ACTIVE POWER LOSS DIMINUTION & VOLTAGE STABILITY ENHANCEMENT BY RED WOLF OPTIMIZATION ALGORITHM

In this paper optimal reactive power dispatch problem (ORPD), has been solved by Enriched Red Wolf Optimization (ERWO) algorithm. Projected ERWO algorithm hybridizes the wolf optimization (WO) algorithm with swarm based algorithm called as particle swarm optimization (PSO) algorithm. In the approach each Red wolf has a flag vector, and length is equivalent to the whole sum of numbers which features in the dataset of the wolf optimization (WO). Exploration capability of the projected Red wolf optimization algorithm has been enriched by hybridization of both WO with PSO. Efficiency of the projected Enriched Red wolf optimization (ERWO) evaluated in standard IEEE 30 bus test system. Simulation study indicates Enriched Red wolf optimization (ERWO) algorithm performs well in tumbling the actual power losses& particularly voltage stability has been enriched.


Introduction
Reactive power problem plays major role in improving secure & economic of power system operation & control. A variety of methodologies [1][2][3][4][5][6] have been implemented to solve the problem, but difficulty found in handling the constraints. Now days various types of Evolutionary algorithms implemented to solve problem [7][8][9][10][11][12][13][14][15]. For last twenty years various types of programming and probabilistic based approach [16][17][18][19][20] has been used to solve the problem. In this work Enriched Red wolf optimization (ERWO) algorithm has been implemented to work out the problem. Both Exploration & Exploitation has been improved. In basic Wolf optimization algorithm (WO) [21], exploration spaces are missing the diversity and the high-quality diversity is needed to upgrade the performance of the algorithm to find an optimal solution. Particle swarm optimization (PSO) [22] has good feature of exploration ability and it has been hybridized with Wolf optimization algorithm (WO) to produce an Enriched version called as Enriched Red wolf optimization (ERWO). PSO will aid to form better preliminary population to WO. In standard IEEE 30 bus test system efficiency of Enriched Red wolf optimization (ERWO) algorithm has been evaluated. Results indicate that Enriched Red wolf optimization (ERWO) algorithm performs well in tumbling the actual power losses& particularly margin index value of voltage stability has been improved.

Modal Analysis for Voltage Stability Evaluation
Power flow equations of the steady state system is given by, Where J R Denote the reduced Jacobian matrix of the system.

Modes of Voltage Instability
Voltage Stability characteristics of the system have been identified through computation of the Eigen values and Eigen vectors.
Where, ξ denote the right eigenvector matrix of JR, η denote the left eigenvector matrix of JR, ∧ denote the diagonal eigenvalue matrix of JR. From the equations (5) and (6), ξi denote the ith column right eigenvector & η is the ith row left eigenvector of JR. λi indicate the ith Eigen value of JR.
reactive power variation of the ith modal is given by, where, Where ξji is the jth element of ξi ith modal voltage variation is mathematically given by, When the value of | λi | =0 then the ith modal voltage will get collapsed.
In equation (8), when ΔQ = ek is assumed , then ek has all its elements zero except the kth one being 1. Then ∆V can be formulated as follows, ƞ 1k is k th element of ƞ 1 At bus k V -Q sensitivity is given by,

Problem Formulation
Minimization of actual power loss and augmentation of static voltage stability margin index (SVSM) is main key to solve optimal reactive power dispatch problem. Voltage stability evaluation has been done through modal analysis method.

Minimization of Real Power Loss
Real power loss (Ploss) minimization is given as, Where n is the number of transmission lines, gk is the conductance of branch k, Vi and Vj are voltage magnitude at bus i and bus j, and θij is the voltage angle difference between bus i and bus j.

Minimization of Voltage Deviation
Formula for reducing the voltage deviation magnitudes (VD) is derived as follows, Where nl is the number of load busses and Vk is the voltage magnitude at bus k.

System Constraints
Load flow equality constraints: where, nb is the number of buses, PG and QG are the real and reactive power of the generator, PD and QD are the real and reactive load of the generator, and Gij and Bij are the mutual conductance and susceptance between bus i and bus j.

Red Wolf Optimization
Red wolf optimization mimics the communal management and hunt deeds of Red wolves in nature.
There are three fittest candidate solutions assumed as , and to lead the population toward promising regions of the exploration space in each iteration of red wolf optimization. is named for the rest of Red wolves and it will assist , and to encircle, hunt, and attack prey, that is, to find Enriched solutions. In order to scientifically replicate the encompassing behavior of Red wolves, the following equations are proposed: Where indicates the current iteration, H ⃗⃗⃗ = 2b ⃗⃗⃗⃗ .

Particle Swarm Optimization
In Particle swarm optimization (PSO) algorithm [22] the positions and velocities of the Particles are modernized as follows: The current position of particle is y t i & search velocity is v t i . Global best-found position is. m t g .
In uniformly distributed interval (0, 1) Rm 1 & Rm 2 are arbitrary numbers. Where cg 1 and cg 2 are scaling parameters.ω t is the particle inertia. The variable ω t is modernized as Maximum and minimum of ω t is represented by ω max and ω min ; maximum number of iterations is given by t max . Until termination conditions are met this process will be repeated.

Enriched Red Wolf Optimization (ERWO) Algorithm for Solving Optimal Reactive Power Dispatch Problem
In this approach red wolves α,β and γ determine the position of the prey. ⃗ ⃗⃗ = 2b ⃗ ⃗⃗⃗ . r 1 ⃗⃗⃗⃗ − b ⃗⃗⃗⃗ Directs the exploration & exploitation process by reducing the value from 2 to 0.When |H ⃗⃗⃗ | < 1 it converged towards the prey & If |H ⃗⃗⃗ | > 1 diverged away. The first best Minimum loss and variables are accumulated as "α" position, score & as like second best, third best accumulated as "β" and " γ" position & score.

Commence
Initialize the parameters Initialize b, H ⃗⃗⃗⃗ and F ⃗⃗ ; beginning positions of Red wolves has been stimulated. i = 1: population size j = 1: n When (i, j) > 0.500 (i) = 1; Else (j) = 0; End if End for Work out the maximum fitness of Red wolves as follows, Primary maximum fitness of the Red wolf is designated as " " Second maximum fitness of the Red wolf is designated as " " Third maximum fitness of the Red wolf is designated as " " While k < maximum iteration For i = 1: population size Exact Location of the existing Red wolf has been revised periodically End for For i = 1: population size Sporadically revise the values of b, H ⃗⃗⃗⃗ and F ⃗⃗ ; At this stage Fitness of Red wolves has been calculated The assessment of red wolves " "," " and " " has to be revised k=k+1; End while Re-examine the value of" "as the optimal characteristic division; End

Simulated Outcomes
The efficiency of the proposed Enriched Red Wolf Optimization (ERWO) algorithm is demonstrated by testing it on standard IEEE-30 bus system, it has 41 transmission lines of which four branches are (6-9), (6-10) , (4-12) , 6 generator buses, 24 load buses , (28-27) -are with the tap setting transformers. Optimal values of the control variables are given arte given in Table 1.  Table 2 indicates the optimal values of the control variables & there is no limit violations in state variables. Static voltage stability margin (SVSM) has increased from 0.2484 to 0.2496. contingency analysis was conducted using the control variable setting obtained in case 1 and case 2 to determine the voltage security of the system. In Table 3 the Eigen values equivalent to contingencies are given. In Table 4Eigen value has been improved for all contingencies. Limit Violation Checking Of State Variables. Comparisons of results are shown in Table 5.     Minimum loss Evolutionary programming [23] 5.0159 Genetic algorithm [24] 4.665 Real coded GA with Lindex as SVSM [25] 4.568 Real coded genetic algorithm [26] 4.5015 projected ERWO 4.2096

Conclusion
Enriched Red wolf optimization (ERWO) approach effectively solved the problem. Exploration & Exploitation has been considerably improved through the proposed methodology. In standard IEEE 30 bus test system proposed technique has been tested, , comparison of the real power loss has been done & proposed methodology reduced the actual power loss considerably with augmentation of static voltage stability margin index.