NOVEL CONSTRAINED SEARCH-TACTIC FOR OPTIMAL DYNAMIC ECONOMIC DISPATCH USING MODERN META-HEURISTIC OPTIMIZATION ALGORITHMS

Transcription

1 NOVEL CONSTRAINED SEARCH-TACTIC FOR OPTIMAL DYNAMIC ECONOMIC DISPATCH USING MODERN META-HEURISTIC OPTIMIZATION ALGORITHMS Authors: Fahad S. Abu-Mouti and M. E. El-Hawary

2 OUTLINE Introduction Problem Formulation Modern Meta-Heuristic Optimization Algorithms ABC SDOA Proposed Constrained-Search Tactic Computational Results 15-unit system Comparisos Summary Future Work 2

3 INTRODUCTION The dynamic economic dispatch (DED) problem exemplifies the practical meaning of optimal operation and control of generation units. The goal of the DED is to determine the optimal power outputs of on-line generating units in order to meet the load demand subject to satisfying various operational constraints over finite dispatch periods. 3

4 INTRODUCTION (CONT D) The DED considers additional practical constraints such as upper bounds on the units' ramping-rates; in reality, units will not respond to steep or instantaneous load variations. The DED is considered a complex, non-convex, and nonlinear optimization problem. Therefore, obtaining a truly optimal solution presents a challenge. 4

5 PROBLEM FORMULATION The DED objective function is as follows: where, 5

6 PROBLEM FORMULATION (CONT D) Output power responses of generator unit due to different fuel cost functions. Without valve-point effect With valve-point effect Cost ($/h) c d e Prohibited operating zone a b 6 Generation (MW/h)

7 PROBLEM FORMULATION (CONT D) The equality constraints is as follows: where, 7

8 PROBLEM FORMULATION (CONT D) The inequality constraints are as follows: or, 8

9 PROBLEM FORMULATION (CONT D) The prohibited operating zones are as follows:, j, j {2, 3,, n i } Nevertheless, the DED problem could be extended to include additional objective function and/or constraints, e.g., emission pollutants and/ or spinning reserve. 9

10 MODERN META-HEURISTIC OPTIMIZATION ALGORITHMS Artificial Bee Colony (ABC) Algorithm It is a population-based optimization approach, introduced in Nov Inspired by the intelligent foraging behavior of the honeybee swarm. The ABC consists of three groups of bees: Employed bees (Eb). Onlooker bees (Ob). Scout bees. Sensory-Deprived Optimization Algorithm (SDOA) It is a population-based optimization approach, introduced in Aug Inspired by the intelligent behaviour/survival instincts of a sensorydeprived human-being. The SDOA consists of: Sensory-deprive person (SDP). Temporarily Parallel (SDP-Parallel). 10

11 ARTIFICIAL BEE COLONY (ABC) ALGORITHM Each cycle of the ABC algorithm comprises these three steps: 1. Sending employed bees to their food-source and evaluating their nectar amount. 2. After sharing the food-source information, onlookers select the food-source region with highest probability rate, and evaluate the nectar amount at that region. 3. Determining the scout bees and sending them into randomly new possible foodsources. 11

12 SENSORY-DEPRIVED OPTIMIZATION ALGORITHM (SDOA) Consider a blind person wants to reach an object, he will rely intuitively on his remaining senses: hearing, tasting, touching, and smelling with various degrees of dependency. However, three of these senses taste, touch, and smell will only provide him with feedback of nearby obstacles. The feedback of the remaining sense hearing could symbolize the slightly-distant obstacles. Utilizing these feedback will assist the blind person towards his goal. 12

13 SENSORY-DEPRIVED OPTIMIZATION ALGORITHM (SDOA) (CONT D) It is clear that the exploitation and exploration processes are present in the previous assumption. However, for the exploration process, the routine is divided into two strategies: 1) Employs hearing in order to receive feedback from an adjacent region of the search space of the remaining senses. 2) Retires the worst-performing sensory-deprived persons (population) and replaces them by those who perform better in a parallel (temporary) search process. This parallel search dynamically diminishes when the number of iterations increases. 13

14 SENSORY-DEPRIVED OPTIMIZATION ALGORITHM (SDOA) (CONT D) Each time the solution will be modified into for sense, it follows this form: For taste, touch, and smell. For hearing. where, u [-1,1] U [-5,5] and u, 14

15 PROPOSED CONSTRAINED-SEARCH TACTIC Each constraint of the DED problem has a degree of dominance affecting the algorithm performance, and -- somehow -- directs the algorithm towards the optimal or quasi-optimal region. The proposed search-tactic utilizes those constraints specifically, the dominant powerbalance constraint to accelerate the algorithm performance towards the optimal feasible region. 15

16 PROPOSED CONSTRAINED-SEARCH TACTIC (CONT D) The following procedures describe the proposed constrained search-tactic for the scenario of a one hour dispatch period. On the other hand, only steps 2 and 3 are utilized when multiple time intervals are considered. 16

17 PROPOSED CONSTRAINED-SEARCH TACTIC (CONT D) 1) The units output power are updated every dispatched hour as follows: 2) The objective function is altered temporary to minimizing the violation of the real power balance equation. The main objective function is retained once the loop (cycle) ( + 1) starts. 3) The handling mechanism for the units prohibited operating zones is as follows: 17

18 PROPOSED CONSTRAINED-SEARCH TACTIC (CONT D) Consider a unit (i) in a solution vector (x i ) operates at a time (t) within a prohibited operating zone (j); 3.1) Divide the solution (x i ) into two sub-solutions by only modifying the unit (i) output according to its violated prohibited operating zone (j). 3.2) Force each one of the two sub-solutions to adjust unit (i) output to operate in its permissible upper and lower limits of the associated prohibited operating zone (j), while taking into account the unit s ramp-rate constraints 3.3) Evaluate both sub-solutions, and select the best based on a designated selection method. 18

19 COMPUTATIONAL RESULTS 15-unit system: Demand = GW Units 2, 5, and 6 have three prohibited operating zones, and unit 12 has 2 prohibited operating zones. The ABC and SDOA parameters are tuned through trial-and-error process. The proposed constrained-search tactic is activated for the first 50 iterations ( ) for both algorithms. 19

20 COMPUTATIONAL RESULTS (CONT D) * with the proposed constrained search-tactic Unit ABC ABC * SDOA SDOA * P 1 (MW) P 2 (MW) P 3 (MW) P 4 (MW) P 5 (MW) P 6 (MW) P 7 (MW) P 8 (MW) P 9 (MW) P 10 (MW) P 11 (MW) P 12 (MW) P 13 (MW) P 14 (MW) P 15 (MW) Total output power (MW) Total P L (MW) Total P L (%) Sys.Viol. (MW) Total operating cost ($/h) 32, , , , Average CPU time (s) An average of 31% reduction in the required CPU time was due to the integration of the offered tactic. 20

21 COMPUTATIONAL RESULTS (CONT D) Both algorithms performances for the 15-unit system. 21

22 COMPUTATIONAL RESULTS (CONT D) Comparison: Statistical measurements obtained after carrying out 30 independent runs with different seeds. With respect to GA results, both algorithms with the proposed constrained-search tactic attained: ~ 0.4% (hourly) reduction in the operating fuel s cost. ~ 98% reduction in the required CPU time. Algorithm Max. ($/h) Avg. ($/h) Min. ($/h) Sys.Viol. (MW) Std.Dev. CPU (s) SA 33, , , GA 33, , , TS 32, , , PSO 32, , , MTS 32, , , ABC * 32, , , SDOA * 32, , ,

23 SUMMARY Presented why the DED occupies a prominent place in power system operation and control. Highlighted, concisely, two modern meta-heuristic optimization algorithms. Proposed a novel constrained-search tactic to solve the DED problem. The main advantage of the proposed search-tactic is reducing (significantly) the degree of randomness in the initial population -- consequently, accelerating the algorithm s performance towards the optimum feasible region. Among all the recorded results, the integration of the offered search-tactic with the SDOA stood for the most economic output power dispatched for the considered system. Although the reduction in operating fuel s cost was smaller than that of CPU time, its significant would exemplify to considerable annual cost saving. 23

24 FUTURE WORK Utilize the proposed constrained-search tactic in solving the DED problem with 24-h period. Evaluate the performance of the proposed tactic with ABC and SDOA in large dimensional problems. Analyze the potential of the SDOA algorithm in high dimensional applications. Utilize the proposed constrained-search tactic in solving the dynamic economic and emission dispatch (DEED) problem. Integrate additional constraints, e.g., spinning reserve and renewable sources in solving the DED and DEED problems. 24

25 THANK YOU 25

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28 SENSORY-DEPRIVED OPTIMIZATION ALGORITHM (SDOA) Since most of the efficient meta-heuristic algorithms, e.g., GA, PSO, ABC, ACO, and FA, are inspired from natural phenomena, other superior algorithms can be derived from nature as well. Inspired by the intelligent behaviour/survival instincts of a sensory-deprived human-being, a new meta-heuristic optimization algorithm is proposed in Aug Deep inside most meta-heuristic algorithms, two important procedures interact with each other sufficiently, i.e., exploitation & exploration. A good balance between these two procedures leads to a superior algorithm. 28