmitted energy for new heating systems (Harvey, 2010) and 1-2% (or less) for cooling
(IDEA, 2008). For the model, a rough “heat loss factor” ( loss) of 2%/100m for heating and
1%/100m was applied to the overall energy transmitted through the network. The impact on
supply temperature across small networks (with cumulative piping runs not exceeding 1km) is
considered negligible, and thus not included in the model analysis. However, the sensitivity to
changes supply temperature should be explored in future work, as a follow-up analysis, and
improvements to the thermal loss modeling aspects should be considered.
Temperature return
The expected return temperature (Tr) along the return line relates to the performance of the
individual buildings and the design of the HXs. The current assumptions of the model are that
the buildings will be tightly managed, and return temperature will be 55 to 65°C (131 to 149 F)
for heating (corresponding with “low” or “high”-temperature systems) and roughly 12°C (54 F)
for cooling. This implies a ΔT of 20 to 25°C (68 to 77 F) for heating and 8°C (46 F) for cooling
(Skagestad, 2002).
Condenser Water Temperature
The estimation of entering condenser water temperature (TECW) for all chillers was based off of
the linear interpolation of ARI Standard 550/590 testing conditions, discussed in Section 3. For
each hour, the TECW was established for the entire set of chillers by entering the system-wide,
cumulative PLR into the TECW estimation function [Equation 5.6 and 5.7]. This allows a
consistent comparison to be made between different configurations under the same loading
conditions.
88
(5.6)
where,
(5.7)
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5.3 Hydraulic Energy Analysis
5.3.1 Hydraulic Modeling
The hydraulic modeling method will use quasi-steady-state analysis, with a focus on operating
costs. The hourly discretization of the overall operating period is sufficiently long and it can be
assumed that the transition between system states during these periods is relatively sluggish
(largely due to an assumption of control valves designed to act slowly); therefore, transient
conditions are not considered.
The model is also inherently non-uniform, as major and minor head losses are key components
of the system design. The water is considered incompressible, with possible transient condition
issues often mitigated by specific case-by-case augmentation of the system based on general
industry standards (using certain slow-acting control valves or implementing bypass lines).
Instead, standard industry assumptions for pipe-sizing were applied to constrain the system
design to reasonable approximations, and to enable consistent and sufficiently accurate
comparisons.
5.3.2 Layout
Building nodes
Each building represents a node in the district energy network. In conventional, centralized
configurations, each building node represents an energy load (a consumer), reducing the thermal
and hydraulic energy content of the process flow. In satellite configurations, each node
represents both a potential energy load as well as a potential energy source. This transforms
each node into an active component in the distribution network. Figure 17 shows a rough
schematic for the potential configuration of satellite district energy nodes.
When a building is scheduled to produce more energy than it needs internally, secondary
distribution pumps installed on site draw flow from the return line through the local HX, which
transfers excess production energy to the process flow (helping charge the supply line).
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When a building node is in net energy consumption mode, it requires more energy to satisfy
demand than is scheduled to be produced on site. In this case, the local distribution pumps are
bypassed, and other distribution pumps on the network provide the pressure difference across
the ETS such that flow passes from the supply line, through the HX, to the return line. During
this process, heat energy is exchanged to satisfy the net internal building demand.
Coordinated control of the disparate distribution pumps, corresponding to the demands and
production schedule, would be crucial for operating the satellite system effectively.
Figure 17: Simplified Building node schematics showing different operating regimes
Distribution Network
The distribution network is comprised of a single supply-return line arrangement, similar to the
conventional configuration. However, the means of production are likewise distributed amongst
the building nodes. Distribution pumps are similarly de-centralized, with pump capacities
equivalent to the production potential at their building node.
Because there is a lack of distinction between either “end” in the satellite configuration, for
clarification purposes, the end pertaining to building 1 will be called the anterior extent, and the
end pertaining to building N will be called the posterior extent (as shown in Figure 18).
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Figure 18: General representation of an example satellite network
5.3.3 Conservation Laws
Flow in the system must adhere to the basic physical laws. At each customer supply junction i
shown in Figure 18, the inflows and outflows must balance in accordance with the mass
conservation expressed in the continuity equation:
As discussed earlier, each customer node requires a specific flow rate to satisfy their energy
demands. In a conventional configuration, these flows are diverted from the main supply line at
specific junctions moving away from the central plant, and the distribution piping can be broken
down into sections of diminishing flow requirements further from the source.
The conservation of mechanical energy in an incompressible hydraulic system is often
represented by a modified Bernoulli equation:
Customer supply junction
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Where the sum of the pressure head (involving pressure p and specific weight γ), velocity head
(involving fluid velocity v and the gravitational constant g), and displacement head (z above a
datum) entering a control volume is equal to the sum of the same components leaving it plus the
frictional losses generated in the control volume (head loss hf).
These conservation laws form the basis of a representative model for each segment of the main
supply piping, which is a function of the total flow, the flow diverted prior to the segment, and
the head losses of the segment itself. These segments define the connections (or „paths‟)
between nodes, and collectively form the overall hydraulic network model. This model can be
used to derive the information required to determine the size of the piping needed under design
conditions (peak loading).
The flow through the first segment of a conventional configuration (and the pumps) is therefore:
However, for satellite DHC configurations, flow through pipe section j (where j = i – 1 and
assuming an ordered set) can be found by determining the imbalance between thermal energy
production and demand for building nodes towards one extent of the network from that position
(all buildings away from pipe j towards either the anterior or posterior critical node) (also
assuming a balanced load schedule):
(5.8)
Therefore, the flow through pipe j can be found rearranging equation 5.2:
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(5.9)
5.3.4 Network Design Flows
For flow to exist in the anterior direction through any pipe length, there must be a net imbalance
in demand at that point towards the anterior extent. In this case, peak flow would occur when
peak demands from all building nodes (towards the anterior extent) coincide. If the sum of these
peaks is lower than the combined production capacity of all units towards the posterior extent,
then the peak flow is “demand-limited towards the anterior extent”. Conversely, if this full
production capacity is insufficient, the flow through the pipe would instead be “production-
limited towards the anterior extent”.
The equivalent comparison can be made for peak flow towards the posterior extent (generating
four distinct cases shown in equation 5.11). The larger of the peak-limited flows towards either
extent through pipe length j would be the overall peak flow for that pipe length, calculated as
follows:
from Equation 5.9,
(5.10)
where,
(5.11)
Sizing each pipe length according to this measure of peak flow enables operational robustness in
case of units going offline for maintenance reasons, or changes to the network configuration.
The effect of this pipe-sizing technique is a network layout with two potential critical customers,
and pipes that increase in size towards center.
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5.3.5 Pressure Losses
Major Head Loss Calculation
The Darcy-Weisbach equation was used to determine the friction losses within the piping
network, as shown here (for SI units) (White, 2003):
(5.12)
The friction factor f is a dimensionless relationship between the ratio of the pipe‟s „roughness‟ e
(based on material properties) to its diameter D (together known as the „relative roughness‟) and
the Reynolds number (Re), which is represented on a Moody diagram in many fluids textbooks
(White, 2003). The Reynolds number is a dimensionless classification of the characteristics of a
given flow, calculated as:
(5.13)
Where µ and ρ are the viscosity and density of the fluid respectively.
For turbulent flow within the operating conditions of a district cooling loop (approximately
5000 ≤ Re ≤ 108, and 10-6 ≤ e/D ≤ 10-2) the friction factor f can be computed using the implicit
Colebrook equation (implemented with an iterative numerical approach method):
However, because the friction losses must be calculated for each hour in the analysis - for each
pipe length - the explicit Swamee and Jain approximation (which is accurate within 1% for these
conditions) was implemented in its place (White, 2003):
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(5.14)
Minor Head Losses
Minor head losses in a district energy network correspond to the control valves, HX, and pipe
deviations. In the satellite configuration, most of these minor losses will occur as flow passes
through the building node ETS.
The LMTD method described in Appendix F allows the energy demand to be related to the
physical form of the HX (the heat exchange surface area AHX, which determines the amount of
material required for construction and is related to the number of layers/overall dimensions of
the HX), which will contribute to determining a characteristic pressure function
(ΔPHX)(Skagestad, 2002).
For the purposes of this study, a consistent ΔT is assumed for all ETS stations. The HXs are
assumed to be of similar construction, such that their characteristic pressure function (ΔPHX) is
assumed to be constant. The loss factor can be input for each building node, and the default
assumption is simply a fixed pressure drop of 35 kPa across the primary side of the HX, with an
additional 15 kPa for valves and fittings (Skagestad, 2002). Each building node therefore
requires a minimum pressure difference of 50 kPa across the ETS for proper function, including
the critical customers at either extent (ΔPcritical).
5.3.6 Pipe-sizing tool
Two separate pipe-sizing tables were generated: one assuming velocity to be the limiting criteria
(default maximum allowable, vmax:3 m/s), and the other assuming the constraining factor is the
major head loss (default maximum allowable, hmax: 0.02 mwater/mpipe)(NRCan, 2011).
Each element of the tables corresponds to the maximum allowable volumetric flow rate
(Qmax_ODPN in m3/hr) based on a particular industry standard pipe diameter (nominal outer
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diameter, DO in mm) and pressure rating (PN) – together these parameters define an actual inner
diameter (DI in mm).
Table A elements
(For velocity limited pipes)
(5.15)
Table B elements
(For head-loss limited pipes)
Attempting to find the flow rate by directly inputting the head loss constraint into the Darcy
Weisbach equation results in an implicit function.
An iterative finite difference Newton-Raphson method was applied to generate the flow rate
tables considering this constraint. The VBA code for the method is shown in Appendix G.
(5.16)
The diameter of a given length of pipe is determined by taking into consideration its peak flow
together with the over-sizing factor. The smallest pipe size able to handle this peak flow is
drawn from both table A and table B.
According to a general rule from the RETScreen guidelines (NRCan, 2011), if both of the
candidates are greater than 400 mm in diameter, then the head-loss limited one should be
selected. If either is smaller than 400 mm in diameter, then the velocity limited candidate should
be selected.
5.3.7 Pumping Requirements
The pumping head required under design conditions must be adequate to satisfy the most
hydraulically remote load (the critical customer). It can be determined by adding the ETS
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pressure head differential for the critical customer together with other minor losses and the
major losses (Equation 5.12).
(5.17)
In a satellite network, pump capacity at each building node i will be determined by the using the
corresponding pipe design flow conditions (j = i and i-1) towards either extent. An assumption
of constant efficiency for the pumps/motors was made to simplify the analysis, which allows the
electricity requirements to be calculated as:
(5.18)
Because the flow rates and distances of the return line directly mirror the supply line, the return
piping can be sized accordingly, and the major head losses in the pump head equation above can
be considered double the supply line‟s (hence the factor of 2).
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5.4 Thermal and Hydraulic Method Summary
The relationships between the thermal and hydraulic energy domains involved in the overall
energy analysis are handled in the methods described in Sections 5.2 and 5.3. Thermal demands
and production potential are converted into characteristic design flows, which contribute to the
functional description of the layout (including pipe sizes). Hydraulic analysis can then be
conducted, providing information on line losses and pumping requirements. Context for these
procedures in the larger model is shown in Figure 19.
Figure 19: High-level breakdown of the methods involved in analyzing the distribution network
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5.5 Aggregate Energy Analysis
The relationships between the component methods, as well as the process for generating a full
set of results for the system as a whole (whether for a particular hour, or aggregated into annual
results), is illustrated in Figure 20.
Figure 20: High-level overview of the methods for aggregating energy results from hourly analyses
For the connected satellite system, the hourly system energy requirements (for hour t) can be
found using:
(5.19a)(5.19b)
Similarly, aggregate individual building results (for building i) can be found using:
(5.20a)(5.20b)
Annual systems energy results are simply found by summation of hourly requirements:
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(5.21a)(5.21b)
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5.6 Financial Analysis
5.6.1 Introduction
The central objective of this study is to assess the financial viability of satellite district energy
networks. This implies a comparison between the satellite configuration and an equivalent base
case conventional configuration. Therefore, the essential parameters are those that inform the
differentiation between the configurations: the additional capital costs for the distribution
network and related equipment, the annual production savings of fuel and electricity (in turn
dependent on prices for natural gas fuel and electricity), the financing structure of the project,
and associated periodic or intermittent costs (outlined in Figure 21).
Figure 21: High-level overview of methods for converting scenario energy results into cost estimates and financial analysis
For this analysis, the differences in costs between the base case configuration (independent
building systems) and the connected satellite configuration are aggregated into a set of cash
flows. A consistent set of cost assumptions and functions is vital.
For a given satellite district energy project to be viable, it must provide adequate savings
potential in order to finance the necessary capital expenditure. Costs and savings associated with
the project are therefore defined by net change in cost from implementing the project. The
cumulative capital cost of a given satellite DHC project is therefore defined as the sum of the
equipment procurement and installation costs beyond what the base case requires:
(5.22)
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The annual costs are a sum of the additional operations & maintenance (O&M), fuel and
electricity costs (which can be negative in case of savings), plus any debt structured into an
ongoing annuity:
(5.23)
5.6.2 Initial Costs
Production Equipment
Production equipment typically accounts for a approximately 25% of the capital costs for a new
DHC system (CDEA, 2008), however, satellite systems largely avoid major capital expenditure
for new production equipment. The cost estimates shown in Equations 5.24a&b were derived
for RETScreen estimations (along with the associated coefficients in Table 6), and can be used
to incorporate replacement units (NRCan, 2011). The model can be configured to assume an
equivalent replacement after the end of life of a unit (YEOL).
(5.24a)(5.24b)
Table 6: Production unit cost estimation coefficients (NRCan, 2011)
low estimate high estimate
cchlr $/kW 110 300
ccond $/kW 25 60
cblr $/GJ
Pumps
The cost function for procuring and installing conventional centrifugal pumps (assumed for both
the heating and cooling networks in this study) was drawn from industry pricing guides and
approximations provided by Enwave (Enwave, 2010):
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(5.25)
Table 7: Pump and motor cost estimate parameters
pump motor
cm $/mmOD 67.50 $/kW 45.10
Cb $ 1,285.70 $ 215.30
ETS
The cost function for the ETS [Equation 5.26] was also drawn from RETScreen resources, and
roughly validated against sample project data from Enwave projects (Enwave, 2010). For
cooling nodes handling peak loads less than 178 tons, a nonlinear cost function was provided;
however, it was decided that for the purposes of this study, individual nodes would not approach
that size, so the function was excluded.
(5.26)
Table 8: ETS cost estimate parameters
heating cooling
cETS $/GJ 29,450 $/ton 252
Piping Network
The procurement and installation of the piping infrastructure itself represents a large portion of
the overall capital cost of a district energy project; however, these costs will vary considerably
depending on case-specific conditions, making generalized cost modeling difficult. Also, as
mentioned in a 2001 study by National Research Council Canada (NRC ,2002), “unfortunately,
details of costs or separation of direct and social costs are rarely given in reported contract
costs... and even harder to quantify.”
Within this model, these costs can be broken down into two main categories: materials and
installation.
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The conventional method for laying the district heating pipes involves digging trenches, laying
supply and return lines (with insulation jackets if necessary) together in a 2-pipe configuration,
and burying. Where open trenches are infeasible, the pipe must be laid through tunnels, which
will incur additional costs (upwards of 2-5 times)(Enwave, 2010).
A major factor in estimating the cost of a piping project is consideration of existing
infrastructure. The position and layout of roads, power conduits, sewers, gas lines, etc. might
complicate the project, require permits for traffic delays, and necessitate more tunnelling.
For both district heating and cooling systems, steel has historically been the predominant
material used in piping networks (Enwave, 2010). However, alternative piping materials have
become more prominent in recent years. One alternative in particular, high-density polyethylene
(HDPE), is now used in many new installations. HDPE pipes can tolerate water at temperatures
up to 120C, making it suitable for the hot water systems assumed in this study.
More urbanized sites (with a high density of existing embedded infrastructure) will result in
piping capital costs upwards of 10 or even 20 times greater than equivalent lengths in a “green-
field” development (depending on tunnelling requirements, additional design, construction
planning, regulatory compliance, scheduling delays and complications, etc.)(Enwave, 2010).
A study conducted in 2001 by the National Research Council (NRC, 2002) investigated the
average costs for laying pipes using trenchless technologies. Appendix H contains a linear
extrapolation of their historic data, and arrived at a current average cost of 4,400 ($/m) for pipe
sizes similar to those used in this study (diameters <300 mm to 1 m). This value roughly
corresponds with the cost estimate provided by Enwave for considerations of complications due
to urban infrastructure density, further validating its use in the study as a conservative
approximation.
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The full cost per meter of pipe can be entered into the model on a case-by-case basis. The pipe
cost estimation method settled on for this study was premised on general bounds set by Enwave
input, with a variable element related to pipe diameter drawn from RETScreen methods:
(5.27)
Table 9: Piping cost estimate parameters (NRC, 2002)
Heating ($/m) Cooling ($/m)
Cm $/mmOD 2.64 2.38
Cb $ 4575.00 4670.00
5.6.3 Cash Flow Analysis
Project Financing
This involves structuring the projects as financial investments, and translating the annual energy
savings into a financial savings balanced against the [resulting] project costs. Cash flow
analysis...
Each scenario must include input for the following project parameters:
Discount rate (rd): corresponding to the context-specific conditions and expectations of
the project (default 8%)
Inflation rate (ri): the macro-economic indicator reflecting an increase in value for
certain goods and services (for this model, it is applied to labour costs)
(default 2% (Enwave, 2009))
Project life (Yproj): the financial horizon for all costs and expected returns (default 25
yrs)
A portion of the capital expenditure for the project is assumed to be drawn from debt.
Repayment of the debt is assumed as a constant annuity cost (Adebt) over the whole debt term
[Equation 5.28] (Fraser, 2008). The relevant variables are:
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Debt ratio (ϒdebt): portion of total capital cost drawn from debt (default 50%)
Debt interest rate (rdebt): defining accruing cost on initial loan (default 6%)
Debt term (Ydebt): period allotted for full repayment of debt and interest accrued (default
10 yrs)
(5.28)
Fuel and Electricity Prices
Costs for the fuel and electricity consumed or saved are largely dependent on their associated
prices. Depending on the price contract structure, these prices can vary depending on time-of-
use, consumption levels and peak demand. They will also change year-to-year, adjusting for
prevailing industry and regulatory conditions (Enwave, 2009). Projecting fuel and electricity
costs is a complex, chaotic and stochastic, which is beyond the scope of this study.
The default method for estimating the energy prices from year to year is to assume electricity
and fuel price projections can be estimated by a fixed annual escalation rate on an initial base
price, (pelec , pfuel, and relec , rfuel).
(5.29a)(5.29b)
Operations and Maintenance (O&M)
It is important to determine whether O&M costs will differ between the conventional and
satellite configurations. A study conducted for IEA Annex VI found that while new O&M costs
arise in district configurations (such as distribution line repair), the overall centralization of
control enables more cost-effective O&M (Skagestad, 2002). However, this aspect of the
financial model is highly variable and difficult to accurately anticipate.
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For this study, additional O&M costs (or savings) can be included (with inflation rates applied
over the course of the project life); however, the default assumption is to anticipate a negligible
net effect, with O&M savings set to null.
(5.30)
Other Costs
Currently set to default negligible amounts, and introduced as periodic or one-time cash flows:
Incentives and grants
Additional income
Rent
Cash Flow Summary
Year 0
(5.31a)
Year 1 to Ydebt
(5.31b)
Year 1 to Yproj
(5.31c)
5.6.4 Financial Metrics
Simple Payback, Equity Payback (yrs)
Simple payback is a rough estimate of the number of years required to make up the initial
capital costs, given the first-year savings potential, and not considering debt payments for the
total capital costs:
(5.32)
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Equity payback represents the specific point in time that the cumulative cash flows become
positive, representing a measure for when the project has accumulated savings in excess of
accumulated costs. It is computed using linear interpolation between the annual cash flows for
which this transition occurs (ya and yb):
(5.33)
Net Present Value (NPV), annual life-cycle savings
The NPV is calculated by discounting and combining all cash flows by the project discount rate
back to year 0. It provides a metric for the overall value of the project:
(5.34)
The annual life-cycle savings is simply the NPV converted to a fixed annuity over the project
life:
(5.35)
Benefit Cost (B-C) ratio
The B-C ratio compares the present worth of the annual cash flows (excluding initial costs) to
the equity portion of the initial costs. It provides a measure of the value of the project, taking
into account the financing strategy:
(5.36)
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Internal Rate of Return (IRR) of equity & assets
The IRR (often referred to as the ROI) provides a measure of an effective interest rate which
would result in the net present worth of all the cash flows equalling zero. A greater IRR implies
a more profitable return on investment. This model applies a numerical approach (specifically, a
finite difference Newton-Raphson method), with 10 iterations, to approximate the IRR.
The equity IRR corresponds with isolating the interest rate associated equating the NPV of the
cash flows as they are, after financing considerations:
(5.37)
The alternative assets IRR includes the full initial cost amount in addition to the following
annual cash flows (including debt payments).
(5.37a)
Incremental IRR
Structuring satellite DHC networks as financial investments and comparing alternative project
configurations involves more than simply assessing each project independently. Selecting from
among different combinations of the same buildings in a given cluster implies mutual
exclusivity:
In these cases, an incremental IRR approach must be taken (Fraser, 2008). This approach
involves first selecting the best IRR from among the possible initial connections (A). Next, each
additional connection (B) is examined as an incremental investment on that base case. The IRR
calculation therefore becomes:
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(5.38)
An important extension of this concept relates to combined heating and cooling networks, where
capital expenditure can be reduced by laying all piping lines together in the same trenches and
tunnels. In this case, the incremental cost of installing the second set of pipes must be assessed
as a mutually exclusive project relative to whichever of the independent network projects was
superior. This topic was further examined in Section 6.5.3.
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Chapter 6 Scenario Analysis Results
6. Scenario Analysis Results
The following sections provide a breakdown of the analysis and results for a representative
scenario. The example will be used to highlight some of the conditions that enable or inhibit
energy savings in a potential satellite configuration, as applied to an existing cluster of
buildings.
This section will contain a comparison of unconnected base cases to its equivalent 2 and 3
building satellite network configurations. Additionally, a more comprehensive assessment of a
4-building satellite network and the benefits of a combined heating/cooling piping configuration
was conducted.
The satellite DHC networks will utilize the existing production equipment of the constituent
buildings.
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6.1 Building Parameters
6.1.1 Basic Information
The representative scenario analysis included subsets of 4 archetypical buildings (shown in
Figure 22): a medium size office tower (Office B), an apartment building (Residential), a large
office tower (Office A), and a small theatre (Event Venue). As shown in Table 10, only Office A
has 2 production units (of each type).
Figure 22: Basic site plan for scenario analysis
Table 10: Building and equipment information for scenario analysis
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6.1.2 Building Demands
Heating
Figure 23: Load duration curves for heating demands of scenario buildings
Cooling
Figure 24: Load duration curves for cooling demands of scenario buildings
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Load Profile Discussion
Drawing on Figures 23 and 24, the load profiles of the 4 sample buildings can be qualitatively
compared to variability metrics shown in Table 26.
Table 11: Profile characteristics of independent buildings
The heating profile of the Event Venue forms a depressed inward curve that implies both
infrequent high loads and frequent low loads relative to the other profiles (since the
corresponding area is much smaller). This is reflected in the high presence of zero-loading
periods and the large deviation from the mean for heating.
Office A exhibits a steep rise past the very low heating loads, implying a smaller portion occurs
in that range. The remaining part of the profile gradually slopes upward, implying fairly equal
distribution of loads among the higher PLR ranges. Together, these factors contribute to the
larger cumulative heating demand, relative to its capacity and the other buildings. Its cooling
load profile follows a similar trend, but is less pronounced. This is reflected in an average
deviation from its mean being substantially lower than the other buildings.
The Residential building spends a substantial portion of the year in low-loading conditions;
however, it has a dramatic rise through the low-medium range. This is reflected in a fairly large
cumulative demand, but a high average deviation from mean. This often relates to the operating
procedures of the building, where even outside of low loading periods, production units may
switch to low loading conditions for brief periods of time if space comfort conditions were
surpassed (Enwave, 2010). Its cooling profile has the most low-loading hours of the sample
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buildings, leading to a low cumulative demand, relative to its system size (also reflected in the
large number of zero-loading hours.
Office B profiles for heating and cooling both exhibit gradual, consistent declines through the
load ranges. Despite this, its cumulative cooling load is the largest (relative to size), implying it
has more frequent medium and high loading hours than the other units.
Overall, it can be seen that the cooling loads tend to have a greater deviation from mean loading
conditions, implying more volatility in their diurnal and annual variations. This relates to the
tendency of cooling demands in moderate climates to have brief, peaking periods, followed by
long base-loading periods (Hutcheon, 1983).
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6.1.3 Production Equipment
Heating
Figure 25: The characteristic power and equivalent performance curves for the constituent boilers
Cooling
Figure 26: The characteristic power and equivalent performance curves for the constituent chillers
The distinctive difference between the convex chiller performance functions and the non-convex
boiler power functions is apparent in Figures 25 and 26. The boilers all appear roughly similar
in efficiency; however, they peak at different capacities. The condenser-relief assumption
provides a significant performance benefit for the VSD chillers, which peak in performance at
around 50% PLR.
Applying the individual power functions to their corresponding building loads provides the
base-case performance results shown in Table 11.
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Table 12: The effective operating efficiencies of the independent buildings, base-case scenario
6.2 Combined Operations Optimization
6.2.1 Production Schedules
Heating
Figure 27: Boiler schedules generated for the 2, 3, and 4-building combined scenarios
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Cooling
Figure 28: Chiller schedules generated for the 2, 3, and 4-building combined scenarios
Discussion
The boiler schedules generated by the heuristic methods developed for this study clearly favour
loading as few units as possible, while avoiding using the least efficient boiler (boiler 3) and
also avoiding operating the largest boiler at inefficient low-loads.
Similarly, the cooling schedules avoid using the less-efficient constant chillers until capacity
constraints require they are brought online.
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6.2.2 Production Performance (4-building case)
Heating
Figure 29: The system heating load bins for the combined 4-building configuration, along with the corresponding 5-boiler schedule performance curve
Cooling
Figure 30: The system cooling load bins for the combined 4-building configuration, along with the corresponding 5-chiller schedule performance curve
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Load Diversity
Table 13: Profile characteristics of the connected 4-building configuration
Comparing the deviation metrics for the combined case (Table 13) to those from the individual
buildings (Table 11), some of the effects of load diversity can be seen. The mean load PLR of
the combined case for both heating and cooling is as high as the highest from the independent
buildings.
The coincidence factor (peak of combined over sum of peaks of the independent, Equation 3.9),
is 0.77 for the heating system and 0.81 for the cooling system, which falls near the upper ranges
for both types, compared to typical district systems (Harvey, 2010). This is likely because a 4-
building network is smaller than most conventional systems (CDEA, 2008).
Both Figure 29 and 30 show performance rising quickly relative to the load, and the majority of
the loading bins are handled by peak efficiency configurations. The significant differences in
performance of the chillers causes the overall performance to decline with increasing load as
those poorer performing chillers must be brought online to handle the capacity. The same is not
true for the boiler schedule, where the peak performance of a unit corresponds with loading
towards capacity, and all of the boilers are roughly equivalent.
The impact of these elements on energy savings potential are discussed in the following
sections.
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6.3 Energy Analysis
6.3.1 Production Savings Details (4-building case)
Heating
Table 14: Heating energy savings results of each independent building connected to the network, and the system as a whole
Cooling
Table 15: Cooling energy savings results of each independent building connected to the network, and the system as a whole
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6.3.2 Network Results (4-building case)
Heating
Table 16: Heating network flows, line losses and piping characteristics
Cooling
Table 17: Cooling network flows, line losses and piping characteristics
Discussion
The pipes are sized according to industry standards and design flows (discussed in Chapter 5.3);
however, this leads to relatively large diameter pipes that result in small line losses for most
flow conditions (Table 16 and 17). This additional flow capacity could serve to aid future
expansion of the network.
Tables 16 and 17 also show that more energy is transferred through the cooling network than the
heating network, which results in higher pumping costs for the cooling case. This may be again
attributable to the greater variability of cooling system loads.
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6.4 Financial Results
6.4.1 Cash Flow Analysis
The connected cooling configuration provides significantly greater energy savings relative to its
base case than does the heating scenario for the same buildings (Table 14 and 15). This is likely
attributable to the more volatile nature of cooling loads, lower demand than for heating in the
Ontario climate (requiring smaller design loads and lower capital expenditure) and consistent
base-loads for specialty purposes (servers, common rooms, etc. that benefit most from load
aggregation)(Hutcheon, 1983). These factors translate into greater annual cost savings (Table
19), and contribute to a better return on investment (Table 20). The relative difference in savings
potential between heating and cooling systems is a recognized trend, and an article by Danny
Harvey highlights that cost improvements in small-scale condensing boilers will further increase
this divide as they become more widely adopted (Harvey, 2006).
Some of these conditions are further explored in reference to this scenario in the following
sections.
Table 18: Financial parameters
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Table 19: Capital costs and first-year annual savings for 4-building scenarios
Figure 31: Cash flow diagram for 4-building heating scenario
Figure 32: Cash flow diagram for 4-building cooling scenario
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Table 20: Financial analysis results of 4-building scenarios over project life
6.5 Summary
6.5.1 Heating
Table 21 provides a summary of the results of analysis of the heating scenarios.
Table 21: Heating scenario results summary and comparison for independent buildings, 2, 3, and 4-building cases
The 2-building heating system connection involved the medium sized office (Office B) and the
residential tower (Residential). The savings relative to the base case for each building were
roughly similar (with the initially poorer performing building having 1.7% greater energy
126
savings). The overall system savings were 4.8% (after line losses were taken into account), with
an overall system efficiency higher than either independent system.
The 3-building heating case included the larger office tower (Office A, contributing 2 additional
boilers) along with the original 2 buildings. The better performance of the new production units
contributed to a significant improvement in the overall system performance and energy savings
seen by the original 2 buildings from the 2-building case. However, these savings were not as
significantly reflected by relative operational improvement at Office A, given that its
independent systems had superior performance to the existing 2-building network to which it
connected (what savings it does have can likely be attributed to load diversity, particularly a
reduction in low-load deviation from the mean). The net effect was a greater return in
investment over the 2-building case.
The 4-building heating case involved the inclusion of a theatre (Event Venue) with lower
demands and poorer performance than the other independent buildings. This meant that it
offered little capacity for the overall system to improve (either from levelling the load or
contributing well-performing production equipment to the schedule), which was reflected by the
negligible marginal improvements of the 3 existing buildings. However, the Event Venue itself
receives large performance gains from connecting to the network, which translate to an increase
in the overall system energy savings, and an improvement in the investment prospects.
The cases are mutually exclusive, and a full investigation of the investment potential for these
scenarios would require selecting the greatest IRR potential from among all 2-building
combinations, and (assuming it is greater than the MARR), comparing incremental IRR
associated with adding each remaining building to the MARR in turn.
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6.5.2 Cooling
Table 22 provides a summary of the results of analysis of the cooling scenarios.
Table 22: Cooling scenario results summary and comparison for independent buildings, 2, 3, and 4-building cases
The connection order for the cooling cases paralleled that of the heating cases.
The 2-building connection generated overall system energy savings of 36% (after line losses),
with a greater portion associated with savings at Office B, despite having a better performing
independent system. This is attributable to the different types and capacities of production
equipment present in either building. The Residential building had an over-sized VSD chiller,
which was benefited the performance of the connected configuration relatively more than the
constant speed chiller provided by Office B. Therefore, Office B gained more by connecting to
the network.
In the 3-building cooling case, the inclusion of a large, well-performing office tower (Office A,
with two constituent chillers) further improves the overall system performance. Similar to the
heating version, the incremental energy savings are mostly associated with further operational
improvement at the original 2 buildings. The cumulative effect of the additional capital costs is
that the IRR of the project is lower than that of the 2-building case (An incremental IRR
assessment would need to be conducted to determine if the 3-building configuration offered
sufficient incremental gains from the 2-building case).
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When the poorly performing Event Venue was added for the 4-building case, it gained very large
energy savings from its independent case, improving the overall system energy savings. The
relative performance of the other buildings actually decreased slightly, which can be attributed
to the overall optimization process of the new system. The production scheduling method was
able to generate proportionally greater gains from the Event Venue relative to the corresponding
losses for the other nodes (minimizing the overall energy requirements). This resulted in an
improvement in the IRR from the 3-building case.
6.5.3 Combined Satellite DHC Configuration
All of the cases for either heating or cooling are mutually exclusive, and structuring an
investment project out of them would require an incremental IRR approach as discussed earlier.
A particular example of this would be the comparison between pursuance of the 4-building
heating and cooling cases independently, and a combined 4-pipe installation that involves
installing both heating and cooling piping lines in the same trenches and tunnels.
Assuming a MARR of 12%, the heating system would not be pursued as an independent project
(Table 21). The cooling system would be a viable investment (Table 22); however, the 4-pipe
option provides an alternative (mutually exclusive) option.
The additional value added by including the heating network (Table 21), less the incremental
costs associated with installing the heating pipes together with a the assumed installation of the
cooling pipes (in a 4-pipe combined configuration), provides capital cost savings of 45% for the
piping network and 10% for the ETS (Figure 33). Using Equation 5.38, the incremental IRR
was found to be 17.2% (with an combined IRR of 18.8%), which is above the MARR, and
suggests the combined 4-pipe configuration is a viable investment opportunity.
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Figure 33: Capital cost breakdown of 4-building heating, cooling and combined configurations
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6.6 Conclusions
The results of the scenario analysis show that a satellite DHC configuration has the potential to
provide energy savings of 7.7% for the heating systems and 43% for the cooling systems. While
these savings can provide a foundation for a viable investment (an IRR of 10.9% and 25.2% for
heating and cooling respectively), particularly when considering a combined piping network
configuration (a combined IRR of 18.8%), the results are limited in relevance to this particular
case.
However, the example scenario can be used to discuss the general conditions that make satellite
DHC viable, and application of the model to a more exhaustive set of scenarios can build upon
these results (Discussed further in Section 8).
Drawn from analysis of the example scenario, the conditions that lead to improved potential
energy savings can be classified under aspects related to the load profiles of the buildings and
those related to the plant equipment.
Load Profiles:
High cumulative demand
High, infrequent peak demand periods
Long, frequent low-loading periods
Fit with other buildings in cluster (large load diversity; similar loading periods)
Plant Equipment, either:
High-performance: contributes to overall system performance of connected
configuration, improving saving potential of other buildings
Poor-performance (oversized, low-efficiency, etc.): benefits internally from higher
system performance, receiving relatively greater operational gains compared to its
independent case than are contributed by its inclusion in the production schedule
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Chapter 7 Building-scale CHP Application
7. Building-scale CHP Application
7.1 Introduction
Satellite DHC systems have the potential to accommodate a variety of energy production
technology, and to integrate symbiotic relationships with other energy flows. CHP is commonly
associated with centralized DHC, which provides the scale of generation necessary for
economically viable power generation (Harvey, 2006). However, small-scale CHP units are
becoming more readily available, and the potential for building-scale application has been
explored in a number of recent studies (Harvey, 2006).
The development of a comprehensive independent building model for the satellite DHC study
provided a platform for exploring the financial viability of CHP applications at the building
level. Cost assumptions for the CHP study are provided in Appendix I.
7.2 First-Year Analysis
7.2.1 Operating Costs and Potential Savings of the CHP System
CHP case-specific variables:
Demand, CHP heating Capacity (GJ/hr)
Operating Cost (without CHP, with CHP) ($/hr)
Fuel Consumption (boilers at D, CHP unit) (GJ/hr)
Heating Performance (boilers at D, CHP unit) (1/efficiency)
Electricity Production (kW)
Unit Price of Electricity, O&M, and Natural Gas ($/kWh) ,
($/GJ)
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Equation 7.1 shows how simplified for of the potential savings [S] associated with running a
CHP unit are dependent on the relationship between the current gas and electricity prices, as
well as the performance of the existing site equipment relative to the performance of the CHP
unit. When the CHP unit is brought online, it generates electricity that can either be used on-site
or sold to the grid, which offers the building direct operational savings. At the same time, the
heat generated can displace a portion of the load on the base system. However, this lowers the
base boilers‟ efficiency and potentially alters their operating configuration. Additional O&M
costs would also be applicable.
Provided,
then for ,
(7.1)
However, when
then , and Equation 7.1 reduces to:
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(7.2)
Therefore, given explicit parameters for the plant and the operating hour, savings are a function
of demand only. Savings of zero would imply a “breakeven” point: where the additional costs
associated with operating the CHP unit are equal to the potential savings generated. In this way,
the optimal operating procedure for the CHP unit can be found by identifying viable regions and
their associated cost savings potential.
However, determining the explicit function component itself involves an optimization
problem, making use of the performance curve functions of the base boilers, which are in turn
by a discontinuous series of polynomials (Chapter 3).
This study avoids this dependence on a set performance-curve definition by directly determining
- independently and for each hour in the year - the costs of operating the default boiler system to
satisfy the heating demand, as well as the costs of running a given CHP system configuration.
Viability and potential savings are then assessed through direct computation.
7.2.2 Operating Procedure for the CHP System
While the CHP unit can satisfy a portion of the building‟s heating demand, it does so with a
typically lower efficiency. This relative increase in the energy required to satisfy the heating
demand can be compounded by a marginal loss of efficiency for the remaining base boilers,
which are satisfying a lower load (as shown in previous section).
Figure 34 highlights a boundary representing breakeven points for an example scenario over the
course of its projected life (and beyond). In a given year (a vertical line on the figure), they
represent operating parameters for the CHP unit – essentially showing the heating demand
thresholds for turning the CHP unit on and off. As a result, when applied to a specific building
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load profile, they also determine the total number of potentially viable operating hours in a
given year for a given scenario.
Essentially, a breakeven point occurs when the electricity savings are sufficient to offset the
marginal increase in fuel and O&M costs. A discussion of common breakeven points and their
associated regions of viable operation (relative to demand) follows, making reference to Figure
34.
Region A [ Demand < CHP_cap ]
The four main possibilities for lower bound breakeven points (where the CHP unit first becomes
viable) occur when for the following regions:
[ Demand ≥ 0 ] Electricity savings are such that the CHP unit is profitable even with no
heating load. This implies that the CHP unit will be viable during any period during the
year.
[ Demand > 0 ] The CHP system requires some heating load to offset fuel costs, but
necessary demand is below minimum system load; therefore, the CHP unit is viable
during any and all heating periods.
[ 0 < Demand < CHP_cap ] In this region, the entire heating load can be satisfied by
CHP unit. The viability depends on the electricity savings offsetting the additional fuel
costs relative to the base case. Since fuel costs and heat output for the CHP unit are
fixed, savings and viability potential increase as demand approaches the CHP unit
capacity - and thus greater heat output utilization.
Region B [ CHP_cap < Demand < blr_cap (or combined peak) ]
[ CHP_cap < Demand < d ] As the heating demand surpasses the CHP unit capacity, it
becomes necessary to activate one of the base boilers. The resulting scheduling
configuration puts lower loads on the boiler than in the base case, resulting in
particularly poor performance. The savings potential is lowest just after demand
surpasses the CHP unit capacity, with improved viability as demand increases.
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[ d < Demand < blr_cap ] As demand approaches the peak performance (and capacity)
of the boiler, the gain in electricity savings from running the CHP unit become relatively
weaker compared to the loss in plant heating efficiency. Potential savings and viability
decrease as demand approaches boiler capacity.
[ Demand = d ] Therefore peak savings in this region occurs when demand
(with either boiler peak independently or combined peak)
Region C & D [ blr_cap < Demand < (blr_cap + CHP_cap) ]
Running the CHP unit prevents the need for the other boiler to be turned on, thus often
improving the overall plant efficiency relative to the default case. These regions offer the
largest cost savings, and remain viable furthest into the project life.
7.2.3 Viability analysis of CHP systems (assessment of a specific
scenario)
From Figure 34, it can be seen that for the 25 year project life of the base case, the CHP unit is
viable for almost all loads above a minimum threshold. Additionally, if the savings provided by
the on-site electricity generation of the CHP unit are higher than the associated costs of fuel and
O&M, the unit will generate a profit in a given hour regardless of heating load. Such a situation
occurs in the first year of the base case in this study, making it a viable option to run the CHP
unit as much as possible in the first year.
The fractured operating schedule shown for later years could also occur earlier if gas prices rise
more quickly than expected (relative to electricity prices).
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Figure 34: Boundary loading conditions for profitable operations of the 1000 kW CHP unit over base project life
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7.2.4 High Level Parameters and Assumptions
High level operating assumptions were handled as initial input parameters or by using
adjustments to the aggregate results from the hourly analysis.
Loading and ―Online‖ Factors
There will be periods of viable hours where the CHP unit will not be operational, whether
because demand for the generated electricity is not sufficient (neither on-site nor grid), or
because of maintenance requirements. An “online factor” of 84% was selected to represent this
parameter, to provide an overall annual loading factor of 80% in the base case, considering only
heating periods (Enwave, 2009).
Fixed versus Variable Output Capacity
The savings potential of the CHP system is largely dependent on the electricity output;
therefore, partial loading cases represent unclear benefits/costs. As such, it was tentatively
assumed that partial-loading would offer only marginal savings with respect to base-load-sized
CHP systems. In practical application, this translated to an assumption that the CHP unit would
only run at full output capacity (when viable to do so)
This assumption is further supported by the implication that the resulting analysis will be
fundamentally conservative in its assessment of the savings potential of a given CHP system
scenario. For example, overproduction of heat during viable low loads is a by-product of this
assumption, and is currently characterized simply as “waste” energy.
More rigorous application of variable CHP performance (for both heat and electricity
production) as a function of loading could be used to optimize operations; however, reliable,
consistent performance curve data was not readily available.
Base Model
This study uses a single-building, two-boiler version of the satellite district heating model
developed for the satellite DHC study.
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The building demand profile was modeled on hourly data-logger records for Mt. Sinai
from September 2009 through August 2010. The profile was linearly scaled to fit the
input peak demand.
The performance curve functions for the typical non-condensing boilers were drawn
from US DOE building modeling software (DOE2, eQuest, etc.).
Parameter Notes
Performance and price information on available CHP production equipment was gathered from
survey results shown in Appendix I. Prices were in USD, which are assumed to be relatively
close to parity with Canadian dollars. For this study, only the reciprocating gas turbine
equipment type was considered (performance data shown in the results table of Test A). Data is
available on gas turbines, natural gas fuel cells, etc; however, these were excluded due to their
high capital costs.
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7.3 Application to Scenarios (life-cycle analysis)
7.3.1 Impact of prices and escalation rates on year-to-year savings
potential
Given a building scenario - with a known heating load profile and existing plant configuration -
the operating costs associated with satisfying the load can be found, both assuming the default
plant configuration (without CHP) and a configuration that incorporates CHP (as per the
heuristics and calculations established in section 7.2).
The potential annual savings of CHP, under the operating parameters given, are derived from
this analysis.
From equation 7.1 in section 7.2, it was shown that Savings for a given year can be found by:
However, prices for natural gas, electricity and O&M change year to year. Therefore, analysis
of the full life-cycle of a project must incorporate these changes. This model incorporates
annual escalation rates associated with each of the input prices for the initial year, as input
parameters ( .the last of which is usually assumed to be equal to inflation)
Therefore, when applied to year y, equation 7.1 becomes:
(7.3)
For a specific hourly demand in a given scenario, the potential electricity production and
associated additional fuel consumption will remain fixed year-to-year. Therefore, the change in
overall savings for a given hourly demand is a function of the initial prices and the escalation
rates as follows.
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(7.4)
Furthermore, a factor representing the necessary energy ratio (of additional fuel consumption to
electricity savings) for maintaining equivalent hourly savings for given loading conditions from
one year (y) to the any other (x) can be expressed as follows:
(7.5)
Therefore, all periods with additional fuel-consumption (over base case) below this threshold
will see an increase in potential savings as prices escalate; and conversely, all periods below the
threshold will see a decline in potential savings – possibly even making the CHP unit nonviable
for the associated loading period (reaching the “breakeven point” discussed in section 7.2).
Figure 35 demonstrates how hourly savings potential varies as a function of demand and price
escalation (represented by years), using results from the base case scenario. It can now be seen
that the viability threshold discussed in Section 7.2 and shown in figure 34 is related to the
savings potential of a given hourly demand.
It can also be seen that certain hourly loading conditions will see periods of increasing potential
savings from year-to-year. For example, the greatest hourly savings potential occurs as demand
approaches the combined capacity of the smaller boiler and the CHP unit operating together
between 10 and 15 years into the project.
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This is caused by the proportionally larger impact a percentage change in the price of electricity
has on the overall savings relative to natural gas (and O&M), due to electricity representing a
larger component base. Therefore, this will have its largest impact during loading conditions
that require the smallest additional fuel cost to realize the electricity savings of the CHP unit
over the default configuration. However, if the fuel price escalates more rapidly than the price
of electricity, then the proportional impact of fuel costs on overall savings will gradually
increase, resulting in diminishing returns over all demand conditions.
Figure 35: A detailed breakdown of the savings potential of a CHP application over the project life
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7.3.2 Scenario Results
Figure 36: Load duration curves for 3 building archetypes compared to capacities of selected CHP units
An analysis of the impact of incorporating a CHP unit into the operations of 3 existing buildings
was conducted. The study assumed the same financial parameters as used for the analysis in
Chapter 6 (Table 18). Each building is also assumed to have the following characteristics:
20,000 MBTU/hr peak demand
2 non-condensing base boilers with 83% peak efficiency (sized 30% and 70% of peak)
The load profiles of the 3 archetypical buildings selected are shown in Figure 36, along with the
heating capacity of 5 reciprocating CHP units (based on actual market information from
Appendix I).
It is clear that “Hospital A” has a large, sustained base-load, while the “Office J” has far less
low loading hours, more zero-load hours, and relatively large, infrequent peak loads. “Municipal
A” falls somewhere in between these two.
As discussed in Section 7.3.1, because the price conditions and production equipment are
equivalent for all cases, hourly savings potential is dependent only on the PLR (and independent
of the building type). Figure 37 compares the cost savings potential (under 3 pricing conditions)
associated with installing and operating a 1000 kW CHP unit against the cumulative energy
required under different loading conditions for each building.
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Figure 37: Single-building 1000kW CHP scenarios - comparison of savings potential and building load bins
The changes in savings potential shown in Figure 37 correspond to the regions discussed in
Section 7.2.2 and shown in Figure 35. It can be seen that the significant base loads of “Hospital
A” correspond with regions of high potential savings with the 1000 kW unit. The other two
buildings may benefit from smaller units, since a greater portion of their cumulative load falls in
loading bins below the high potential regions.
Figure 38 provides a visual representation of the effective operations of each building under the
1000 kW CHP unit case. As the years pass and the fuel prices change, the benefit of the
electricity savings diminishes relative to the rising additional fuel costs, and the savings
potential for various loading regions diminishes (as shown in Figure 35). The impact on
scheduling the CHP unit depends on the load profile (shown in Figure 37). Therefore, “Hospital
A” is able to justify running the CHP unit for more hours of the year, further into the project life
than the other buildings, as it has greater base-loads during which less excess heat is generated
and the operational efficiency for heat generation is not impacted as significantly.
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Hospital A
Municipal A
Office J
Figure 38: Energy consumption breakdown for 1000 kW CHP scenarios
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Table 23 provides the results of the analysis. The difference in savings potential for each
building while using the 1000 kW CHP unit reflects the assessment above, with “Hospital A”
offering greatest returns on the investment. The greatest return on investment for “Municipal A”
corresponds with installation of the 300 kW unit, while the 100 kW unit is best suited for
“Office J”, from an investment-return standpoint. It is possible that larger units might be more
favourable if NPV is considered the paramount metric.
Table 23: Single-building scenario results for incorporating a selection of CHP units
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7.4 Conclusions
Identifying Buildings with high potential savings
High potential for savings are associated with the presence of the following conditions:
large base-load (significant portion of year at or above low loads – few zero loading
periods)
stable electricity demands (either throughout, or at least coinciding with space demands)
low operational efficiency
Selecting a CHP unit
After identifying a building, the optimal CHP capacity must be selected. This will be a balance
between the decreasing capital costs per unit of output capacity and the loading potential for the
unit given the building‟s demand profile, as they relate to the fuel prices. Higher capacity units
will also be more susceptible to unfavourable energy price conditions in the future (dependent
on anticipated escalation rates).
Key parameters for gauging the suitability for a particular CHP unit (and relative sensitivity to
price factors) are:
the total annual demand for the building
the operational performance for the boilers and the CHP unit
the cumulative demand for loads lower than the CHP unit capacity
and number of hours during which loading falls below the CHP unit
These parameters allow a rough estimation of the additional fuel consumption and the electricity
generation potential. Projects with a high CHP capacity relative to the total demand will result
in greater overproduction and a larger reduction in plant performance. This makes them more
sensitive to changes in fuel prices and differences in equipment performance.
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7.5 Future Work
Equipment variations
Tests of same building archetype (i.e. a hospital), at multiple efficiencies, sizes of
boilers, CHP capacity, etc.
Fuel price variations
Fixed building and base equipment specs
Years/price changes independent, so evaluate on a per-year basis for high-resolution
analysis
Test at fixed price ratios (and provide “equivalent project year” where appropriate)
Follow up with table of effects on full project life (perhaps even on multiple building
types as well)
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Chapter 8 Conclusions and Directions for Future Work
8. Conclusions and Directions for Future Work
8.1 Conclusions
Chapters 3-5 demonstrated that by focusing on each of the core components of a DHC network
(the building demand profiles and production equipment; the aggregate building cluster and
network layout; the net energy benefits and associated financial balance for DHC
configurations) and developing the component analytical procedures towards a modular
structure for the implementation, a functional “satellite DHC model” was created that could
incorporate analysis of distributed generation potential – something lacking in most
conventional high-level simulation tools and research (discussed in the literature review in
Section 1.5).
Chapter 4 elaborated on the operations optimization problem, which is both a vital component
of DHC production savings, and a dynamic field of research in its own right. This study
develops a novel approach that offers consistent solution schedules based on standard industry
practices and heuristic refinement. The result is compatible with the computation constraints of
the larger model, and offers a platform for further development.
Chapter 6 provided a detailed examination of a 4-building satellite DHC scenario, applying the
model developed for the study. It demonstrated the financial viability of such a scenario,
highlighting the conditions that made it a viable investment. The satellite scenario configuration
provided 7.7% and 43% energy savings for the heating and cooling systems respectively, over
the base unconnected cases. This contributed to an IRR of 10.9% for the heating network
scenario, and a 25.2% IRR for the cooling network. Capital cost savings associated with laying
heating and cooling pipes together would enable a combined project to have an IRR of 18.8%
(this corresponds to an incremental IRR of 17.2% for inclusion of the heating network, making
it a more economically viable option for expansion).
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Such configurations can aid the growth of existing centralized DHC systems by offering an
alternative approach to expanding the network: planting satellite DHC hubs among existing
building clusters outside of the immediate feasible reach of conventional connections.
Re-iterating the conclusions from Section 6.6, the following conditions increase the potential for
satellite DHC systems to offer significant energy savings and a viable investment platform:
Load Profiles:
High cumulative demand
High, infrequent peak demand periods
Long, frequent low-loading periods
Fit with other buildings in cluster (large load diversity; similar loading periods)
Plant Equipment, either:
High-performance: contributes to overall system performance of connected
configuration, improving saving potential of other buildings
Poor-performance (oversized, low-efficiency, etc.): benefits internally from higher
system performance, receiving relatively greater operational gains compared to its
independent case than are contributed by its inclusion in the production schedule
Chapter 2 explores the life-cycle environmental impacts of DHC – specifically assessing the
energy, emissions, and thermal impacts of Deep Lake Water Cooling in Toronto. The system
was found to have average GHG emissions of 0.060 kgCO2e/tonhr during the period covering
November 2008 to October 2009, which was 74% less than the baseline conventional
configuration. The report reflects supplementary analysis techniques important in the
application (and perhaps future development) of the satellite DHC model, when using it to
assess the role of such networks in the greater societal context. It also represented the potential
of alternative generation technology to be incorporated into DHC networks.
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Alternative generation of thermal energy and the relationship with other energy domains was
further explored in Chapter 7. Through the integration of CHP unit production scheduling into a
single-building version of the satellite DHC model, scenario investigation demonstrated that
CHP installation and operation in existing buildings could be economically viable. Results
showed IRR upwards of 20% for 3 example building archetypes (considering existing CHP unit
technology and prices). Savings potential was contingent on a number of factors including:
sufficient loading conditions for the CHP (particularly large, sustained base-loads)
a relative difference in electricity and gas prices that favours saving electricity
low impact on effective heating efficiency (either due to large, flexible systems, a low-
efficiency baseline, or incorporation of a small CHP unit)
The following section explores the connections between these elements, the potential for future
development of the satellite DHC concept and model, and the larger role as part of a multi-
domain energy system.
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8.2 Directions for Future Work
The results of this study demonstrate the significant savings potential of satellite DHC networks,
using development of a comprehensive energy model to evaluate scenarios and assess the root
conditions underlying the energy savings. However, a more thorough and exhaustive
experimental strategy should be implemented to generate more statistically meaningful results,
using the model methods.
Preliminary results shown in this section may help inform future directions for study and
application of this model. These include aspects where sensitivity analysis or rigorous
conditional experimentation might yield meaningful results.
In particular, the model could be used to investigate and find a clear connection between
potential energy savings and the conditions discussed in section 6. The results of such analysis
could be applied to Geographical Information Systems (GIS) data to classify regions of high
potential, perhaps identifying specific areas of existing building stock where a satellite DHC
system might be particularly beneficial. This could in turn lead to more rigorous case studies,
and overall progress in a less-explored aspect of DHC research.
8.2.1 Conditions for Energy Savings
The satellite approach involves augmenting existing building systems, and while the overall
system savings reflect the financial viability of the project as a whole, those savings represent an
aggregate value. Analyzing the root causes of the savings requires exploration of the specific
energy savings attributable to each individual component that makes up the system whole.
Of particular interest would be creation of a generalized “Load Diversity Indicator” that could
be drawn from solid statistical analysis of a large batch of scenarios, relative to some of the load
diversity metrics discussed earlier, or derived from some new technique.
Figure 39 and 40 show the energy savings associated with individual buildings from a variety of
scenarios. A general trend correlating the initial performance of the building (relative to the
152
other buildings in its cluster) and its eventual energy savings is apparent for both heating and
cooling systems, with relatively little apparent correlation related to the number of buildings in a
given configuration (Figure 41 narrows in on the impact of increasing the number of buildings,
and a general trend of diminishing returns to scale is seen).
If the well-defined correlation implied by this preliminary finding holds up under more rigorous
rounds of batch scenario testing, such a metric could be applied directly to GIS data, calculating
building node potential based on its immediate neighbours, and eventually characterizing whole
regions based on DHC energy savings potential.
This would be particularly useful, because it is drawn directly from the existing state of the
building stock, and does not rely on additional data for central plant performance possibilities. It
could represent a possibility for a load diversity indicator.
Figure 39: Individual building heating energy savings resulting from satellite DHC connection
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Figure 40: Individual building cooling energy savings resulting from satellite DHC connection
Figure 41: Changes in energy savings and performance resulting from consecutive addition of identical buildings to a satellite DHC scenario
Changes in unit cost parameters for fuel and electricity have a large impact on determining the
financial viability of DHC networks, as suggested by the results shown in Figure 42 (and as seen
in the CHP analysis as well). A full sensitivity analysis could be incorporated into future studies
of scenarios, or future development of the model. Additionally, price variations with time of day
and under different contract structures could also prove to have a significant impact on results.
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Figure 42: Impact of changes in fuel escalation rates on financial viability of example satellite DHC scenarios
Figure 43 shows a particularly important consideration for DH configurations: boiler efficiency
is strictly limited by thermodynamics, reflected by a hard cap on potential additional savings
depending on initial boiler performance. Harvey notes that as high-performance condensing
boilers become more cost-effective for individual buildings to install, DH networks will offer
little advantage specifically for energy savings (Harvey, 2010).
This suggests that a study of satellite DH configurations involving condensing boiler systems
would be useful, as well as examination of inclusion of alternative energy sources and other
benefits of DH connections.
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Figure 43: Building savings associated with connecting to a satellite DH network, measured against initial performance
Further analysis in these specific areas could also provide valuable information on the effect of
changing conditions and how the model might be improved:
Sensitivity to changes in the local environment
Sensitivity to the presence of a disparity in type, performance or capacity of existing
production equipment.
Sensitivity to changes in supply and return temperatures, building operations, and
condenser systems
Impact of including explicit warm-up and shut-down costs
8.2.2 Model Development
Additionally, the methodology used in this study can be built upon to further refine the model
procedures. In particular, the modular structure of the model was intentionally designed to make
it suitable for implementation on a more robust platform. Whether implemented using a general-
purpose high-level programming language (such as Python), a numerical computing platform
(such as Matlab), or incorporated into an existing framework (such as TRNSYS), the
computational needs for a more robust testing platform make the transfer necessary (for
generation and analysis of a large number of scenarios).
Some particular directions for development include:
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Further development of the heuristic optimization method, perhaps augmenting the
deterministic heuristic base with stochastic methods of refinement (whether Lagrange,
genetic algorithms, gradient descent, or some other method)
Dynamic modeling considerations for hydraulic elements and thermal loads, including
transient behaviour
Incorporation of new production equipment options, and changes to existing
assumptions for auxiliary equipment.
Environmental impact assessment (including materials flow and resource use, emissions,
etc.)
8.2.3 Satellite Systems in the Larger Context of Urban Energy Systems
A final direction proposed for future work involves the relationship and integration with other
energy systems. Satellite DHC systems offer a less constrained direction for DHC system
analysis, particularly with respect to their role in the larger context of DMG systems.
The model could be further adapted to handle consideration of CHP, using the analysis in
Section 7 as a starting point. Alternative production technology, thermal storage components,
and new network design elements could also be incorporated.
High-level research into the implications on resiliency and integration of such configurations
into real urban systems would also compliment this direction of study. An aggregation of
information on existing cases studies would also prove beneficial.
Another potential benefit of distributed generation and control strategies in district networks is
improved resiliency to failure events. A study assessing the costs of lost production or isolated
customers due to failures in existing distribution network or plants could be conducted, with
specific consideration for mitigation effects a distributed system might provide (if any).
157
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160
Appendix Material
161
Appendix A
The change-point temperature is found using linear regression methods of load vs. outdoor
temperature.
The linear regression is applied to all hours of temperature-dependent loads. Independent aspect
is modeled using normal and student-t probability distributions. The central limit theorem is
used to characterize different building archetypes from sample groups (of N >= 30) to Normal
distributions N(mean, variance). [see pg. 12] This is done for each hour of a typical weekend-
day and weekday, the result is relative to the design load for a given day based on temperature
(or otherwise) (found earlier).
The yearly profiles are restored using Energy Consumption Indicators (ECI), specifically, for
heating (HCI), and degree-days.
Aggregate load is found by summation of the normal distributions (not overly straightforward
given above).
Note that above method is among most thorough I found. A more typical (but similar) method is
to use a “typical day” profile, normalize it, and multiply by something like effect * number of
degree-days.
162
Appendix B
The results of the comparison are shown in the figure below.
Figure 44: Comparison of chiller power curves from different sources
TRNSYS calculations for constant speed chillers:
163
Appendix C
Convexity of a function (f) is defined as:
For all x and y
or for production equations in the context of this study:
For all L
For a twice differentiable function, convexity can be practically verified when the second
derivative is strictly non-negative over the entire range. This is true for the chiller power
function as long the following equation holds:
Examining each element of the equation above will find that P(L) is strictly convex given that:
c3 is strictly positive for all cases
Lcap is strictly positive for all cases,
Tcws and Tchws terms are balanced in the numerator and denominator
164
Appendix D
Proof of “full-loading condition” for boiler scheduling.
Note: Here P = dF/dt
so shift ΔL onto B and evaluate next step of ΔL,
If
then
therefore,
More generally,
if
then
therefore,
165
Appendix E
Proof that Optimal Loading Occurs at Equal Marginal Power for Chillers
Note: Here P = dE/dt
Let,
If , then according to the convexity proof (Appendix C),
For (m) other chillers,
where,
So,
Therefore,
Therefore, power saved across other chillers will always be less than power added on chiller 1
(same line of reasoning works for reverse)
166
Appendix F
The Log Mean Temperature Difference (LMTD) method relates the heat exchange rate (L) of a
HX to the properties of the heat-exchange material (heat transfer coefficient UHX and area AHX)
and assumed operating conditions:
Where the LMTD represents the driving factor behind the energy transfer in a HX and is
determined by the inlet and outlet conditions of both air flows as follows:
However, when the temperature differences are nearly equivalent, the LMTD will generate
errors, in which case it may be more suitable to simply use one of the differences (TM from
Figure 16) in its place.
167
Appendix G
VBA code for flow and head loss approximations
*******************************
Numerical method for approximating
flow given a head loss constraint
*******************************
Sub Button6_Click()
'iterative method for estimating velocity of a pipe given
'head loss, distance and material properties
Dim Va, Vb, ha, hb, h, Vi As Double
h = Cells(10, 5) 'allowable head loss
Va = 10 'high initial guess (m/s)
Vb = 0
ha = 0 'initiate approximation variables
hb = 0
Vi = 0
i = 0 'counter1
j = 0 'counter2
k = 0 'counter3
'rough iterations to get within +/- 0.1 m/s
Do While (h - ha) > 0
Va = Round(Va - 0.1, 1)
ha = headloss(Va)
j = j + 1
Loop
Vb = Va
Va = Va + 0.1
'fine-tuned iterations until within 0.01%
Do While Abs(hb - h) > 0.0001
i = i + 1
ha = headloss(Va) 'Darcy-Weisbach estimation
hb = headloss(Vb) 'current best guess
168
'new approximate Vi based on linear interpolation:
Vi = Va + (h - ha) * (Vb - Va) / (hb - ha)
'reset variables for next iteration
Va = Vb
Vb = Vi
Loop
Cells(25, 5) = Vi
End Sub
Function headloss(ByVal Velocity As Double)
Dim rho, mew, g, Pi, D, e, L As Double
rho = Cells(5, 5) 'water density
mew = Cells(7, 5) 'dynamic viscosity of water
g = Cells(6, 5) 'acceleration due to gravity
Pi = 3.14159265
D = Cells(12, 5) 'Diameter
e = Cells(16, 5) 'roughness of pipe material
L = Cells(19, 5) 'length for pipe
Re = Velocity * D * rho / mew 'estimate for Reynold's number
f = 0.25 / ((Log(e / (3.7 * D) + 5.74 / Re ^ 0.9)) / Log(10)) ^ 2 'Swamee-Jain approx
headloss = f * L * Velocity ^ 2 / (D * 2 * g) 'Darcy-Weisbach estimation
'Cells(21, 10) = v
'Cells(22, 10) = Re
'Cells(23, 10) = f
'Cells(25, 10) = Diameter
'Cells(24, 10) = headloss
End Function
**********************
BATCH APPROACH
****************
Sub Button2_Click()
'iterative method for estimating velocity (V) of a BATCH of pipes given
'head loss, distance and material properties
'outputs flow in m3/s
169
Dim iter As Long, max_iter As Long
iter = 1
max_iter = 0
num_row = 29
Do
If Cells(num_row, 3) = "" Then
Exit Do
End If
max_iter = max_iter + 1
num_row = num_row + 1
Loop
Do While iter <= max_iter
Dim Va, Vb, ha, hb, h, Vi As Double
h = Cells(10, 5) 'allowable head loss in m_watercolumn
Va = 10 'high initial guess (m/s)
Vb = 0
ha = 0 'initiate approximation variables
hb = 0
Vi = 0
i = 0 'counter1
j = 0 'counter2
k = 0 'counter3
'rough iterations to get within +/- 0.1 m/s
Do While (h - ha) > 0
Va = Round(Va - 0.1, 1)
ha = headloss_batch(Va, iter)
j = j + 1
Loop
Vb = Va
Va = Va + 0.1
'fine-tuned iterations until within 0.01%
Do While Abs(hb - h) > 0.0001
i = i + 1
ha = headloss_batch(Va, iter) 'Darcy-Weisbach estimation
hb = headloss_batch(Vb, iter) 'current best guess
170
'new approximate Vi based on linear interpolation:
Vi = Va + (h - ha) * (Vb - Va) / (hb - ha)
'reset variables for next iteration
Va = Vb
Vb = Vi
Loop
Cells(28 + iter, 6) = Vi * (Cells(28 + iter, 3) / 1000 / 2) ^ 2 * 3.14159265
iter = iter + 1
Loop
End Sub
Function headloss_batch(ByVal Velocity As Double, Iteration As Long)
Dim rho, mew, g, Pi, D, e, L As Double
rho = Cells(5, 5) 'water density
mew = Cells(7, 5) 'dynamic viscosity of water
g = Cells(6, 5) 'acceleration due to gravity
Pi = 3.14159265
D = Cells(28 + Iteration, 3) / 1000 'Diameter
e = Cells(16, 5) 'roughness of pipe material
L = Cells(19, 5) 'length for pipe
Re = Velocity * D * rho / mew 'estimate for Reynold's number
f = 0.25 / ((Log(e / (3.7 * D) + 5.74 / Re ^ 0.9)) / Log(10)) ^ 2 'Swamee-Jain approx
headloss_batch = f * L * Velocity ^ 2 / (D * 2 * g) 'Darcy-Weisbach estimation
'Cells(21, 10) = v
'Cells(22, 10) = Re
'Cells(23, 10) = f
'Cells(25, 10) = Diameter
'Cells(24, 10) = headloss
End Function
171
Appendix H
Linear extrapolation of trenchless piping costs using (NRC, 2002) data.
172
Appendix I
CHP cost estimates based on industry survey (Harvey, 2006)
173
Appendix J
Scheduling garbage collection
(removes eliminated configurations and re-establishes superset schedule for next round)
*************************************
Iteratively excise schedule of suboptimal sets
*************************************
Sub Heuristic_iter()
'vectors of binary tags for removing configs
'new removal tags (in) and removal commands (out)
Dim remov_i(40) As Integer 'refreshed each time
Dim remov_o(40) As Integer 'iteratively evolves
Dim conf As Integer 'number of configs total
Dim i, j, m As Integer 'counters
conf = Cells(2, 7)
m = 0
'run through an clear old set of config commands
i = 0
Do While i < conf
If Cells(2, 9 + i) = 1 Then
Cells(2, 9 + i) = 0
End If
i = i + 1
Loop
'main loop for iterating in different configs
Do While m <= conf
i = 0
'full pass from new tags to complete output commands for next config
Do While i < conf
remov_i(i) = Cells(1, 9 + i)
remov_o(i) = Cells(2, 9 + i)
j = i
'finding the corresponding config to remove by finding first '0' going backwards
If remov_i(i) = 1 Then
174
Do While j > 0
If remov_o(j) = 0 Then
remov_o(j) = 1
Exit Do
End If
j = j - 1
Loop
End If
i = i + 1
Loop
'output new config commands to spreadsheet (remov_o)
i = 0
Do While i < conf
If remov_o(i) = 1 And Cells(2, 9 + i) = 0 Then
Cells(2, 9 + i) = remov_o(i)
End If
i = i + 1
Loop
m = m + 1
Loop
End Sub
175
Appendix K
[LCA of DLWC report attached]
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