1. 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 Janeiro COPPE Brazil * Also with CEPEL/Eletrobrás CEPEL

2. NSF Workshop on Applied Mathematics for Deregulated Electric Power Systems - Washington - November 2003 2 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

3. NSF Workshop on Applied Mathematics for Deregulated Electric Power Systems - Washington - November 2003 3 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)

4. NSF Workshop on Applied Mathematics for Deregulated Electric Power Systems - Washington - November 2003 4 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

5. NSF Workshop on Applied Mathematics for Deregulated Electric Power Systems - Washington - November 2003 5 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

6. NSF Workshop on Applied Mathematics for Deregulated Electric Power Systems - Washington - November 2003 6 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

7. NSF Workshop on Applied Mathematics for Deregulated Electric Power Systems - Washington - November 2003 7 Decomposed Approach Placement Problem Location Type Control Structure Parameters Coordinated Tuning Problem Parameter..Adjustment Placement Decisions Performance of Tuned Controllers Integer Programming Problem Branch-and-bound Metaheuristics Etc. Continuous Optimization Problem Non-linear programming Metaheuristics Etc. Benders Decomposition

8. NSF Workshop on Applied Mathematics for Deregulated Electric Power Systems - Washington - November 2003 8 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.

9. NSF Workshop on Applied Mathematics for Deregulated Electric Power Systems - Washington - November 2003 9 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 LocationType Control Structure Parameters

10. NSF Workshop on Applied Mathematics for Deregulated Electric Power Systems - Washington - November 2003 10 GA Aided Control System Design Genetic Algorithm Software Performance Index Evaluation (Fitness Function) Software for Control System Simulation Linear Analysys Etc.

11. NSF Workshop on Applied Mathematics for Deregulated Electric Power Systems - Washington - November 2003 11 GA Aided Control System Design S C S C S C S C Population of Potential Solutions Time Simulation Eigenanalysis Other Methods...... Performance Index Evaluation (Fitness Function ) Genetic Operators Selection Crossover Mutation

12. NSF Workshop on Applied Mathematics for Deregulated Electric Power Systems - Washington - November 2003 12 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

13. NSF Workshop on Applied Mathematics for Deregulated Electric Power Systems - Washington - November 2003 13 Flow Chart of the Optimization Strategy Genetic Algorithm Load Factor Increase Program Initialization and Ending Load Flow

14. NSF Workshop on Applied Mathematics for Deregulated Electric Power Systems - Washington - November 2003 14 Results: System Loadability Saturation Relatively Small Improvement Saturation Relatively Small Improvement

15. NSF Workshop on Applied Mathematics for Deregulated Electric Power Systems - Washington - November 2003 15 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

16. NSF Workshop on Applied Mathematics for Deregulated Electric Power Systems - Washington - November 2003 16 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:

17. NSF Workshop on Applied Mathematics for Deregulated Electric Power Systems - Washington - November 2003 17 Problem Formulation m : number of operating conditions n : system order : closed-loop system eigenvalue damping ratio K,, T : controllers parameters Fitness Function:

18. NSF Workshop on Applied Mathematics for Deregulated Electric Power Systems - Washington - November 2003 18 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 L 3 ) NRFS: reverse flow (decrease L 3, increase L 10, 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

19. NSF Workshop on Applied Mathematics for Deregulated Electric Power Systems - Washington - November 2003 19 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

20. NSF Workshop on Applied Mathematics for Deregulated Electric Power Systems - Washington - November 2003 20 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

21. NSF Workshop on Applied Mathematics for Deregulated Electric Power Systems - Washington - November 2003 21 Results Scenario 2 Scenario 1 Scenario 3 Damping enhancement constrained by low- damped multivariable zero Closed-loop eigenvalues

22. NSF Workshop on Applied Mathematics for Deregulated Electric Power Systems - Washington - November 2003 22 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

23. NSF Workshop on Applied Mathematics for Deregulated Electric Power Systems - Washington - November 2003 23 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

24. NSF Workshop on Applied Mathematics for Deregulated Electric Power Systems - Washington - November 2003 24 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