AMELIORATED PARTICLE SWARM OPTIMIZATION ALGORITHM FOR SOLVING OPTIMAL REACTIVE POWER DISPATCH PROBLEM

In this paper, an Ameliorated Particle Swarm Optimization (APSO) algorithm has been proposed to solve the optimal reactive power dispatch problem. Particle Swarm Optimization (PSO) is swarm intelligence-based exploration and optimization algorithm which is used to solve global optimization problems. But due to deficiency of population diversity and early convergence it is often stuck into local optima. Diversity upsurges and avoids premature convergence by using evolutionary operators in PSO. In this paper the intermingling crossover operator is used to upsurge the exploration capability of the swarm in the exploration space. Particle Swarm Optimization uses this crossover method to converge optimum solution in quick manner. Thus the intermingling crossover operator is united with particle swarm optimization to augment the performance and possess the diversity which guides the particles to the global optimum powerfully. Proposed Ameliorated Particle Swarm Optimization (APSO) algorithm has been tested in standard IEEE 30 bus test system and simulation results shows clearly the improved performance of the projected algorithm in reducing the real power loss and static voltage stability margin has been enhanced.


Introduction
Reactive power optimization plays a key role in optimal operation of power systems. Many numerical methods [1][2][3][4][5][6][7] have been applied to solve the optimal reactive power dispatch problem. The problem of voltage stability plays a strategic role in power system planning and operation [8]. So many Evolutionary algorithms have been already proposed to solve the reactive power flow problem [9][10][11]. In [12,13], Hybrid differential evolution algorithm and Biogeography Based algorithm has been projected to solve the reactive power dispatch problem. In [14,15], a fuzzy based technique and improved evolutionary programming has been applied Http://www.granthaalayah.com ©International Journal of Research -GRANTHAALAYAH [203] to solve the optimal reactive power dispatch problem. In [16,17] nonlinear interior point method and pattern-based algorithm has been used to solve the reactive power problem. In [18][19][20], various types of probabilistic algorithms utilized to solve optimal reactive power problem. In this paper, an Ameliorated Particle Swarm Optimization (APSO) algorithm has been proposed to solve the optimal reactive power dispatch problem. Particle Swarm Optimization (PSO) [21] has been used efficaciously in solving many optimization problems, for its simplicity and fast convergence rate. Swarm intelligence is the subdivision of artificial intelligence and based on collective behaviour of self-organized system [22,23]. The optimize value of the function using Particle Swarm Optimization Algorithm is hang on in the exploration and exploitation of the particles during searching in the exploration space [24].There are also problem in PSO like when it applies to various global optimization problems it may get held in the local optimization due to early convergence because the diversity shrinkages with the time for a large population [25] , So we apply various evolutionary operator to get the global optimal solution [26][27][28][29][30][31].The intermingling crossover is a crossover operator which is applied in basic PSO to discover the exploration area . The intermingling crossover operator is a improved crossover operator, which is apply to the PSO to optimize the function. The proposed Ameliorated Particle Swarm Optimization (APSO) algorithm has been evaluated in standard IEEE 30 bus test system. The simulation results show that our proposed methodology outperforms all the entitled reported algorithms in minimization of real power loss.

Modal Analysis for Voltage Stability Evaluation
Modal analysis is one among best methods for voltage stability enhancement in power systems. The steady state system power flow equations are given by.
J R is called the reduced Jacobian matrix of the system.

Modes of Voltage Instability
Voltage Stability characteristics of the system have been identified by computing the Eigen values and Eigen vectors. Let Where, ξ = right eigenvector matrix of JR η = left eigenvector matrix of JR ∧ = diagonal eigenvalue matrix of JR and From (5) and (8), we have Or Where ξi is the ith column right eigenvector and η the ith row left eigenvector of JR. λi is the ith Eigen value of JR.
The ith modal reactive power variation is, where, Where ξji is the jth element of ξi The corresponding ith modal voltage variation is If | λi | =0 then the ith modal voltage will collapse. In (10), let ΔQ = ek where ek has all its elements zero except the kth one being 1. Then,

Problem Formulation
The objectives of the reactive power dispatch problem is to minimize the system real power loss and maximize the static voltage stability margins (SVSM).

Minimization of Real Power Loss
Minimization of the real power loss (Ploss) in transmission lines is mathematically stated as follows.
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
Minimization of the voltage deviation magnitudes (VD) at load buses is mathematically stated as follows.
Minimize VD = ∑ |V k − 1.0| nl k=1 (15) Where nl is the number of load busses and Vk is the voltage magnitude at bus k.

System Constraints
Objective functions are subjected to these constraints shown below.
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.
Generator bus voltage (VGi) inequality constraint: Load bus voltage (VLi) inequality constraint: Switchable reactive power compensations (QCi) inequality constraint: Reactive power generation (QGi) inequality constraint: Transformers tap setting (Ti) inequality constraint: Transmission line flow (SLi) inequality constraint: Where, nc, ng and nt are numbers of the switchable reactive power sources, generators and transformers.

Particle Swarm Optimization (PSO)
PSO is a population-based optimization tool, where the system is initialized with a population of random particles and the algorithm searches for optima by updating generations. Suppose that the search space is D-dimensional. The position of the i-th particle can be represented by a Ddimensional vector = ( 1 , 2 , . . , ) and the velocity of this particle is = ( 1 , 2 , . . , ).The best previously visited position of the i-th particle is represented by = ( 1 , 2 , . . , ) and the global best position of the swarm found so far is denoted by = ( 1 , 2 , . . , ). The fitness of each particle can be evaluated through putting its position into a designated objective function. The particle's velocity and its new position are updated as follows: Where ∈ {1,2, . . , }, ∈ {1,2, . . , }N is the population size, the superscript t denotes the iteration number, is the inertia weight, r 1 and r 2 are two random values in the range [0,1],c 1 and c 2 are the cognitive and social scaling parameters which are positive constants.
These both equations are used to update the velocity and position of a particle in the exploration space. The equation (24) is used to balance the search abilities of the particle in the search space. The equation (25) uses the velocity obtained in first equation to get the new position of the particle.
Crossover is a Genetic operator which is used after selection in Genetic Algorithm to get the new children using two or more than two parent. It is used to get the healthier solution than current solution. There are various improved version of crossover available to get the value of newfangled species. Intermingling crossover is also a improved operator which is used to get the new healthier child by using current parent. This operator is applied in PSO to optimize the multidimensional function and upsurge the probing capability of the PSO, So that Particle Swarm Optimization optimizes the functions efficiently and did not jammed in the local optima.

Proposed Ameliorated Particle Swarm Optimization (APSO) algorithm
Although the crossover operator is a conception of Genetic Algorithm but apart from genetic algorithm it has been used in many algorithms with some alterations. The crossover operator takes two or more than two parent and produce one or more than one child .The produced new child after crossover is superior to their parents. There are various improved crossover technique, The intermingling crossover operator is one of the improved crossover operator in which two particles are used to create a minimum and maximum range values which lies in the function's bounded region and the new particle is produced within the calculated minimum and maximum range values, Then we compute the fitness value of that new particle and compare it with the current particle and modernize the N_POP of the population of the particles.

Start
Select two arbitrary particles from N_POP x 1 and x 2 Compute x new =(x 1 -x 2 ) Compute k 1 =min(x 1 , x 2 ) Compute k 2 =max(x 1 , x 2 ) k min =k 1 -b*x new ; k max =k 2 +b*x new ; Where "b" is an arbitrary selected integer within range Now select an arbitrary particle from the range N_new=(k max -k min ) *rand +k min Now compute the fitness of newly produced particle N_new

Start
Initialize particle with Arbitrary Position and Velocity Set P_best i =X i ,g_best=min(P_best i ) Initialize Generation as g=0; While ( < max _ ) For (i=1 to N_POP) For (j=1 to D_POP) Compute +1 using equation (11) Compute +1 using equation (12) If +1 and +1 are in exploration range then; Calculate fitness for corresponding particle x i ; Apply intermingling crossover to compute the new particle N_new Compute fitness value for newlyproduced particle Compare the fitness value for x i and N_new; If Fitness (N_new) is superior than x i then Modernize the particle in N_POP g=g+1; End for End for End of while Print the value of g_best. End

Simulation Results
The efficiency of the proposed Ameliorated Particle Swarm Optimization (APSO) algorithm is demonstrated by testing it on standard IEEE-30 bus system. The IEEE-30 bus system has 6 generator buses, 24 load buses and 41 transmission lines of which four branches are (6-9), (6-10) , (4)(5)(6)(7)(8)(9)(10)(11)(12) and  -are with the tap setting transformers. The lower voltage magnitude limits at all buses are 0.95 p.u. and the upper limits are 1.1 for all the PV buses and 1.05 p.u. for all the PQ buses and the reference bus. The simulation results have been presented in Tables 1, 2, 3 &4. And in the Table 5 shows the proposed algorithm powerfully reduces the real power losses when compared to other given algorithms. The optimal values of the control variables along with the minimum loss obtained are given in Table 1. Corresponding to this control variable setting, it was found that there are no limit violations in any of the state variables. Optimal Reactive Power Dispatch problem (ORPD) together with voltage stability constraint problem was handled in this case as a multi-objective optimization problem where both power loss and maximum voltage stability margin of the system were optimized simultaneously. Table  2 indicates the optimal values of these control variables. Also it is found that there are no limit violations of the state variables. It indicates the voltage stability index has increased from 0.2472 to 0.2486, an advance in the system voltage stability. To determine the voltage security of the system, contingency analysis was conducted using the control variable setting obtained in case 1 and case 2. The Eigen values equivalents to the four critical contingencies are given in Table 3. From this result it is observed that the Eigen value has been improved considerably for all contingencies in the second case.    Minimum loss Evolutionary programming [32] 5.0159 Genetic algorithm [33] 4.665 Real coded GA with Lindex as SVSM [34] 4.568 Real coded genetic algorithm [35] 4.5015 Proposed APSO method 4.1268

Conclusion
Ameliorated Particle Swarm Optimization (APSO) algorithm has been successfully solved optimal reactive power dispatch problem. In this paper the intermingling crossover operator is used to upsurge the exploration capability of the swarm in the exploration space. Particle Swarm Optimization uses this crossover method to converge optimum solution in quick manner. Thus the intermingling crossover operator is united with particle swarm optimization to augment the performance and possess the diversity which guides the particles to the global optimum powerfully. Proposed Ameliorated Particle Swarm Optimization (APSO) algorithm has been tested in standard IEEE 30 bus test system and simulation results shows clearly the improved performance of the projected algorithm in reducing the real power loss and static voltage stability margin has been enhanced.