Optimal Capacitor Placement on Radial Distribution Feeders in Presence of Nonlinear Loads Using Binary Particle Swarm Op

1. Optimal Capacitor Placement on Radial Distribution Feeders in Presence of Nonlinear Loads Using Binary Particle Swarm Optimization Presented by Tamer Mohamed Khalil

2. 2 Power distribution from electric power plants to ultimate consumers is accomplished via the transmission sub-transmission, and distribution lines. I2R loss in a distribution system is significantly high compared to that at high-voltage transmission system.

3. 3 The I2R losses can be separated to active and reactive component of branch current, where the losses produced by reactive current can be reduced by the installation of shunt capacitors.

4. 4 At present, harmonic distortion is increasing in distribution power systems due to the proliferation of nonlinear distorting loads. Capacitor significantly influences the propagation of system harmonics.

5. 5 Therefore, the optimal selection and placement of capacitor banks must be integrated with the estimation of harmonic levels to avoid excessive harmonic distortion.

6. 6 Particle Swarm Optimization Particle: Xi = [xi1,xi2 ,……,xid]. Population: pop = [X1, X2,…,Xn]. Particle best: PBi =[ pbi1, pbi2, ….,pbid ]. Global best: GB=[gb1, gb2, …..,gbd ]. Particle velocity: Vi = [ vi1,vi2,….., vid ].

7. 7 The i-particle position is updated by

8. 8 Binary Particle Swarm Optimization:

9. 9 System Model at Fundamental and Harmonic Frequencies

10. 10 System Model at Fundamental and Harmonic Frequencies

11. 11 System Model at Fundamental and Harmonic Frequencies

12. 12 Problem Formulation

13. 13 Formulation of Capacitor Placement Using Binary PSO

14. 14 Formulation of Capacitor Placement Using Binary PSO At l-level and k-iteration: popk =[Xk1, Xk2,… ,Xki,….,Xkn]. Xki =[xki1,xki2,…,xkij ,…, xkiJ]. (J represents the candidate buses) xkij = [xkij1 , xkij2,… xkijr,… xkijR ]. (R represents the maximum integer)

15. 15 Formulation of Capacitor Placement Using Binary PSO Each particle i represented in (J,R) dimensions by:

16. 16 Formulation of Capacitor Placement Using Binary PSO The number of capacitors placed at load level l at bus j at iteration k in particle i represented by : = xlkij1 +2 xlkij2 +… + r xlkijr +…+R xlkijR

17. 17 Illustrative examples: The first is IEEE 9-bus radial distribution feeder with nonlinear loads. The second is IEEE 34-bus radial distribution feeder with nonlinear loads.

18. 18 IEEE 9-bus radial distribution feeder

19. 19 Optimal Number of 300 kvar Capacitors for Different Load Levels, using Exhaustive Search (ES) and Binary PSO (# Fixed- and * Switched-Type Capacitors)

20. 20 The simulation results clear that: Before capacitor placement: The maximum THD at each load level within the permissible limits, the minimum rms voltage is 0.872 and the annual total cost of the system losses is $ 252873.5.

21. 21 After optimal capacitor placement without voltage constrains: applying the exhaustive search shows a net saving of 13.77%, applying the binary PSO shows a net saving of 13.81%. with voltage constrains: applying the exhaustive search shows a net saving of 13.45%, applying the binary PSO shows a net saving of 13.49%.

22. 22 IEEE 34-bus Radial Distribution Test System One-line Diagram of IEEE 34-Bus Radial Distribution Feeder

23. 23

24. 24 Optimal Solution for Different Cases

25. 25 The THD at each bus in each case

26. 26 Peak power losses in each case

27. 27 Yearly benefits in each case

28. 28 Conclusion We have proposed the binary PSO for solving the capacitor placement problem in the presence of harmonics. The effectiveness of the proposed algorithm in solving the capacitor placement problem and the effect of harmonics on optimal capacitor placement have been demonstrated through two test systems.

29. 29 Conclusion The simulation results indicate that when the harmonics effects ignored, the yearly benefits are greater than that when the harmonics effects are taken into account.

30. 30 Conclusion However, the limits of THD prevent possible harmonic amplification or resonance conditions which may result in considerable future cost caused by additional stress on equipment insulation, increased capacitor failure and interference with communication systems.

31. 31 Conclusion Therefore, from a long-term point of view, the presented solution when taken the harmonics effect into consideration and putting limits to the maximum THD be more economical than that when the harmonics effects are ignored.