AEEICB-2016 PAPER ID- 187 Voltage Stability Enhancement and Voltage Deviation Minimization Using Ant-Lion Optimizer Algorithm Indrajit N. Trivedi 1 Siddharth A. Parmar 2 R. H. Bhesdadiya 3 Pradeep Jangir 4 GEC Gandhinagar, Gujarat 1 L.E. College Morbi, Gujarat 2,4 School of Engineering, RK University, Rajkot, Gujarat 3 1

OUTLINE Previous Paper Concept Problem Formulation Proposed System Ant-Lion Optimizer Algorithm Results & Discussion Conclusion References

Previous Paper Concept The 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 Antlion Optimizer technique.

Set of Equality Constraints Set of Inequality Constraints 4. 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

Standard IEEE 30-Bus Test System The 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 28-27. 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

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

Ant-Lion Optimizer Algorithm The Ant Lion Optimizer was developed by Seyedali Mirjalili in 2015.ALO based on the hunting mechanism of ant lions in nature. Five main steps of hunting prey such as the random walk of ants, building traps, entrapment of ants in traps, catching preys, and re-building traps are implemented [5].

Pseudo Code of Antlion Algorithm Initialize the first population of ants and antlions randomly Calculate the fitness of ants and ant lions Find the best antlions and assume it as the elite (determined optimum) while the end criterion is not satisfied for every ant Select an antlion using Roulette wheel Update c and d using equations Equation 𝑐 𝑡 = 𝑐 𝑡 𝐼 and 𝑑 𝑡 = 𝑑 𝑡 𝐼 Create a random walk and normalize it using Equation X(t)=[0, cum sum(2r( 𝑡 1 )-1),cum sum(2r( 𝑡 2 )-1),…,cum sum(2r( 𝑡 𝑛 )-1)] and 𝑥 𝑖 𝑡 = ( 𝑥 𝑖 𝑡 − 𝑎 𝑖 )∗( 𝑑 𝑖 − 𝑐 𝑖 𝑡 ) ( 𝑑 𝑖 𝑡 − 𝑎 𝑖 ) + 𝑐 𝑖 Update the position of ant using Equation 𝐴𝑛𝑡 𝑖 𝑡 = 𝑅 𝐴 𝑡 + 𝑅 𝐸 𝑡 2 end for Calculate the fitness of all ants Replace an ant lion with its corresponding ant it if becomes fitter Equation 𝐴𝑛𝑡𝑙𝑖𝑜𝑛 𝑗 𝑡 = 𝐴𝑛𝑡 𝑖 𝑡 𝑖𝑓 𝑓 𝐴𝑛𝑡 𝑖 𝑡 >𝑓( 𝐴𝑛𝑡𝑙𝑖𝑜𝑛 𝑗 𝑡 ) Update elite if an antlion becomes fitter than the elite end while Return elite

RESULTS ALO 799.1545 Ant Lion Optimizer Method Cost Method description 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 ALO 799.1545 Ant Lion Optimizer FA 799.7657 Firefly Algorithm PSO 799.7036 Particle Swarm Optimization BHBO [2] 799.9217 Black-Hole-Based Optimization

RESULTS Method Voltage Deviation Method description ALO 0.1222 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 ALO 0.1222 Ant Lion Optimizer FA 0.1474 Firefly Algorithm PSO 0.1506 Particle Swarm Optimizer BHBO [2] 0.1262 Black-Hole-Based Optimization

RESULTS Method Lmax Method description ALO 0.1140 Ant Lion Optimizer 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 ALO 0.1140 Ant Lion Optimizer FA 0.1184 Firefly Algorithm PSO 0.1180 Particle Swarm Optimizer BHBO [2] 0.1167 Black-Hole-Based Optimization

Voltage Deviation (P.U) RESULTS Table 5: Optimal settings of control variables obtained by ALO.  Variables Min Max Initial Case 1 Case 2 Case 3 𝐏 𝐆𝟏 50 200 99.2230 177.0808 176.422 159.945 𝐏 𝐆𝟐 20 80 48.7252 49.012 48.347 𝐏 𝐆𝟓 15 21.3119 21.829 21.160 𝐏 𝐆𝟖 10 35 21.0305 19.974 25.810 𝐏 𝐆𝟏𝟏 30 11.9525 14.073 22.839 𝐏 𝐆𝟏𝟑 12 40 12.0000 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) - 901.951 799.1545 ----------- ------------ Voltage Deviation (P.U) 1.1496 0.1222 Lmax 0.1723 0.1140

Conclusion The Antlion Optimizer, Firefly 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. ALO 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 ALO approach have fast convergence characteristics and it gives the competitive results compared with FA and PSO methods which confirms the effectiveness of proposed algorithm.

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