REDUCTION OF REAL POWER LOSS BY IMPROVED SHUFFLED FROG-LEAPING ALGORITHM

This paper presents Improved Shuffled Frog-Leaping (ISFL) algorithm for solving optimal reactive power problem. A new search-acceleration parameter has been introduced into the formulation of the original shuffled frog leaping (SFL) algorithm to create an adapted form of the shuffled frog algorithm for solving the reactive power problem. The shuffled frog-leaping algorithm draws its formulation from two other search techniques: the local search of the ‘particle swarm optimization’ technique; and the competitiveness mixing of information of the ‘shuffled complex evolution’ technique. Proposed Improved Shuffled Frog-Leaping (ISFL) algorithm has been tested in standard IEEE 30,57,118 & Practical 191 Utility (Indian) System bus test systems and simulation results show clearly about the better performance of the proposed algorithm in reducing the real power loss & control variables within the limits.


Introduction
To till date various methodologies has been applied to solve the Optimal Reactive Power problem. Many types of mathematical methodologies like linear programming, gradient method [1][2][3][4][5][6][7][8] has been utilized to solve the reactive power problem, but those techniques found difficult in handling the constraints in the reactive power problem. After that various types of evolutionary algorithms [9][10][11][12] has been applied to solve the reactive power problem. But some algorithm good in exploration means, it lacks in exploitation and few algorithm's good in exploitation but lack in exploration. Speed of convergence is poor for some algorithms even though they got good tradeoff between exploration and exploitation. This paper presents Improved Shuffled Frog-Leaping (ISFL) algorithm for solving optimal reactive power problem. A new search-acceleration parameter has been introduced into the formulation of the original shuffled frog leaping (SFL) algorithm [13][14][15] to create an adapted form of the shuffled frog algorithm for solving the reactive Http://www.granthaalayah.com ©International Journal of Research -GRANTHAALAYAH [147] power problem. The shuffled frog-leaping algorithm draws its formulation from two other search techniques: the local search of the 'particle swarm optimization' technique; and the competitiveness mixing of information of the 'shuffled complex evolution' technique. Proposed Improved Shuffled Frog-Leaping (ISFL) algorithm has been tested in standard IEEE 30,57,118 & Practical 191 Utility (Indian) System bus test systems and simulation results show clearly about the better performance of the proposed algorithm in reducing the real power loss & control variables within the limits.

Active Power Loss
Main objective of the reactive power dispatch problem is to minimize the active power loss and mathematically written by, Where F-objective function, PLpower loss, gk -conductance of branch, Vi and Vj are voltages at buses i,j, Nbr-total number of transmission lines in power systems.

Voltage Profile Improvement
Objective function (F) has be rewritten to minimize the voltage deviation in PQ buses as follows, Where VD -voltage deviation, ω v -is a weighting factor of voltage deviation.
And the Voltage deviation given by: Where Npq-number of load buses Equality Constraint the power balance equation with respect to the equality constraint of the problem is written as follows: Where PG-total power generation, PDtotal power demand.

Inequality Constraints
The inequality constraint with upper and lower bounds on the active power of slack bus (Pg), and reactive power of generators (Qg) are written as follows: Q gi min ≤ Q gi ≤ Q gi max , i ∈ N g (6) Upper and lower bounds on the bus voltage magnitudes (Vi) is given by: Upper and lower bounds on the transformers tap ratios (Ti) is given by: Upper and lower bounds on the compensators (Qc) is given by: Where N is the total number of buses, Ng is the total number of generators, NT is the total number of Transformers, Nc is the total number of shunt reactive compensators.

Shuffled Frog-Leaping Algorithm
The shuffled frog-leaping algorithm (SFL) is a memetic metaheuristic that is designed to seek a global optimal solution by performing a heuristic search. It is based on the evolution of memes carried by individuals and a global exchange of information among the population. In essence, it combines the benefits of the local search tool of the particle swarm optimization and the idea of mixing information from parallel local searches to move toward a global solution. The SFL algorithm has been tested on several combinatorial problems and found to be efficient in finding global solutions. The SFL algorithm involves a population of possible solutions defined by a set of frogs (i.e. solutions) that is partitioned into subsets referred to as memeplexes. The different memeplexes are considered as different cultures of frogs, each performing a local search. Within each memeplex, the individual frogs hold ideas, that can be influenced by the ideas of other frogs, and evolve through a process of memetic evolution. After a number of memetic evolution steps, ideas are passed among memeplexes in a shuffling process. The local search and the shuffling processes continue until convergence criteria are satisfied.
First, an initial population of 'P' frogs is created randomly. For S-dimensional problems, each frog i is represented by S variables as Xi=(xi1, xi2, . . . . . . , xiS). The frogs are sorted in a descending order according to their fitness. Then, the entire population is divided into m memeplexes, each containing n frogs (i.e. P=m6n). In this process, the first frog goes to the first memeplex, the second frog goes to the second memeplex, frog m goes to the mth memeplex, and frog m+1 goes to the first memeplex, and so on. Within each memeplex (figure 1b), the frogs with the best and the worst fitness are identified as Xb and Xw, respectively. Also, the frog with the global best fitness is identified as Xg. Then, an evolution process is applied to improve only the frog with the worst fitness (i.e. not all frogs) in each cycle. Accordingly, the position of the frog with the worst fitness is adjusted as follows: Where rand () is a random number between 0 and 1; and Dmax is the maximum allowed change in a frog's position. If this process produces a better frog (solution), it replaces the worst frog. Otherwise, the calculations in equations (10) and (11) are repeated with respect to the global best frog (i.e. Xg replaces Xb). If no improvement becomes possible in this latter case, then a new solution is randomly generated to replace the worst frog with another frog having any arbitrary fitness. The calculations then continue for a specific number of evolutionary iterations within each memeplex. The main parameters of the SFL algorithm are: number of frogs P, number of memeplexes, and number of evolutionary iterations for each memeplex before shuffling.
Begin; Generate random population of P solutions (individuals); For each individual i E P: calculate fitness (i); Sort the whole population P in descending order of their fitness; Divide the population P into m memeplexes; For each memeplex; Determine the best and worst individuals; Improve the worst individual position using Equations- (10) & (11); Repeat for a specific number of iterations; End; Combine the evolved memeplexes; Sort the population P in descending order of their fitness; Check if termination=true; End;

Improved Shuffled Frog-Leaping (ISFL) Algorithm
In the SFL algorithm, each memeplex is allowed to evolve independently to locally search at different regions of the solution space. In addition, shuffling all the memeplexes and re-dividing them again into a new set of memeplexes results in a global search through changing the information between memeplexes. As such, the SFL algorithm attempts to balance between a wide search of the solution space and a deep search of promising locations that are close to a local optimum.
As expressed by equation (10), each individual frog (solution) in a memeplex is trying to change its position towards the best frog within the memeplex or the overall best frog. As shown in this equation, when the difference in position between the worst frog Xw (i.e. the frog under evolution) and the best frogs (Xb or Xg) becomes small, the change in frog Xw's position will be very small, and thus it might stagnate at a local optimum and lead to premature convergence. To overcome such an occurrence, this Improved Shuffled Frog-Leaping (ISFL) algorithm proposes that the right-hand side of equation (10) be multiplied by a factor C called the 'search -acceleration factor', as follows: Assigning a large value to the factor C at the beginning of the evolution process will accelerate the global search by allowing for a bigger change in the frog's position and accordingly will widen the global search area. Then, as the evolution process continues and a promising location is identified, the searchacceleration factor, C, will focus the process on a deeper local search as it will allow the frogs to change its positions. The searchacceleration factor, which can be a positive constant value, linear, or nonlinear function of time, provides the means to balance between global and local search.

Simulation Results
In standard IEEE 30-bus, 41 branch system validity of proposed Improved Shuffled Frog-Leaping (ISFL) algorithm has been verified and the system has 6 generator-bus voltage magnitudes, 4 transformer-tap settings, and 2 bus shunt reactive compensators. 2, 5, 8, 11 and 13 are considered as PV generator buses, Bus 1 is taken as slack bus and others are PQ load buses. Primary variables limits are given in Table 1.   Table 2 the power limits of generators buses are listed.  Table 3 shows the proposed Improved Shuffled Frog-Leaping (ISFL) algorithm successfully kept the control variables within limits. Table 4 narrates about the performance of the proposed Improved Shuffled Frog-Leaping (ISFL) algorithm. Table 5 list out the overall comparison of the results of optimal solution obtained by various methods.    At that Improved Shuffled Frog-Leaping (ISFL) algorithm has been tested in standard IEEE-57 bus power system. The reactive power compensation buses are 18, 25 and 53. Bus 2, 3, 6, 8, 9 and 12 are PV buses and bus 1 is selected as slack-bus. The system variable limits are given in Table  6.
The preliminary conditions for the IEEE-57 bus power system are given as follows: Pload = 12.108 p.u. Qload = 3.012 p.u. The total initial generations and power losses are obtained as follows: ∑ P G = 12.148 p.u. ∑ Q G = 3.3123 p.u. Ploss = 0.25832 p.u. Qloss = -1.2041 p.u. Table 7 shows the various system control variables i.e. generator bus voltages, shunt capacitances and transformer tap settings obtained after optimization which are within the acceptable limits. In Table 8, shows the comparison of optimum results obtained from proposed methods with other optimization techniques. These results indicate the robustness of proposed approaches for providing better optimal solution in case of IEEE-57 bus system.    Then Improved Shuffled Frog-Leaping (ISFL) algorithm has been tested in standard IEEE 118bus test system [24]. The system has 54 generator buses, 64 load buses, 186 branches and 9 of them are with the tap setting transformers. The limits of voltage on generator buses are 0.95 -1.1 per-unit., and on load buses are 0.95 -1.05 per-unit. The limit of transformer rate is 0.9 -1.1, with the changes step of 0.025. The limitations of reactive power source are listed in Table 9, with the change in step of 0.01.  The statistical comparison results have been listed in Table 10 and the results clearly show the better performance of proposed Improved Shuffled Frog-Leaping (ISFL) algorithm in reducing the real power loss.

Conclusion
In this paper Improved Shuffled Frog-Leaping (ISFL) algorithm successfully solved the optimal reactive power problem. The shuffled frog-leaping algorithm draws its formulation from two other search techniques: the local search of the 'particle swarm optimization' technique; and the competitiveness mixing of information of the 'shuffled complex evolution' technique. Proposed Improved Shuffled Frog-Leaping (ISFL) algorithm has been tested in standard IEEE 30,57,118 & Practical 191 Utility (Indian) System bus test systems and simulation results show clearly about the better performance of the proposed algorithm in reducing the real power loss & control variables within the limits.