OPCHAIN-WATER - Integrated Water Resources Planning System ...

OPCHAIN-WATER - Integrated Water Resources Planning System

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OPCHAIN-WATERINTEGRATED WATER RESOURCES

PLANNING SYSTEM

Ing. Jesús Velásquez-Bermúdez, Dr. Eng. Chief Scientist DecisionWare - DO Analytics

[email protected]

Julio de 2019

mailto:[email protected]


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INDEX

1. OPCHAIN-W&E&G: WATER & ELECTRICITY & GAS SUPPLY CHAIN OPTIMIZATION

1.1. OPCHAIN-WATER: INTEGRATED WATER RESOURCES PLANNING SYSTEM

1.2. OPCHAIN-E&G: ELECTRICITY & GAS SUPPLY CHAIN OPTIMIZATION

1.1. OPCHAIN-SGO: SMART GRIDS OPTIMIZATION

2. STOCHASTIC OPTIMIZATION & RISK MANAGEMENT

3. MODELING HYDRO-CLIMATIC VARIABLES

4. WATER RESOURCES MODELING

4.1. TOPOLOGY 4.2. HYDROELECTRIC POWER PLANTS

4.2.1. WATER FLOW

4.2.2. HYDRO GENERATION CURVES 4.2.3. PUMPING-STORAGE

4.3. EXTREME EVENTS 4.3.1. SPILLAGE

4.3.2. MINIMUM OPERATING CURVES 4.3.3. MINIMUM FLOWS

4.3.4. FLOODS

4.4. UNDERWATER WATER ACUIFERS 4.5. AQUEDUCTS

4.6. EWER SYSTEMS 4.7. WATER TREATMENT SYSTEMS

5. WATER RESOURCES & RISK MANAGEMENT


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INTEGRATED WATER RESOURCES PLANNING SYSTEM

1. OPCHAIN-W&E&G: WATER & ELECTRICITY & GAS SUPPLY CHAIN OPTIMIZATION

OPCHAIN-W&E&G is a Decision Support System of technical and economic planning tools that exploits the

latest computer technologies coupled with the advanced mathematical modeling. The power of algorithms used for optimization, like Nested Benders Decomposition (NBD) or Generalized Stochastic Dual Dynamic Programming

(G-SDDP), joint with the ability to represent precisely the relation of cost and volume, provides confidence in optimal results that cannot be provide by simpler approaches; its services for generation of models, coupled with

spreadsheets, databases, multidimensional analysis tools, visualization software and Monte-Carlo simulation models to generate probabilistic scenarios; providing an ideal place to develop quickly and comprehensively

optimization studies of the of water, electrical, smart grids and natural gas systems.

HYDRAULIC MODEL

ELECTRIC MODEL

CENTRALHIDRÁULICA

CIRCUITODEMANDA

~VE

VC

~

VERTIMIENTOEMBALSE

VERTIMIENTOCENTRAL

RIO

CONEXIÓN

EMBALSE

HAF

BARRADRGO

BARRA 5

BARRA 6

BARRA 2BARRA 1

TERMOELECTRICA

CENTRAL HIDRÁULICA

EMBALSE

PROYECTO INDUSTRIAL

INTERCONEXIÓNCOMERCIAL

DEMANDAVEGETATIVA

Multi Tecnología (Gas - Fuel Oil)

~

NATURAL GAS MODEL

BARRA 3BARRA 4

BARRA 1

TERMOELÉCTRICA

EMBALSE

YACIMIENTO

REFINERÍAINDUSTRIA

NODO DEMANDAGAS-ELECTRICIDAD

NODO GAS 1

NODO GAS 2

NODO GAS 3

BARRA 2

~

CENTRAL HIDRÁULICA

OPCHAIN-E&G - MODULES

OPCHAIN-W&E&G is composed by three models that can be integrated according to the needs of the end user.

=

+

HYDRAULIC

GAS

HYDRAULIC&

ELECTRICITY&

GAS

+

ELECTRICITY

OPCHAIN-E&G


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Considering that a MP (Mathematical Programing) model is based on standard algebra; then it is possible to join two MP problems to obtain a new MP model.

1.1. OPCHAIN-WATER: INTEGRATED WATER RESOURCES PLANNING SYSTEM

For optimum management watershed, the hydraulic model may be use individually (OPCHAIN-WATER)

1.2. OPCHAIN-E&G: ELECTRICITY & GAS SUPPLY CHAIN OPTIMIZATION

OPCHAIN-ELE (ELEctricity Supply Chain Optimization) corresponds to a set of mathematical models designed

to support the decisions of the various actors involved in the electricity supply chain, in terms of sectoral planning and business generation. According to the structure of modern electricity markets, the support of the business

decision-making power generation should be seen from two different points of view. ▪ Central agents: formed by the regulator, supervisor, planner and market operator ▪ Generators: agents that operate power plants.

OPCHAIN-GAS corresponds to a mathematical model designed to support the decisions of the various actors

involved in the chain of supply of natural gas at the level of sectoral planning. OPCHAIN-ELE and OPCHAIN-

GAS together make OPCHAIN-E&G a set of optimization model to dispatch the electricity and gas systems.

OPCHAIN-E&G is designed to allow its users to parameterize the model according to the complexity of its supply

chain and optimization requirements thereof.


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The table presents a resume of the optimization model that integrates OPCHAIN-ELE

OPCHAIN-ELE MATHEMATICAL MODELS

Model Description

DISPATCH SIMULATION IN POWER PLANTS

E&G

The central model OPCHAIN-E&G corresponds to the standard integrated representation (equations) of the electricity

and gas supply chains; these equations gives rise to variations of the model according to the techno-economic concepts that support a specific modeling. The have at least three type of “similar” models to represent the electricity & gas market in the medium term.

EDI Economic Dispatch: Dispatch of plants minimizing the operation cost of the interconnected system, it simulates a perfect electricity market, may be include the gas system.

ERD Economic Regulated Dispatch: Dispatch of plants minimizing the operation cost plus the regulated cost of the interconnected system and includes representatives of regulatory aspects of the electricity market being simulated. It may use to simulate a regulated electricity market.

NCD Nash-Cournot Equilibrium Dispatch: Dispatch of plants oriented to the simulation of competitive electricity markets with agents that can influence, with their decisions, on transactions occurring in the market. Two type of agents are considered: price makers and prices takers.

FIN Integrated simulation of economic/regulated dispatch plus financial modeling (ALM). Oriented to use in valuation of electric assets and/or to analyze the financial health of the agents in a market.

OPTIMIZATION OF AGENTS DECISIONS

STRATEGIC PLANIFICATION

SCD Supply Chain Design, associated with strategic planning (long-term) decisions related to design supply chain, in relation to capacity of reservoir, transfers, power plants and other elements of an electrical system.

TACTICAL PLANIFICATION

ETRM Energy Trade and Risk Management, optimal medium/long term decisions related to marketing energy and coverage of financial risks.

MAN Oriented to optimize the decisions associated to preventive maintenance of multiple central generation plants. It can be applied to all plants in: i) a region, ii) a national grid, or iii) a set of plans that control an agent.

OPERATIVE PLANIFICATION

UC Unit Commitment associated with operational planning (short term) decisions related to dispatch plants hourly, or more detailed periods, respecting all non-linear and discrete constraints that are part of the dispatch.

STOCHASTIC PROCESSES MODELS

HID-SIM Synthetic generation of water intake based on a model of Fiering-Matalas type.

HID-KAL Projected short-term hydrological contributions via a DUAL Kalman Filter

HID-ML Projected short-term hydrological contributions via a Machine Learning Model

PSPOP Projected electricity prices short-term competitive markets through S-ARIMAX-GARCH models

HID-SIMMONTE CARLO

Synthetic Generation

Optimal Network

E&G-SCDSupply Chain Design

Forecast InflowsHours - Days

E&G-PSPOTStatistical Models

ARIMA-GARCH

Forecast Spot Prices

Hours - Days

E&G-ERDEconomic

Regulated Dispatch

MaintenancePlanning

CommercialsPolicies

Scheduled Operation

HistoricalHydrology

Historical Spot Prices

KALMANState Estimation

DUAL KALMAN FILTER

E&G-ETRMEnergy Trading

&Risk Management

E&G-UCUnit

Commitment

E&G-MANMaintenance Optimization

OPCHAIN-ELE - MODELS CONNECTIVITY FOR A ELECTRICITY GENERATOR

Forecast Spot PricesMonths - Years

SyntheticInflowsMonths - Years

The diagram below shows the design of the integrated use of the models described above to support the decision-

making of a generator agent.


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More information:

▪ Electricity & Natural Gas - Advanced Supply Chain & Market Optimization

https://www.linkedin.com/pulse/electricity-natural-gas-advanced-supply-chain-jesus-velasquez/

1.3. OPCHAIN-SGO: SMART GRIDS OPTIMIZATION

OPCHAIN-SGO is a decision support system orient to Smart Grids Optimization. More information:

▪ Smart Grids Optimization & Renewables Energies https://www.linkedin.com/pulse/smart-grids-optimization-jesus-velasquez/

2. STOCHASTIC OPTIMIZATION & RISK MANAGEMENT

Traditionally, Stochastic Dynamic Programming (SDP) and Multi-Stage Stochastic Programming (MS-SP) has been part of the mathematical methods used to optimize the use of water resources; initially, Stochastic Dynamic

Programming (SDP) models was the most used; later, the models based on Nested Benders Stochastic

Decomposition (NBSD) are the “standard”. OPCHAIN-W&E&G incorporate as basic large-scale methodology

the Generalized Stochastic Dual Dynamic Programming (G-SDDP) that it is oriented to solve large-scale dynamic

stochastic optimization problems.

All models of OPCHAIN-W&E&G can be modeled using MS-SP, this is a decision of the end-user, not a decision

of the mathematical modeler.

The power of the optimization solvers (GUROBI, IBM CPLEX, XPRESS) and the power of current computers

(multiples CPUs and multiples and multiples GPUs) allows the analysis of problems based on stochastic optimization models, leaving aside the traditional deterministic models. The modeling of random events in

optimization models is supported in:

▪ We don’t know what will happen ▪ We know what can happen

Random events are modeled based on scenarios, which are assigned to probabilities of occurrence.

STOCHASTIC OPTIMIZATION ENVIRONMENT

MULTI-STAGE DECISION PROCESS

STOCHASTIC PROCESS

RISKRISK MANAGEMENTSOLUTION STRATEGY

DETERMINISTIC MODEL

CORE

Scenario H

Scenario 1

Scenario 2

ARBOL DE DECISIONES DE MULTIPLES ETAPAS

t = 1 t = 2 t = 3 t = 4

..

..

.

While several decades ago to solve problems of stochastic optimization of large size using lots of scenarios seemed

unattainable, technological advances in all directions (speed of the processor, cache memory capacity and memory


https://www.linkedin.com/pulse/smart-grids-optimization-jesus-velasquez/


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RAM, "solvers" speed, networks of high-speed communications,...) made the stochastic optimization a viable methodology to face the problem of handling uncertainty in decision-making process.

Stochastic optimization is necessary when we want to manage financial risks related to the investment and

operation of general industrial systems; a case known is related to the management of resilient supply chains to face disasters, which cannot be achieved with deterministic models. The use of MS-SP implies the definition by

the user of five fundamental aspects:

1. The “core” deterministic model, all W&E&G models can be converted in a stochastic optimization model.

2. The dimensions of uncertainty (the number of random parameters, i.e. water inflows, demand, oil prices, …)

that define the random environment of decisions (scenarios). The user can select many uncertainty dimensions, according to the situation or to the model.

3. The decision-making process is represented by a multi-stage tree that is configured by the user.

TWO-STEP EQUIPROBABLE DECISION TREE

t = 1 t = 2

Scenario Demand 10

Scenario Demand 1

Scenario Demand 2

Decisions

Invesment

Decisions

Simulated Operations

0.10

0.10

Scenario Demand

t = 1 t = 2

Decisions

Invesment

Decisions

Simulated Operations

1.0

DETERMINISTIC “DECISION TREE”

4. The policy of risk management, financial or operational, that the user wants to include in the analysis.

5. The methodology of mathematical problem solution, which can be: i) default or ii) selected the user according

to the format of the problem.

More detailed information at: ▪ Stochastic Programming & Risk Management: Fundamentals

https://www.linkedin.com/pulse/stochastic-programming-fundamentals-jesus-velasquez/

▪ Water Resources & Risk Management https://www.linkedin.com/pulse/water-resources-optimization-risk-management-jesus-velasquez/

3. MODELING HYDRO-CLIMATIC VARIABLES

For the generation of synthetic scenarios of the variable climatic variables, there are two requirements: i) short term (hours, days) and ii) medium/long term (weeks, months). Short-term specific models for each renewable

source, should be built, it is not considered in detail in this part.

For medium/long term, there are two alternatives to generate synthetic scenarios: 1. Statistical synthetic generation model of climatic variables (type Fiering-Matalas),

2. Generate synthetic series of climatic variables based on mixing of historical series


https://www.linkedin.com/pulse/water-resources-optimization-risk-management-jesus-velasquez/


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3. Generate synthetic series based on the historical series having the ENSO (El Niño Southern Oscillation) series

as an instrumental variable, this is the standard method in OPCHAIN-WATER.

ENSO events have proven to be determinants of climatological variables (water inflow, wind speed and solar

luminosity) mainly in the Pacific Sea area; therefore; ENSO is a main variable to forecast events that may occur in the Pacific countries, but its effect impact all the world.

The importance of ENSO events has led to large amount of investigation by multiple organizations, which have multiple models oriented to forecast ENSO events in the short/medium term. Two types of models are used: i)

Dynamic: based on the physical modeling of the dynamics of the process; and ii) Statistics: based on empirical evidence of the process adjusted through statistical models.

SYNTHETIC GENERATION OF CLIMATOLOGICAL VARIABLES

SISTEMA

DE

INFORMACIÓN

OPCHAIN-ELE

Series de Tiempo Sintéticas Aportes Hídricos – Índice ENOS

Minimice Sh=1,H St=1,T e2t,h

ENOSt,h = a + St=1,T Sp=1,P bp,h E-HISt,p + et,h

Sp=1,P bp,h = 1

bp,h ≥ 0

E-SINt,h = Sp=1,P bp,h E-HISt,p

Q-SINt,i,h = Sp=1,P bp,h Q-HISt,p,i

Historic Series:▪ ENOS▪ Climatologic Variables

MATHEMATICAL MODEL FOR GENERATION OF MIX OF HISTORICAL SERIES

Plants Dispatch

Spot PriceMarginal Cost

IRI ENSOForecast

ENSO Events

IRI

Synthetic Series:▪ ENOS▪ Climatologic Variables

The International Research Institute for Climate and Society (IRI, http://iri.columbia.edu/, Columbia University)

integrates all the predictions based on a Bayesian Ensemble Model that dynamically modifies the a-posteriori

probability to be the correct for each of the models. DW methodology is based on integrating the ENSO forecast

of the IRI with the observed historical series of climatological variables. OPCHAIN-ENOS uses an optimization

model of which results are the convex combination of historical series that “best” represent a synthetic scenario generated from the statistical characteristics of the IRI forecast.

http://iri.columbia.edu/


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More information: ▪ Forecasting & Synthetic Generation of Hydro-Climatic Variables

https://www.linkedin.com/pulse/forecasting-synthetic-generation-hydro-climatic-jesus-velasquez/

4. WATER RESOURCES MODELING

4.1. TOPOLOGY

OPCHAIN-WATER may be use isolated, because it includes all types of hydraulic components: reservoirs,

hydroelectric plants, pumping stations, pumping storages, rivers, spillage channels, connection points, demands

(irrigation, aqueducts, environmental, industrial, …). The components can be linked to form any topology.

HYDROELECTRICPOWER PLANT

DEMAND

~VE

VC

~

RESERVOIR SPILLAGE

PLANT SPILLAGE

RIVER

CONNECTION

RESERVOIR

HEE

HEC

HCC

HKE

HKC

HEK HCK

VEE

VCE

HAF

(m,n)

(c,p)

(cb,bc)

ATU

BUSDRGO

GHI

HKK

HYDRAULIC SYSTEM

4.2. HYDROELECTRIC POWER PLANTS

Hydroelectric plants are modeled independently of the reservoirs so that connectivity plant-reservoir and reservoir-

plant must be set.

4.2.1. WATER FLOW

The regulation capacity of reservoir is simulated in detail, so such consistently represent the dispatch of power

plants considering its ability to regulate the water resource multi-year, annual, hourly, ....

In the graph the continuous line represents the movement of water to aggregate level (monthly, weekly) and the

dotted line, movements to detailed level (hours or less), in this way becomes coherent movements of reservoirs for different uses.

https://www.linkedin.com/pulse/forecasting-synthetic-generation-hydro-climatic-jesus-velasquez/


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WATER FLOW TROUGH WATER SYSTEM

~

~

SbBLO HCEt,p,m,b

HEEt,n,m

HEEt,m,n SbBLO HECt,m,p,b

HEKt,m,cb

HEKt,cb,m

HAFt,r

VEEt,n

VEEt,m

SbBLO VCEt,p,b

PODBt,b × VEEt,m

HYDDROELECTRICCONNECTION

RESERVOIR

Aggregate Period

Hourly Block

4.2.2. HYDRO GENERATION CURVES

For the conversion of the hydraulic energy into electrical energy, two physical aspects are considered:

1. The generation of electrical energy in the turbine. It is considered that the productivity of the turbine does

not have a linear behavior with respect to the flow. The proposed solution consists of the piecewise linearization of the efficiency curve. For a modeling adjusted to reality, should be considered if the function

of productivity does not have economies of scale, i.e. that the gradient of the curve is always decreasing;

then, it is not required binary variables to ensure correct modeling. All the curves presented in the graph have this feature.

HYDRO GENERATION CURVES

NOMINAL FLOW (%)

PR

OD

UC

TIV

ITY

(%

)

2. The head energy in the reservoir. The solution is a piecewise linearization of the relationship between the

volume of the reservoir and the height of the water, which not present economies of scale in the conversion

of the height of the reservoir volume.


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The combination of the two linearization allows to generate a convex hull of the curve of hydro generation curve as a function of the height of the water in the reservoir and the flow in the turbine. If the hull is non-convex,

must be necessary to include binary variables in the modeling.

HYDRO GENERATION CURVE

G = f(V,Q)

HYDRO-GENERATIONG (MW)

RESERVOIR VOLUMEV (MM)

TURBINE OUTFLOWQ (M3/S)

% D

For more information: ▪ Electricity & Natural Gas - Advanced Supply Chain & Market Optimization


4.2.3. PUMPING-STORAGE

OPCHAIN-WATER includes pumping-storage generation systems to take advantage of time differences in

electric rates that allow for certain projects generate when fees (or marginal costs) hours are high and pumping to reservoir water at times of low rates. This process can be simulated with little detail for short/medium-term

planning and detail for real-time operations (unit commitment) including the detailed modeling of the pumps used

to raise water. The graph presents the modeling system.

BAR

HYDROELECTRIC

~LOWERRESERVOIR

~UPPER

RESERVOIR

PUMPINGSTATION

NATURALSTREAMFLOW

NATURALSTREAMFLOW

HEC

ATU GHI

HCE

HEBQEB

QCE

HBEQBE

GEB

PUMPING STORAGE CONNECTIVITY



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For special reservoirs, it is possible to establish rules of operation established based on agreements or laws that

must be observed when using the water resources, if it is possible.

For more information about pumping systems, the reader can access:

▪ Oil Pipelines Real-Time Optimization https://www.linkedin.com/pulse/oil-pipelines-real-time-optimization-jesus-velasquez/

4.3. EXTREME EVENTS

Extreme events are those that produce risks, for this reason it is important to analyze the way of modeling of such events that are related with: spillage, minimum flow rates and minimum levels in the hydraulic system.

It is quite common that the spillage between to reservoirs, the minimum flow rates and minimum levels should

be managed using soft constraints, which involve subjective penalties in the objective function. This is due to that

in many cases the format of the problem cannot be solved by the selected solver or by the mathematical methodology. For example, the standard NBD only solves linear problems that ever has feasible solutions.

The problems arising from the penalties are concentrated on the fact that they are “mathematical tricks” to control

the representation of the physical solution of problem which ends up altering the representativeness of the economic solution (dual variables).

For example, this can lead to wrong decisions, when the economic variables are used to estimate the spot price of an energy market; the marginal cost of the demand equation is considered a "proxy" of the electricity spot

price. But due to the penalties the marginal cost may be negative, its value depends on the value of the penalization and the amount of streamflow arriving to the reservoir.

The best solution is to impose objective penalties, this means that they are associated with real economic cost and not one that invent the modeler or end user. However, make economic sense to these violations is not a

trivial process. More detailed information at: ▪ Water Resources & Risk Management


4.3.1. SPILLAGE

To be exact the modeling of the spillage of reservoirs must include binary variables. The distortion is greater when

shedding moves water from a basin of lower productivity to a basin of higher productivity. OPCHAIN-WATER

has no problem to model exactly such situations.

The modeling adjusted to reality implies that spillage (VEEt) is equal to zero if the volume of water in the reservoir

(NEMt) is below to the reservoir capacity (CEMB). This logical condition requires the following equations for its modeling.

VEEt = 0 si NEMt < CEMB

0 ≤ CEMBt - NEMt ≤ BVEt ×

VEEt ≤ (1 – BVEt) ×

NEMt = NEMt-1 - HEEt - VEEt + AHIDt

BVEt {0,1}

https://www.linkedin.com/pulse/oil-pipelines-real-time-optimization-jesus-velasquez/



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~ ~

HEEt

VEEt

P-VEEMW/mcs

P-HEEMW/mcs

NEMt

SPILLAGE MODELING

VEEt = 0 si NEMt < CEMB

0 ≤ CEMBt – NEMt ≤ BVEt ×

VEEt ≤ (1 – BVEt) ×

NEMt = NEMt-1 - HEEt - VEEt + AHIDt

BVEt {0,1}

~ ~

where HEEt represents the net water transferred to other reservoirs (less inputs output) and AHIDt the

streamflow arriving to the reservoir. The binary variable BVEt ensures that logical condition that controls the

spillage of the reservoir is met.

If the productivity (MW/mcs) via the reservoir is greater than the productivity via the shedding (P-HEE > P-VEE) the logical conditions are not required; otherwise, the associated restrictions are required. When these restrictions

shall be replaced by the spillage penalization, the dual variables are distorted, and it is possible that the physical

constraint is violated by the mathematical model. The distortion that is generated depends on the value of the penalty which is a subjective factor that has no theoretical support.

The problem arises because of the difficulty which introduces the binary variable in the formulation, which

eliminates the use of certain types of methodologies, as in the case of methods based on NBD that only can solve linear problems.

4.3.2. MINIMUM OPERATING CURVES

Conventionally, this approach includes in the model "soft" constraints that penalize the objective function when a

reservoir operates below the “minimum operating curve” (MOPt). The conventional modeling means to include a restriction that assessing the violation of minimum operating curve (VMIt), to be subsequently included in the

objective function using a subjective penalization factor. The equation included in the model is:

"minimum operating" ≤ final level + "violation of minimum operating"

MOPt NFt + VMIt

where NFt represent the volume of the reservoir at the end of period t.

This approach entails serious distortions since it doesn’t work as the modeler and the user think, incurring overruns

cost that can be significant.

The detailed analysis of this case will be presented in: ▪ Water Resources & Risk Management




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4.3.3. MINIMUM FLOWS

The modeling of this condition entails problems since it is possible that there is no feasible solution in times of

low water.

The conventional modeling means to include a restriction that assessing the violation of minimum flow (MFLt), to be subsequently included in the objective function by means of a subjective factor. Algebraic modeling is

presented below.

MFLt FLOt + VFLt

where FLOt represent the flow in a point of the water resource system and VFLt the violation of the minimum flow.

To avoid the subjective penalization, at least two alternatives modeling can be managed; including the model

restrictions on:

▪ The likelihood of violation of the minimum flow, this modeling would require binary variables ▪ The CVaR violation of the minimum flow, this case only requires continuous variables and linear constraints.

4.3.4. FLOODS

Flood control modeling can be done using subjective penalizations, as in the previous cases, or to include probabilistic modeling, including in the model restrictions on:

▪ The likelihood of flood, this modeling would require binary variables ▪ The CVaR of the flood, this case only requires continuous variables and linear constraints.

4.4. UNDERWATER WATER AQUIFERS

In edition. If the lector requires information about it please send an email to: [email protected]

4.5. AQUEDUCTS


4.6. SEWER SYSTEMS


4.7. WATER TREATMENT SYSTEMS


5. WATER RESOURCES & RISK MANAGEMENT

More detailed information at:

▪ Water Resources & Risk Management







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