1 ICEES-2016 PAPER ID- PS 28 Voltage Stability Enhancement and Voltage Deviation Minimization Using BAT Optimization Algorithm Indrajit N. Trivedi 1 Siddharth A. Parmar 2 Motilal Bhoye 3 Pradeep Jangir 4 Narottam Jangir 5 Arvind Kumar 6 GEC Gandhinagar, Gujarat 1 L.E. College Morbi, Gujarat 2,3,4,5 S. S. College, Bhavnagar, Gujarat 6 1 3rd International Conference on Electrical Energy Systems at SSN College of Engineering

2 OUTLINE Previous Paper Concept Problem Formulation Proposed SystemBAT Optimization Algorithm Results & Discussion Conclusion References

3 Previous Paper ConceptThe objective of the OPF problem is to determine the optimal settings of control variables of a power system by optimizing a particular objective while satisfying certain operating constraints [1]. Earlier deterministic optimization techniques [2] : Gradient Based Methods Linear Programming Interior Point Methods Newton Based Methods Highly non-linear and multi-modal optimization problem [3]. No criterion to decide whether a local solution is also the global solution. Need of development of Stochastic optimization techniques. One of them is BAT Optimization technique.

4 Set of Equality Constraints Set of Inequality Constraints4. Problem Formulation The OPF problem can be formulated as a non-linear constrained optimization problem as follows[1]: Minimize J(x, u) Vector of State Variables Vector of Control Variables Subject to g(x, u) = 0 & h(x, u) ≤ 0 Set of Equality Constraints Set of Inequality Constraints

5 Standard IEEE 30-Bus Test SystemThe standard IEEE 30-bus test system selected in this work has the following characteristics[4]: six generators at buses 1,2,5,8,11 and 13. four transformers with off-nominal tap ratio at lines 6-9,6-10,4-12 and nine shunt VAR compensation buses at buses 10,12,15,17,20,21,23,24 and 29. The Maximum and Minimum Limits of Generators, Transformers and Compensators are shown in Table 5 [4]. Fig. 1 Standard IEEE 30 Bus Test System

6 Control Parameters Used In BAT OptimizerTable 1 : Control Parameters used in BAT Optimizer Sr. No. Parameters Value 1 Population (No. of Search Agents) (N) 50 2 Maximum iterations count (t) 500 3 No. of Variables (dim) 6 4 Random Number [0,1]

7 BAT Optimizer AlgorithmThe BAT Optimization Algorithm was developed by Xin-She Yang in 2010. Bats are fascinating creatures. They are the single mammals having wings and innovative skill of finding location according to sound called echolocation. Bats utilizes echolocation to a definite angle; from all the types, micro-bats utilizes more echolocation as compared to mega-bats. Micro-bats utilizes echolocation for finding food, evade hurdles, and discover its resting cracks in the night.

8 Pseudo Code of BAT AlgorithmObjective function f(x), x = (x1, , xd)t Initialize the bat population xi (i=1,2,3, . . .,n) and vi Define pulse frequency fi at xi Initialize pulse rates ri and the loudness Ai while(t Generate new solutions by adjusting frequency, and updating velocities and locations/solutions [equations (5.1) to (5.3)] if(rand > ) Select a solution among the best solutions Generate a local solution around the selected best solution end if Generate a new solution by flying randomly If (rand < Ai&f(xi) < f(x*)) Accept the new solutions Increase ri and reduce Ai Rank the bats and find the current best x* end while Post process results and visualization

9 BAT Optimization AlgorithmRESULTS Case 1: Minimization of Generation Fuel Cost: The objective function J represents the total fuel cost of all generator units and it is expressed as follows[1]: J= 𝑖=1 𝑁𝐺 𝑓 𝑖 ($/ℎ) (1) Where, 𝑓 𝑖 is the fuel cost of the 𝑖 𝑡ℎ generator. 𝑓 𝑖 , can be expressed as follow: 𝑓 𝑖 = 𝑎 𝑖 + 𝑏 𝑖 𝑃 𝐺𝑖 + 𝐶 𝑖 𝑃 𝐺𝑖 2 ($/ℎ) (2) Where, 𝑎 𝑖 , 𝑏 𝑖 and 𝐶 𝑖 are cost coefficient. Table 2 : Optimal Values for Case 1. Method Cost Method description BOA BAT Optimization Algorithm FPA Flower Pollination Algorithm PSO Particle Swarm Optimization BHBO [2] Black-Hole-Based Optimization

10 BAT Optimization AlgorithmRESULTS Case 2:Voltage Deviation Minimization Here the goal is to increase voltage profile simultaneously by reducing the voltage deviation of PQ buses from 1.0 p. u. Hence, the objective function may be calculated as given below [1]: (3) Where, w is an appropriate weighting factor. (4) (5) Table 3 : Optimal Values for Case 2. Method Voltage Deviation Method description BOA 0.108 BAT Optimization Algorithm FPA 0.185 Flower Pollination Algorithm PSO 0.151 Particle Swarm Optimizer BHBO [2] 0.126 Black-Hole-Based Optimization

11 BAT Optimization AlgorithmRESULTS Case 3: Voltage stability enhancement Thus, the objective function may be given as [1]: (6) Where, (7) (8) Table 4 : Optimal Values for Case 3. Method Lmax Method description BOA 0.116 BAT Optimization Algorithm FPA 0.117 Flower Pollination Algorithm PSO 0.118 Particle Swarm Optimizer BHBO [2] Black-Hole-Based Optimization

12 Voltage Deviation (P.U)RESULTS Table 5: Optimal settings of control variables obtained by BOA.  Variables Min Max Initial Case 1 Case 2 Case 3 𝐏 𝐆𝟏 50 200 𝐏 𝐆𝟐 20 80 49.012 48.347 𝐏 𝐆𝟓 15 21.829 21.160 𝐏 𝐆𝟖 10 35 19.974 25.810 𝐏 𝐆𝟏𝟏 30 14.073 22.839 𝐏 𝐆𝟏𝟑 12 40 12.001 13.040 𝐕 𝐆𝟏 0.95 1.1 1.05 1.1000 1.038 1.100 𝐕 𝐆𝟐 1.04 1.0882 1.022 1.088 𝐕 𝐆𝟓 1.01 1.0622 1.014 1.068 𝐕 𝐆𝟖 1.0703 1.006 1.098 𝐕 𝐆𝟏𝟏 1.0825 1.004 𝐕 𝐆𝟏𝟑 1.0958 T11 1.078 1.0140 0.983 1.035 T12 1.069 0.9866 0.939 0.996 T15 1.032 1.0458 0.971 1.002 T36 0.9972 0.966 0.969 QC10 5 2.8048 3.051 1.856 QC12 2.0604 3.552 4.979 QC15 2.2544 3.925 5.000 QC17 4.7050 4.221 QC20 4.7442 3.230 QC21 2.6848 4.999 2.334 QC23 3.8919 4.485 4.161 QC24 2.9886 4.597 1.669 QC29 4.1214 2.479 Fuel cost ($/h) - Voltage Deviation (P.U) 1.1496 0.108 Lmax 0.1723 0.116

13 Conclusion The BAT Optimization Algorithm, Flower Pollination Algorithm and Particle Swarm Optimization Algorithm are successfully applied to standard IEEE 30-bus systems to solve the optimal power flow problem for the various types of cases. BOA proves its effectiveness in terms of maximum efficiency extraction from unknown search space and in minimum computational time. The results gives the optimal settings of control variables with different methods which demonstrate the effectiveness of the particular technique. The results shows that the solutions obtained from the BOA approach have fast convergence characteristics and it gives the competitive results compared with FPA and PSO methods which confirms the effectiveness of proposed algorithm.

14 References H.R.E.H. Bouchekara, Optimal power flow using black-hole-based optimization approach, Appl. Soft Comput. (2013). Bouchekara, M.A. Abido, M. Boucherma, Optimal power flow using Teaching-Learning-Based Optimization technique, Electr. Power Syst. Res. 114(2014) 49–59. H.R.E.H. Bouchekara, M.A. Abido, A.E. Chaib, R. Mehasni, Optimal power flow using the league championship algorithm: a case study of the Algerian power system, Energy Convers. Manag. 87 (2014) 58–70. Lee K, Park Y, Ortiz J. A united approach to optimal real and reactive power dispatch. IEEE Trans Power Appar Syst 1985;104(5): 1147–53. Yang X-S, “Bat algorithm:literature review and application”, Int J Bio-inspired Comput 2010;5(3):141-9. O. Alsac, B. Stot, “Optimal load flow with steady-state security”, IEEE Trans. PowerApp. Syst. PAS-93 (3) (1974) 745–751. C.A. Belhadj, M.A. Abido, “An optimized fast voltage stability indicator”, in: Elec-tric Power International Conference on Engineering, PowerTech, Budapest,1999, pp. 79–83. M.R. AlRashidi, M.E. El-Hawary, “Applications of computational intelligence techniques for solving the revived optimal power flow problem”, Electr. PowerSyst. Res. 79 (4) (2009) 694–702. S. Frank, I. Steponavice, S. Rebennack, “Optimal power flow: a bibliographic survey I. Formulations and deterministic methods”, Energy Syst. 3 (3) (2012)221–258.

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