1. STUDY OF USING PARTICLE SWARM FOR OPTIMAL POWER FLOW IN IEEE BENCHMARK SYSTEMS INCLUDING WIND POWER GENERATORS by Mohamed A. Abuella A Thesis Submitted in Partial Fulfillment of the Requirements for the Master of Science Degree Department of Electrical and Computer Engineering Southern Illinois University Carbondale 2012 1

2. THE OUTLINE 2 3. The main aim of the thesis is to obtain the optimal economic dispatch of real power in systems that include wind power. Model considers intermittency nature of wind power. Solve OPF by PSO. IEEE 30-bus test system. 6-bus system with wind-powered generators. 3 4. MOTIVATION: The Growing Importance of Wind Energy: 4 5. MOTIVATION: 5 Fluctuations of oil prices; One of the most competitive renewable resources. Abundance of wind power everywhere; The Cost of Wind Energy: 6. MOTIVATION: 6 The Optimal Economic Dispatch of Wind Power: Its a challenging topic to search about. ECE580 Wind Energy Power Systems ECE488 Power Systems Engineering Spring 2011 7. STATEMENT OF THE PROBLEM 2 i i i i i iC a P b P c ,w i i iC d w Conventional-thermal generators Wind-powered generators 7 The objective function of the optimization problem in the thesis is to minimize the operating cost of the real power generation. 8. STATEMENT OF THE PROBLEM In similar fashion, , , , , , (underestimation)( ) ( ) ( ) r i i p i p i i av i w p i i W w C k W w k w w f w dw Since Weibull probability distribution function (pdf) of wind power.( )Wf w , , , , 0 ( ) (overestimation) ( ) ( ) i r i r i i i av w r i i W C k w W k w w f w dw 8 9. STATEMENT OF THE PROBLEM The model of OPF for systems including thermal and wind-powered generators: ,min ,max , min max m , ax , , , : ( ) ( ) ( ) ( ) : 0 r M N N N i i i i i i i i i i i i i r i M N i i i i i i i line i lin i i ipw i e Minimize J C p w w w Subjectto p p p w w p w L V V V C S C S C Particle Swarm Optimization (PSO) algorithm is used for solving this optimization problem. 9 2 i i i i i iC a P b P c , iw i iC d w , ,, (underestimation)( ) ( ) r i i w p i i W w p i k w w f w dwC , 0 , ( ) ( ) (overestimation) i r i w r i i Wk w w f w dwC Where: 10. PROBABILITY ANALYSIS OF WIND POWER: The wind speeds in particular place take a form of Weibull distribution over time, as following: Weibull probability density functions (pdf) of wind speed for three values of scale factor c ( / ) ( 1) ( ) ( ) kv c k V k v f v e c c 0 5 10 15 20 25 30 35 40 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 Wind speed v Probability C=25 C=15 C=5 10 11. PROBABILITY ANALYSIS OF WIND POWER: The cumulative distribution function (cdf) of Weibulll distribution is: Weibull pdf and cdf of wind speed for c=5 m/s ( / ) 0 ( ) 1 k v v c v vF f d e 11 0 0.1 1 wind speed v pdf 0 5 10 15 0 0.5 1 cdf cdf pdf 12. The captured wind power can be assumed to be linear in its curved portion: PROBABILITY ANALYSIS OF WIND POWER: The captured wind power w 0; ( )i ov v or v v ( ) ; ( ) i r r i v v w v v i rv v v ;rw r ov v v 3 2 m p RP C A v The captured wind power 12 13. The linear transformation (in terms of probability) from wind speed to wind power is done as following: PROBABILITY ANALYSIS OF WIND POWER: Pr{ 0} 1 exp exp k k i ov v W c c Pr{ } exp exp kk or r vv W w c c 13 While for the continuous portion: 1 (1 ) (1 ) ( ) exp kk i i i W r klv l v l v f w w c c c 1 ( )W v w b f w f a a Q ( ) Where : , r i r i v vw l w v 14. PROBABILITY ANALYSIS OF WIND POWER: Probability vs. Wind power for C=10, 15 and 20 14 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.2 0.4 0.6 0.8 1 w/wr Probability C=10 C=15 C=20 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 C=10 W/Wr Comulative.Probability C=15 C=20 The probability density function pdf of wind power The cumulative distribution function (cdf) of wind power , , , (underestimation)( ) ( ) r i i w p i p i i W w C k w w f w dw , , 0 ( ) ( ) (overestimation) iw r i r i i WC k w w f w dw 15. PROBABILITY ANALYSIS OF WIND POWER: , , , ( ) ( ) r i i w p i p i i W w fC k w w dww , , 0 ( () ) iw r i r i i WC k w w f dww , ,: ( ) ( ) ( ) ( ) M N N N i i wi i p i i r i i i i i i Minimize J C p C w C w C w 1 expPr{ 0} exp k k i ov v c c W exp xPr{ } e p k r k or vv c c W w 1 (1 ) (1 ) ) exp( kk i W i i r klv l v l w v c f w c c Then, plug the transformed wind power equations in the model: 15 16. OPTIMAL POWER FLOW (OPF) 1 1 cos( ) 0 sin( ) 0 n i i j ij i j ij j n i i j ij i j ij j P V V Y Q V V Y : ( ) Subject to: ( ) 0 ( ) 0 Min J g h x,u x,u x,u The optimal power flow (OPF) is a mathematical optimization problem set up to minimize an objective function subject to equality and inequality constraints. While: ( ) 0g x,u 1 1 , 1 , 1 ,[ , ,..., , ,..., , ,...., ]T G L L NL G G NG line line nlP V V Q Q S Sx Where: 16 , ,( ) ( ) ( ) ( ) ( ) M N N N i i wi i p i i r i i i i i i J C p C w C w C w x,u 1 2 , 1 1 ,[ ,..., , ,..., , ,...., , ,... ]T G NG G G NG NT C C NCV V P P T T Q Qu 17. OPTIMAL POWER FLOW (OPF) min max min max min max 1,....., 1,....., 1,....., Gi Gi Gi Gi Gi Gi Gi Gi Gi P P P i NG V V V i NG Q Q Q i NG Where: Generator Constraints: Whereas: Transformer Constraints: min max 1,.....,i i iT T T i NT While: Shunt VAR Constraints: min max 1,.....,Ci Ci CiQ Q Q i NC Finally: Security Constraints: min max max , , 1,....., 1,....., Li Li Li line i line i V V V i NL S S i nl On the other hand, for inequality constraints ( ) 0 :h x,u 17 18. OPTIMAL POWER FLOW (OPF) 2 2 2 lim 2 lim lim max 1 1 , , 1 1 1 ( ) ( ) ( ) ( ) NL NG nl P G G V Li Li Q Gi Gi S line i liau ng e i i i i J J P P V V Q Q S S By using penalty function principle, all constraints are included in the objective function ( ):J x,u , , ,andP V Q S Where: are penalty factors. 18 19. PARTICLE SWARM OPTIMIZATION (PSO) PSO suggested by Kennedy and Eberhart (1997). 20. PARTICLE SWARM OPTIMIZATION (PSO) 1 1 2* * ( ) * ( )i i i i i k k k k k k v w v c U pbest x c U gbest x PSO Searching Mechanism: 1 1 i i i k k k x x v max min max max ( ) * w w w w iter iter Where: 20 21. PARTICLE SWARM OPTIMIZATION (PSO) PSO Algorithm Flowchart 21 22. PARTICLE SWARM OPTIMIZATION (PSO) ( , )Min J x u Implementation of PSO for Solving OPF: . . ( , ) 0S T g x u 1[ , , , ]G G L lineP Q V Sx Where: ( , ) 0h x u [ , , , ]G G cP V T Qu 1 1 ( ) * ( , ) NG NS i i a g Gu i i i J F P h x u 1; ( , ) 0 0; ( , ) 0 i h h x u x u 22 Since: 2 2 2 lim 2 lim lim max 1 1 , , 1 1 1 ( ) ( ) ( ) ( ) NL NG nl P G G V Li Li Q Gi Gi S line i line i i i aug i J P P V V QJ Q S S 23. STUDY CASES AND SIMULATION RESULTS OPF Main Flowchart 23 24. STUDY CASES AND SIMULATION RESULTS Using Sensitivity Matrices to Select the Most Control Variables: 24 25. STUDY CASES AND SIMULATION RESULTS Using Power Flow algorithm to satisfy the equality constraints g(x,u)=0 25 26. STUDY CASES AND SIMULATION RESULTS Using PSO algorithm to find the minimum cost 26 27. STUDY CASES AND SIMULATION RESULTS IEEE 30-BUS TEST SYSTEM: 27 28. STUDY CASES AND SIMULATION RESULTS Study of Base Case: VL3 VL4 VL6 VL7 VL9 VL10 VL12 VL14 VL15 VL16 VL17 VL18 VL19 VL20 VL21 VL22 VL23 VL24 VL25 VL26 VL27 VL28 VL29 VL30 0.9 0.95 1 1.05 1.1 1.15 P.U. Load Bus Voltages Upper limit Lower limit PG1 (MW) PG2 (MW) PG3 (MW) PG4 (MW) PG5 (MW) PG6 (MW) Losses (MW) Cost ($/hr) 176.94 48.71 21.27 21.09 11.83 12.00 8.4382 798.43 100 200 300 400 500 600 700 797.5 798 798.5 799 799.5 800 800.5 801 Iterations Cost 28 29. STUDY CASES AND SIMULATION RESULTS Application of Sensitivity Analysis for OPF : 29 The order of most effective control variables is: 30. STUDY CASES AND SIMULATION RESULTS Using combinations of the most effective control variables for Base Case OPF: 30 The order of most effective control variables is: 31. STUDY CASES AND SIMULATION RESULTS 6-BUS SYSTEM INCLUDING WIND-POWERED GENERATORS 31 32. STUDY CASES AND SIMULATION RESULTS 6-BUS SYSTEM INCLUDING WIND-POWERED GENERATORS 1 (1 ) (1 ) ) exp( kk i W i i r klv l v l w v c f w c c 32 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.2 0.4 0.6 0.8 1 w/wr Probability C=10 C=15 C=20 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 C=10 W/Wr Comulative.Probability C=15 C=20 , ,: ( ) ( ) ( ) ( ) M N N N i i wi i i i i i p r ii i i Minimize J C p C w w C wC 33. STUDY CASES AND SIMULATION RESULTS The Effect of Wind Power Cost Coefficients The Effects of Reserve Cost Coefficient kr (and kp=0): 33 34. STUDY CASES AND SIMULATION RESULTS The Effects of Penalty Cost Coefficient kp (and kr=0): 34 35. STUDY CASES AND SIMULATION RESULTS The Effects of Reserve Cost Coefficient kr and Penalty Cost Coefficient kp: 35 (a) kr=20 36. STUDY CASES AND SIMULATION RESULTS The Effects of Reserve Cost Coefficient kr and Penalty Cost Coefficient kp: 36 37. Conclusion and Further Work The implementation of PSO algorithm to find OPF solution is useful and worth of investigation. PSO algorithm is easy to apply and simple since it has less number of parameters to deal with comparing to other modern optimization algorithms. PSO algorithm is proper for optimal dispatch of real power of generators that include wind- powered generators. The used model of real power optimal dispatch for systems that include wind power is contains possibilities of underestimation and overestimation of available wind power plus to whether the utility owns wind turbines or not; these are the main features of this model. Conclusion 37 38. Conclusion and Further Work The probability manipulation of wind speed and wind power of the model is suitable since wind speed itself is hard of being expected and hence the wind power as well. In IEEE 30-bus test system, OPF has been achieved by using PSO and gives the minimum cost for several load cases. Using OPF sensitivity analysis can give an indication to which of control variables have most effect to adjust violations of operating constraints. The variations of wind speed parameters and their impacts on total cost investigated by 6-bus system. Conclusion 38 39. Conclusion and Further Work PSO algorithm needs some work on selecting its parameters and its convergence. PSO can be applied in wind power bid marketing between electric power operators. The same model can be adopted for larger power systems with wind power. The environment effects and security or risk of wind power penetration can be included in the proposed model and it becomes multi-objective model of optimal dispatch. Fuzzy logic is worth of investigation to be used instead probability concept which is used in the proposed model, especially when security of wind power penetration is included in the model. Further Work 39 40. Conclusion and Further Work Using the most effective control variables to adjust violations in OPF needs more study. The incremental reserve and penalty costs of available wind power can be compared with incremental cost of conventional-thermal quadratic cost; this comparison could lead to useful simplifications of an economic dispatch model that includes thermal and wind power. Further Work 40 41. Thank You for Listening Any Question ? 41