Power system security enhancement through effective allocation, control and integration of demand response program and FACTS devices By Ashkan Yousefi This thesis is presented for the degree of Doctor of philosophy of The University of Western Australia Energy Systems Centre School of Electrical, Electronics and Computer Engineering 2013
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Power system security enhancement
through effective allocation, control and
integration of demand response program
and FACTS devices
By
Ashkan Yousefi
This thesis is presented for the degree of Doctor of philosophy of The
University of Western Australia
Energy Systems Centre
School of Electrical, Electronics and Computer Engineering
2013
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1
ACKNOWLEDGEMENTS
I would like to express my sincere gratitude to my supervisor and my co-supervisor, Dr
Herbert H.C. Iu and Dr Tyrone Fernando, for providing the opportunity to undertake
this research, along with their excellent guidance and constant support.
I would like to thank the staff at the Energy Systems Centre for their assistance and the
use of the facilities of the centre.
I would like to express my love to my family for their unconditional love and
encouragement during my study.
Finally, I would like to express my special appreciation to the University of the Western
Australia for providing the SIRF scholarship.
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ABSTRACT
This thesis is devoted to the development of a new approach for using the FACTS
devices and demand response programs to improve the power system security and
reliability.
The key objectives of the research reported in this thesis are:
-Optimal allocation of demand response program
-Optimal allocation of FACTS devices
-Congestion management in transmission lines using demand response program
-Congestion management in transmission lines by effective integration of FACTS and
dispatchable demand response program
-Facilitating large penetration of wind power generation into the system by effective
utilisation of dispatchable demand response program
To be able to cover the above objectives, the thesis first developed a method to find the
optimal location of static var compensator (SVC) and thyristor control series
compensator (TCSC). A multi-objective optimisation is developed and optimised using
non-dominated genetic algorithm to find the optimum location for installing the FACTS
devices in the network.
In SVC allocation, the objective function covers minimising the SVC installation cost,
voltage deviation, maximising the load ability of the transmission lines and minimising
the active power loss.
In the case of TCSC allocation, the objectives are minimising the investment cost,
maximising the loadability of transmission system and minimising the transmission
active power loss. To optimise the proposed multi-objective functions non-dominated
sorting genetic algorithm which is one of the well-developed member of evolutionary
algorithm methods is selected.
After determining the optimal location and sizes of SVC and TCSC in the electricity
network, a multi-objective approach is applied to find the optimum location for
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dispatchable demand response program. In this case, maximising the available
transmission capacity, minimising the expected energy not supplied, minimising the
active power loss and minimising the total DR capacity in the network are considered as
objectives for allocation of demand response program.
After successful allocation of SVC, TCSC and demand response program an approach
for transmission lines congestion management is proposed by effective participation of
demand response program. In the next step, the congestion management algorithm is
developed using effective combination of FACTS and demand response program. A
formulation for coordinating both FACTS device controllers and demand responses
through constrained optimization is proposed to achieve congestion management in the
transmission lines with minimum cost. This coordination can enhance the power system
security and provide an effective tool for system operator to mitigate the congestion in
transmission lines during high peak demand or major contingencies in the system.
In the final step of the research, the role of demand response program in providing the
support for the large integration of renewable energy into the electricity network is
investigated.
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LIST OF PRINCIPAL SYMBOLS
|V| System voltage magnitudes
Θ System phase angles
U System Control variables
α Delay angle which is calculated based on the applied voltage to the TCR
Xtcr Effective reactance of the thyristor controlled reactor at the nominal
frequency
XL Reactance of the reactor at the nominal frequency
|Vhsvc| High voltage node for the SVC
Vsvcref Voltage reference value for the SVC
asvc Slope reactance of the SVC
Isvc SVC current
Bsvcmax Maximum susceptance of the SVC
Bscvmin Minimum susceptance of the SVC
g2k Index indicating violation of line flow limits
si Total power flow in transmission line i
simax The maximum limit for the line i
L Total number of transmission lines
|Vnk| The voltage magnitude at load bus n in operating condition k
𝑉𝑟𝑒𝑓𝑛𝑘 The nominal or reference voltage at bus n
N The number of buses in the transmission network
Ysl,i The element (sl, i) of the nodal admittance matrix of the power system
kE Vector function of system
|V|k Vector of system voltage magnitudes
θk Vector of system phase angle
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uk Vector of control variables in operating condition k
Vik Nodal voltage at node i in operating condition k
Yi,jk Element (i, j) of the network nodal admittance matrix in operating
condition k
PiSP Specified active power load demand at node i
|Vik| Voltage magnitude at node i
Vi maxk Maximum voltage allowable value in operating condition k
gimin Minimum value obtained for the objective functions
gimax Maximum value obtained for the objective functions
Gi𝑚 Selected values for multi objective optimisation
Ysl,i Element (sl, i) of the admittance matrix of the power system
PDi Real load in load area
QDi Reactive load in load area
PDi0 Original real load demands at bus i in the load area
QDi0 Original real load demands at bus i in the load area
|Vi| Voltage magnitudes at bus i
Gij Real part of the ijth element of bus admittance matrix
Bij Imaginary parts of the ijth element of bus admittance matrix
δij Voltage angle difference between bus i and bus j
𝑁 The total number of load loss events in a year
𝐸𝑃𝑁𝑆𝑗 Expected power not supplied in the jth event
𝑇𝑗 Duration of the outage in the jth event
Ysl,i Element (sl, i) of the admittance matrix of the power system
GiP The real power generation at bus i
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iV Voltage magnitudes
δij Voltage angle difference between bus i and bus j
𝑇𝐷𝑅𝑃 Total DR programs capacity
𝐷𝑅𝑃 The amount of load participating in the demand response at the nth
load bus
TB Total number of load buses with demand response programs
E Elasticity of the demand
0D Initial demand value (MWh)
D Demand value (MWh)
Electricity price ($/MWh)
0 Initial electricity price ($/MWh)
( )LR t Reduction level requested from the aggregator
( )fin t Penalty for not responding to aggregator request
max ( )LR t Maximum value agreed in the contract between the aggregator and DR
participants
( ( ))B L t Customer revenue for using ( )L t
( )E t Elasticity of the load
0 ( )t Market price prior to demand response implementation
PreDi Power provided by responsive demand i
max,PGj l Maximum power block l offered by generator
NreD Number of responsive demands
NL Number of lines
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NGj Number of blocks offered by generator j
fr Risk coefficient
Pr j Outage probability of generator j
Prl Outage of line l probability
( )CO RI The function represents the risk.
upGjP Increment in the schedule of generator j
downGjP Decrement in the schedule of generator j
downreDiP Decrement in the schedule of responsible demand i
upjr Price offered by generator j to increase its schedule
downjr Price offered by generator j to decrease its schedule
DikP Power block k that demand i is willing to buy at price Dik
Dik Price offered by demand i to buy power block k
Gjl Price offered by generator j to sell power block l
GjlP Power block l that generator j is willing to sell at price Gjl
fdP The fixed load based on demand forecasting.
DikP Power block k that demand i is willing to buy at price Dik
Dik Price offered by demand i to buy power block k
Gjl Price offered by generator j to sell power block l
GjlP Power block l that generator j is willing to sell at price Gjl
fdP Fixed load based on demand forecasting
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(.)mE Emission function of a unit
(.)mLE Slope of segment m in a linearized emission curve
(.)F Fuel cost function of a unit
(.)ME Number of segments for the piecewise linearized fuel cost curve
(.)MF Number of segments for the piecewise linearized fuel cost curve
(.)P Hourly generation of a unit
mLG Slope of segment m in linearized fuel cost curve
(.)mP Generation of segment m in a linearized fuel cost curve
(.)mq Generation of segment m in a linearized emission curve
(.)u Unit status indicator where 1 means on and 0 means off
iRUP Ramping up limit of a unit
iRAD Ramping down limit of a unit
( )SPI t Total amount of spinning reserve
TIU Number of hours a unit has been on at the start of the scheduling period
TIC Number of hours a unit has been off at the start of the scheduling period
(.)HT Number of hours a unit needs to remain on if it is on at the beginning of
the scheduling period (.)LU Minimum up time of a unit
(.)LT Minimum down time of a unit
( , )mD i t Power block that demand i is willing to buy at the price of ( , )m i t
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GLOSSARY
FACTS Flexible alternating current transmission system
TCSC Thyristor Controlled Series Capacitor
SVC Static VAR compensator
EENS Expected Energy Not Supplied
ATC Available Transmission Capacity
DR Demand Response
NSGA Non dominating sorting algorithtm
ISO Independent System Operator
EPRI Electric Power Research Institute
TCR Thyristor controlled reactor
TSC Thyristor switched capacitors
MOV Metal Oxide Varistor
STATCOM Static Synchronous Compensator
UPFC Unified Power Flow Controller
TCVR Thyristor Controlled voltage regulator
SSSC Static Synchronous Series Compensator
TCPAR Thyristor controlled phase angle reactor
TCPST Thyristor Controlled Phase Shifting Transformer
FERC Federal Energy Regulatory Commission
DLC Direct load control
DB Demand Bidding
EDRP Emergency Demand Response Program
CAP Capacity market program
A/S Ancillary-services market program
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TOU Time of Use
CPP Critical Peak Pricing
RTP Real Time Pricing
CAISO California Independent System Operator
ERCOT Electric Reliability Council of Texas
LaaR Loads Acting as a Resource Program
IEA International Energy Agency
NYISO New York Independent System Operator
DASR Day-ahead scheduling reserve
FERC Federal Energy Regulatory Commission
MOGA Multi Objective Genetic Algorithm
OPF Optimal Power Flow
NERC North American Electric Reliability Council
TTC Total Transfer Capability
TRM Transmission Reliability Margin
CBM Capacity Benefit Margin
ETC Existing Transmission Commitments
RPF Repeated power flow
CPF Continuation Power Flow
SCOPF Security constrained optimal power flow
DSM Demand Side Management
NAS Natrium Sulfur
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Contents Chapter 1 ......................................................................................................................... 19
1.1 Objectives ......................................................................................................... 22
1.2 Outline of the thesis .......................................................................................... 22
1.3 Contributions of the thesis ................................................................................ 25
1.4 Publications ...................................................................................................... 25
Chapter 2 Steady-state models of flexible AC transmission system devices ............ 27
2.1 Basic Mechanisms of Compensation ............................................................... 28
2.1.1 Power system stability .............................................................................. 28
2.1.2 Power system static security ..................................................................... 28
2.2 Steady-state models of power system elements ............................................... 28
2.3 Power system nodal formulation ...................................................................... 29
2.4 Modelling of the FACTS devices ..................................................................... 30
2.4.1 Static VAr compensator (SVC) ................................................................. 30
2.4.2 Thyristor controlled series compensator (TCSC) ..................................... 35
2.5 Applications of FACTS devices in power system ............................................ 41
2.5.1 The role of FACTS for congestion management ...................................... 43
Chapter 3 Demand response program ........................................................................ 45
3.1 Definition of demand response program .......................................................... 45
3.2 Benefits of DR programs .................................................................................. 46
3.3 Demand response in electricity market ............................................................ 46
3.4 Different types of demand management programs .......................................... 47
3.4.1 Incentive-based demand response programs ............................................. 48
3.4.2 Time-based programs ................................................................................ 51
3.5 Applications of demand response programs for power system planning and
operation ...................................................................................................................... 54
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3.5.1 The role of DR programs for transmission line planning ......................... 55
3.5.2 The role of DR for providing ancillary services ....................................... 55
3.6 Review of demand response programs in electricity markets .......................... 56
3.6.1 Electric Reliability Council of Texas ........................................................ 56
3.6.2 California ISO (CAISO) ........................................................................... 58
3.6.3 PJM Interconnection ................................................................................. 58
3.6.4 New York ISO (NYISO) ........................................................................... 59
3.7 Summary of the demand response program in the U.S. electricity market ...... 59
Chapter 4 Multi-objective approach for optimal allocation of FACTS devices ........ 61
4.1 FACTS allocation overview ............................................................................. 62
4.2 Problem formulation ......................................................................................... 64
4.2.1 Cost ........................................................................................................... 64
4.2.2 Loadability index ...................................................................................... 64
4.2.3 Voltage deviation index ............................................................................ 65
4.2.4 Active power losses................................................................................... 65
4.2.5 Equality constraints ................................................................................... 66
4.2.6 Inequality constraints ................................................................................ 66
4.3 Multi-objective optimisation ............................................................................ 67
4.4 Implementation of NSGA-II method ............................................................... 68
4.4.1 Initial population ....................................................................................... 69
4.4.2 Fitness evaluation ...................................................................................... 70
4.4.3 Iterative process ........................................................................................ 71
4.4.4 Selection of final solution ......................................................................... 72
4.5 Numerical Studies ............................................................................................ 75
4.6 TCSC allocation ............................................................................................... 79
4.6.1 Objective function formulation for TCSC allocation................................ 80
4.6.2 Numerical results for TCSC placement .................................................... 86
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4.6.3 Conclusion ................................................................................................ 89
Chapter 5 Multi-objective demand response allocation ............................................ 90
5.1 Problem formulation ......................................................................................... 91
5.1.1 Expected energy not supplied (EENS) ...................................................... 91
5.1.2 Active power loss ...................................................................................... 92
5.1.3 Available transmission capacity ................................................................ 92
5.1.4 Total DR programs capacity ..................................................................... 95
5.1.5 Equality constraints ................................................................................... 95
5.1.6 Inequality constraints ................................................................................ 96
5.2 Variables and their representation .................................................................... 96
5.2.1 Fitness evaluation ...................................................................................... 97
5.2.2 Iterative process ........................................................................................ 98
5.2.3 Selection of final solution ....................................................................... 100
5.3 Numerical Studies .......................................................................................... 101
5.4 Conclusion ...................................................................................................... 103
Chapter 6 Congestion management using demand response program .................... 104
6.1 Congestion management ................................................................................ 105
6.1.1 Preventive congestion management methods ......................................... 105
6.1.2 Corrective congestion management methods.......................................... 107
6.2 Modelling demand response program ............................................................ 108
6.3 Auction-based market clearing ....................................................................... 114
6.4 Congestion management by generation and demand re-dispatch .................. 115
6.5 Numerical studies ........................................................................................... 116
6.6 Conclusion ...................................................................................................... 122
Chapter 7 Hybrid approach for congestion management using combination of
demand response and FACTS devices .......................................................................... 123
7.1 Introduction .................................................................................................... 123
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7.2 Problem formulation ....................................................................................... 124
7.2.1 Congestion management formulation ..................................................... 125
7.3 Numerical studies ........................................................................................... 129
7.4 Conclusion ...................................................................................................... 135
Chapter 8 Facilitating large integration of wind power generation through effective
utilisation of demand response program ....................................................................... 136
8.1 Introduction .................................................................................................... 136
8.2 Problem formulation ....................................................................................... 140
8.2.1 Market clearing formulation ................................................................... 140
8.3 Representative study ....................................................................................... 145
8.4 Conclusion ...................................................................................................... 153
Chapter 9 Conclusions ............................................................................................. 154
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List of Figures:
Fig. 2.1: Typical SVC connection .................................................................................. 31
Fig. 2.2: Thyristor controlled reactor ............................................................................. 31
Fig. 2.3: Typical VAr compensator ................................................................................ 33
Fig. 2.4: SVC schematic diagram ................................................................................... 33
Fig. 2.5: V-I characteristic of the SVC ........................................................................... 34
Fig. 2.6: Schematic diagram of the TCSC ...................................................................... 35
Fig. 2.7: The reactance versus delta angle characteristic of the TCSC ........................... 37
Fig. 2.8: Typical V-I characteristics for a single-module TCSC .................................... 38
Fig. 2.9: The correlation between TCSC reactance and line current .............................. 39
Fig. 2.10: Typical V-I capability characteristics for TCSC with two modules............... 40
Fig. 2.11: Typical X-I capability characteristics for a typical TCSC with two modules 40
Fig. 2.12: Effective FACTS devices for voltage control ................................................ 42
Fig. 2.13: Effective FACTS devices for reactance and angle ........................................ 42
Fig. 3.1: Time-based and Incentive-based Demand Response Programs 53
Fig. 4.1: NSGA II procedure 69
Fig. 4.2: Representation of a power system and the sample string for SVC locations and
sizes ................................................................................................................................. 70
Fig. 4.3: The selection procedure for optimal allocation of the SVC ............................. 74
Fig. 4.4: IEEE 14 bus test system ................................................................................... 75
Fig. 4.5: Flowchart of the proposed algorithm ................................................................ 85
Fig. 4.6: IEEE 30 bus test system ................................................................................... 86
Fig. 5.1: Representation of sample power system and string for DR locations and sizes
97
Fig. 5.2: Flowchart of the proposed algorithm. ............................................................... 99
Fig. 5.3: Single line diagram of the IEEE 30 bus test system ....................................... 101
Fig. 6.1: The elasticity of the typical elastic and inelastic load 110
Fig. 6.2: Linear representation of price versus quantity................................................ 110
Fig. 6.3: Non-linear representation of price versus quantity ......................................... 111
Fig. 6.4: IEEE 30-bus system ........................................................................................ 116
Fig. 6.5: The load curve before and after DR program implementation ....................... 118
Fig. 6.6: Total cost of market operation in three scenarios of demands ($/hour) ......... 121
Fig. 7.1: Typical demand response offer to the market. 126
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Fig. 7.2: Two step market clearing procedure............................................................... 128
Fig. 7.3: IEEE 30-bus system ........................................................................................ 129
Fig. 8.1: Load profile and wind generation in CAISO 139
Fig. 8.2: Approximated cost function by the piecewise blocks .................................... 141
Fig. 8.3: Typical price-quantity offer package of the DR aggregator ........................... 143
Fig. 8.4: Summary of the market clearing procedure with demand response and NAS
battery ............................................................................................................................ 145
Fig. 8.5: Load profile before and after DR implementation ......................................... 152
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List of Tables:
Table 2.1: FACTS devices and their applications ........................................................... 41
Table 2.2: Various type of FACTS and their applications .............................................. 43
Table 3.1: Provided spining reserve by demand side resources in different markets
across the U.S 56
Table 3.2: Summary of active demand response programs for providing spinning
reserve in ERCOT ........................................................................................................... 57
Table 3.3: Summary of demand response programs for providing non-spinning reserve
......................................................................................................................................... 57
Table 3.4: Comparison of the conventional generators and demand response programs
in providing ancillary services ........................................................................................ 58
Table 3.5: Utility companies with active DLC program ................................................. 60
Table 4.1: Three contingencies in IEEE 14 bus network 76
Table 4.2: The installation cost, location and size of the SVCs ...................................... 77
Table 4.3: The comparison between active power loss before and after SVC installation
......................................................................................................................................... 78
Table 4.4: The comparison between voltage deviation index before and after SVC
installation ....................................................................................................................... 78
Table 4.5: The comparison between loadability index of transmission lines before and
after SVC installation ...................................................................................................... 79
Table 4.6: Selected severe contingencies in the IEEE 30 bus system ............................ 87
Table 4.7: The locations and sizes of the TCSC based on the optimisation outcome .... 87
Table 4.8: The comparison of active-power loss before and after TCSC installation .... 88
Table 4.9: The security margin comparison before and after TCSC installation ........... 88
Table 4.10: The ATC comparison before and after TCSC installation........................... 88
Table 5.1: Selected buses and the amount of DR programs 102
Table 5.2: The comparison between active-power loss before and after DR
implementation .............................................................................................................. 102
Table 5.3: The comparison between EENS before and after DR implementation ....... 102
Table 5.4: The comparison between ATC before and after DR implementation. ........ 103
Table 6.1: Loads in three scenarios of demand 117
Table 6.2: Load demands due to various incentives and penalties ............................... 119
Table 6.3: The auction results for generators ................................................................ 119
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Table 6.4: The auction results for generators and responsible demands....................... 120
Table 6.5: Generator increment and decrement to release the congestion .................... 120
Table 6.6: Generators and Responsible demands increment and decrement to release the
congestion ..................................................................................................................... 121
Table 7.1: Load demand with power factor 0.9 130
Table 7.2: selected buses for Demand response implementation ................................. 131
Table 7.3: selected buses for demand response implementation .................................. 131
Table 7.4: Facts devices data ........................................................................................ 131
Table 7.5: The Auction Results for Generators participated in electricity market ....... 132
Table 7.6: Generation increment and decrement for all generators due to congestion
management (MW) ....................................................................................................... 133
Table 7.7: demand response contribution for congestion management (MW) ............. 134
Table 7.8: Total cost of market operation and redispatch cost in different scenarios and
system states .................................................................................................................. 134
Table 8. 1: Cost function and generation limit for conventional generators in IEEE 57
bus system 146
Table 8.2: The pollution cost function for IEEE 57 bus generators.............................. 146
Table 8.3: Cost function and generation limit for conventional generators in IEEE 30
bus ................................................................................................................................. 147
Table 8.4: The pollution cost function for generators in IEEE 30 bus ......................... 147
Table 8.5: Self and cross elasticity values . .................................................................. 148
Table 8.6: Demand side resources contribution for three different participation levels in
IEEE 57 bus system ...................................................................................................... 148
Table 8.7: Conventional generators contribution for three different participation levels
in IEEE 57 bus system .................................................................................................. 149
Table 8.8: Demand side resources contribution for three different participation levels in
IEEE 30 bus system ...................................................................................................... 149
Table 8.9: Conventional generators contribution for three different participation levels
in IEEE 30 bus system .................................................................................................. 150
Table 8.10: Total Market Cost for different demand side participation level in........... 153
Table 8.11: Total Market Cost for different demand side participation level in........... 153
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Chapter 1
Many countries around the world are introducing programs aimed at reducing the
emissions produced by the power plants and increasing the utilization of renewable
generation. Among different types of renewable energy technologies, wind power is
expected to be one of the most popular types of renewable in the near future [1].
However, high penetration of wind power can introduce new challenges and reduce
the power system security [2-7]. Some of the major challenges which arise as a result
of large integration of renewable generation are summarised as follows:
Lack of wind power and demand correlation
Congestion in transmission lines
Impacts on transient stability of the system
Protection system maloperation in distribution networks
Addressing these issues require considerable research on the identified problems. This
thesis focuses on lack of correlation between the demand and the wind power
generation as well as transmission congestion management in power systems. A
comprehensive approach is proposed to address these issues by effective utilisation of
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FACTS devices and demand response programs. In this research, a day–ahead
network constrained market clearing formulation is developed in which demand side
resources can participate in the market in addition to the conventional generators. In
the next step, an integrated approach using combination of FACTS and dispatchable
demand response program is proposed to provide additional flexibility for system
operator to maintain the system security during peak demand or major contingencies
in the network. To be able to achieve this goal, potential barriers are determined and
required milestones are identified. Summary of the achieved milestones are reported in
the following:
In the first step, different types of demand response programs and its application for
the power system operation are reviewed and the summary of the literature review is
presented. In the next step, various types of flexible AC transmission system devices
and their applications for power system are reviewed through extensive literature
review. As part of this step, the steady state model of popular FACTS devices
including thyristor controlled series compensator (TCSC) and the static var
compensator (SVC) are presented which used for FACTS simulation in later stages of
this research.
In the next step, a multi-objective algorithm is developed for optimum allocation of
TCSC and SVC in the electricity network. The TCSC allocation considers four
objectives including power loss reduction, investment cost minimisation, security
margin improvement and available transmission capacity enhancement. Another
multi-objective allocation problem is also developed for SVC allocation that considers
network active-power loss, capital cost of SVCs and system voltage deviation as the
main objectives for optimisation. The outcomes of the proposed algorithm can
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determine the optimum location and sizes of the TCSC and SVC in the electricity
network.
The next stage of the thesis is dedicated to optimum allocation of demand response
program. As different factors are involved for effective allocation of demand response
program, a multi-objective optimisation is formulated which considers expected
energy not supplied (EENS), active power loss, available transmission capacity (ATC)
and total DR programs capacity as the main objectives for demand response program
allocation. In addition, the demand response elasticity based model is developed by
adding incentive and penalty factors to the existing mathematical model to provide
additional control for the market operator to have two factors to control the capacity of
responsive demands. These additional control factors can provide an opportunity for
system operator to encourage demand response program participants at specific load
nodes that has a considerable impact on the power system security enhancement.
In the next stage, an integrated approach is developed using combination of FACTS
and event-driven dispatchable demand response program to manage the congestion in
the transmission lines during the peak periods or major contingencies in the network.
A constrained optimisation is developed as part of this stage for effective coordination
of FACTS and demand side resources.
The final part of the thesis focuses on the role of demand side resources in enabling
the power system for large integration of renewable energy especially the wind power
generation. A day-ahead network-constrained market clearing formulation is proposed
in which dispatchable demand side resources can reduce the need for ramping
up/down services by conventional generators. This approach can provide a cost
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effective solution for operation of power system with large amount of renewable
energy and enhance the system security and reliability. The presented methods in this
thesis can provide additional tool for system operator to maintain the power system
security in electricity networks with large integration of renewable energy.
1.1 Objectives
a) Developing a mathematical model for demand response program
b) Developing a comprehensive multi-objective approach for demand response
program allocation
c) Determining the optimal size and location of static var compensator in the
electricity network through multi-objective approach
d) Determining optimal location and sizes of TCSC in the electricity network by
using multi-objective optimisation
e) Proposing an integrated approach for transmission congestion management
through effective combination of demand response program and FACTS devices
f) Proposing a comprehensive approach to mitigate the lack of correlation between
power system load profile and wind power generation using demand response
programs in electricity networks with high penetration of wind power
generation
1.2 Outline of the thesis
This thesis is organised in nine chapters. Starting with the background and scope of the
research, the first chapter presents the objectives, outline and the contributions of the
thesis.
Chapter 2 focuses on general overview of the previously reported steady-state models
for FACTS devices. In this chapter, a comprehensive review for the FACTS devices and
their applications in power system operation are presented.
In Chapter 3, a comprehensive overview of the demand response programs is presented
and reviewed. The successful experiments of demand response programs in different
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countries are also reviewed in this chapter. Chapter 2 and 3 provide a foundation for the
subsequent chapters.
Chapter 4 develops a multi-objective approach to find the optimal allocation of SVC
and TCSC in the electricity network. This Chapter presents a comprehensive approach
to find optimum locations and sizes of TCSCs (Thyristor controlled Series
Compensator) and static var compensator (SVC) in the power system. The approach
comprises two main parts. In the first part, a mixed continuous-discrete multi-objective
optimization problem is formulated in which TCSCs locations and sizes are the
variables. The second part develops an optimization method based on NSGA II (Non-
dominated Sorting Genetic Algorithm) to solve the problem. Non-dominated sorting
genetic algorithm (NSGA II) is used for determining the optimal location of TCSCs.
This is done by considering power loss reduction, investment cost minimisation,
security margin improvement and available transmission capacity enhancement in the
allocation objectives. A similar multi-objective approach is also used for optimum
allocation of SVC with considering network active-power loss, capital cost of SVCs and
system voltage deviation.
In chapter 5 is developed a comprehensive solution for optimal allocation of the demand
response programs in the electricity network. The outcomes of this chapter can
determine the optimum amount and the location of the demand response programs in
the electricity network. An approach for optimally selecting the locations of DR
programs in the network together with their capacities to achieve the maximum
technical benefits from the programs is proposed. The method is based on the
constrained optimization of multi-objective function formed in terms of the expected
energy not supplied (EENS), active power loss, available transmission capacity (ATC)
and total DR programs capacity. This multi-objective function is then optimised based
on a heuristic method to find the amount and locations of DR programs. The presented
approach is a general one in principle and can be customised and extended to design DR
programs with technical and economic objectives other than those considered in this
research.
Chapter 6 develops a method for transmission line congestion management using
demand side approach. In the proposed method, a non-linear mathematical model for
______________________________________________________________________
24
incentive-based event-driven demand response program is used for modelling demand
side resources. A coordination process between the generators, demand response
participants and independent system operator is proposed to release the congestion in
the electricity network. In addition, to evaluate the effectiveness of the proposed method
in contingency condition, critical contingencies are identified and considered to verify
the effectiveness of the proposed approach in the contingency condition.
A hybrid approach is proposed in chapter 7 for transmission lines congestion
management in a restructured market environment using combination of dispatchable
demand response (DR) program and flexible alternating current transmission system
(FACTS) devices. A two-step market clearing procedure is formulated which
conventional generators and demand side resources can bid to the market. In the first
step, generation companies bid to the market for maximizing their profit, and the ISO
clears the market based on social welfare maximisation. Network constraints including
those related to congestion management are presented in the second step of the market-
clearing procedure. A re-dispatch formulation for the second step is developed using
mixed integer optimisation technique in which demand responses and FACTS device
controllers are optimally coordinated with conventional generators.
A day-ahead network-constrained market clearing formulation is presented in chapter
eight that considers a combination of conventional generators and demand side
resources. The proposed approach can provide flexible load profile and reduce the need
for ramp up/down services by the conventional generators. This method can potentially
facilitate large penetration of renewable generation by shifting the wind power
generation from the off-peak periods to the high-peak hours. The proposed approach
can mitigate some of the challenges that arise because of large-scale wind power
penetration into the electricity network.
The overall conclusion in chapter 9 summarises the main features and advances of the
research reported in this thesis.
______________________________________________________________________
25
1.3 Contributions of the thesis
1. Development of a comprehensive multi-objective approach for demand response
programs allocation
2. Optimum allocation of static var compensator (SVC) in the electricity network
to minimise the investment cost, voltage deviation, the active power loss and
also maximising the transmission system loadability
3. Optimal allocation of TCSC in the electricity network to minimise the
investment cost, the active power loss and maximise the loadability of
transmission lines
4. Development of a non-linear incentive based demand response model by adding
penalty and incentive factors which can potentially increase the control of the
market operator on amount and availability of demand side resources
5. Proposal of an integrated approach for transmission congestion management
through effective combination of demand response program and FACTS devices
6. Proposal of a comprehensive approach to mitigate the lack of correlation
between power system load and wind power generation in electricity networks
with high penetration of renewable energy
1.4 Publications
This thesis is supported by eight publications as follows:
1- Ashkan Yousefi, Herbert H.C Iu, Tyrone Fernando, “An Approach for Providing
Spinning Reserve using Demand Response Program”, International Journal of
Electrical Power and Energy Systems, 2013 (under review).
2- Ashkan Yousefi, Herbert H.C Iu, Tyrone Fernando and Hieu Trinh, “An
Approach for Wind Power Integration Using Demand Side Resources”, IEEE
Transactions on Sustainable Energy, vol.4, no.4, pp.917,924, Oct. 2013.
3- Ashkan Yousefi, Herbert H.C Iu, Tyrone Fernando, “Optimum Scheduling of
Spinning Reserve by Integration of Demand Response Program”, AJEEE:
Australian Journal of Electrical & Electronics Engineering, Volume 10 Issue
2 (2013).
4- Ashkan Yousefi, Herbert H.C Iu, Tyrone Fernando, “Optimal locations and sizes
of static var compensators using NSGA II”, AJEEE: Australian Journal of
Electrical & Electronics Engineering, Volume 10 Issue 3 (2013).
5- A. Yousefi, T. T. Nguyen, H. Zareipour, and O. P. Malik, "Congestion
management using demand response and FACTS devices," International Journal
of Electrical Power and Energy Systems, vol. 37, pp. 78-85, 2012.
______________________________________________________________________
26
6- T. T. Nguyen and Ashkan Yousefi, "Demand side solution for transmission
congestion relief in competitive environment," International Review on
Modeling and Simulations, vol. 4, pp. 171-179, 2011.
7- T. T. Nguyen and Ashkan Yousefi, "Multi-objective demand response allocation
in restructured energy market," in Innovative Smart Grid Technologies (ISGT),
2011 IEEE PES, 2011, pp. 1-8.
8- T. T. Nguyen and Ashkan Yousefi, "Multi-objective approach for optimal
location of TCSC using NSGA II," in Power System Technology
(POWERCON), 2010 International Conference on, 2010, pp. 1-7.
______________________________________________________________________
27
Chapter 2 Steady-state models of
flexible AC transmission system
devices
Demand growth together with the requirement for providing transmission access for
generation companies leads to the need for transmission system reinforcement or
expansion. However, practical constraints, which arise from environmental
consideration and investment decision in competitive electricity markets, can prevent, or
defer the construction of new transmission lines. Consequently, the transmission system
capacity would not be adequate to meet the requirements related to demand growth.
With limited capacity, transmission congestion can arise, depending on the demand and
/or contingency. To certain extent, FACTS devices can enhance the transmission
capacity of the existing system without the need for additional transmission lines. With
FACTS device installation, transmission congestion can be eliminated or mitigated [8-
10]. The effectiveness of FACTS devices needs detailed evaluation based on system
simulation. In the context of dispatch and congestion management in electricity market,
FACTS devices are represented in terms of steady-state models in a single-phase
equivalent form[11]. Although, there has been some research on representing stability
constraints in dispatch calculations, using dynamic models [12, 13], the focus of the
thesis is on steady-state operation. The steady-state FACTS devices models are in the
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28
form that directly augments the steady-state power network model to a set of equations
and inequalities for use in dispatch calculation together with congestion evaluation and
management. This chapter reviews the FACTS devices operating principles and control
objectives based on which the FACTS models are explained[14].
2.1 Basic Mechanisms of Compensation
Transmission line capacity is usually limited by some factors including thermal limit of
transmission lines, power system security and system stability. These limitation factors
are briefly reviewed in the following section.
2.1.1 Power system stability
Power system stability is the capability of a power system, for a specific initial
operating condition, to recover a state of operating equilibrium after a system
disturbance and/or contingency, with most system variables bounded so that the entire
system remains intact [15]. Generally, stability margin is reduced during high peak
periods. Stability would be lost if the system loading exceeds its upper limit which
depends mainly on the type of disturbance.
2.1.2 Power system static security
The other major factor in limiting the transmission line capacity is referred to as power
system static security. The power system should be managed in a way that satisfies the
static security criteria, which are specified in terms of voltage limitations and maximum
transmission capacity of the transmission lines in steady-state operating condition[16].
2.2 Steady-state models of power system elements
Modelling each individual components or items of plant in the system is a major
milestone in power system analysis. In power system studies, different models are used
for different studies. For the purpose of this thesis, the steady state model will be
______________________________________________________________________
29
discussed in more details. There are different levels for presenting power system and its
components in the steady-state mode. If the focus is on system operating unbalances,
then phase variable models are required in the analysis and evaluation for most of the
steady-state system studies. The system voltage and current variables are represented by
positive-phase sequence, and the system elements are modelled based on single-phase
equivalent in positive sequence [11].
2.3 Power system nodal formulation
This model is developed on the key assumption that the network operates in steady-state
mode at the supply frequency, and the voltages and the currents are represented in
phasor forms. This allows the system elements to be modelled by their
impedances/admitances at the supply frequency. Based on balanced operating condition,
the system elements are represented by a single-phase equivalents expressed in the
positive-phase sequence. The network model, which is combined with nodal operating
constraints at individual load nodes and generator nodes, are converted to set of
nonlinear equations. Inequality constraints are used for considering generator reactive-
power limits and transformer tap position ranges. They are given in the following in a
compact form. The power system nodal formulation can be explained in a compact form
as per equation (2.1).
0uθVf ),,(
(2. 1)
where
f is a function of |V|, θ and u which is explained in a vector form;
System voltage magnitudes and phase angles are explained by |V| and θ
Control variables are summarised in vector u
The control variables in (2.1) are the control signals of the controlling tools such as off-
nominal tap position of a load-tap-changing transformer (LTC). In addition to these
equality constrains, there are other inequality constrains that can be considered for
power flow calculations. These inequalities constrains are summarised and presented in
a short form as follows:
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30
0uθVh ),,( (2. 2)
In (2.2), h is a vector function of |V|, θ and u.
2.4 Modelling of the FACTS devices
The flexible AC transmission systems which is known as FACTS are power electronic
devices are used for improving the efficiency and enhancing the controllability of the
electricity network. The FACTS devices were introduced for the first time by the
Electric Power Research Institute (EPRI) to improve the controllability on the power
system and enhancing the dynamic response of the power system elements.
The major benefits of the FACTS for power system can be summarized as increasing
the control on the voltage nodes and the power flow in electricity network [14]. In
addition, these power electronic devices have considerable effects on improving the
dynamic responses of the power system which is not a main focus of this research. This
section reviews two of the popular FACTS devices which are the static VAr
compensator (SVC) and thyristor-controlled series compensator (TCSC) [11] [14].
2.4.1 Static VAr compensator (SVC)
The first SVCs were installed for compensation of large fluctuating caused by large
industrial loads, such as switching of large motors in factories. Later, the SVC
applications are focused on voltage improvement and increasing the control on
transmission lines [17].
The SVC is made of advanced power electronic tools and used for providing shunt
compensation in the network. Fig. 2.1 explains the typical SVC structure and its main
components.
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31
Fig. 2.1: Typical SVC connection
In many cases, the SVC is connected to the transmission network through coupling
step-up transformer. At the low-voltage side of the transformer, three types of elements
are connected, including fixed harmonic filters, thyristor switched capacitors and
thyristor controlled reactor [14]. The brief review of each item is presented as follows:
2.4.1.1 Thyristor controlled reactor (TCR):
A schematic diagram of the single-phase TCR, including the thyristor pair and the
reactor is shown in Fig. 2.2.
Fig. 2.2: Thyristor controlled reactor
The controlled switching of the thyristors combined with the linear reactor enables
the effective supply-frequency for TCR, which is a function of the delay angle, to
Thyristor switched
capacitors
Harmonic
Filter
Controlled
reactor
Low-voltage bus
Transformer
High-voltage bus
XL
______________________________________________________________________
32
change continuously from the predefined reactance value of the reactor to the value
that the thyristor operates on fully non-conducting mode [11, 14]. The effective
value of the TCR is shown in equation (2.3):
sin2-2-π
π)( Ltcr XX (2. 3)
where
α is the delay angle which is calculated based on the applied voltage to the TCR,
and can varies from 2
π0 ;
Xtcr is the effective reactance of the thyristor controlled reactor at the nominal
frequency;
XL is the reactance of the reactor at the nominal frequency.
2.4.1.2 Thyristor switched capacitors (TSCs):
TSC has the ability to provide inductive and capacitive output for the network.
2.4.1.3 Fixed harmonic filters:
The filters can provide low-impedance paths and capacitive compensation for harmonic
currents generated from the TCR. Variation of the thyristor firing angle α yield to the
TCR reactance change that eventually changes the effective reactance of the SVC. In
other words, the SVC can change from the capacitive mode to the reactive one by
changing the firing angle. Schematic diagram of an SVC is shown in Fig. 2.3. The SVC
generally considered as a device that can provide a capacitive or inductive mode by
either generating or absorbing the reactive power.
______________________________________________________________________
33
Fig. 2.3: Typical VAr compensator
Generally, the SVC is not connected directly to the transmission lines and a coupling
transformer is required for connecting an SVC to the high voltage level. Fig 2.4
demonstrates an SVC connection to the high voltage line.
Fig. 2.4: SVC schematic diagram
V-I characteristic of the steady-state operational mode of the SVC is shown in Fig. 2.5.
A steady-state model for the SVC should be able to reproduce the above characteristic.
Coupling
transformer
High voltage line Vhsvc
SVC
Isvc
Vlsvc
Transmission line
C
XL
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34
Fig. 2.5: V-I characteristic of the SVC
Based on this explanation the voltage magnitude at the high-voltage side can be
explained as per equation (2.4):
svcsvcsvcrefhsvc IaVV || (2. 4)
where
|Vhsvc| and Vsvcref are high-voltage node and the reference value for the SVC
respectively;
asvc is the SVC slope reactance
Isvc is the SVC current
The SVC current phasor can be considered as possible reactive power contribution by
ignoring the active-power loss of the SVC. If the current lags the voltage by 90°, the
SVC operates in inductive mode. The SVC runs in a capacitive mode when the voltage
and the current angle is 90°lead. Based on V-I characteristics in Fig. 2.5, It can be seen
that the operating constraints of the SVC depends on its susceptance. The SVC
susceptance is explained in equation (2.5).
hsvc
svcsvc
V
IB
(2. 5)
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35
Based on V-I characteristics of Fig. 2.5, the SVC operating constraints can also be
explained based on its susceptance as per equation (2.6).
maxmin svcsvcsvc BBB (2. 6)
where Bsvcmax and Bscvmin are the maximum and minimum susceptance of the SVC,
respectively. The control ability of the SVC is valid just between these operating limits
[14].
2.4.2 Thyristor controlled series compensator (TCSC)
The other FACTS device that is used for improving the power system efficiency is
thyristor controlled series compensator. The TCSC is connected in series to the
transmission lines and it has a crutial role in improving the loadability of the
transmission line. TCSC can have a significant contribution for power system stability
improvement and have a noticeable effect on enhancing the power transfer capability.
Fig. 2.6 demonstrates a typical TCSC [14, 18]:
Fig. 2.6: Schematic diagram of the TCSC
TCSC can be modelled by capacitors connected in series with a transmission line.
TCSC is able to reduce the transmission line impedance and facilitate the transfer of
additional power via the existing transmission lines. In addition, TCSC is able to
enhance the loadability of the transmission lines and improve the voltage profile. In
other words, TCSC can be used as an effective tool to enhance the security of the power
system. The main elements of the TCSC are a series capacitor that is connected in
parallel with a TCR. In addition to these a metal-oxide varistor (MOV) is connected in
parallel with the series capacitor play a role of protection. In Fig. 2.6, the reactance of
the series capacitor and the reactor of the TCR are denoted by XC and XL , respectively.
XC
XL
MOV
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36
Basically, TCSC has three operation modes which can be useful in different operational
condition [19]:
2.4.2.1 Bypassed-thyristor mode:
In this mode, the TCSC acts as a combination of parallel capacitor and reactor. The net
reactance of the TCSC can be calculated by bypassX which is explained in equation (2.7).
L Cbypass
L C
X XX
X X
(2. 7)
If the TCSC is operated in the inductive mode, the XL value can varies in the following
range:
0 L CX X (2. 8)
2.4.2.2 Blocked-thyristor mode:
The TCSC is controlled to block the current through TCR branch, and acts as a fixed-
series capacitor.
2.4.2.3 Partially conducting thyristor mode:
In this mode which is the most controllable mode in comparison to other modes, the
firing angles of the TCSC can vary in a range to shift the TCSC from the capacitive
mode to the inductive mode or vice versa. In the partially conducting thyristor mode,
the effective reactance of the TCSC is calculated based on parallel circuit consisting of a
fixed capacitive reactance, XC, and a variable inductive reactance, Xtcr(α) [14]. The
effective reactance of the TCSC can be calculated as per equation (2.9):
Ctcr
tcrC
tXX
XXX
)(
)()(csc
(2. 9)
Fig. 2.7 demonstrates the correlation between effective reactance and the firing angle of
the TCSC. In Fig. 2.7, 𝛿𝐿𝑚𝑎𝑥and 𝛿𝐶𝑚𝑎𝑥are the delay angle limits in the inductive and
capacitive areas. The delay angle between 𝛿𝐿𝑚𝑎𝑥 to 𝛿𝐶𝑚𝑎𝑥 is not permitted, and XLmax
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37
and XCmax are maximum limits of the inductive and capacitive reactance modes of the
TCSC.
Fig. 2.7: The reactance versus delta angle characteristic of the TCSC
The other constraint on the operation of a TCSC is imposed by MOV, which limits the
TCSC operation in the inductive zone.
XLmax
maxC π/2 maxL
Operation inhibited
maxmax CL
Inductive area
max0 L
Capacitive area
2/max C
Xtcsc
0
XC
Xbypas
s
Xcmax
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38
Fig. 2.8: Typical V-I characteristics for a single-module TCSC
Continuous operation
Transient operation in long-term
Transient operation in short-term
Fig. 2.8 [14, 20, 21] shows a V-I characteristics of the typical TCSC. This
characteristic is derived based on different constrains in TCSC operation such as
thyristor delay angle and voltage limits.
Fig. 2.9 shows the operational constraints of the TCSC in terms of the relationship
between reactance and lines current [20]. As it is shown, the voltage compensation can
be achieved because of changes in compensating impedance. The TCSC limitation is
dynamic, and it varies based on reactance boundaries as shown in Fig. 2.9. It is
necessary to note that reactance boundaries are not fixed values and could be change
based on transmission line currents [14, 22].
Harmonic limitation
Current
Full
Thyristor conduction
Maximum
firing
Firing
limitation
(delay)
0
(Cap
acit
ive
area
) (I
nduct
ive
area
) V
olt
age
Maximum
thyristor
current
MOV protection level
______________________________________________________________________
39
The other limitation in the operation of the TCSC is a gap in the control range between
block reactance and the bypass reactance that are denoted by XC and Xbypass respectively.
Fig. 2.9: The correlation between TCSC reactance and line current
One of the alternatives to bypass this gap is to split the TCSC operation into multiple
sections which each of which section can simulate the TCSC for both inductive and
capacitive modes [23]. Figs.2.10 shows the V-I characteristics of the typical TCSC.
Fig. 2.11 shows the reactance versus the line current for the operation of the TCSC. As
it can be seen, the operational boundary of the TCSC can be limited if the current
increases in the transmission lines. The dependency of operational range of TCSC to the
transmission line currents is demonstrated in Fig 2.11.
current
1
Imax 0
Cap
acit
ive
area
Induct
ive
area
Rea
ctan
ce
C
bypass
X
X
0
______________________________________________________________________
40
Fig. 2.10: Typical V-I capability characteristics for TCSC with two modules
Both TCSC modules operate in a capacitive region
One TCSC module operates in a capacitive region, the other one in an inductive
region
Both TCSC modules operate in an inductive region
Fig. 2.11: Typical X-I capability characteristics for a typical TCSC with two modules
Both TCSC modules operate in a capacitive region
One TCSC module operates in a capacitive region, the other in an inductive
region
Both TCSC modules operate in an inductive region
Current
0
Cap
acit
ive
area
area
area
Induct
ive
area
V
olt
age
In
duct
ive
area
Imax
Current
0
Cap
acit
ive
area
Rea
ctan
ce
______________________________________________________________________
41
As it is shown, the transition between the capacitive and inductive zone can be smoother
by increasing the number of modules [11, 14, 24]. The following table summarises and
compares different FACTS devices and the general applications of each type.
Table 2.1: FACTS devices and their applications
Type of FACTS Features
Static VAr Compensator (SVC) Reactive power compensation,
Voltage control
Thyristor-controlled series compensator
(TCSC)
Power control, voltage control, series
impedance control, transient stability
Unified Power flow Controller (UPFC) Power control, voltage control, reactive
power compensation, transient stability
In the next section, application of each type of FACTS devices and practical
experiments in using FACTS devices and practical experiments at restructured
electricity network are presented and discussed [25].
2.5 Applications of FACTS devices in power system
FACTS devices are generally divided into two broad groups from controlling the active
power transfer capability of the transmission lines. First group of FACTS as presented
in Fig 2.12 can be used for voltage control such as SVC, static synchronous
compensator (STATCOM), Unified Power Flow Controller (UPFC) and Thyristor
Controlled voltage regulator (TCVR). The second group of FACTS as presented in Fig
2.13 can be used for controlling line reactance and angle such as TCSC, static
synchronous series compensator (SSSC), UPFC, Thyristor controlled phase angle
reactor (TCPAR) and Thyristor Controlled Phase Shifting Transformer (TCPST).
______________________________________________________________________
42
Fig. 2.12: Effective FACTS devices for voltage control
Fig. 2.13: Effective FACTS devices for reactance and angle
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43
Table 2.2 summarise the main application of various FACTS devices in the electricity
network. This table also categorises FACTS devices based on major impacts of each
group on power system.
Table 2.2: Various type of FACTS and their applications
Principle Type of FACTS Devices
Major effects on the power
system
Load
flow stability
Power
quality
Series
compensation
FSC
(fixed series compensator)
TPSC (Thyristor protected
series compensator)
TCSC (Thyristor controlled
series compensator)
●
●
●
●
●
●
●
●
●
Shunt
compensation
SVC (Static var compensator)
STATCOM (Static
synchronous compensator)
●
●
●
●
Load flow
control
UPFC (Unified Power flow
controller) ● ● ●
2.5.1 The role of FACTS for congestion management
As mentioned in previous sections, the congestion is one of the major problems for both
vertically integrated and deregulated power systems. In vertically integrated systems
the duration, place and type of congestion were determined before generator dispatch.
However, in the electricity market, the congestion problem is more complicated and
many uncertainties might affect the congestion problem in the system.
The congestion in the restructured environments has serious impacts on the electricity
market performance such as [26-29]:
Preventing new contracts in the market
Market Power in some parts of the network
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44
Load shedding
The majority of the researches related to FACTS devices for congestion management.
Some of the research focused on operation cost minimisation using FACTS devices. In
[30-43], the FACTS device allocation and its effects for minimising the cost of
operation is considered. The main aims of these researches are cost minimisation by
improving the available transmission capacity and congestion relief. The major
differences of these researches can be summarised into four different areas:
Different kind of markets (pool, bilateral and hybrid)
Different type of FACTS devices
Different optimisation methods
In [44-50] the available transmission capacity (ATC) maximisation is considered. In
[10], the FACTS devices are used for congestion management and also the cost
allocation of each market participant for providing the capital cost of FACTS devices
are considered. Most of the papers in congestion management section consider the
thermal limits of the transmission lines and the role of FACTS for improving the load
ability of transmission system. However, in [51] the voltage profile and the transmission
line load ability enhancement considered simultaneously. In [52], the location marginal
price minimisation is considered as an objective function for congestion management.
In [53-55] the congestion management is considered and the number and size of the
FACTS devices are optimised to satisfy the proposed object. In [56], the effect of
FACTS devices in minimising the cost of locational marginal price is presented.
In [57], the economic studies for European electricity network are implemented to
analyse the effects of FACTS devices for transmission line enhancement. The results of
these studies confirm that FACTS devices can be a feasible solution for congestion
management in midterm.
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45
Chapter 3 Demand response
program
The aim of this chapter is to introduce demand response (DR) programs and have a brief
overview on each time-based and incentive-based programs. This chapter covers the
following topics:
• Definition of demand response program
• Different types of demand management programs
• The role of DR in power system operation
• The role of demand response in electricity market
3.1 Definition of demand response program
Demand response program is defined as changes in electricity consumers demand in
response to price signals or incentives, which are offered by utilities or market operators
[58]. In some electricity markets, DR programs are defined as changes in electricity
consumption by retail customers from their normal load in response to electricity price
______________________________________________________________________
46
change, or to incentive payments. These programs are designed to reduce lower
electricity usage at times of high wholesale market price or to maintain the power
system security and reliability[59].
3.2 Benefits of DR programs
The main advantages of DR programs are those of optimising the utilisation of the
existing power network and deferring / avoiding network expansion, and this goal can
be achieved if the customers [60] :
a) Reduce the electricity consumption during high price periods and participate in
demand management programs
b) Invest in advanced energy-efficient tools to reduce their consumption
In addition, demand response has influence on pricing interactions between customers
and suppliers in connecting the retail and wholesale markets in the deregulated market
environment. Policy makers in most of the major electricity markets in the U.S
modifying the rules to allow large electricity consumers to participate in the wholesale
electricity market[61].
3.3 Demand response in electricity market
In the fully developed electricity market, both supply and demand sides have an active
role in the wholesale and retail electricity market. In the current wholesale market,
demand side does not have a considerable role, and market operators try to develop new
rules to increase demand-side participation and deploy these market based tools to
improve the economical and technical performance of the electricity market [62]. The
result of study by Federal Energy Regulatory Commission (FERC) showed that shifting
______________________________________________________________________
47
five to eight percent of electricity demand to off-peak hours in the U.S. could save up to
$15 billion a year [58].
The result of research by the federal energy regulatory commission confirmed that 3-5
percent of annual U.S. peak load can be reduced through implementation of demand
response program and this reduction could potentially leads to significant improvement
in market efficiency [63].
Another study conducted by the New England independent system operator showed that
there are two ways to respond to the escalating electricity demand. The first is to reduce
demand, and the second is to develop new supply sources. As a result of complex
environmental policies, the electricity sector cannot significantly expand the
conventional generators and increase the transmission capacity by adding new
infrastructure. Therefore, many utilities and market operators focus on the first option to
postpone constructing new power plants and transmission lines.
3.4 Different types of demand management programs
Basically, DR programs are classified into two broad sections which are:
a) Incentive-based demand response programs:
Incentive-based demand response programs are categorised into different subsections
including:
Direct load control
Demand bidding
Emergency demand response programs
Capacity market programs
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48
Ancillary-services market programs
b) Time-based demand response programs:
Time-of-use
Critical-peak pricing
Real-time pricing
Incentive-based demand response programs are structured to lower the electricity
consumption during system peak load periods or system emergency cases such as
contingencies. Customers who participate in incentive-based demand response
programs receive reduced electricity tariff or separate incentives for load reduction or
shifting their demand. The incentive-based programs can be triggered for either
reliability or economic reasons [59, 64].
The second category of demand response program is focused on time-based programs.
Different types of time-based rates are currently in operation all over the world. Time-
based programs are designed to reduce the system load in peak hours and transferring
the electricity consumption from the peak periods to the off-peak hours. The brief
review of each sub-group can be found in the following section.
3.4.1 Incentive-based demand response programs
These programs do not rely on natural responses of customers to price change, which
are not easy to predict. Incentive-based demand response programs can provide an
effective tool for electric utilities and/or market operators to enhance reliability and
improve the electricity market efficiency. The incentive-based demand response
programs are briefly reviewed in the following section.
______________________________________________________________________
49
3.4.1.1 Direct load control (DLC)
Direct load control (DLC) is a well-known program in various electricity markets in
which a system operator is able to shut down customer’s electrical equipment in a short
notice. DLC program is typically triggered during or after contingency in the electricity
network. DLC has been in operation for at least a decade in different electricity systems
around the world and its effectiveness on improving the power system operation is
proven in various electricity markets [58] [65].
3.4.1.2 Interruptible/Curtailable (I/C)
Participated electricity customers in interruptible/curtailable service rates receive a
discounted rate or credit to reduce their load during system contingencies. If customers
do not curtail, they can be penalised. It is necessary to note that I/C program is different
from emergency demand response program and capacity program. These programs are
offered by utility company and load serving entity to apply the load reduction when
necessary and participated customers must comply with utility company request [58].
3.4.1.3 Emergency demand response program (EDRP)
Participants in emergency demand response program is developed as a market based
tool. Emergency demand response program receive credit for demand reduction during
contingencies or high peak periods. In this program participants are not penalised for
not responding to the market operator invoke for load reduction [59]. New York
independent system operator introduced an emergency demand response program to
provide flexibility for system operator in emergency situations [66].
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50
3.4.1.4 Capacity market program (CAP)
In capacity-market program, participants sign a contract to provide pre-specified load
reductions in emergency cases, and if they do not respond to the request, they have to
pay the predefined penalty. Capacity market program is considered as an insurance for
power system. Participants in capacity market program have to provide the required
facilities to confirm that the claimed reduction is achievable for at least four hours[67].
Capacity market program has been successfully in operation in New York since 2002
and played an effective role in electricity network restoration after the August 14, 2003,
blackout. The other successful example of this category is implemented in ISO New
England and had considerable effect on preventing blackout in the U.S southwest
connection during the summer 2005 [58].
3.4.1.5 Demand bidding program (DB)
Demand bidding program encourages large electricity customers to reduce their load at
the prespecified amount that they offered to the market. These programs enabled the
system operator to control the electricity price during emergency cases. If customer bids
are accepted, the offered capacity will be dispatched, and the participants shall reduce
their load to the prespecified amount. DB program is an attractive option for customers
because they have the opportunity to receive higher payments for load reduction during
high electricity market price [68].
3.4.1.6 Ancillary service program (AS)
The last category of incentive-based demand response is ancillary-service program.
Ancillary service programs allow customers to participate in operating reserve market to
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51
provide their available capacity for the spinning reserve market. If their bids are
accepted, participants receive the market clearing price to provide standby capacity for
the system operator. If the load reduction is requested by the market operator the
additional credit which is equals to the spot electricity market price will be paid to the
AS provider. The participants in this program shall be equipped with on line
communication channels to connect to the control centre to adjust their load in
emergency condition such as rapid load change or major contingency in the network.
The typical loads which are able to participate in AS program are large industrial
processes loads that can reduce their loads quickly without any stress on equipment.
California Independent System Operator (CAISO) and Electric Reliability Council of
Texas (ERCOT) are the leaders in implementing ancillary services program. One
example for ancillary service participant in CAISO market is large water pumps
operated by California Department of Water Resources. Another example from
ancillary services category that is already in operation is Loads Acting as a Resource
(LaaR) program. The minimum requirements for LaaR program participants are the load
monitoring system and real-time control facilities [67, 69].
3.4.2 Time-based programs
The second major group of demand response programs are dedicated to the time-based
programs. After electricity industry restructuring, market operators developed programs
to promote active participation of electricity customers in the electricity market.
Time-based programs can connect and link the wholesale and retail market. In fact,
these programs can reflect the variation of electricity price change in wholesale market.
Three major time based programs are time-of-use (TOU), critical peak pricing (CPP)
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52
and real-time pricing (RTP). Brief review of these programs are presented in the
following section [70].
3.4.2.1 Time-of-use rates
Time-of-use (TOU) program was initially designed for residential customers.
Significant number of customers in the U.S adopted some types of TOU rates in various
electricity markets. TOU rates and intervals varies based on the time of the year and
geographic locations [71].
3.4.2.2 Critical peak pricing
Critical peak pricing (CPP) is a program that is designed to trigger load reduction
during system contingencies or very high electricity price. The load reduction for
participants in CPP are triggered in a limited number of days [72].
3.4.2.3 Real-time pricing (RTP)
This program is able to reflect the electricity price variations in the wholesale electricity
market to the retail customers. The first real time pricing program was introduced in
California to improve the reliability of the power system. According to the study
conducted by the national grid in the U.S, more than 70 utilities in North America offer
RTP on either a pilot or approved programs [58, 73]. DR programs are divided into two
main categories and different subsections, which are presented in Fig. 3.1.
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53
Fig. 3.1: Time-based and Incentive-based Demand Response Programs
Demad Response (DR) programs
Time - based programs
Time of Use (TOU)
Real Time Pricing (RTP)
Critical Peak Pricing(CPP)
Incentive - based programs
Direct Load Control (DLC)
Interruptible/Curtailable (I/C) Services
Demand Bidding /Buy Back (DB)
Emergency Demand Response Program (EDRP)
Capacity Market Program (CAP)
Ancillary Service (A/S) Markets
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54
3.5 Applications of demand response programs for power system planning and
operation
In the strategic plan of the International Energy Agency (IEA) for 2008–2012, demand
side activities are considered as the preferred option in all energy policy decisions,
because of its potential benefits including enhancing the power system reliability,
security and emission reduction [74]. Demand response program can have significant
role for power system operation and need to be considered as an effective tool in power
system planning. Prior to electricity industry deregulation, most regions in the United
States designed generation and transmission expansion plans solely based on
conventional resources. However, deregulation in electricity industry during 1990s in
most parts of the U.S such as California and the state of New York encouraged the
policy makers to choose integrated resource planning to use variety of resources
including demand response programs[75, 76]. The NYISO (New York Independent
System Operator) has introduced the SCR (Special Case Resources) program and utilize
it during reserve shortage cases [66]. The PJM interconnection developed the day-ahead
scheduling reserve (DASR) market and is intended to provide incentives for demand
resources to provide day-ahead scheduling reserves [77]. The Electric Reliability
Council of Texas (ERCOT) introduced the load acting as a resource (LAAR) program,
which allows customers who satisfy certain performance requirements to provide
operating reserve [69]. The ISO New England started the real-time DR program in
2005, which requires customers to commit mandatory load reductions on a predefined
triggers from the ISO [63].
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55
3.5.1 The role of DR programs for transmission line planning
Demand response programs have a significant potential to defer installation of new
transmission lines to increase the available transmission capacity during peak periods.
The significant positive impacts of demand response programs in increasing the
available transmission capacity and congestion management in the transmission lines
are addressed in the literature [60, 78-82].
3.5.2 The role of DR for providing ancillary services
Demand response programs also have significant potential to provide ancillary services
such as spinning reserve for the electricity network. Participants in this program have to
be able to reduce their load in emergency cases and be equipped with specific
communication and control facilities to interrupt the load.
It is essential to note that, providing local spinning reserve that is distributed in the
electricity network can enhance the reliability level of the power system. Table 3.1
summarise some of the major ancillary services that is provided by demand response
program in electricity markets across the U.S.
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56
Table 3.1: Provided spining reserve by demand side resources in different markets
across the U.S [58]
Market
Name Regulation Spinning
Non-
Spinning
Non-
Spinning
Long Term
Non-
Spinning
Replacement
ISO-NE N/A N/A DR active DR active N/A
NYISO N/A DR active DR active DR active N/A
PJM DR active DR active DR active N/A N/A
MISO N/A N/A N/A DR active N/A
ERCOT N/A DR active DR active DR active DR active
CAISO N/A DR active DR active DR active N/A
As it is shown in Table 3.1, demand response program has permitted to participate in
non-spinning and slower reserve services in most markets.
3.6 Review of demand response programs in electricity markets
In recent years, technology development in control, communications, and metering
result in considerable expansion in demand response programs in various electricity
markets in the U.S. and other countries. This section reviews some of the implemented
DR programs in major electricity markets around the world [58].
3.6.1 Electric Reliability Council of Texas
Electric Reliability Council of Texas (ERCOT) responsible to increase the reliability of
electricity network in the state of Texas. ERCOT was established in 2001 based on
combining 10 control areas into one single control area. In ERCOT, DR programs are
allowed to provide spinning reserve and non-spinning reserve services. According to the
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57
statistics, ERCOT is integrated 1100 MW of demand side resources for providing the
spinning reserve in the market. This approach helped the market operator to prevent the
blackout in 2006. Table 3.2-3.4 summarises active demand response programs in
ERCOT [58, 69].
Table 3.2: Summary of active demand response programs for providing spinning
reserve in ERCOT
Program type Provided services The minimum requirements
Voluntary load
response
Curtailment or reduction in
response to Market Price
Metering and/or curtailment
technology.
Load Acting as a
Resource (LaaR)
ERCOT Ancillary Services
(AS)
Advance metering
Curtailment technology.
Table 3.3: Summary of demand response programs for providing non-spinning reserve
Type of Service Metering Participants benefits Response time
Non-Spinning
Reserve
Telemetry
&
advanced
metering
Market clearing price in
non-spinning reserve
market and energy when
invoked
Within 30 minutes
Replacement
Reserve
Telemetry
&
advanced
metering
Market clearing price in
replacement market and
energy when invoked
Negotiable with
Market operator
Voluntary Load
Response
Negotiable
with
Market
operator
Market-clearing price Negotiable with
Market operator
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58
Table 3.4: Comparison of the conventional generators and demand response programs
in providing ancillary services
Type of
Service
Regulation
Down
Regulation
Up
Spinning
Reserve
Non-
spinning
Reserve
Replacement
Generation
Resources
Active Active Active Active Active
Load with
response
capability
within 10
minutes
N/A N/A Active Active Active
3.6.2 California ISO (CAISO)
The California market operator has one of the most advanced demand response
programs, and it is one of the leading independent system operators to promote demand
side participation. In CAISO electricity market, demand response programs varies from
residential air conditioning systems to large water pumps with 80,000 horsepower. The
California market operator strategic plan aims to reduce five percent of power system
peak by the use of demand side resources[67]
3.6.3 PJM Interconnection
PJM Interconnection is one of the major market operators in the U.S and provides
electricity to approximately 51 million people in 13 states. The PJM has a peak demand
of 135,000 MW, which equals to approximately 16 percent of the total US/Canadian
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59
demand. PJM market has a comprehensive program to enhance the reliability of
transmission system by providing distributed spinning reserve and other reliability
services using demand response program [77].
3.6.4 New York ISO (NYISO)
NYISO is responsible to monitor the reliability level of electricity network and manages
10,775 miles of transmission system in the state of New York. NYISO has initiated a
program to enhance the reliability of the electricity network by integrating demand side
resources. The NYISO deployed 1,750 MW of demand side resources to provide
spinning reserve for the electricity network [83].
3.7 Summary of the demand response program in the U.S. electricity market
The result of the study by Federal Energy Regulatory Commission (FERC) summarised
the active DR programs in various electricity markets in the U.S [58]. Table 3.5
summarise the direct load control participants in industrial level in the U.S electricity
market.
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Table 3.5: Utility companies with active DLC program
Name of Utility Number of participants in DLC
Florida Power and Light 740570
Progress Energy Florida 401720
Detroid Edison 347750
Baltimore Gas and Electric 338568
Northern State Power 283317
Duke Power 207794
Southern California Edison 166318
Public Service Electric & Gas 119310
Dairyland Power Cooperative 112656
Sacramento Municipal Utility District 104079
As it is shown in Table 3.5, the Florida Power and Light Company has the highest
number of customers enrolled in DLC program in comparison with other utilities based
on the study results by federal energy regulatory commission [84].
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61
Chapter 4 Multi-objective
approach for optimal allocation of
FACTS devices
This chapter focuses on finding an optimal location and sizes of FACTS devices. The
proposed approach is applied to two types of FACTS devices including SVC and
TCSC. In the first part, SVC allocation is considered, and in the next step the optimal
location of TCSC is investigated and discussed. As part of the FACTS device
allocation, a comprehensive literature review is conducted and in the next step, the
multi-objective problem is formulated. Later, an optimisation technique is applied to the
developed multi-objective FACTS device allocation to determine the optimum amount
and the number of FACTS devices. The proposed method is verified using standard
IEEE networks.
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62
4.1 FACTS allocation overview
With the worldwide restructuring and deregulation of power systems, sufficient
transmission capacity and reliable operation have become more valuable for both
system planners and operators. Building new transmission circuits to enhance the
transmission capacity of a network is very expensive, time consuming and many
constraints have to be satisfied for new transmission lines development. As a result,
there is a significantly increased potential for the application of FACTS devices due to
their flexibility and relatively lower costs in power system security enhancement. It has
been generally acknowledged that the effectiveness of FACTS in providing voltage and
reactive power flow control functions depend importantly on their locations and ratings.
The problem of determining the optimal locations and sizes of FACTS is a nonlinear
and complex problem [85]. To identify the buses at which FACTS should be located is
a combinatorial problem with discrete variables.
There are several methods to find optimal locations of FACTS devices in both vertically
integrated and unbundled power systems. There have been various optimisation
methods previously proposed to solve the FACTs device allocation problem where only
a limited number of objectives is included [86]. In general, optimal FACTS device
allocation problem is to determine the optimal sizes and locations of new FACTS
devices in order to optimise a set of objective functions subject to a range of operating
constraints. According to the characteristics of FACTS devices, various criteria have
been considered in allocation problem. Some of the reported objectives are: long term
voltage stability enhancement [87, 88], network loadability enhancement [89], loss
reduction, voltage profile improvement [90], and overall system cost minimisation.
Each of the above mentioned objectives improves power system network operation.
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63
However, improvement in one objective does not guarantee the same improvement in
the others. For instance, satisfying the voltage magnitude constraint might not meet the
power flow security constraints. Therefore, none of the mentioned technical objectives
can be neglected in FACTS device allocation. On the other hand, allocation of the
FACTS devices based on one or more technical objectives without considering the
economic objective expressed in terms of cost of FACTS devices are not a practical
one. Consequently, both technical and economic objectives should be represented in
formulating the FACTS device allocation problem.
In previous efforts, to achieve the mentioned goals, some simplifications have been
made. In [91], a multi-objective genetic algorithm (MOGA) approach has been
implemented for FACTS device allocation, in which only two objectives have been
considered for optimisation including line overload and voltage violation, and these
objectives have been combined to form a single objective function.
A key problem in multi-objective function optimisation is to select the optimal solution
that is non-inferior one often referred to as Pareto optimal solution. There have been
proposed optimisation procedures based on GA by which Pareto optimal solution is
obtained. In [91], a genetic algorithm referred to as NSGA (non-
dominated sorting genetic algorithm) was proposed in which a new selection operator
was developed, and chooses only non-inferior solutions in the search. Subsequent
development led to its improvement [91].
The NSGA II, which has better algorithm for ranking incomparison with NSGA, is used
for solving a multi-objective optimization problem to find the locations and sizing of
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64
FACTS. The objective functions to be optimised in this problem formulation are
network active-power loss, capital cost of FACTS, voltage deviation and loadability.
These objective functions are to be optimised subject to sets of equality and inequality
constraints, which include the power flow equations and operating limits. The solution
to the multi-objective constrained optimisation problem determines the optimal
locations, and sizing of the SVCs. In the following section, the mathematical concept of
multi-objective allocation of SVC is discussed. Four groups of objective functions are
considered in this research.
4.2 Problem formulation
4.2.1 Cost
In general, the cost of each SVC can be expressed in terms of a nonlinear function of its
reactive-power rating. If the cost of the ith SVC is denoted by fi(qi) where 𝑞𝑖 is the
reactive power rating of the SVC, then the total cost function to be minimised is:
)(1
1
T
i
ii qfg (4. 1)
where T is the number of SVCs. For example, a cost function of an SVC in a quadratic
form which can be expressed as follows[92]:
cbqaqqf iiii 2)( (4. 2)
where a, b and c are constants.
4.2.2 Loadability index
The severity of the system loading under normal and contingency cases can be
described by a line power flow index as follows:
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65
L
ii
skfkg
1
)(22
(4. 3)
where g2kis the index indicating violation of line flow limits, and )(2 i
k sf is a function
defined as follows[93]:
f2k(si) = {
1; if sik ≤ si
max
exp (λ |1-si
k
simax|) ; if si
k > simax (4. 4)
where si is the total power flow in transmission line i ; simax the maximum limit for the
line i, and λ is a small positive constant. Superscript (k) indicates operating condition
including normal condition and contingencies. The notation L in (4.3) is the total
number of transmission lines.
4.2.3 Voltage deviation index
To have a good voltage performance, the voltage deviation from each load bus must be
made as small as possible. The voltage deviation index to be minimised can be
expressed as follows:
2N
1n
k
refn
k
n
k
3 VVg
(4. 5)
where |Vnk| is the voltage magnitude at load bus n in operating condition k and 𝑉𝑟𝑒𝑓𝑛
𝑘 is
the nominal or reference voltage at bus n. N is the number of buses in the transmission
network and n is the node identifier, i.e. Nn ,...,1 .
4.2.4 Active power losses
Minimising the active-power loss is equivalent to minimising the slack node active-
power. Active-power at the slack node,Psl , is expressed as :
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66
*
4 ,Resl sl sl i i
i
g P V Y V
(4. 6)
where Ysl,iis the element (sl, i) of the nodal admittance matrix of the power system. It is
noted that the active-power loss minimisation is considered only for the base case.
4.2.5 Equality constraints
Equality constraints consist of power flow equations applied for individual power
network nodes, which is written in a compact form as follows:
0u,θ,VE kkkk (4. 7)
where kE is a vector function; |V|kand θk are the vectors of system voltage magnitudes
and phase angles, and uk is the vector of control variables in operating condition k such
as generator excitation control and SVC reference signals. An example for active-power
equation at a load node is given in the following:
0PV.YVRe sp
i
*
j
k
j
k
ji,
k
i
(4. 8)
where Vik is the nodal voltage at node i in operating condition k. Yi,j
k is element (i, j) of
the network nodal admittance matrix in operating condition k. PiSP is the specified
active-power load demand at node i . In addition to above equality constraints, the
optimisation is subject to inequality constraints that are described as follows.
4.2.6 Inequality constraints
In general, the inequality constraints can be written in the compact form:
hk(|V|k, θk, uk) ≤ 0 (4. 9)
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67
where hk is in general a nonlinear vector function relating to operating conditions such
as power flow constraints, generator reactive power and controllers limits: An example
for inequality constraint is that of voltage magnitude constraint:
0VV k
maxi
k
i (4. 10)
where |Vik| and Vi max
k are voltage magnitude at node i and its maximum allowable
value in operating condition k respectively.
4.3 Multi-objective optimisation
Many real-world problems involve simultaneous optimisation of several objective
functions. Generally, these functions are non-commensurable, and often represent
conflicting objectives. Multi-objective optimisation with such conflicting objective
functions gives rise to a set of optimal solutions, instead of one optimal solution. The
reason for the multiple optimal solutions is that no one can be considered better than
any other with respect to all objective functions. One of the optimal solutions is known
as the Pareto-optimal solution. The definition of Pareto optimal or Pareto non-
dominated solution is explained through an example in the following:
A multi-objective optimisation problem is stated as per equation (4.11).
Minimise F(x) = (f1(x), … , fm(x)) (4. 11)
Subject to a set of equality and/or inequality constraints
In a multi-objective minimisation problem, a feasible solution denoted by vector X is
said to be non-dominated if and only if, for any other vector denoted by Y, every single
objective function value determined by vector X is less than or at most equal to that
determined by vector Y, and at least one of the objective functions determined by vector
X is less than the corresponding objective function determined by vector Y. A Pareto-
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68
optimal solution cannot be improved with respect to any objective without worsening at
least one other objective. In this research, the NSGA-II [94], which incorporates the
concept of Pareto optimality into its search algorithms ,and can find optimal trade-offs
among the multiple conflicting objectives simultaneously, has been implemented and
applied to solve the FACTS device allocation problem.
4.4 Implementation of NSGA-II method
The basic idea of the NSGA II algorithm is to subdivide the population in each
generation into a number of subsets referred to as fronts, which are ranked in terms of
levels. Each level consists of some members, and based on ranking method, the whole
population is divided to various levels. For each front, there is one non-dominated
solution, which satisfies Pareto optimality condition. In this way, for the entire
population, there is a set of non-dominated solutions derived from the individual fronts.
In the second generation starting from the initial population, these ranked fronts are then
reproduced through crossover and mutation operators. Individual elements in the fronts
with a high level in the ranking have a high probability of being selected for
reproduction. The solutions in the first level front are assigned the highest priority, and
then those in the second level and so forth. The crossover and mutation procedures are
the same as those used in GA. Fig. 4.1 shows the procedure of one NSGA II iteration. In
the first step the population is divided into two sections and after first iteration the off
springs are ranked into various groups, first three fronts in the ranking are selected, and
the algorithm is continued up to satisfaction of stoping criteria.
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69
Fig. 4.1: NSGA II procedure
4.4.1 Initial population
The multi-objective optimisation with NSGA II algorithm in common with the variables
of the optimisation problem to be coded as a string of binary digits of finite length. The
variables representing the SVCs locations and sizing are grouped into a string with the
structure shown in Fig. 4.2. The first part of the structure is for the coding of the SVCs
locations. Each gene in this part is associated with a node in the power system. The
gene value of 1 means that the node has an SVC, and the gene value of 0 corresponds to
the node having no SVC. The number of nodes determines the length of the first part in
the power system. The second part of the structure comprises a number of blocks of
binary numbers. Each block is associated with a node in the power system that
represents the reactive-power rating of the SVC connected to the node. The number of
blocks in the second part is the number of nodes in the power system. The length in
each block is determined by the maximum power rating and accuracy required. Fig. 4.2
shows a power system and a sample string for SVC locations and sizing.
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70
Fig. 4.2: Representation of a power system and the sample string for SVC locations and
sizes
4.4.2 Fitness evaluation
The fronts are formed from the current population using an iterative process described
in the following. In forming the first front, the entire population is considered from
which the first non-dominated solution is identified. The second member of the first
front is then selected from the reduced population in which the first non-dominated
solution is excluded. The second member is the non-dominated solution belonging to
the reduced population. The process is repeated for a finite number (based on the size of
the case study) of times to form level-1 front. The same procedure is then applied to
form level-2 front from the remaining population where level-1 front individuals are
excluded. Successive fronts with lower ranks are constructed iteratively.
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71
Individual fronts are assigned fitness values accordingly to their levels. Level-1 front
has the largest fitness value. Lower fronts are then assigned smaller fitness values.
Having formed the fronts together with their fitness values, it is required to assign
fitness value for each member of each front. The requirement in this fitness value
assignment is to maintain diversity. This means that the fitness value distribution over
the individuals in each front is a non-uniform one. Various schemes can be designed to
form the distribution of fitness values. For example, the present research implements a
scheme based on a clustering algorithm which will assign low fitness values to the
individuals in close proximity to one another as measured by the norms of the
differences between the vectors representing these individuals[91]. The assignment of
fitness values for the individuals in each front also takes account of the fitness value of
the front so that the lowest fitness value of an individual in a front will still be greater
than that of another individual in a front with a lower rank.
4.4.3 Iterative process
The population is reproduced according to the fitness values. Since individuals in the
first front have the highest fitness values, they always get more copies than the rest of
the population. The efficiency of NSGA lies in the way by which a mapping from
objective function values to fitness values of individuals in a population is achieved
using the Pareto optimal criteria. In principle, the method can be applied to any number
of objective functions encountered in a constrained optimisation problem. The flow
chart of the proposed algorithm is shown in Fig. 4.3. Either reaching the maximum
number of allowed iterations or finding no other new non-dominated solution in a
predefined number of successive iterations has been considered as the termination
criterion. The key aspect in the flowchart of Fig.4.3 is the application of the OPF
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72
(optimal power flow) for evaluation of individual objective functions, which are
essential to the NSGA II procedure. The input to the OPF in terms of SVCs sizes and
locations are those given in each possible solution vector in individual iteration. Outputs
of this step will be used to rank possible solutions in different fronts. Then, a new
population will be reproduced from the individuals with fitness values above a specified
threshold. Finally, a max-min approach is used to determine the best compromising
solution.
4.4.4 Selection of final solution
The final solution will be one of the vectors in the front with level 1 in the population of
the last generation. An obvious choice for the final solution is that which satisfies the
Pareto optimality condition. However, the system planners can have the flexibility of
selecting a solution in level-1 front, which deviates from the Pareto optimality condition
in meeting their practical planning requirements and conditions. The system planners
can formulate criteria based on which the most suitable solution is selected. In this
research, a min-max approach is used to select the suitable locations and sizes of SVCs.
Each possible solution in the front with level 1 has an associated vector of values of
objective functions that can be normalised using the following expressions[93]:
G1m=
g1m -g1min
g1max -g1min
(4. 12)
G2m=
g2m -g2min
g2max -g2min
(4. 13)
G3m=
g3m -g3min
g3max -g3min
(4. 14)
G4m=
g4m -g4min
g4max -g4min
(4. 15)
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73
Where g1min, g2min
, g3min and g4min are the minimum values, and
g1max, g2max
, g3maxand g4max
are the maximum values obtained for the objective
functions. G1𝑚, G2𝑚
, G3𝑚 and G4𝑚
are selected values for multi objective optimisation.
The notation m is the identifier of an element in the front. It is noted that the result of
this normalisation shows the level of contentment for each objective function.
Afterwards, a min-max approach, summarised in (4.16), is applied to select the final
multi-objective SVCs placement and sizing.
m
k
m
k
mm GGGGMaxMin 4321 ,,, (4. 16)
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74
Fig. 4.3: The selection procedure for optimal allocation of the SVC
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75
4.5 Numerical Studies
The modified IEEE 14-bus test system has been used to demonstrate the application of
the proposed formulation and evaluate the effectiveness of the NSGA II in solving the
SVC allocation problem. Fig. 4.4 shows the single line diagram of the test system. The
information related to lines, transformers, generators, synchronous condensers, network
peak load in normal condition, and lines power rating of the test system can be found in
[70].
Fig. 4.4: IEEE 14 bus test system
It is required that contingencies are to be taken into account in determining the optimal
SVC allocation in relation to maintaining system security following the loss of one or
more transmission circuits. In the present study, the loss of only one transmission line in
each contingency is considered. In this research, three line outage as per Table 4.1 is
considered and ranked based their impacts on loss of load in IEEE 14 bus test system.
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Table 4.1: Three contingencies in IEEE 14 bus network
Line Number
1-2 1
1-5 2
2-3 3
The goal of this section is to find the best locations and sizes of SVCs which are
previously described. The optimisation is to be carried out with respect to two
parameters: location and size. The optimal locations of SVCs is considered as a discrete
decision variable, where all load buses except those which have a generator and
synchronous compensator are candidates to be the optimal locations of SVCs. The
problem is formulated as a multi–objective optimisation considering the cost, voltage
deviation index, power loss and loadability index. Here, these objectives are optimised
at the same time, using NSGA II. In this study, the max-min method is applied to find,
among possible solutions, the most suitable one. The number of SVCs to be installed in
the network as found from the solution of the optimisation problem is two with their
optimal places and sizes given in Table 4.2.
To be able to achieve the presented results in Table 4.2, the optimisation is conducted
with respect to two parameters: location and size. The optimal location of SVC is
considered as a discrete decision variable, where all load buses except those which have
generator and synchronous compensator are candidates to be the optimal location of
SVC. The problem is formulated as a multi–objective optimisation considering the
minimisation of cost, voltage deviation index, power loss and maximisation of power-
flow security. Here, these objectives are optimised at the same time, using NSGA II
which has been described in section 4.4.
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In this study, two sets of initial population and number of iterations are considered and
compared. First set considers the initial population of 200 and the maximum number of
iterations of 100. The initial population of 150 and the maximum iteration of 200 are
also considered for the second set. The Probabilities of mutation and crossover
operators are set to 0.1 and 0.6, respectively. To select the best multi-objective solution,
the max-min method is applied to find among possible solutions, the most suitable one.
The number of SVCs to be installed in the network as found from the solution of the
optimisation problem is two with their optimal places and sizes given in Table 4.2.
Table 4.2: The installation cost, location and size of the SVCs
Cost of SVC installation(U.S $) 245156
SVC locations Bus 9 and Bus 14
SVC size (MVAr) 18MVAr and 14 MVAr
Comparison between the objective functions in normal and contingency states before
the SVC installation and those after the SVC installation is summarised in Tables 4.3 -
4.5.
Comparison between the objective functions both in normal and contingency states
before the SVC installation and those after the SVC installation is summarised in Tables
4.3 - 4.5. It can be seen that the active power loss, voltage deviation index and power-
flow security are improved by optimal locations and sizes of SVCs in the network.
Sensitivity studies have also been performed with various values for the parameters of
NSGA II algorithm. These studies indicate that improvements in the objective
functions, if there are any, are minimal in comparison with those in Tables 4.3 - 4.5. As
it can be seen, the voltage deviation index can be improved by 36.93% during line 2-3
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outage. In addition, optimal allocation of SVC can reduce transmission active power
loss by 5.63% during Line 1-5 outage.
Table 4.3: The comparison between active power loss before and after SVC installation
Transmission Loss before SVC installation
No contingency 3.759 MW
Line 1-2 outage 3.940 MW
Line 1-5 outage 3.870 MW
Line 2-3 outage 3.791 MW
Transmission Loss after SVC installation
No contingency 3.624 MW
Line 1-2 outage 3.718 MW
Line 1-5 outage 3.702 MW
Line 2-3 outage 3.553 MW
Table 4.4: The comparison between voltage deviation index before and after SVC
installation
Before SVC installation
No contingency 0.024537
Line 1-2 outage 0.024887
Line 1-5 outage 0.024378
Line 2-3 outage 0.025021
After SVC installation
No contingency 0.01539
Line 1-2 outage 0.01596
Line 1-5 outage 0.01480
Line 2-3 outage 0.01578
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Table 4.5: The comparison between loadability index of transmission lines before and
after SVC installation
Before SVC installation
Line 1-2 outage 1.028167
Line 1-5 outage 1.024389
Line 2-3 outage 1.029473
After SVC installation
Line 1-2 outage 1.024246
Line 1-5 outage 1.020298
Line 2-3 outage 1.026767
It can be seen that the active power loss, voltage deviation index and power-flow
security are improved by optimal locations and sizes of SVCs in the network.
4.6 TCSC allocation
It has been generally acknowledged that the effectiveness of TCSCs depends
importantly on their locations and sizes. The problem of determining the optimal
locations and sizes of TCSCs is a nonlinear and complex one. To identify the lines in
which TCSCs should be located is a combinatorial problem with discrete variables.
There are several methods to find optimal locations of TCSC devices in both vertically
integrated and unbundled power systems. There have been various optimization
methods previously proposed to solve the TCSC device allocation problem where only
a limited number of objectives is included. In general, optimal TCSC allocation
problem is to determine the optimal sizes and locations of new installed TCSC devices
in order to optimize a set of objective functions subject to a range of operating
constraints. According to the characteristics of TCSC devices, various criteria have been
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considered in allocation problem. Some of the reported objectives are: network load
ability enhancement [92], ATC enhancement, congestion management [90], loss
reduction, and economic factors which minimised the overall system cost function [95].
In [96], a multi-objective genetic algorithm (MOGA) approach has been implemented
for TCSC allocation, in which only two objectives have been considered including line
overload and voltage violation reduction, and these objectives have been combined to
form a single objective function. The combination causes some problems such as: the
possible benefits of TCSC devices being not fully utilized. Against the above
background, the present research proposes to apply an optimisation procedure based on
NSGA II (Non-dominated Sorting Genetic Algorithm) [91]. The objective functions
which are considered in the TCSC allocation problems are power loss, investment cost,
loadability index and available transmission capacity [97].
4.6.1 Objective function formulation for TCSC allocation
In this section, the mathematical concept of multi-objective allocation of TCSCs is
presented. The four groups of objective functions will be considered in this research as
explained in the following:
4.6.1.1 Cost
In general, the cost of each TCSC can be expressed in terms of a nonlinear function of
its capacity in MVAr. However, TCSC is supposed to carry rated transmission line
current. Its rating will be decided by maximum current carrying capacity of a
transmission line. As a result, the size of TCSC will be directly proportional to its
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reactance limit. The cost of the ith TCSC is denoted by fi(si) where si is the rating of
the TCSC in MVAr.
The total cost function to be minimised is:
𝐠𝟏 = ∑ 𝐟𝐢(𝐬𝐢)𝐓𝐢=𝟏 (4. 17)
where T is the number of TCSCs. For example, a cost function of an TCSC in a
quadratic form is:
𝐟𝐢(𝐬𝐢) = 𝐚𝐬𝐢𝟐 + 𝐛𝐬𝐢 + 𝐜 (4. 18)
Where a, b and c are constants.
4.6.1.2 Line flow limit index
The severity of the system loading under normal and contingency cases can be
described by a line power flow index as follows:
𝐠𝟐𝐤 = ∏ 𝐟𝟐
𝐤(𝐬𝐢)𝐋𝐢=𝟏 (4. 19)
where g2k is the factor indicating violation of line flow limits, and 𝑓2
𝑘(𝑠𝑖) is a function
which defined as follows:
𝐟𝟐𝐤(𝐬𝐢) = {
𝟏; 𝐢𝐟 𝐬𝐢𝐤 ≤ 𝐬𝐢
𝐦𝐚𝐱
𝐞𝐱𝐩 (𝛃 |𝟏 −𝐬𝐢
𝐤
𝐬𝐢𝐦𝐚𝐱|) ; 𝐢𝐟 𝐬𝐢
𝐤 > 𝐬𝐢𝐦𝐚𝐱 (4. 20)
where 𝑠𝑖 is the total power flow in transmission line i ; 𝑠𝑖𝑚𝑎𝑥 the maximum limit for the
line i, and β is a small positive constant. Superscript (k) indicates operating condition,
including normal condition and contingencies. The notation L in (4.19) is the total
number of transmission lines.
4.6.1.3 Active Power Losses
Minimising the active-power loss is equivalent to minimising the slack node active-
power. Active-power at the slack node,Psl , is expressed as per equation (4.21).
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82
𝐠𝟒 = 𝐏𝐬𝐥 = 𝐑𝐞 {𝐕𝐬𝐥 [∑ 𝐘𝐬𝐥,𝐢 . 𝐕𝐢𝐢 ]∗} (4. 21)
where Ysl,i is the element (sl, i) of the admittance matrix of the power system. It is noted
that the active-power loss minimisation is considered only for the base case.
4.6.1.4 Available transmission capacity
Available transmission capacity (ATC) was defined by North American Electric
Reliability Council (NERC) as a measure of the available transfer capability in
transmission network. Adequate ATC is required to ensure all power transactions to be
achieved successfully. Calculation of ATC involves four components: total transfer
capability (TTC), transmission reliability margin (TRM), capacity benefit margin
(CBM), and existing transmission commitments (ETC). Mathematically, available
transmission capacity can be formulated as per equation (4.22) [93]:
𝐀𝐓𝐂 = 𝐓𝐓𝐂 – 𝐓𝐑𝐌 – 𝐂𝐁𝐌 – 𝐄𝐓𝐂 (4. 22)
where TTC refers to the maximum power which can be transferred from one power
control area to other areas (source/sink), which cause no thermal overloads, voltage
limit violations or voltage collapse. TRM is the amount of transmission capability
necessary to ensure that the interconnected system is secure under a reasonable range of
uncertainty. Furthermore, CBM is the amount of the transmission transfer capability
which is reserved by load serving entities in order to ensure access to generation via
interconnected systems considering generation reliability requirements and finally ETC
is the existing transmission commitment. TTC is commonly used as the basis for the
evaluation of ATC because other components are either known for a giving operating
condition or specified by the power company. Therefore, maximising the ATC in (4.22)
is equivalent to maximising the following:
𝐓𝐓𝐂 – 𝐄𝐓𝐂 (4. 23)
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Several methods have been developed for TTC calculation. These approaches can be
classified in three groups as follows:
i) Repeated power flow (RPF) method;
ii) Continuation power flow (CPF) method;
iii) Security constrained optimal power flow (SCOPF) method.
In this research, RPF method is used to evaluate TTC in IEEE 30 bus test system.
Repeated power flow (RPF) method enables the increase in the transfer of power by
increasing the load with uniform power factor at every load bus in the load area (sink)
and increasing the injected real power at generator buses in the generation area (source)
in incremental steps until the power flow calculation fails to converge or when the
power flow and/or voltage solution violates their specified operating limits. The
mathematical formulation of TTC using RPF can be expressed as follows:
Maximize λ at following equations
𝐏𝐃𝐢 = 𝐏𝐃𝐢𝟎 . (𝟏 + 𝛌 . 𝐊𝐃𝐢) (4. 24)
𝐐𝐃𝐢 = 𝐐𝐃𝐢𝟎 . (𝟏 + 𝛌 . 𝐊𝐃𝐢) (4. 25)
where PDi (real load in load area) and QDi (reactive load in load area) and PDi0 , QDi
0 are
original real and reactive load demands at bus i in the load area and KDi is a constant
used to specify the change rate in the load as λ varies [93].
Subject to:
𝐏𝐆𝐢 − 𝐏𝐃𝐢 − ∑ |𝐕𝐢|. |𝐕𝐣|(𝐆𝐢𝐣 𝐜𝐨𝐬 𝛅𝐢𝐣 + 𝐁𝐢𝐣 𝐬𝐢𝐧 𝛅𝐢𝐣) = 𝟎𝐧𝐣=𝟏 (4. 26)
𝐐𝐆𝐢 − 𝐐𝐃𝐢 − ∑ |𝐕𝐢|. |𝐕𝐣|(𝐆𝐢𝐣 𝐬𝐢𝐧 𝛅𝐢𝐣 − 𝐁𝐢𝐣 𝐜𝐨𝐬 𝛅𝐢𝐣) = 𝟎𝐧𝐣=𝟏 (4. 27)
|𝐕𝐢|𝐦𝐢𝐧 ≤ |𝐕𝐢| ≤ |𝐕𝐢|𝐦𝐚𝐱 (4. 28)
𝐒𝐢𝐣 ≤ 𝐒𝐢𝐣 𝐦𝐚𝐱 (4. 29)
𝐐𝐠𝐞𝐧𝐢𝐦𝐢𝐧≤ 𝐐𝐠𝐞𝐧𝐢 ≤ 𝐐𝐠𝐞𝐧𝐢𝐦𝐚𝐱
(4. 30)
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84
where λ is scalar parameter representing the increase in the area’s load or generation.
λ = 0 corresponds to the base case ,and λ = λmax corresponds to the maximum
transfer; |Vi| , |Vj| are voltage magnitudes at bus i and j; Gij; Bij are real and imaginary
parts of the ijth element of bus admittance matrix; δij is voltage angle difference
between bus i and bus j ,and Sij is apparent power flow in line ij ; Qgeni is generator
reactive power.
TTC level in each case (normal or contingency) is calculated as per equation (4.31):
SinkAreaj
0
DiSinkAreaj
maxDi P)(λPTTC (4. 31)
where )(λPSinkAreaj
maxDi
is the sum of the loads in the sink area when λ = λmax ,and
SinkAreaj
Di0P is the sum of the loads in the sink area when λ = 0. The equality and in
equality constraints such as power flow constraints, generator reactive power and
controller limits are similar to the SVC allocation which explained previously.
Summary of the optimisation procedure for TCSC allocation is presented in Fig. 4.5.
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85
Fig. 4.5: Flowchart of the proposed algorithm
Generating first
population
(set of possible solutions)
Determine TCSC
cost
Determine
Power loss
Determine
ATC
Determine
Line flow limit
Determine TCSC
cost
Determine
Power loss
Determine
ATC
Determine
Line flow limit
Iteration=Iteration+1
Set of non-dominated
solutions
Decision Making
Analysis
Termination
Criteria?
NO
YES
Iteration=1
Non-dominated sorting, Assignment of fitness value to each solution
Reproduction, Crossover, Mutation, Generating a set of off spring
Final Solution
Non-dominated sorting, Assignment of fitness value to each solution
Choosing solutions for the new population
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4.6.2 Numerical results for TCSC placement
The IEEE 30-bus test system selected to demonstrate the application of the proposed
formulation and evaluate the effectiveness of the NSGA II in solving the TCSC
allocation problem. This test system was selected for TCSC placement exercise because
of higher number of generators and load buses as well as capability to be divided into
generation and load area. Fig. 4.6 shows the single line diagram of the test system with
the red line divide the IEEE 30 bus to into two parts i.e. generation and load area. The
information related to lines, transformers, generators, synchronous condensers, network
peak load in normal condition, and lines maximum powers of the test system are based
on the IEEE 30 bus test system[24, 70].
Fig. 4.6: IEEE 30 bus test system
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A contingency analysis is carried out to show the effectiveness of the method during the
contingency condition and to emphasis on benefits of optimal allocation of TCSC in the
network. Three contingencies are selected and listed in Table 4.6.
Table 4.6: Selected severe contingencies in the IEEE 30 bus system
Contingency number
Line
1 4-12
2 6-10
3 23-24
The main goal of this section is to find the best locations and sizes of TCSCs which
optimise all objective functions as described in previous parts. The optimisation is made
on two parameters: location and size. The locations of TCSCs are considered as discrete
decision variables. The problem is formulated as multi–objective optimisation
considering the minimisation of cost, active power loss, security margin improvement
and ATC enhancement. Values in Table 4.7 present the optimal places and sizes of
TCSCs to be installed.
Table 4.7: The locations and sizes of the TCSC based on the optimisation outcome
NO TCSC location TCSC size (MVAr)
1 Line 2-6 7.33
2 Line 27-28 10.327
Comparison between security margin, active power loss, and ATC in the normal and
contingency situation before and after TCSC installation is summarised in Table 4.8 to
Table 4.10. It can be seen that the active power loss, security margin and ATC of the
network are improved considerably.
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Table 4.8: The comparison of active-power loss before and after TCSC installation
Transmission Loss before TCSC installation
No contingency 3.006 MW
Line 4-12 outage 2.976 MW
Line 6-10 outage 2.765 MW
Line 23-24 outage 2.974 MW
Transmission Loss after TCSC installation
No contingency 2.231 MW
Line 4-12 outage 2.155 MW
Line 6-10 outage 2.113 MW
Line 23-24 outage 2.211 MW
Table 4.9: The security margin comparison before and after TCSC installation
Line flow limit before TCSC installation
Line 4-12 outage 1.1885
Line 6-10 outage 1.2209
Line 23-24 outage 1.4153
Line flow limit after TCSC installation
Line 4-12 outage 1.0209
Line 6-10 outage 1.0345
Line 23-24 outage 1.0983
Table 4.10: The ATC comparison before and after TCSC installation
ATC before TCSC installation
No contingency 70.25 MW
Line 4-12 outage 30.03 MW
Line 6-10 outage 50.14 MW
Line 23-24 outage 60.96 MW
ATC after TCSC installation
No contingency 86.85 MW
Line 4-12 outage 42.62 MW
Line 6-10 outage 69.62 MW
Line 23-24 outage 79.33 MW
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4.6.3 Conclusion
In this chapter, an approach has been proposed to determine the optimal sizes and
locations of SVC and TCSC, based on a multi-objective function. In this method, the
allocation problem has been formulated according to various technical and economical
considerations such as voltage deviation, active power loss and installation cost. Also,
in contrast to previous research, the cost objective function has been considered, besides
other objectives, to reach a cost-effective and practical solution. In addition, NSGA II
method which has been utilised to find the optimal solution has been found to be robust,
and offer good convergence property in achieving the solution. The results confirm that
the optimal allocation of SVC and TCSC can play a considerable role in improving the
performance of the network in terms of lowering the active power loss and increasing
the security margin of the network.
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Chapter 5 Multi-objective
demand response allocation
With the continued increase in the demand for the electrical energy and lack of enough
transmission capacity, power system security has become an issue of increased
importance in power system operation. To meet the load demand in a power system
and satisfy the stability and reliability criteria, both the existing transmission lines and
generation units must be utilised more efficiently, or new lines and generation units
should be added to the existing system. The latter is often costly and impractical. The
reason is that building a new power line or generator in many countries is a time
consuming process and sometimes an impossible task, due to environmental problems.
Therefore, the first alternative i.e. maximising system utilisation provides an
economically and technically attractive solution to power system security problem.
The integrated use of demand and supply side resources can be a solution for enhancing
the utilisation factor in the electricity network. In addition, reliability enhancement and
power system security improvement could be achieved by effective utilisation of
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91
demand side resources. Considerable research has been done on the impacts of demand
response on generation and transmission system reliability [98]. However, few
researches have focused on the allocation problem. The optimal allocation of DR has a
considerable impact on enhancing the electricity network performance. In this research,
the DR program is optimally designed to maximise the available transmission capacity
(ATC), minimise the expected energy not supplied (EENS), minimise active power loss
and minimise the total DR programs capacity. In this study, EENS represents an index
of composite system reliability, which is considered as an important network operator’s
concern. The focus of the current research is that of determining the optimal DR
locations and their capacities to optimize specified objectives subject to operating
constraints
5.1 Problem formulation
As it is mentioned in the previous section, four objective functions are considered in
formulating the optimisation problem. The objective functions are those of ATC,
expected energy not supplied (EENS), total active power loss and total DR programs
capacity. The decision variables in this optimisation problem are locations and the
amount of DR programs to optimise the four objective functions. The details of the
objective functions are presented in the following:
5.1.1 Expected energy not supplied (EENS)
The expected energy not supplied is chosen in this research as an index for composite
system reliability. The EENS can be calculated by (5.1):
j
N
j
j TEPNSEENS .
1
(5. 1)
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92
where
𝑁 The total number of load loss events in a year
𝐸𝑃𝑁𝑆𝑗 Expected power not supplied in the jth event.
𝑇𝑗 Duration of the outage in the jth event.
𝐸𝑃𝑁𝑆𝑗 is evaluated based on the annual failure rates of the items of power system ,the
outage of which leads to loss of load supply.
5.1.2 Active power loss
In steady-state operation, there are always the active and reactive-power balances.
Minimizing the active-power loss is therefore, equivalent to minimizing the slack node
active-power. Active-power at the slack node Pslis expressed as:
*
, .Re i
i
islslsl VYVP (5. 2)
where Ysl,iis the element (sl, i) of the admittance matrix of the power system. To reduce
the amount of computation, the base case network configuration and maximum load
demand condition are adopted in forming the objective function for active-power loss.
5.1.3 Available transmission capacity
ATC was defined by North American Electric Reliability Council (NERC) as a measure
of the transfer capability in transmission network. Adequate ATC is required to ensure
that all economic transactions can be successfully achieved. Calculation of ATC
involves four components: total transfer capability (TTC), transmission reliability
margin (TRM), capacity benefit margin (CBM), and existing transmission commitments
(ETC). Mathematically, ATC is defined as:
ETCCBMTRMTTCATC (5. 3)
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In (5.3), TTC refers to the maximum power that can be transferred from generation area
to the load area (source/sink), which causes no thermal overloads, voltage limit
violations or voltage collapse. TRM is the amount of transmission capability necessary
to ensure that the interconnected system is secure under a reasonable range of
uncertainty. CBM is the amount of the transmission transfer capability which is
reserved by load serving entities in order to ensure access to generation via
interconnected systems considering generation reliability requirements, and finally.
ETC is the existing transmission commitment. TTC is commonly used as the basis for
the evaluation of ATC because other components are either known for a given operating
condition or specified by the transmission company. Therefore, maximising the ATC in
(5.3) is equivalent to maximising the following equation.
ETCTTC (5. 4)
Several methods have been developed for TTC calculation. These approaches can be
classified in three groups as follows:
i) Repeated power flow (RPF) method;
ii) Continuation power flow (CPF) method;
iii) Security constrained optimal power flow (SCOPF) method.
In this research, RPF method is used to evaluate TTC because of ease of
implementation and time convergence. The Repeated power flow (RPF) method enables
the increase in the transfer of power by increasing the load with uniform power factor at
every load bus in the load area (sink) and increasing the injected active power at
generator buses in the generation area (source) in incremental steps until the power flow
calculation fails to converge or when the power flow and/or voltage solution violates
their specified operating limits. The mathematical formulation of TTC using RPF is
expressed in the following:
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94
Maximise λ
Subject to:
0sincos.)(2
ijijijij
n
j
jiDiGi BGVVPP (5. 5)
0cossin.)(2
ijijijij
n
j
jiDiGi BGVVQQ (5. 6)
maxmin iii VVV (5. 7)
maxijij SS (5. 8)
maxmin genigenigeni QQQ (5. 9)
where λ is a scalar parameter representing the increase in the area’s load or generation,
λ = 0 corresponds to the base case and λ = λmaxcorresponds to the maximum transfer;
GiP and GiQ are the real and reactive power generation at bus i ; iV , Vj are voltage
magnitudes at bus i and j ; ijG and ijB are real and imaginary parts of the thij element
of bus admittance matrix; δij is voltage angle difference between bus i and bus j ,and
Sij is apparent power flow in line ij ; Qgeni is the reactive power of the thi generator. In
the power flow in (5.5) and (5.6), PDi (active load in load area) and QDi (reactive load in
load area) are calculated as:
).1.(0
DiDiDi KPP (5. 10)
).1.(0
DiDiDi KQQ (5. 11)
where PDi0 and Q
Di
0 are base real and reactive load demands at bus i in the load area ,and
KDi is a constant used to specify the change rate in the load as λ varies. Inequalities
(5.7) and (5.8) impose the voltage limits of the buses and the thermal limits of
transmission lines, respectively. The load demands in the source area, if there are any,
have their values kept fixed at those in the base case. TTC level in each case (normal or
contingency) is calculated as follows:
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95
)( max
SinkAreaj
DiPTTC (5. 12)
where )( maxSinkAreaj
DiP is the sum of the loads in the sink area when λ = λmax. In terms of
generation to meet the demand as specified in (5.10) and (5.11), optimal power flow
(OPF) is performed to determine the optimal generation schedule for each iteration. The
OPF objective is to minimise the total generation cost, with the assumption that the cost
functions for individual generators are specified.
5.1.4 Total DR programs capacity
This objective function is the total DR programs capacity in the power system that is
formed as follows:
1
TBTDRP DRP
nn
(5. 13)
TDRP
Total DR programs capacity
DRP
The amount of load participating in the demand response at the nth load bus
TB
Total number of load buses with demand response programs
5.1.5 Equality constraints
Equality constraints consist of power flow equations applied for individual power
network nodes, which is written in a compact form as follows:
0,, uVE (5. 14)
In (5.14), |V|kand θk are the vectors of system voltage magnitudes and phase angles,
and ukis the vector of control variables such as generator excitation control. In addition
to above equality constraints, the optimisation is subject to inequality constraints that
are described in the following section.
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96
5.1.6 Inequality constraints
In general, the inequality constraints can be written in the compact form as follows:
0,, uVH (5. 15)
In (5.15), H is in general a nonlinear function that relates to operating conditions such
as power – flow constraints, generator reactive power and controllers limits. An
example for inequality constraint is that of voltage magnitude constraint:
0max ii VV (5. 16)
In (5.16), |Vik| and Vi max
k are voltage magnitude at node i and its maximum allowable
respectively
5.2 Variables and their representation
The multi-objective optimisation with NSGA II algorithm requires the variables of the
optimisation problem to be coded as a string of binary digits of finite length. The
variables representing the DR program locations and sizing are grouped into a string
with the structure shown in Fig 5.1. The first part of the structure is for the coding of the
DR program locations. Each gene in this part is associated with a bus in the power
system. The gene value of 1 means in that bus DR program has been implemented. The
length of the first part is given by the number of load buses in the power system. The
second part of the structure comprises a number of blocks of binary numbers. Each
block is associated with a load bus in the power system that represents the size of the
DR program assigned to the bus. The length in each block is determined by the
maximum amount and accuracy required.
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Fig. 5.1: Representation of sample power system and string for DR locations and sizes
5.2.1 Fitness evaluation
The fronts are formed from the current population using an iterative process described
in the following. In forming the first front, the entire population is considered from
which the first non-dominated possible solution is identified. The second possible
solution of the first front is then selected from the reduced population in which the first
non-dominated possible solution is excluded. The process is repeated for a finite
number of times to form level-1 front. The same procedure is then applied to form level-
2 front from the remaining population where level-1 front individuals are excluded.
Individual fronts are assigned fitness values accordingly to their levels. Level-1 front
has the largest fitness value. Lower fronts are then assigned smaller fitness values.
Having formed the fronts together with their fitness values, it is required to assign
fitness value for each element of each front. The requirement in this fitness value
assignment is to maintain diversity. This means that the fitness value distribution over
the individuals in each front is a non-uniform one. Various schemes can be designed to
form the distribution of fitness values. For example, the present research implements a
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98
scheme based on a clustering algorithm that will assign low fitness values for the
individuals in close proximity to one another as measured by the norms of the
differences between the vectors representing these individuals. The assignment of
fitness values for the individuals in each front also takes account of the fitness value of
the front so that the lowest fitness value of an individual in a front will still be greater
than that of another individual in any other front with a lower rank.
5.2.2 Iterative process
The population is then reproduced according to the fitness values. Since individuals in
the first front have the highest fitness values, they always get more copies than the rest
of the population. The efficiency of NSGA II lies in the way by which a mapping from
objective function values to fitness values of individuals in a population is achieved
using the Pareto optimal criteria. In principle, the method can be applied to any number
of objective functions encountered in a constrained optimisation problem. The flow
chart of the proposed algorithm is shown in Fig. 5.2. Either reaching the maximum
number of allowed iterations or finding no other new non-dominated solution in a
predefined number of iterations has been considered as the termination criterion. The
key aspect in the flowchart of Fig. 5.2 is the essential application of the OPF (optimal
power flow) for evaluation of individual objective functions, which are used for the
NSGA II procedure. The inputs to the OPF in terms of DR programs sizes and locations
are those given in each possible solution vector in individual iteration. Outputs of this
step will be used to rank possible solutions in different fronts. Finally, a max-min
approach described in the following section is used to determine the compromising
solution.
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Fig. 5.2: Flowchart of the proposed algorithm
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100
5.2.3 Selection of final solution
The final solution will be one of the vectors in the front with level 1 in the population of
the last generation. An obvious choice for the final solution is that which satisfies the
optimality condition. However, the system planners might prefer to have the flexibility
of selecting a solution level-1 front that deviates from the Pareto optimality condition in
meeting their practical planning requirements and conditions. The system planners can
formulate criteria based on which the most practical solution is selected. In the current
research, a min-max approach is used to select the suitable locations and sizes of DR
programs. Each possible solution in the front with level 1 has an associated vector of
values of objective functions that can be normalised using the following expressions:
min1max1
min11
1gg
ggG m
m
(5. 17)
min2max2
min22
2gg
ggG m
m
(5. 18)
min3max3
min33
3gg
ggG m
m
(5. 19)
min4max4
min444
gg
ggG m
m
(5. 20)
where g1min, g2min
, g3minand g4min
are the minimum values and
g1max, g2max
, g3max and g4max
are the maximum values obtained for the objective
functions. The notation m is the identifier of an element in the front. It is noted that the
result of this normalisation shows the level of contentment for each objective function.
Afterwards, a min-max approach, summarised in (5.21), is applied to select the final
multi-objective DR program placement and sizing.
mmmm GGGGMaxMin 4321 ,,, (5. 21)
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5.3 Numerical Studies
The proposed algorithm has been tested on the modified IEEE-30 bus test system,
which has six generator buses, 21 load buses, 41 lines, and four tie-lines as represented
in Fig. 5.3 [70].
Fig. 5.3: Single line diagram of the IEEE 30 bus test system
It is assumed that all load buses could have DR programs up to 10% of their demand.
The design results are shown in Table 5.1 in terms of the buses selected for DR
programs together with their sizes. Sensitivity design studies have also been performed
with various values for the parameters of NSGA II algorithm. These studies indicate
that improvements in the objective functions, if there are any, are minimal in
comparison with those in Tables 5.2 to Tables 5.4. Table 5.2 shows the active power
loss in the electricity network with and without DR programs. Moreover, three
contingencies are also considered to show the effectiveness of the method in the
contingency situation.
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In Table 5.3 is summarised the EENS of the network before and after DR
implementation, and finally Table 5.4 illustrates the noticeable effect of DR on ATC
enhancement in normal and contingency conditions.
Table 5.1: Selected buses and the amount of DR programs
Bus Number Initial Demand(MW) DR program sizes (MW)
4 76 5.434
8 300 6.45
10 58 4.147
21 175 7.2625
19 95 5.8425
12 112 3.528
Table 5.2: The comparison between active-power loss before and after DR
implementation
Transmission Loss before DR installation (MW)
No contingency 27.30
Line 4-12 outage 27.82
Line 6-10 outage 27.99
Line 27-28 outage 35.29
Transmission Loss after DR installation (MW)
No contingency 26.36
Line 4-12 outage 26.88
Line 6-10 outage 27.02
Line 27-28 outage 34.54
Table 5.3: The comparison between EENS before and after DR implementation
EENS before DR installation (MWh) 484771
EENS after DR installation (MWh) 436942
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Table 5.4: The comparison between ATC before and after DR implementation
ATC before DR installation (MW)
No contingency 122.4426
Line 4-12 outage 74.37881
Line 6-10 outage 87.97862
Line 27-28 outage 82.64034
ATC after DR installation (MW)
No contingency 127.75
Line 4-12 outage 79.35
Line 6-10 outage 91.12
Line 27-28 outage 89.47
5.4 Conclusion
A flexible design procedure based on multi-objective function optimization using
NSGA II algorithm has been developed and presented in this chapter for optimally
allocating DR programs in terms of their locations and sizes. Network security
constraints are included in optimizing the objective functions related to ATC, EENS and
active-power loss. The design procedure is a flexible and general one that can be
extended in a straightforward manner to incorporate other objective functions including
those of an economic nature and constraints encountered in system operation. The
effectiveness of the procedure developed and DR programs has been illustrated with a
representative design study based on an IEEE 30 bus power system, the results of which
confirm the noticeable improvements of the objective functions chosen in the DR
program design.
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Chapter 6 Congestion
management using demand
response program
According to North American Electricity Reliability Council (NERC) Operating Policy,
demand response (DR) programs are recognised as one of the contingency reserve
services. This market based tools are very valuable when the operating margins
available to the independent system operator (ISO) reduced considerably with
increasing market competition. In addition, demand side management (DSM) strategic
plan of International Energy Agency (IEA), for 2004–2009 confirms that, ‘‘demand side
activities should be active elements and the first choice in all energy policy decisions
designed to create more reliable and more sustainable energy systems”. At the moment,
different independent system operators (ISOs) in Europe, Oceania and North America
are continuing development of a demand response program with the objective of
changing electricity demand of large power users. ISOs in different power market
around the world try to use DR programs to enhance the security of the power system.
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The role of demand response programs in a restructured power system and its effects in
congestion management was addressed in this chapter. In this approach, Day-Ahead
Demand Response Program (DADRP) and Interruptible /Curtailable (I/C) loads are
modelled based on load elasticity and used to release transmission congestion in a least-
cost manner by considering different load scenarios. The present research proposes an
integrated framework for congestion management, using DADRP and I/C programs as
an effective tools for congestion management. To achieve this goal, a market auction
with combining DADRP and I/C programs are designed.
6.1 Congestion management
The electricity network is congested when one or some of the transmission lines reached
to its maximum limits or the voltage in some buses exceeds its limitations [29].
Although, the congestion problem is not a new problem in the power system, it has
become more severe in a restructured market environment. There are different
congestion management methods apply in different electricity markets around the world
[27, 28]. Generally, these methods can be categorised into two major groups, which are
as follows:
Preventive congestion management methods
Corrective congestion management methods
6.1.1 Preventive congestion management methods
These methods are applied before finalising the electricity market. The Preventive
congestion management methods are categorised into three different sub sections apply
for different time lines. The time line for each category varies from short term to long
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106
term solutions. One of the most popular methods of this group is reserving the
transmission line capacity method and is used for bilateral contracts. In the following,
different methods for congestion management based on the preventive congestion
management methods will be discussed in details [28].
6.1.1.1 Congestion management using the transmission right
In this method, transmission line capacity will be assigned to different customers in the
market based on six months or 12 months contracts. This method is very effective in
electricity markets with considerable bilateral contracts. If the congestion occurs in the
market, the system operator priorities customers with reserved transmission capacity.
This approach can potentially reduce the probability of congested transmission lines
[99].
6.1.1.2 Point to point method
In the point to point method some of the nodes are considered as power injection and
some nodes are considered as power consumption points. In the next step, maximum
transferable power between these two points is calculated and required transfer capacity
will be reserved for power transaction [28].
6.1.1.3 Area to area method
In this method, the network is divided into different areas then the maximum
transferable power between two sections can be calculated with considering the
maximum thermal limitations of transmission lines, transformer limitations and voltage
stability [28].
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6.1.1.4 Congestion management methods based on the ATC
The available transmission capacity can be calculated as per equation (6.1) [100]:
ATC TTC TRM CBM ETC (6. 1)
The TTC equals to the total transfer capacity between two points or two areas in the
transmission system. The factors that affect the total transfer capacity (TTC) include
thermal limitation of the transmission lines, voltage limitation on buses and the stability
limits. The transmission reliability margin (TRM) is a reliability index. This index
shows that the power transfer is not exceeded the reliability margin of the line. The
other terms which can affect this index are load forecast errors and contingency in the
electricity network. The capacity benefit margin (CBM) index is also similar to TRM
and considers a security margin for transmission lines. The, existing transmission
capacity (ETC) shows the existing transferable power from one area to other or from
one point to other point. In this method, the system operator calculates the ATC for
different areas and publishes this information before the actual operation time. This
information will be published via the specific gateway. In the next step, the system
operator recalculate the ATC based on the received information from the market
participants. During the transmission congestion the system operator might ask for
improving or cancelling some of the contracts to be able to recover the available
transmission capacity to the normal level [101].
6.1.2 Corrective congestion management methods
The corrective congestion management alternatives focuses on eliminating the
congestion when occurs during system operation, through online control actions. Some
of the usual corrective congestion management methods include, the controlling actions
from phase shifters, transformer tap changing, revising the FACTS device reference
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108
value and generator re-dispatch [8, 39, 40, 102]. Although, the preventive actions can
help the system operator to prevent the congestion in transmission lines, the corrective
actions have to be applied in some cases such as major generator or transmission line
outages or any other major contingency in the system.
6.2 Modelling demand response program
In order to analyse the impact of demand response program on load profile
characteristics, development of responsive load economic models are necessary. There
are several models available to show the relationship between the price and demand.
These models can be used for simulating different type of customers such as linear,
logarithmic, exponential and hyperbolic [103]. One of the important steps associated
with modelling the demand response participants is to determine how the reduced load
by participants would be recovered after predefined reduction by the market. Basically,
load reductions by DR participants are divided into two categories.
Non-transferable loads: Load reduction without recovering it later. For example,
lighting load, air conditioning loads are examples of loads which cannot be shifted to
another hours.
Transferable loads: some types of loads can be rescheduled and shifted as required.
Some of industrial processes can be rescheduled and shifted based on request. The
Elasticity is defined as the demand sensitivity with respect to the price, and it is
explained as follows [103]:
0
0
.D dD
ED dp
(6. 2)
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109
where
E Elasticity of the demand
0D Initial demand value (MWh)
D Demand value (MWh)
Electricity price ($/MWh)
0 Initial electricity price ($/MWh)
Based on this definition if the electricity price increases or if the independent system
operator considers incentive payment in some intervals, the electricity customers react
to these changes based on equation (6.2). Some types of loads are not capable to be
transferred from one period to another. These type of loads known as “self elasticity",
and it has negative value. In other hand, some loads could be able to shift from the peak
period to the off-peak hours known as multi period loads and they have positive
elasticity values. The equation (6.3) shows the self and cross elasticity:
0
0
( ) ( )( , ) .
( ) ( )
j dD iE i j
D i dp j
( , ) 0 ,
( , ) 0 ,
E i j if i j self elasticity
E i j if i j cross elasticity
(6. 3)
The self and cross elasticity can be explained for each hour of a day with 24 by 24
matrices as per equation (6.4) [64, 104].
(1) (1,1) (1,2) .... .... .... (1,24) (
(2) (2,1) (2,2) .... .... ....
(3) .... ..... ( , ) .... ....
.... (23,1) .... (23, ) .... (23,24)
(24) (24,1) .... (24, ) .... (24,24)
d E E E
d E E
d E i j
E E j E
d E E j E
1)
(2)
( )
....
(24)
j
(6. 4)
The self elasticity is shown in the diagonal items of this matrix, and the off-diagonal
items correspond to the cross elasticity. For instance, Column j of this matrix shows
how a change in price during the single period j affects the demand during all other
periods. The elasticity for the electricity sector generally varies by a value between -1
and +1. Fig. 6.1 shows the elasticity of inelastic and elastic load and Fig. 6.2 shows the
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110
elasticity of the typical customers to the price based on linear model. This figure
explains the relation between quantity and price for any commodity including the
electricity from customer point of view.
Fig. 6.1: The elasticity of the typical elastic and inelastic load
Fig. 6.2: Linear representation of price versus quantity
The equation (6.5) shows the relationship between the price and quantity based on
linear function that is shown in Fig. 6.2.
0
0
( ) ( )( , ) .
( ) ( )
j dD iE i j
D i dp j
(6. 5)
In the equation (6.5) ( )
( )
dD i
dp j is constant, which means if the price increases from $1 to
$2, it has similar effect on changing from $100 to $101. The non-linear modelling can
highlight this difference and leads to the accurate model for elasticity.
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111
Fig. 6.3: Non-linear representation of price versus quantity
Three factors including incentive, penalty and elasticity are considered in this research
to form the mathematical model that can be used to form the price quantity offer by the
demand response aggregators. The steps for developing the mathematical demand
response formulation are explained in the following:
The load change at the ith bus arising after load reduction by demand response
participants can be expressed as follows:
0( ) ( ) ( )L t L t L t (6. 6)
In (6.6), 0 ( )L t and ( )L t are the load at the ith location before and after demand response,
respectively.
If ( )IN t is paid as incentive to the customer for each unit of load reduction, the total
incentive for participating in DR program will be calculated based on equation (6.7).
The incentive amount is a fixed value that is determined by the market operator. The
amount of penalty is also assumed to be a fixed amount, and for the purpose of this
chapter the penalty is set to be 1.5* IN(t) [79].
0( ( )) ( )[ ( ) ( )]P L t IN t L t L t (6. 7)
If the customers participating in the DR program do not respond to the minimum load
reduction as required in the contract, the customers will have to pay the penalty. If the
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112
reduction level requested from the aggregator and penalty for the same period are
denoted by ( )LR t and ( )fin t , respectively, then the total penalty ( ( ))TFIN L t is calculated
as follows:
0( ( )) ( ).{ ( ) [ ( ) ( )]}TFIN L t fin t LR t L t L t (6. 8)
The requested load reduction level, ( )LR t , is limited to the maximum value max ( )LR t as
agreed in the contract between the aggregator and DR participants. If the customer
revenue is considered as ( ( ))B L t for using ( )L t , the customer net benefit can be
calculated as follows:
( ) ( ( )) ( ) . ( ) ( ( )) ( ( ))S t B L t L t t P L t TFIN L t (6. 9)
In (6.9), ( )t is the price that should be notified or forecasted by the demand response
aggregator or demand response participants prior to the day for implementing DR
program. To maximize the customer’s net benefit,( )
S
L t
in equation (6.9) is set to zero.
( ) ( ( )) ( ) ( ) ( ( )) ( ( ))
0( ) ( ) ( ) ( ) ( )
S t B L t t L t P L t TFIN L t
L t L t L t L t L t
(6. 10)
From (6.10),
( ( ))
( ) ( ) ( )( )
B L tt IN t fin t
L t
(6. 11)
In general, various forms of customer revenue function have been proposed for
expressing the customer revenue in terms of demand [63, 104-106]. In this paper, an
exponential function of demand elasticity as given in [107] is adopted for deriving the
optimal demand response:
1( )
00 0 1
0
( ) ( ) ( )( ( )) ( ( )) 1
( )1 ( )
E ii L i L i
B L i B L iL iE i
(6. 12)
In (6.12), ( )E t is the elasticity of the load and 0 ( )t is the market price prior to demand
response implementation. Differentiating equation (6.12) yields to:
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113
1
1
( )
0
10
( ) 1
10
10 0
( )( ( )) ( )1
( ) ( )1 ( )
( ). ( ) 1 ( )( ) .
( ) ( )1 ( )
E t
E t
tB L t L t
L t L tE t
t L t L tE t
L t L tE t
(6. 13)
Simplifying equation (6.13) and substituting into equation (6.11) yields to equation
(6.14).
1 1
1
0
( ) ( )
1
0 0
( ) ( ) ( )(1 ( ) ).
( )
( ) ( )1 ( ) .
( ) ( )
E t E t
t IN t fin tE t
t
L t L tE t
L t L t
(6. 14)
Rearranging equation (6.14) leads to:
1( )
10 0
( ) ( ) ( ) ( ) 1
( ) ( ) 1 ( )
E tt IN t fin t L t
t L t E t
(6. 15)
The second term of the right hand side of equation (6.15) can be discarded for small
amount of elasticity, and finally the demand response model can be achieved as follows:
( )
00
( ) ( ) ( )( ) ( ).
( )
E tt IN t fin t
L t L tt
(6. 16)
In this research, it is assume that the aggregators submit the offers to the wholesale
market on behalf of the demand response participants and NAS battery owners. The
demand response formulation in (6.16) is used to form the price-quantity offer package
to the market. The aggregated package comprises a number of power blocks each of
which with block size and bidding price. The details of the market clearing formulation
with considering demand side resources are explained in the following section.
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114
6.3 Auction-based market clearing
Customers can bid their capacity and associated price at which they would be willing to
curtail their loads on a day-ahead auction dispatch (DADRP). The market clearing
formulation can be presented according to equation (6.17).
)(.1 1
,,1 1 1
,,1
,, ).().().(: RICOr
fD DiG reD DiGj N
i
N
kkDikDi
N
j
N
i
N
kkreDikreDi
N
llGjlGj PPPMin
(6. 17)
Subject to
DikDikDikDi NNPP ,.....,1,,.....,10 max
,,
(6. 18)
GjlGlGjlGj NNjPP ,.....,1,,.....,10 max
,,
(6. 19)
G
N
l
lGjj
N
l
lGj
N
l
lGjj NjPuPPuGjGjGj
,......,11
max
,
1
,
1
min
,
(6. 20)
reDireDkreDikreDi NkNiPP ,...,1,,......,10 max
,, (6. 21)
G GjreD DiD Di N
j
N
l
lGj
N
i
N
k
kreDi
N
i
N
k
kDi PPP1 1
,
1 1
,
1 1
, (6. 22)
reD
N
i
L
lliliii
RN
j
L
lljljjj
RI1 1
P rP r)1()P r.(
1
)
1
P rP r)1()P r.((
(6. 23)
reDiLlRjiljj
u ,,}1,0{,,, (6. 24)
Gj Nju ,......,11,0 (6. 25)
where ,PGj l Power block l that generator j is willing to sell at price ,Gj l up to a maximum
of max,PGj l ;
,PreDi kPower block k that responsive demand i is willing to sell; PreDi
Power
provided by responsive demand I; max,PGj l Maximum power block l offered by generator ;
NreDNumber of responsive demands; NL
Number of lines; NGjNumber of blocks offered
by generator j; fr Risk coefficient; Pr joutage probability of generator j; Prl outage of line
l probability; ( )CO RI the function represents the risk. The objective function is presented
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115
in (6.17). The set of constraints are presented in (6.18) to (6.22). The set of constraints
(6.18) specifies the sizes of responsible demand bids. Constraint (6.22) states that the
production should be equal to the demand balance considering the responsible demands.
Equation (6.23) is explaining the risk factor.
6.4 Congestion management by generation and demand re-dispatch
The congestion management formulation using demand response and conventional
generators are presented as follows:
reDi
down
reDi
down
iGj
up
Gj
up
j
down
Gj
down
j PrPrPrMin )()(: (6. 26)
Subject to:
NnBPPPPn
nnnnm
mnnm
down
D
A
D
down
G
A
G ,......,10)(
(6. 27)
nnmmnnmnm mNnPBP ,,.......,1)( maxmax (6. 28)
GGjj
down
Gj
A
GjGjj NjPuPPPu ,........,1maxmin (6. 29)
n
nGj
down
Gj
down
G NnPP ,........,1 (6. 30)
NnPPn
nGj
A
Gj
A
G ,.......,1
(6. 31)
NnPPn
nDi
down
reDi
down
D ,.....,1
(6. 32)
NnPPn
inDi
A
D
A
D ,.......,1
(6. 33)
The objective function for congestion management is presented in (6.26), and the
constraints are presented in (6.27) to (6.33). Whereup
GjP increment in the schedule of
generator j;down
GjP decrement in the schedule of generator j; downreDiP decrement in the
schedule of responsible demand I; upjr price offered by generator j to increase its
schedule;downjr price offered by generator j to decrease its schedule
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116
6.5 Numerical studies
A case study based on the modified IEEE 30-bus system is presented. Transmission
capacity limits of the lines are supposed to be 70% of the values given in [24].
Fig. 6.4: IEEE 30-bus system
Three scenarios of the demands are considered; in scenario 1, all the demands are
considered to be in their peak value during the 24-hour period. In scenarios 2 and 3, two
sets of random numbers are generated for determination of the loads in every load bus.
These random numbers are generated by uniform distribution in the range of 0–1 with
considering a typical load duration curve. The load demands in three scenarios are
presented in Table 6.1.
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Table 6.1: Loads in three scenarios of demand
Bus Number Scenario 1 Scenario 2 Scenario 3
1 0 0 0
2 21.7 20.12 20.21
3 2.4 1.55 1.67
4 7.6 6.84 3.38
5 0 0 0
6 0 0 0
7 22.8 13.75 14.31
8 30 25.17 21.48
9 0 0 0
10 5.8 4.02 4.49
11 0 0 0
12 11.2 7.15 11.02
13 0 0 0
14 6.2 4.40 4.71
15 8.2 5.87 3.68
16 3.5 2.003 2.27
17 9 8.25 5.007
18 3.2 2.87 2.45
19 9.5 7.93 6.81
20 2.2 1.69 1.24
21 17.5 9.77 7.81
22 0 0 0
23 3.2 3.06 1.68
24 8.7 6.59 5.12
25 0 0 0
26 3.5 2.31 1.73
27 0 0 0
28 0 0 0
29 2.4 1.91 1.517
30 10.6 7.62 8.072
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A typical load curve is selected to test and analyse the effect of DADRP and I/C
programs. The load curve is divided into three intervals; low-load period, off-peak
period, and peak period. In this study, three values of incentives and penalties are
considered for DR programs. The incentive value is assumed to be 30, 40 and
60$/MWh and the penalty value is assumed to be 60, 80 and 110 $/MWh for all
customers. The load curves before and after implementation of DR program is presented
in Fig. 6.5 for different incentive and penalty values.
Fig. 6.5: The load curve before and after DR program implementation
In this study, seven high load buses are selected as the candidates for implementing DR
programs. These selected buses and the reduction amount are provided in Table 6.2.
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119
Table 6.2: Load demands due to various incentives and penalties
Responsible
Demand
Number
Bus
Number
Initial
Demand
30$ /MWh
Incentive
60$/MWh
Penalty
40$/MWh
Incentive
80$/MWh
Penalty
60$/MWh
Incentive
110$/MWh
Penalty
1 7 22.8 21.44 20.440 20.10
2 8 30 28.38 27.84 26.76
3 12 11.2 10.53 10.041 9.87
4 17 9 8.46 8.068 7.938
5 19 9.5 8.93 8.51 8.37
6 21 17.5 16.45 15.68 15.43
7 30 10.6 9.96 9.50 9.34
The market clearing results for generators and demand response programs are presented
in Table 6.3 and Table 6.4. In addition, increment and decrement for generators and
demand response programs are shown in Table 6.5 to 6.6.
Table 6.3: The auction results for generators
Generator Number Bus Number Production (MW)
1 1 44.73
2 2 58.26
3 13 15.77
4 22 22.31
5 23 15.79
6 27 32.324
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120
Table 6.4: The auction results for generators and responsible demands
Generator Number Bus Number Production (MW)
1 1 43.714
2 2 57.099
3 13 14.970
4 22 21.988
5 23 14.970
6 27 29.88
Responsible
Demand(DADRP)
Bus Number Production(MW)
1 7 1.35
2 8 1.785
3 12 0.666
4 17 0.535
5 19 0.565
6 21 1.041
7 30 0.630
Table 6.5: Generator increment and decrement to release the congestion
Generator
Number
Bus
Number
Without _DR
Decrement Increment
1 1 0 9.6682
2 2 43.625 0
3 13 0 18.1375
4 22 0 4.7225
5 23 0 3.84
6 27 0 7.2403
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121
Table 6.6: Generators and Responsible demands increment and decrement to release the
congestion
Generator
Number
Bus
Number
With _DADRP
Decrement Increment
2 2 27.1722 0
3 13 0 14.077
4 22 0 0.8656
5 23 0 4.289
6 27 0 4.0355
Responsible
Load
Number
Bus
Number
Decrement Increment
1 8 3.54 0
2 21 0.3648 0
Total cost of market for various scenarios and three load demands are presented and
compared in Fig. 6.6.
Fig. 6.6: Total cost of market operation in three scenarios of demands ($/hour)
0
10000
20000
30000
40000
50000
60000
70000
WITHOUT DR DADRP I/C DADRP+I/C
Demand 1 62010.47157 31527.05265 34983.58604 31563.10236
Demand 2 20310.08069 11991.16423 15478.60441 12068.78006
Demand 3 9059.438286 8635.814622 8820.775138 8698.644935
Tota
l Co
st($
)
Total Market Cost
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122
6.6 Conclusion
In this chapter, DR program as a new tool for congestion management was considered.
In this regard, auction-based dispatch method, which is adopted in some electricity
markets and as a relatively simple procedure, was implemented. Then, two different
types of this method were compared from economical viewpoint. In the first type, the
congestion was relieved just by increment and decrement of initial production of
generators, which was determined in market auction. In another type, congestion was
relieved by decrement in initial production of generators and reduction of demands,
which was achieved by I/C and DADRP implementation. Comparison of these two
auction-based mechanisms was performed on IEEE 30-bus system. The results indicate
that congestion management by generation and demand re-dispatch can considerably
reduce the congestion costs.
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123
Chapter 7 Hybrid approach for
congestion management using
combination of demand response
and FACTS devices
7.1 Introduction
Congestion may be relieved, in many cases by cost-free means such as network
reconfiguration, operation of transformer taps and operation of flexible alternating
current transmission system (FACTS) devices [9, 42, 108-111]. In other case, however,
it may not be possible to remove or relieve congestion by cost-free means, and some
non-cost-free control methods, such as re-dispatch of generation and curtailment of
loads, are required [112, 113]. Since there is a wide range of events which can lead to
transmission system congestion, a key function in system operation is to manage and
respond to operating conditions in which system voltages and/or power flow limits are
violated [28]. A congestion management method proposed in this chapter is based on a
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124
combination of FACTS devices and demand response programs. In addition , deploying
combination of demand response resources and FACTS at appropriate locations would
allow generation to operate at a lower cost as the congestion is reduced and also
transmission network investment can be postponed while maintaining the existing level
of security [60, 114, 115]. A two-step market clearing procedure is formulated in this
chapter. In the first step, generation companies bid to the market for maximizing their
profit, and the ISO clears the market based on social welfare maximization without
considering the electricity network constraints. In the second step, the ISO will consider
network losses and network constraints. The electricity market-clearing procedure
considered in the present chapter is similar to the one used by the Ontario electricity
market operator [65, 116].
7.2 Problem formulation
The market clearing formulations are presented in the following section:
1 1 1 1
: ( ) ( )
GjDi GDNN NN
Dik Dik Gjl Gjl
i k j l
Maximise P P
(7. 1)
Subject to:
min max 1,..., , 1,...,Dik Dik Dik D DiP P P i N k N (7. 2)
min max , 1,...,Gjl Gjl Gjl G GjP P P j N l N (7. 3)
1 1 1 1
GjDi GDNN NN
Dik fd Gjl
i k j l
P P P
(7. 4)
where DikP Power block k that demand i is willing to buy at price Dik up to a maximum
of maxDikP ; Dik Price offered by demand i to buy power block k ;
Gjl price offered by
generator j to sell power block l ;GjlP Power block l that generator j is willing to sell at
priceGjl up to a maximum of
maxGjlP ;
fdP the fixed load based on demand forecasting. The
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125
objective function in (7.1) represents the social welfare, and it has two terms. The first
term consists of the sum of accepted demands times their corresponding bidding prices,
and the second term is the sum of acceptable production bids times their corresponding
bidding prices. The block of constraints in (7.2) specifies the size of the demand bids.
The block of constraints in (7.3) limits the sizes of the production bids. The equality
constraint in (7.4) ensures that the production should be equal to the total demand. The
solution of the constrained optimisation problem described in (7.1)–(7.4) specifies the
power produced by every generator and the power supplied to customers together with
the market prices.
7.2.1 Congestion management formulation
In the previous section, the dispatch calculations are performed without taking into
account the electricity network limitations such as thermal limit of transmission lines
and voltage constraints. To manage the congestion due to such limits, the following
constrained optimisation problem is to be solved.
: ( ) .upup down down down down
j j Gj Di reDi iGj
j G i reD
Minimize r P r P r P d
(7. 5)
Subject to:
, , 0E V u (7. 6)
, , 0H V u (7. 7)
whereupjr is price offered by generator j to increase its output schedule for congestion-
management;up
GjP is increment in the schedule of generator j ; downreDiP is decrement in the
schedule of responsive demand block i ; downDir is price offered by responsible demand i to
decrease its demand;downjr is price offered by generator j to decrease its pool power
______________________________________________________________________
126
schedule; down
GjP is decrement in the schedule of generator j ; id is binary value; V is
vector of voltage magnitudes; is vector of phase angles and u is vector of control
variables.
E and H in (7.6) and (7.7) are the sets of equality and inequality constraints. Vector u
in (7.6) and (7.7) is the control vector comprising active-power generation
increments/decrements, demand response commitments, input references to generator
excitation controllers and network controllers including those of FACTS devices.
The objective function in (7.5) has two parts. The first part is the sum of the payments
received by the generators for changing their output as compared to the original
generation schedule, and the second term shows the total payment received by demand
response participants to reduce their load. Each demand response service provider
submits to the system operator a bidding curve to specify prices and capacity. Typically,
the bidding comprises a number of power blocks each of which with block size and
bidding price as shown in Fig. 7.1.
),(1
tiD ),(2
tiD ),(3
tiD ),(4
tiD
),(1
ti
),(2
ti
),(3
ti
),(4
ti
Load Reduction
(MW)
Offered Cost
($/MW)
Fig. 7.1: Typical demand response offer to the market
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127
The set of equality constraints in (7.6) includes the power-flow equations for
generator nodes and load nodes. For each generator node, the nodal active–power is the
algebraic sum of power generation as determined after market clearing and the
increment/ decrement supplied by ancillary service providers at the node. For each load
node, the total nodal active-power is the algebraic sum of load demands before the
demand response and the decrement after demand response at the node.
The nodal reactive-power at each load node used in forming the power-flow equation
is determined from the active-power together with a specified power factor.
The set of inequality constraints denoted by H in (7.7) is related to operating limits
that include:
i. Power-flow constraints for transmission circuits. These constraints are required
in congestion management.
ii. Nodal voltage constraints. These are related to network voltage security.
iii. Generator reactive power limits.
iv. Power system controllers limits.
For the purpose of this research, network controllers based on FACTS devices in the
form of TCSCs and SVCs are considered. The functions of these controllers include
those for mitigating congestion and/or enhancing network voltage security. The
operating limit constraints on these FACTS device controllers, which are to be
included in the set of inequalities in (7.7) are expressed in (7.8) and (7.9).
min maxTCSC TCSC TCSCX X X (7. 8)
min maxSVC SVC SVCB B B (7. 9)
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128
For each TCSC, TCSCX in (7.8) is the TCSC reactance variable that is a controllable
quantity.
Solution of the problems (7.5)–(7.7) provides the modified generation levels,
demand response commitments, generator and network controller input references
that satisfy system operating constraints.
The details of the two steps for market clearing with congestion management are
summarised in the flowchart in Fig. 7.2.
Fig. 7.2: Two step market clearing procedure
ISO
Receives information
From market participants
Market clears without
Considering network constraints
ISO finalize the market
Violation?
No
Yes
ISO analyze network congestion and
Determine
Power loss
Congestion management
Procedure using
Responsive Determine
Generation re-dispatchNon-
Dominated sorting,
Assignment of fitness
value to each solution
FACTS Reproduction,
Crossover, Mutation,
Generating a set of
offspring
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129
7.3 Numerical studies
A case study based on the modified IEEE 30 bus system that is shown in Fig. 7.3 is
presented in this section. Line, generator, and demand data can be found in [117]. In
this paper, load demands are presented in Table 7.1. Seven load buses as specified in
Table 7.2 are selected for demand response participation based on their potential to
reduce the transmission line congestion according to generation shift factor.
The data for generator bidding are presented in Table 7.3. The data for the TCSC
and SVC in the system of Fig. 7.3 in terms of their reactance/susceptance limits is
shown in Table 7.4 [118].
Fig. 7.3: IEEE 30-bus system
SVC
TCSC
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130
Table 7.1: Load demand with power factor 0.9
Bus Number Demand Value
1 0
2 21.7
3 7.6
4 7.6
5 0
6 0
7 22.8
8 30
9 0
10 5.8
11 0
12 11.2
13 0
14 6.2
15 8.2
16 7.8
17 9
18 3.2
19 9.5
20 11.6
21 17.5
22 0
23 12.5
24 8.7
25 0
26 3.5
27 0
28 0
29 2.4
30 10.6
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131
Table 7.2: selected buses for Demand response implementation
Responsible Demand Number Bus Number
1 7
2 8
3 12
4 17
5 19
6 21
7 30
Table 7.3: selected buses for demand response implementation
Gen
Number
1
Gene
Number
2
Gen
Number
3
Gen
Number
4
Gen
Number
5
Gen
Number
6
Quantity (MW) 10 10 10 10 16 16
Price ($) 352 352 704 704 704 704
Quantity (MW) 20 20 20 20 32 32
Price ($) 990 990 1540 1540 1606 1606
Quantity (MW) 30 30 30 30 48 48
Price ($) 1892 1892 3520 2464 2728 2728
Quantity (MW) 40 40 - 40 64 64
Price ($) 3080 3080 - 3520 4026 4026
Quantity (MW) 50 50 - - - -
Price ($) 4532 4532 - - - -
Table 7.4: Facts devices data
Type of FACTS TCSC SVC
Operating limit (p.u) 0.105 0.105TCSCX 0.15 0.15SVCB
noitacoL Line 28 (bus10-bus 22) Bus 30
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132
Using the software system developed and system data given in previous section, the
results of market clearing together with congestion management are obtained and
discussed. In the first step, the electricity market is cleared without considering the
electricity network.
The generator schedule is presented in Table 7.5. Subject to network constraints
including those arising from congestion, the generator schedule and load demands
would be augmented, drawing on the solution of the constrained optimisation
problem. The problem will be formed and solved for three options the benefits of
which are compared.
Option 1. Without demand response and with FACTS devices. In this case, demand
response is not considered for congestion management.
Option 2. With demand response and with FACTS devices.
Option 3. With demand response and without FACTS devices
Results of generation re-dispatch (generation increment or decrement) for
congestion management for options 1-3 as indicated in Table 7.6. These results were
derived based on two step market clearing which is explained in Fig 7.2.
Table 7.5: The Auction Results for Generators participated in electricity market
Generator Number Bus Number Generation (MW)
1 1 35
2 2 33.37
3 22 36
4 27 36
5 23 18.39
6 13 32.24
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133
Table 7.6: Generation increment and decrement for all generators due to congestion
management (MW)
Generator
number Bus Number
Without DR
With
FACTS
With
DR
With
FACTS
With
DR
Without
FACTS
Generation increment
1 22 16.24 8.36 12.24
2 27 12.18 9.83 71.8
3 23 0.22 0 0.22
Generator
number Bus Number
Without DR
With
FACTS
With DR
With
FACTS
With
DR
Without
FACTS
Generation decrement
1 1 0.4 0.79 0.4
2 2 12.16 6.67 41.6
3 23 0 0.29 0
4 13 12.89 6.96 10.59
Total amount of re-dispatch for generators without using demand response (option
1) is 54.1 MW. With the generation price biddings adopted in the study, the total
amount of generation re-dispatch using option 2 is reduced significantly to 32.9MW.
This represents a reduction of about 21.19 MW. This reduction is a consequence of
using combination of incentive-based demand response programs and FACTS
devices. However, if the power system does not have FACTS devices, the
generation re-dispatch amount is reduced to 37.76 MW as indicated in the results in
column 5 (option 3) of Table 7.6. The load reduction associated with each
responsive demand is presented in Table 7.7. This table shows the demand response
locations and the reduction level that is achieved based on the solution of the
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134
optimisation problem presented in section 7.3. The total cost of market operation in
three different options are presented in Table 7.8.
Table 7.7: demand response contribution for congestion management (MW)
Responsible
demand number
Bus Number With DR
With FACTS
With DR
Without FACTS
1 7 1.4 1.6
2 8 1.6 2.2
3 12 0.8 0.8
4 17 0.4 0.6
5 19 0.6 0.8
6 21 1.2 1.2
7 30 0.4 0.8
Table 7.8: Total cost of market operation and redispatch cost in different scenarios and
system states
Without DR
With FACTS
With DR
With FACTS
With DR
Without FACTS
Total market cost
($/h) 19150 17761 19364
Total redispatch
cost($) 4849 3460 5063
Comparison of different options shows that using the combination of DR and
FACTS devices can reduce the total market cost (including market clearing and
congestion cost) up to 10.3%. The re-dispatch costs are shown separately in Table
7.8 for comparison purpose. In fact, total market cost is lower when the market
operator deployed the combination of FACTS and DR programs.
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135
7.4 Conclusion
This chapter has developed a methodology for transmission congestion management
in which the traditional approach of using conventional generators and/or FACTS
devices is augmented by demand responses. The method proposed draws on a mixed
integer optimization required of DR dispatches. The effectiveness of the method is
illustrated with a representative market clearing study in which various options of
using FACTS devices and/or DR are compared.
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136
Chapter 8
Facilitating large integration of
wind power generation through
effective utilisation of demand
response program
8.1 Introduction
Many countries and regions around the world are introducing policies aimed at reducing
the emissions produced by the energy sector and increasing the utilization of renewable
energy. Among various types of renewable generations, wind generation is projected to
take a considerable share of green power generation. The U.S. Department of Energy
has presented a scenario in which wind energy is expected to supply 20% of the U.S.
electricity demand in 2030 [119]. Integration of large portion of wind power in the
electricity grid can potentially challenge the power system security in different ways.
______________________________________________________________________
137
These challenges arise as a result of integrating large amount of high uncertainty, high
volatility, and low predictability wind power source. Some of the major technical
challenges for power systems with high penetration of wind power are summarized as
follows [2-7]:
Voltage stability
Transient stability
Available transfer capacities from/to windy areas
Response during contingencies
Impacts on distribution networks, and
Lack of wind power and demand correlation.
These issues require considerable research attention in order to be able to achieve
high wind penetration without compromising the power system security. In order to
overcome the mentioned problems additional resources are required for electricity
network. Demand side resources could be an effective solution to overcome the
mentioned challenges. In the previous studies, a significant volume of technical
literature focuses on demand response [81, 120-124] and the associated benefits for
electricity network which include the improvement in the operation of renewable
generation [93], providing ancillary services for the market [125, 126] and enabling
infrastructure for utilizing large amount of renewable resources [127]. In [128], a
day-ahead network constrained market clearing formulation is proposed in a form of
mixed integer linear programming to schedule the energy and spinning reserve
provided by generating units and demand response program. The role of demand
side management to enhance power system transient stability is investigated in
[129]. This approach is investigated in a power system with high renewable
generation level. A comprehensive central DR algorithm for frequency regulation in
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138
micro grids is studied in [130]. It is shown that the proposed comprehensive demand
response (DR) central strategy can enhance the system stability in the presence of
wind power generation. An event-driven demand response scheme for power system
security enhancement is investigated in [131]. The proposed approach is able to
provide key setting parameters such as the amount of demand reductions at various
locations to prevent power system from experiencing voltage collapse.
In order to overcome the mentioned problems additional resources are required for
electricity network. Effective utilization and integration of demand side resources
and FACTS could be an effective solution to overcome the mentioned challenges.
FACTS devices and their associated benefits for efficient operation of electricity
markets have been widely addressed in the literature [132-135]. FACTS devices can
benefit the power system in many ways including congestion management [136],
transient stability [134, 137] and voltage stability[138]. In addition, demand side
resources including demand response programs and energy storage systems can also
play a major role to enhance the power system security. Significant number of
technical literature focuses on demand response [81, 120-123] and the associated
benefits for electricity network including improvement in the operation of renewable
generation [93], providing ancillary services for the market [125, 126], enabling
infrastructure for utilizing large amount of renewable resources [127], network
reliability enhancement [139], improving the loadability of the transmission lines,
providing ancillary services for the market [125, 126] and enabling infrastructure for
supporting large amount of renewable resources [127]. There are several examples
which have been reported for application of demand response programs. The use of
demand-side resources to respond to the operating reserves deficiency or major
emergencies in power systems has investigated in [140]. In the U.K., DR program is
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139
actively encouraged to compete with conventional generators to provide all types of
reserve services for the power system [141]. The main aim of this chapter is to
propose a comprehensive approach through effective utilisation of demand side
resources to mitigate some of the challenges which arise as a result of large
integration of wind power to the electricity network. To achieve this aim, a
constrained optimization is proposed to clear the electricity market that allows
conventional generators and demand side resources to offer their capacity. In the
next step, a centralized event-driven approach is proposed to maintain the system
security after major contingency or disturbance to the system. To achieve this aim,
the required amount of emergency demand response program is triggered to recover
the power system security. Fig. 8.1 shows the wind power generation and load
variation in a summer day in California ISO.
Fig. 8.1: Load profile and wind generation in CAISO [142]
As it can be seen, wind power is dropping off when the load is ramping up and when
the load is ramping down wind power is starting to rise. This characteristic increases
0
5000
10000
15000
20000
25000
30000
35000
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24Time (hour)
Lo
ad
(M
W)
0
200
400
600
800
1000
1200
1400
1600
1800
2000
Win
d P
ow
er
(MW
)
Base load profileWind Generation
______________________________________________________________________
140
a need for additional ramping capability from the conventional generators in the
power system with high penetration of wind power. The main contribution of this
chapter is to develop a day-ahead network-constrained market clearing formulation
in which dispatchable demand side resources including demand response and
Natrium Sulfur (NAS) battery can participate in the market. Using the proposed
approach, it is possible to have a flexible demand and reduce the need for ramping
up/down services by conventional generators. This method can provide flexible load
profile at a minimum cost and facilitate large-integration of wind generation in the
power system. In other words, the proposed approach facilitates shifting the wind
generation from the off-peak periods to the high-peak hours.
8.2 Problem formulation
8.2.1 Market clearing formulation
The objective function of the proposed method is to minimize the total cost while
satisfying the equality and inequality constraints [143].
( )
1
( )1
1
( )
1 1
( , ). ( )
( ). ( ) ( ). ( , )
( ). ( , )
( ). ( ) ( , ). ( )
( , ). ( , )D
m mMF i
iN
m
ME ii
m i m mtm
N NSD i
m m
i m
P i t b i
F i u t ST i b i t
SH i c i t
MINE i u t q i t LE i
D i t i t
1
T
(8. 1)
where; (.)mE Emission function of a unit; (.)mLE Slope of segment m in a linearized
emission curve; (.)F Fuel cost function of a unit; (.)ME Number of segments for the
piecewise linearized fuel cost curve; (.)MF Number of segments for the piecewise
linearized fuel cost curve; (.)P Hourly generation of a unit; mLG Slope of segment m
______________________________________________________________________
141
in linearized fuel cost curve; (.)mP Generation of segment m in a linearized fuel cost
curve; (.)mq Generation of segment m in a linearized emission curve; (.)u Unit status
indicator where 1 means on and 0 means off; iRUP Ramping up limit of a unit; iRAD
Ramping down limit of a unit; ( )SPI t Total amount of spinning reserve;TIU Number
of hours a unit has been on at the start of the scheduling period; TIC Number of
hours a unit has been off at the start of the scheduling period; (.)HT Number of hours
a unit needs to remain on if it is on at the beginning of the scheduling period; (.)LU
Minimum up time of a unit; (.)LT Minimum down time of a unit; ( , )mD i t Power
block that demand i is willing to buy at the price of ( , )m i t .
The first line of the objective function is related to the fuel cost, start up and shut
down cost. The typical fuel cost function for conventional generators are used in this
paper and formulated as follows:
2( , ) ( ). ( , ) ( ). ( , ) ( )F i t i P i t i P i t i (8. 2)
This cost function can be approximated by a set of piecewise blocks, as it shown in
Fig. 8.2.
)(1 iP)(iP g )(iP g)(2 iP
Power Generation (MW)
)(1 mb
)(2 mb
)(3 mb
)(3 mb
Co
st ($
)
Fig. 8.2: Approximated cost function by the piecewise blocks
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142
The mathematical explanation of the linear approximation of the fuel cost function
is represented in equation (8.3):
( )
1
( ). ( ) ( , ). ( )
MF i
i m m
m
F i u t P i t LG i
(8. 3)
The second part of the conventional generator cost is related to the start up and shut
down cost. The start up cost comprises of two separate values which are cold start
up and hot start up.
The cost of shut down is constant for each unit and is modelled using shut down
indicator. The second line of the objective function is dedicated to emission cost.
The polynomial function is used to consider the emission cost in this paper. The
following quadratic function is considered for cost of emission.
2( , ) ( ). ( , ) ( ). ( , ) ( )mE i t ea i P i t eb i P i t ec i (8. 4)
The emission function can be approximated by a set of piecewise blocks and the
mathematical representation can be explained as follows:
( )
1
( ). ( ) ( , ). ( )
ME i
m i m m
m
E i u t q i t LE i
(8. 5)
The third line of the objective function dedicated to demand side resources. The
demand side offer package comprises the power blocks and associated price as it is
shown in Fig. 8.3.
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143
),(1
tiD ),(2
tiD ),(3
tiD ),(4
tiD
),(1
ti
),(2
ti
),(3
ti
),(4
ti
Load Reduction
(MW)
Offered Cost
($/MW)
Fig. 8.3: Typical price-quantity offer package of the DR aggregator
The objective function is subject to the following constraints.
8.2.1.1 Load balance
Total generation including demand side resources and conventional generators must
satisfy the load.
1
( )
0
( , ). ( , ) (1 ). ( )
( ) ( ) ( ). ( ) ,
( )
N
i
E t
P i t u i t L t
t IN t fin tL t i t
t
(8. 6)
8.2.1.2 Generation unit output limit
( )
1
( , ). ( , ) ( , ) ( , ). ( , ) ,
MF i
m
m
P i t u i t P i t P i t u i t i t
(8. 7)
8.2.1.3 Ramping up/down constraints
( 1) ( ) ,i i iP t P t RUP i t (8. 8)
( ) ( 1) ,i i iP t P t RAD i t (8. 9)
It is required that a unit stays “ON” for minimum number of hours based on the
following formulation.
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144
( )
1
max[ , ( ) 1]
1
(1 ( , )) 0
( , ) ( , ) 1,
( ) 1,...,
( ) max 0,min[ , ( ) ( ,0). ( ,0)
HT i
t
T t LU i
m t
u i t i
b i t C i m i
t HT i T
HT i T LU i TIU i u i i
(8. 10)
In addition, if a unit is shut down, it will remain off for a minimum number of hours
as per equation (8.11).
( )
1
max[ , ( ) 1]
1
( , ) 0 ,
( , ) ( , ) 1,
( ) 1,...,
( ) 0, [ , ( ) ( ,0).(1 ( ,0))]
LT i
t
T t LT i
m t
u i t i
C i t b i m i
t LT i T
LT i Max Min T LT i TIC i u i
(8. 11)
The relation between unit status, start up and shut down indicators are explained as
follows:
( , 1) ( , 1) ( , 1) ( , )b i t c i t u i t u i t i (8. 12)
It is also necessary to consider a scenario that a specific unit may not be start up or
shut down at a given hour.
( , ) ( , ) 1 ,b i t c i t i t (8. 13)
8.2.1.4 Spinning reserve
Spinning reserve shall be sufficient to reduce the possibility of any loss of load in
the system. Total required reserve in the system denoted by ( )SPI t . Maximum
capacity of all synchronized units minus the total generation output in specific hour
can be given by the equation (8.14)
1
( )
00
( , ). ( , ) ( ) (1 ) ( )
( ) ( ) ( )( )
( )
N
i
E t
P i t u i t SPI t L t
t IN t fin tL t
t
(8. 14)
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145
The details of the market clearing procedure are summarized in Fig. 8.4.
Demand Response Participants
NAS
battery
owners
Demand Response Aggregators
Generator Company 1,..,N
offer
Independent Market Operator
The generators and the demand response aggregators
schedules are determined
Fig. 8.4: Summary of the market clearing procedure with demand response and NAS
battery
8.3 Representative study
Case studies based on the modified IEEE 30 and IEEE 57 bus systems are presented
in this section. Table 8.1 to Table 8.4 summarise the generator information for the
IEEE 30 and IEEE 57 bus test systems. Details of the mentioned test networks can
be find in [24, 70, 126]. The required spinning reserve for the system is considered
as 10% of the total system load. Two NAS batteries are installed on bus 8 and bus
21 for IEEE 30 and three NAS batteries are installed on bus 3, 9 and 12 for IEEE 57
bus system. Details of the installed NAS batteries can be found in [144].
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146
Table 8. 1: Cost function and generation limit for conventional generators in IEEE
57 bus system
Generator
bus
( )a i ( )b i ( )c i ( , )P i t ( , )P i t
1 680 16.5 0.077 575 0
2 450 19.7 0.01 100 0
3 370 22.6 0.25 140 0
6 480 27.7 0.01 100 0
8 660 25.92 0.02 550 0
9 665 27.7 0.01 100 0
12 670 27.9 0.032 410 0
Table 8.2: The pollution cost function for IEEE 57 bus generators
Generator bus ( )i ( )i ( )i
1 0.00509 -0.4069 30.03
2 0.00344 -0.3813 32.06
3 0.00344 -0.3813 32.06
6 0.00465 -0.3902 33.05
8 0.00465 -0.3902 33.05
9 0.00312 -0.3952 35.006
12 0.00312 -0.3986 36.002
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147
Table 8.3: Cost function and generation limit for conventional generators in IEEE
30 bus
Generator
bus
( )a i ( )b i ( )c i ( , )P i t ( , )P i t
1 320 2 0.02 80 0
2 225 1.75 0.0175 80 0
22 175 1 0.0625 50 0
27 240 3.25 0.00834 55 0
23 330 3 0.025 30 0
13 335 3 0.025 40 0
Table 8.4: The pollution cost function for generators in IEEE 30 bus
Generator bus ( )i ( )i ( )i
1 10.33 -0.3713 0.00409
2 10.39 -0.3802 0.0033
22 30.91 -0.3852 0.00456
27 30.91 -0.3876 0.0046
23 36.01 -0.3906 0.00354
13 34.05 -0.3613 0.00354
The uniform elasticity values are considered for all load nodes with demand
response participants. Table 8.5 shows the self and cross elasticity values.
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148
Table 8.5: Self and cross elasticity values [145]
Peak Off-Peak Low
Peak -0.12 0.018 0.014
Off-Peak 0.018 -0.12 0.01
Low 0.014 0.01 -0.12
Three different participation levels for demand response participants are considered
in this study including 10%, 15% and 20% participation level. The participation
level of 20% means that 20% of the total load can participate in the demand
response program. The results of market clearing for IEEE 30 and IEEE 57 bus
system are presented in Table 8.6- Table 8.9.
Table 8.6: Demand side resources contribution for three different participation
levels in IEEE 57 bus system
Bus
Number
Initial
Generation
10%
Participation
15%
Participation
20%
Participation
3 41 37.9 35.1 34.2
8 150 138.8 128.4 125.3
9 121 111 103.6 101
12 377 348.8 322.7 315
13 18 16.6 15.4 15
14 10.6 9.9 9.3 8.8
18 27.2 25.1 23.2 22.7
27 9.4 8.7 8 7.8
29 17 15.7 14.5 14.2
38 14 13.3 12 11.7
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149
Table 8.7: Conventional generators contribution for three different participation
levels in IEEE 57 bus system
Bus
Number
Initial
Generation
10%
Participation
15%
Participation
20%
Participation
1 142.6 140.6 138.7 138.1
2 87.8 75.1 63.6 60
3 45 44.4 43.8 43.6
6 72.9 61.4 50.9 47.7
8 459.8 452.6 446 444
9 97.6 80 64.5 59.7
12 361.5 353.2 345.6 343.3
Table 8.8: Demand side resources contribution for three different participation
levels in IEEE 30 bus system
Bus
Number
Initial
Demand
10%
Participation
15%
Participation
20%
Participation
7 22.8 20.8 19.5 19.1
8 30 27.3 26 25.3
12 11.3 10.7 10 9.8
17 9 8.6 8.3 7.8
19 9.5 9.1 8.6 8.3
21 17.5 16.1 15.3 14.4
30 10.6 9.7 9.1 8.7
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150
Table 8.9: Conventional generators contribution for three different participation
levels in IEEE 30 bus system
Bus
Number
Initial
Generation
10%
Participation
15%
Participation
20%
Participation
1 41.6 42 41.6 41
2 55.4 55.9 55.4 54.8
13 16.2 15.9 15.4 15
22 22.8 22.5 22.3 22
23 16.3 15.6 15.1 14.7
27 40 31.4 27.7 26.5
Table 8.6 shows the demand side resources contribution in three load reduction
scenarios for the IEEE 57 bus system. As it is shown, increasing the participation
level does not lead to a uniform load reduction by demand side resources. In other
words, the demand side resources allocation plays a crucial rule to determine the
amount of contribution by these resources. This trend highlights the importance of
demand side resources allocation in the electricity market.
As it is shown in Table 8.6 and Table 8.8, the load reduction pattern is not similar
for three considered scenarios. In fact, increasing the participation level from 10% to
15% leads to more load reduction than escalating the participation level from 15%
to 20%. For example based on the provided information in Table 8.6 increasing the
participation level from 10% to 15% lead to 10.4 MW load reduction in bus 8
whereas changing the participation level from 15% to 20% in the same bus result to
3.1MW reduction. This trend highlights the importance of the demand side
resources participation level.
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151
The presented results in Table 8.8 are also emphasizes on the importance of
participation factor by demand side resources. As shown in Table 8.8, the demand
side resources allocation and participation level can play the important role to
achieve the optimum contribution by demand side resources. For instance based on
the provided information in Table 8.8 increasing the participation level from 10% to
15% yield to 1.3MW load reduction on the bus 7. However, increasing the
participation level from 15% to 20% on the same bus results to 0.4 MW load
reduction. Table 8.7 and Table 8.9 focuses on the committed generation by
conventional generators. Based on the provided information in these tables,
increasing the participation level yields to noticeable generation reduction by
conventional generator units. It is necessary to note that the generation reduction in
different scenarios depends on three factors including cost of generation by
generation unit, demand side resources location and participation level. As an
example, in Table 8.7 the generation output on bus 9 reduces by 17.6% in a scenario
with 10% participation level. Whereas, the generator unit in bus 1 dropped by 1.4%
under the same scenario which shows a significant difference. One of the main
advantages of integrating demand side resources in energy market is providing
flexible load profile for the system. This flexibility is result of shifting the load from
high peak hours to off peak periods. In other words, load reduction in peak demand
and load recovery in off peak periods can provide a flatten load profile for the
system. This trend can improve the system load factor and reduces the need for
ramp up/down services by the conventional generators. The base load profile for
IEEE 57 bus system and the demand curve for 15% participation level by demand
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152
side resources are shown in Fig. 8.5. This figure demonstrates the effects of
dispatchable demand side resources on the system load profile.
Fig. 8.5: Load profile before and after DR implementation
As it is shown, the load reduces by 5.2% during the peak hours as a result of
demand side resources participation. Some part of this reduction can be recovered in
the off peak hours. As it is discussed, the active demand side participation is able to
flatten the load profile and facilitate the large-integration of wind power into the
system. Table 8.10 and 8.11 show the total cost of market in IEEE 30 and IEEE 57
bus systems. As it is shown, the total cost of market is reduced as a result of
demand side resources integration into the electricity market. This trend is achieved
as a result of generation reduction by expensive generator units in the system. Based
on the provided information in Table 8.11, the total cost of market operation
reduced by 11% during peak time for the 15% participation level in comparison
with base case.
750
800
850
900
950
1000
1050
1100
1150
1200
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
LOA
D (
MW
)
TIME(HOUR)
BASE LOAD
LOAD PROFILE AFTER15% DEMAND SIDEPARTICIPATION
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153
Table 8.10: Total Market Cost for different demand side participation level in
IEEE 30 bus system
Demand Side Participation Level Total Market Cost ($)
Without demand side participation 4616
Participation Level 10% 4336
Participation Level 15% 4168
Participation Level 20% 4064
Table 8.11: Total Market Cost for different demand side participation level in
IEEE 57 bus system
Demand Side Participation Level Total Market Cost ($)
Without demand side participation 41737
Participation Level 10% 39237
Participation Level 15% 36993
Participation Level 20% 36307
8.4 Conclusion
This chapter presents an approach for increasing the power system capability by
using demand side resources to accommodate more wind power generation. The
constraint optimization is developed for market clearing with considering demand
side resources. The simulation results confirm the effectiveness of demand side
resources on providing flexible load profile for the system and total cost reduction.
The simulation results also verify the importance of demand response location and
participation level in providing flexible load profile.
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154
Chapter 9 Conclusions
The original contributions or advances made in the research and presented in the body
of this thesis are summarised in the following:
The first advance relates to the development of a multi-objective approach to find the
optimal allocation of SVC and TCSC in the electricity network. The presented approach
can find the optimum locations and sizes of TCSC (Thyristor controlled Series
Compensator) and static var compensator (SVC) in the power system. A novel approach
has been proposed to determine the optimum sizes and locations of SVCs and TCSCs,
based on optimisation of multi-objective function. In this method, the allocation problem
has been solved according to different technical and economical considerations. Also, in
contrast to some previous research, the cost objective function has been considered,
besides other objectives, to achieve a practical solution. NSGA II method [91] which has
been utilised to find the optimal solution has been found to be robust, and offer good
convergence property in achieving the solution. The results of comparative studies
confirm that the optimal allocation of SVC and TCSC play a considerable role in
improving the power system performance.
The research has led to the second original contribution in which a comprehensive
solution is proposed for optimal allocation of the demand response programs in the
electricity network. The outcomes of this research can determine the optimum amount
______________________________________________________________________
155
and the location of the demand response programs in the electricity network. A flexible
design procedure based on multi-objective function optimisation using NSGA II
algorithm has been developed and presented in this part of the research for optimally
allocating DR programs in terms of their locations and sizes. Network security
constraints are included in optimizing the objective functions related to ATC, EENS and
active-power loss. The design procedure is a flexible and general one which can be
extended in a straightforward manner to incorporate other objective functions including
those of an economic nature and constraints encountered in system operation. The
effectiveness of the procedure developed and DR programs has been illustrated with a
representative design study based on an IEEE standard systems, the results of which
confirm the noticeable improvements of the objective functions chosen in the DR
program design.
In the third advance made in the research, a non-linear mathematical model for
incentive-based event-driven demand response program is used for modelling demand
side resources. A coordination process between the generators, demand response
participants and independent system operator is proposed to release the congestion in
the electricity network. In addition, to evaluate the effectiveness of the proposed method
in contingency condition, critical contingencies are identified and considered to verify
the effectiveness of the proposed approach in the contingency condition. The results
confirm that using demand response programs can considerably reduce the congestion
cost in the electricity market.
One of the key developments in this research is effective integration of FACTS and
demand response programs for transmission line congestion management. This key
development has led to the fourth advance. A hybrid approach is proposed for
transmission lines congestion management in a restructured market environment using a
combination of dispatchable demand response (DR) program and flexible alternating
current transmission system (FACTS) devices. This advancement has developed a
methodology for transmission congestion management in which the traditional approach
of using conventional generators and/or FACTS devices is augmented by demand
responses. The method proposed draws on a mixed integer optimisation required of DR
dispatches. The effectiveness of the method is illustrated with a representative market
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156
clearing study in which various options of using FACTS devices and/or DR are
compared.
Finally, a day-ahead network-constrained market clearing formulation is presented
which considers a combination of conventional generators and demand side resources.
The proposed approach can provide flexible load profile and reduce the need for ramp
up/down services by the conventional generators. This method can potentially facilitate
large penetration of renewable generation by shifting the wind power generation from
the off-peak periods to the high-peak hours. The proposed approach can mitigate some
of the challenges that arise as a result of large-scale wind power penetration into the
electricity network. This approach can be used as a powerful tool to reduce the need for
ramping requirements by the conventional generators and support the system with high
penetration of wind power. Simulation results verified the considerable economic and
technical benefits of the presented approach.
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157
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