Multiobjective optimisation in load dispatch of electric power system by EAs

1
Multiobjective optimisation in load dispatch of
electric power system by EAs
INGENET
Case Studies Open Day
8th June 2001

• B. Galván, G.Winter, B.Gónzalez (CEANI)
• M. Cruz (UNELCO)

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CONSUMERS DISCOMFORT
POLLUTANTS
G
G
POLLUTANTS
FUEL
G
THE LOAD DISPATCH PROBLEM
G
RELIABILITY
G
FUEL
G
LOAD DEMAND CURVE
MULTIOBJECTIVE
MWh
1
24
12
Hour
3
Index

• Part I
• Short Review
• Part II
• INGEnet Test Case
• INGEnet research
• INGEnet results
• Future research

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Multiobjective optimisation in load dispatch of
electric power systemsPart I Short review
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Short review

• Equal incremental cost criterion (Steimberg
  Smith (1943), Kirckmayer (1958).
• Kuhn.Tucher approach (1951)
• Dynamic Programming (DP) (1957)
• Nonlinear ProgrammingGauss Seidel, Squires
  (1960), Carpentier (1962)
• Lagrange Multipliers Newton-Raphson (1960
  1970)
• Partial enumeration methods (DP based) (1980
  1990)
• Priority list methods (1943-1957)(1990 -)
• Lagrangian Relaxation (1989)

Traditional Approaches
Many methods, each of them involve his own
difficulties, only guarantee local optimal
solutions
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Short review

• Expert Systems
• Neural Networks
• Monte Carlo Optimisation (Simulated Annealing)
• Evolutionary Algorithms (EAs)
• Genetic Algorithms (1975, 1989)
• Evolution Strategies (1973)
• Flexible Evolution (2001)

Artificial Intelligence approaches
EAs Robustness, efficiency and flexibility
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Evolutionary Algorithms
Short review

• Maintain a set of solution candidates
• Undergoing Selection procedure
• Sampling methods

• By analogy to Natural Environment
• Set of Solutions Population
• Each solution Individual

• Mimic Natural Evolution
• Successive populations (Generations)
• Survival of the fittest (Selection)

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Short review

• Genetic Algorithms
• Selection Crossover Mutation
• Evolution Strategies
• Self-Adaptation of some parameters
• Flexible Evolution
• Self-Adaptation of the algorithm and some
  parameters

Evolutionary Algorithms
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EAs in Electric Power Systems
Short review
Problems with
Evolutionary Algorithms

• Complex and Large search spaces
• Multiple, often conflicting, objectives

EAs characteristics desirables for this kind of
problems
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Electric Power System Applications Search Results
Genetic Algorithms (single and multiobjective)
Geographical distribution of the authors Europe
(1) 570 publications compiled 211 from Europe
(37)
SOURCES 1.- Jarmo T. Alexander, Indexed
Bibliography of Genetic Algorithms in Power
Engineering. Report 99-1-power. University of
Vaasa. Finland 2.- CEANI search 2001.
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Electric Power System Applications Search Results
Short review
Genetic Algorithms (single and multiobjective)
Genetic Algorithms (multiobjective only)
(2000) 75 Multiobjective
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Electric Power System Applications Search Results
Short review
Multiobjective (all methods)
51.8 of all multiobjective applications
computed with GAs
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European Community (EC)Source CORDIS
Short review

• All Databases
• Multiobjective or Multicriteria
• Partners search (3)
• Projects (29)
• Publications (23)

Only 4 related to Electric Power Systems
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Multiobjectives Considered
AREA
Objective
Economic Dispatch
Cost
NOx
Environmental Impact
SO2 , CO2
Particles
Reliability
Engineering
Security
Load Shedding
Contingency Analysis
Generation Reallocation
Line loss
System
Line flow
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Multiobjectives Considered
AREA
Objective
Economic Dispatch
Cost
NOx
Environmental Impact
SO2 , CO2
Particles
Reliability
Engineering
Security
Load Shedding
Contingency Analysis
Generation Reallocation
Line loss
System
Line flow
Expert System and Fuzzy Logic
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Multiobjectives Considered
AREA
Objective
Economic Dispatch
Cost
NOx
Environmental Impact
SO2 , CO2
Particles
Reliability
Engineering
Security
Load Shedding
Contingency Analysis
Generation Reallocation
Line loss
System
Line flow
Genetic Algorithms
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Multiobjective optimisation in load dispatch of
electric power systemsPart II INGEnet
activities
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Multiobjective Considered
AREA
Objective
Economic Dispatch
Cost
NOx
Environmental Impact
SO2 , CO2
Particles
(1997) Good Hybrid Approach Genetic Algorithms
Heuristics local method Find Pareto Fronts
using a two-obj. Selection Method
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Multiobjective Considered
AREA
Objective
Economic Dispatch
Cost
NOx
Environmental Impact
SO2 , CO2
Particles
(1997) Good Hybrid Approach Genetic Algorithms
Heuristics local method Find Pareto Fronts
using a two-obj. Selection Method
Strong influence on final results
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Multiobjective Considered
AREA
Objective
Economic Dispatch
Cost
NOx
Environmental Impact
SO2 , CO2
Particles
(2000-2001) INGEnet Genetic Algorithms
Heuristics local method Find Pareto Fronts
using a two-obj. Selection Method
To eliminate or reduce the need of the local
search method
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Multiobjective Considered
AREA
Objective
Economic Dispatch
Cost
NOx
Environmental Impact
SO2 , CO2
Particles
(2000-2001) INGEnet Genetic Algorithms
Heuristics local method Find Pareto Fronts
using a two-obj. Selection Method
To eliminate or reduce the need of the Heuristics
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Multiobjective Considered
AREA
Objective
Economic Dispatch
Cost
NOx
Environmental Impact
SO2 , CO2
Particles
(2000-2001) INGEnet Genetic Algorithms
Heuristics local method Find Pareto Fronts
using a By-objective Selection Method
Last advances in Multiobjective analysis
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Summary

• To define a close to real Multiobjective
  test-case
• To eliminate or to reduce the need of
  non-evolutionary processes helping GAs
• Local search method
• Heuristics
• To Explore the efficiency of last multiobjective
  methods
• Non-Dominated Sorting
• Strength Pareto
• To explore the application of new Evolutionary
  Optimization methods Flexible Evolution

INGEnet
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• To define a close to real Multiobjective
  test-case

Minimizing

• Industry side
• Fuel Cost
• Social side
• NOx emission
• SO2 emission
• Particles emission

INGEnet Results
Search Space 240 Real variables
INGEnet Database Test Case Description
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Summary

• To eliminate or to reduce the need of
  non-evolutionary processes helping GAs
• Local search method
• Heuristics

Eliminated
Reduced
INGEnet Results
Defining clear rules to repair unfeasible
solutions using constraints
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Summary

• To Explore the efficiency of last multiobjective
  methods
• Non-Dominated Sorting
• Strength Pareto

New Method developed
INGEnet Results
FLEXIBLE SELECTION RULES
SELECTED NON DOMINATED SOLUTIONS
POPULATION SOLUTIONS
EVOLUTIONARY OPERATORS
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Flexible Evolution Methodology
Population t
SOLUTION 1
SOLUTION 2
Learning Engine
SOLUTION 3
...
SOLUTION N
DE
Decision Engine
Selection Engine
Population t1
DE
Decision Engine
SOLUTION 1
SOLUTION 2
Sampling Engine
SOLUTION 3
...
SOLUTION N
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Flexible Evolution Methodology
Population t1
SOLUTION 1
SOLUTION 2
SOLUTION 3
...
SOLUTION N
DE
Decision Engine
Selection Engine
Population t2
DE
Decision Engine
SOLUTION 1
SOLUTION 2
Sampling Engine
SOLUTION 3
...
SOLUTION N
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Flexible Evolution Methodology
Population t2
SOLUTION 1
SOLUTION 2
SOLUTION 3
...
SOLUTION N
DE
Decision Engine
Selection Engine
Population t3
DE
Decision Engine
SOLUTION 1
SOLUTION 2
Sampling Engine
SOLUTION 3
...
SOLUTION N
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Flexible Evolution Methodology

• Self-Adaptation
• Algorithm
• Parameters

• All existing Selection Operators considered
  (Selection Engine)
• All existing Crossover and Mutation operators
  considered (Sampling Engine)
• Multiple learning methods (Learning Engine)
• Probabilistic Decisions (Decision Engine)
• Collective and Individual memory included
  (Solutions)
• Only Two parameters (Population size and Number
  of Generations)

All operators playing a Cooperative-Competitive
game during the search
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Mono-objective Optimization of Load Dispatch
Example of Results
FUEL COST MINIMIZATION FOR A SET OF GENERATION
UNITS IN A TIME PERIOD
Problem

• Which generation units must be put on and when?
  (UNIT COMMITMENT)
• What power output must have each one of the
  generation units? (ECONOMIC DISPATCH)

In every hour of the study period (1 day or 1
week)
We achieve the minimum fuel cost in the entire
study period
Result
t 1
t 2
t M
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Mono-objective Optimization of Load Dispatch
Example of Results
Results obtained with single loop Flexible
Evolution
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Mono-objective Optimization of Load Dispatch
Example of Results
Results obtained with single loop Flexible
Evolution
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Mono-objective Optimization of Load Dispatch
Example of Results
Enhanced Results (A First Double Loop Strategy)
Let Pt(U) be the population and the ?
best individuals of Pt(U). Then the algorithm
with the double loop strategy is Establish GA
parameters population size, maximum number of
generations, crossover rate, mutation rate t
0 Generate Pt(U) While not stop criterion
do ? Eliminate genotype duplicates ?
Evaluate the AEF ? Extract
? Set ? selection
? Set ? crossover
? Set Pt1(U) ? mutation
? Set
Od Evaluate the FEA with the best
individual Print the best solution
The FEA return, for each individual U, the best
real solution obtained for the design that U
represents, and its fitness function value.
Tournament (41)
One point crossover
Uniform mutation
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Mono-objective Optimization of Load Dispatch
Example of Results
Enhanced Results (A First Double Loop Strategy)

• Binary chromosome

ui 1 if the generator goes to be at a fixed
power Pi (during the whole study period) ui 0
if its power can vary between 0 and its maximum
power

• Real chromosome

t 1
t 2
t M
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Mono-objective Optimization of Load Dispatch
Example of Results
Results obtained with double loop Flexible
Evolution
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Mono-objective Optimization of Load Dispatch
Example of Results
Results obtained with double loop Flexible
Evolution
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Mono-objective Optimization of Load Dispatch
Example of Results
Binary chromosome
Results obtained with double loop Flexible
Evolution
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Mono-objective Optimization of Load Dispatch
Example of Results

• It is shown that the flexible agent is capable of
  self-adapting to the proposed problem. It selects
  in each optimisation step the more suitable
  operators and obtains solutions of a great
  quality in the most of the cases.
• Moreover, the double loop strategy has proved to
  be an efficient learning tool that activates
  sensitively the FEA convergence.
• The best solutions obtained with both algorithms
  are better than the best solution obtained in
  INGEnet until now the T54.5-R3 whose value is
  729.995,45.

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Multi-objective Optimization of Load Dispatch
Example of Results
FUEL COST AND ENVIRONMENTAL IMPACT MINIMIZATION
FOR A SET OF GENERATION UNITS IN A TIME PERIOD
Problem

• Which generation units must be put on and when?
  (UNIT COMMITMENT)
• What power output must have each one of the
  generation units? (ECONOMIC DISPATCH)

In every hour of the study period (1 day or 1
week)
We achieve the minimum fuel cost and
environmental impact in the entire study period
Result
t 1
t 2
t M
41
Multi-objective Optimization of Load Dispatch
Example of Results
Same (and short) number of Objective Function
evaluations
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Future research

• Generation/Network expansion planning
• Optimal strategies to replace obsolete/high-pollu
  tant generation units.
• Computer-aided multicriteria decision making
• Dynamic load dispatch under uncertainty and
  incomplete information
• Emergency Analysis
• Developing progressive official regulations
  taken into account real industry possibilities of
  evolution.

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End