placement and coordinated tuning of control devices for capacity and security enhancement using...
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Placement and Coordinated Tuning of Control Devices for Capacity and Security Enhancement Using Genetic Algorithms and Other Metaheuristics
Djalma M. Falcão* Glauco N. Taranto
Federal University of Rio de JaneiroCOPPE Brazil
* Also with CEPEL/Eletrobrás CEPEL
2NSF Workshop on Applied Mathematics for Deregulated Electric Power Systems - Washington - November 2003
Summary
Motivation Power System Controls Placement and Coordinated Tuning GAs and Other Metaheuristics Approach Examples
FACTS placement for loadability improvement FACTS tuning for damping control PSS tuning for damping control in a large scale power
system Ongoing Work Future Work Conclusions
3NSF Workshop on Applied Mathematics for Deregulated Electric Power Systems - Washington - November 2003
Motivation
New Scenario Regulatory uncertainty Difficulties in line and plant construction
Power systems must operate reliably and efficiently under a variety of operating conditions
Robust control Coordinated tuning Wide-area control
Available Technology / Challenges Computer, Communication, and Control Wide-Area Monitoring Systems (WAMS) New design and optimization technologies
(metaheuristics)
4NSF Workshop on Applied Mathematics for Deregulated Electric Power Systems - Washington - November 2003
Power System Controls
Available Controllers Generators: AVRs, Governors, PSSs, etc. OLTC transformers FACTS HVDC links Automatic Generation Control and Coordinated Voltage
Control Control Strategies
Mostly local or task oriented Placed and designed on an ad hoc basis Present situation requires a better use of available control
System-wide performance Robustness in the presence of component losses
5NSF Workshop on Applied Mathematics for Deregulated Electric Power Systems - Washington - November 2003
Placement & Coordinated Tuning
Placement Problem Location (branch, bus, generator, etc.) Type: FACTS (TCSC, SVC, UPFC, etc.), PSS, etc. Control Structure Parameters (range)
Coordinated Tuning (given a set of controllers) Parameter adjustment
Combined Placement & Tuning More complex and larger problem “Global” optimization
6NSF Workshop on Applied Mathematics for Deregulated Electric Power Systems - Washington - November 2003
Combined Placement and Tuning
Mixed-Integer Nonlinear Programming Problem “Unfriendly” Characteristics
Large scale: thousands of variables Non-convex functions Some functions may not be available explicitly Design bounds not easily determined
Possible Approaches Two stage solution approach
Propose a potential solution for the placement problem Coordinated tuning of controller for that potential solution
Simultaneous solution approach using Metaheuristics
7NSF Workshop on Applied Mathematics for Deregulated Electric Power Systems - Washington - November 2003
Decomposed Approach
Placement Problem• Location • Type• Control Structure• Parameters
Coordinated TuningProblem
• Parameter ..Adjustment
PlacementDecisions
Performance of Tuned Controllers
Integer Programming Problem• Branch-and-bound• Metaheuristics • Etc.
Continuous Optimization Problem• Non-linear programming• Metaheuristics • Etc.
Bender’s Decomposition
8NSF Workshop on Applied Mathematics for Deregulated Electric Power Systems - Washington - November 2003
Metaheuristic(Free On-Line Dictionary of Computing)
A top-level general strategy which guides other heuristics to search for feasible solutions in domains where the task is hard
Metaheuristics have been most generally applied to problems classified as NP-Hard or NP-Complete by the theory of Computational Complexity
Metaheuristics would also be applied to other combinatorial optimization problems for which it is known that a polynomial-time solution exists but is not practical
Examples of Metaheuristics are Tabu Search, Simulated Annealing, Genetic Algorithms, Particle Sworm Optimization, etc.
9NSF Workshop on Applied Mathematics for Deregulated Electric Power Systems - Washington - November 2003
Metaheuristics Approach
Placement and tuning problem can be solved simultaneously Potential solutions are coded in a “computational structure”
Population of potential solutions are evolved according to metaheuristic rules
Global optimization is not assured but usually finds good “engineering solutions”
Deals nicely with multiobjective problems Very large computation requirements: high performance
computing may be required
Location Type Control Structure Parameters
10NSF Workshop on Applied Mathematics for Deregulated Electric Power Systems - Washington - November 2003
GA Aided Control System Design
Genetic Algorith
m
Software
Performance Index Evaluation
(Fitness Function)Software for
Control System Simulation
Linear AnalysysEtc.
11NSF Workshop on Applied Mathematics for Deregulated Electric Power Systems - Washington - November 2003
GA Aided Control System Design
S
C
S
CS
C
S
C
Population of Potential Solutions
Time Simulation
Eigenanalysis
Other Methods
.
.
Performance Index
Evaluation(Fitness Function)
Genetic Operators• Selection• Crossover• Mutation
12NSF Workshop on Applied Mathematics for Deregulated Electric Power Systems - Washington - November 2003
Example 1: Optimal Location of Multi-Type FACTS Devices by Means of GAs
Gerbex, Chekaoui & Germond, IEEE PWRS, August 2001
Steady-state modeling: Load Flow model Performance index (fitness function): System
Loadability Constraints: Thermal and Voltage Limits FACTS Devices considered: TCSC, TCPST, TCVR,
SVC Test System: IEEE 118 bus
13NSF Workshop on Applied Mathematics for Deregulated Electric Power Systems - Washington - November 2003
Flow Chart of the Optimization Strategy
Genetic Algorithm
Load Factor Increase
Program Initialization and Ending
Load Flow
14NSF Workshop on Applied Mathematics for Deregulated Electric Power Systems - Washington - November 2003
Results: System Loadability
SaturationRelatively Small Improvement
SaturationRelatively Small Improvement
15NSF Workshop on Applied Mathematics for Deregulated Electric Power Systems - Washington - November 2003
Example 2: Robust Decentralized Control Design using GAs in Power System Damping Control
Taranto & Falcão, Proceedings of IEE, Part C, Jan. 1998
Linearized dynamic model: Small-Signal Stability model
Performance index (fitness function): Sum of the Spectrum Damping Ratio for all operating conditions
Constraints: Bounds on controllers parameters and minimum damping ratio
Test System: Hypothetical 12 bus, 6 generators system
16NSF Workshop on Applied Mathematics for Deregulated Electric Power Systems - Washington - November 2003
Test System
Hypothetical 12 bus and 6 generators power system
SVC and TCSC All generators modeled
with six variables with identical parameters
Five operating conditions Two low-frequency
electromechanical inter-area oscillatory modes:
Mode 1: B A + C Mode 2: A C
Controllers structure:
17NSF Workshop on Applied Mathematics for Deregulated Electric Power Systems - Washington - November 2003
Problem Formulation
m: number of operating conditions
n: system order
: closed-loop system eigenvalue damping ratio
K, , T : controllers parameters
Fitness Function:
18NSF Workshop on Applied Mathematics for Deregulated Electric Power Systems - Washington - November 2003
Results
Nominal: controllers designed using classical control techniques
GA: controllers designed using GA
NDFS: direct flow (generators 3, 4, 5, 6 are exporting; main load L3)
NRFS: reverse flow (decrease L3 , increase L10 , reverse flow in TCSC)
Weak 1: NDFS with a weaker tie in the SVC transmission path
Weak 2: NDFS with a weaker tie in the TCSC transmission path
Weak 3: NRFS with a weaker tie in the TCSC transmission path
Damping ratio for closed-loop eigenvalues
19NSF Workshop on Applied Mathematics for Deregulated Electric Power Systems - Washington - November 2003
Example 3: Simultaneous Tuning of Power
System Damping Controllers Using GA
Bomfim, Taranto & Falcão, IEEE PWRS, February 2000
Linearized dynamic model: Small-Signal Stability model
Performance index (fitness function): Sum of the Spectrum Damping Ratio for all operating conditions
Constraints: Bounds on controllers parameters and minimum damping ratio
Problem Formulation: similar to example 2 Test System: Brazilian interconnected power
system
20NSF Workshop on Applied Mathematics for Deregulated Electric Power Systems - Washington - November 2003
Test System
Equivalent of the Brazilian South-Southeastern System
Model: 1762 AC buses 2515 AC branches 57 synchronous
generators 22 PSSs DC link not modeled
dynamically 450 state variables
Three operating scenarios considered
Controllers structure: identical to example 2
21NSF Workshop on Applied Mathematics for Deregulated Electric Power Systems - Washington - November 2003
Results
Scenario 2
Scenario 1
Scenario 3Damping enhancement
constrained by low-
damped multivariable
zero
Closed-loop eigenvalues
22NSF Workshop on Applied Mathematics for Deregulated Electric Power Systems - Washington - November 2003
Comments
The GA based tuning process has shown robustness in achieving controllers satisfying the design criteria in a large-scale realistic power system
Large computation time Approximately 8h in a Pentium 4 processor Most of time spent in the eigenvalue calculations (QR)
Parallel implementation on a Cluster of PCs: considerable reduction in computing time
Combination of GAs approaches with other design methods:
Pole placement LMI
23NSF Workshop on Applied Mathematics for Deregulated Electric Power Systems - Washington - November 2003
Ongoing Work
Experiments with other objective functions Frequency domain based Time domain based
Simultaneous tuning of PSS and AVRs Objective: higher performance of the excitation system Performance Index: combination of frequency and time
domain features Difficulties: higher computation time requirements
24NSF Workshop on Applied Mathematics for Deregulated Electric Power Systems - Washington - November 2003
Future Work
Improvements in the GA-based methodology aimed to solve the combined placement and tuning problem
Tests with other metaheuristics and hybrid formulations
New challenges: Ability of the control system to respond properly to
catastrophic events Integrated analysis of control and protection systems