Meleagris Gallopavo Algorithm for Solving Optimal Reactive Power Problem

Received Jan 10, 2018 Revised Feb 16, 2018 Accepted Feb 24, 2018 In this paper, Meleagris Gallopavo Algorithm (MGA) is proposed for solving optimal reactive power problem.As a group-mate Meleagris gallopavo follow their poultry to explore food, at the same time it prevent the same ones to eat their own food. Always the overriding individuals have the lead to grab more food and Meleagris gallopavo would arbitrarily pinch the high-quality food which has been already found by other Meleagris gallopavo. In the region of the mother Meleagris gallopavo, Poults always search for food. In the Projected Meleagris Gallopavo Algorithm (MGA) additional parameters are eliminated, in order to upsurge the search towards global optimization solution.Proposed Meleagris Gallopavo Algorithm (MGA) has been tested on two modes a. with the voltage stability Evaluation in standard IEEE 30 bus test system, b. Without voltage stability Evaluation in standard IEEE 30, 57,118 bus test systems & practical 191 test system. Simulation results show clearly the better performance of the proposed Meleagris Gallopavo Algorithm (MGA) in reducing the real power loss, enhancement of static voltage stability Index and particularly voltage profiles within the specified limits. Keyword:


INTRODUCTION
The main objective in optimal reactive power problem is to minimize the real power loss and to keep the voltage profile within the limits. Various mathematical techniques [1 -8] have been utilized to solve the problem but have the complexity in managing inequality constraints. Start form genetic algorithm & all Evolutionary algorithms [9][10][11][12][13][14][15][16][17][18][19][20] have been applied serially to solve the reactive power problem. But they also had their own advantages & disadvantages in Exploration & Exploitation. This paper proposes Meleagris Gallopavo Algorithm (MGA) to solve reactive power problem. In this projected algorithm both exploration & exploitation has been augmented equally in order to reach near to global optimum solution. As a groupmate Meleagris Gallopavo follow their poultry to explore food, at the same time it prevent the same ones to eat their own food. Always the overriding individuals have the lead to grab more food and Meleagris Gallopavo would arbitrarily pinch the high-quality food which has been already found by other Meleagris Gallopavo. In the region of the mother Meleagris Gallopavo, Poults always search for food. In the Projected Meleagris Gallopavo Algorithm (MGA) additional parameters are eliminated, in order to upsurge the search  (MGA) in reducing the real power loss, enhancement of static voltage stability Index and particularly voltage profiles are within the specified limits.

VOLTAGE STABILITY EVALUATION 2.1. Voltage Stability Evaluation by Modal Analysis
For voltage stability enhancement in power systems Modal analysis methodology [25] has been used. The steady state system power flow equations are given by. Where J R is called the reduced Jacobian matrix of the system.

Modes of Voltage Instability
By computing the Eigen values and Eigen vectors voltage Stability characteristics of the system have been identified.
Where, ξ = right eigenvector matrix of JR η = left eigenvector matrix of JR ∧ = diagonal eigenvalue matrix of JR and From the equations (5) and (8), we can write, 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 given by, where, Where ξji is the jth element of ξi The corresponding ith modal voltage variation is mathematically given by, When | λi | =0 then the ith modal voltage will get collapsed. In Equation (8), assume ΔQ = ek where ek has all its elements zero except the kth one being 1. Then, ƞ 1k k th element of ƞ 1 V-Q sensitivity at bus k is given by,

PROBLEM FORMULATION
The key objectives of the reactive power dispatch problem is to minimize the system real power loss and also to maximize the static voltage stability margin (SVSM).

Minimization of Real Power Loss
Real power loss (Ploss) Minimization in transmission lines is mathematically 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
At load buses minimization of the voltage deviation magnitudes (VD) is stated as follows, Where nl is the number of load busses and Vk is the voltage magnitude at bus k.

System Constraints
These are the following constraints subjected to objective function as given 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 Load bus voltage (V Li ) inequality constraint: Switchable reactive power compensations (Q Ci ) inequality constraint: Reactive power generation (Q Gi ) inequality constraint: Transformers tap setting (T i ) inequality constraint: Transmission line flow (S Li ) inequality constraint: Where, nc, ng and nt are numbers of the switchable reactive power sources, generators and transformers.   male Meleagris Gallopavo) to explore food, at the same time it prevent the same ones to eat their own food. Always the overriding individuals have the lead to grab more food and Meleagris Gallopavo would arbitrarily pinch the high-quality food which has been already found by other Meleagris Gallopavo. In the region of the mother Meleagris Gallopavo Poults always search for food. In the Projected Meleagris Gallopavo Algorithm (MGA) additional parameters are eliminated, in order to upsurge the search towards global optimization solution.
Always advantages for the dominant individuals in grab the food. Better fitness poultry will have high priority for food access when compared with worse fitness values poultry. It has been simulated that the poultry with better fitness values can explore for food in a wider range of places than that of the with poultry worse fitness values. This can be articulated mathematically as follows. , Where (0, 2 )is a Gaussian distribution [21] with mean 0 and standard deviation 2 , ,which is used to shun the zero-division-error & the smallest constant. , a poultry index, is arbitrarily selected from the poultry group, f is the fitness value of the corresponding y. Hens, follow their group-mate poultry to explore for food. Furthermore, they would also arbitrarily steal the good food found by other Meleagris Gallopavo. Dominant Meleagris Gallopavo would have high advantage in competing for food than the more passive ones. This phenomenon can be formulated mathematically as follows, Where Rand is a uniform random number over 1 ∈ [0, 1], is an index of the poultry, which is the ith Meleagris Gallopavo's group-mate, while 2 ∈ [0, 1], is an index of the Meleagris Gallopavo, which is arbitrarily chosen from the swarm 1 ≠ 2 .
Around the mother Meleagris Gallopavo, Poults move to forage for food. This is formulated by, Where , , stands for the position of the i-th Poults's mother ∈ [1, ]. FL[ ∈ (0,2)] is a parameter, & it indicates that the Poults would follow its mother to forage for food. Consider the individual differences, the FL of each Poult would arbitrarily choose between 0 and 2 Meleagris Gallopavo group has wide range of exploration & it lead to have global search ability Number of parameters is reduced but the exploration and exploitation of exploration space can be done by all individual of population. The multi steps are separated be two steps. The first step is diversification (Exploration) in which Meleagris Gallopavo group's first step is reduced due to the largest area search ability; this reduced form is used to exploring the global optima. Each individual of Meleagris Gallopavo population move to the other position by the best Meleagris Gallopavo and the other Meleagris Gallopavo. The second one is intensification (exploitation) & it evaluates the value from the first step. Since the poultry and Poults group have the local exploration ability, the both group will be utilized to exploit the existing position from the first step. Alike to the first step, each individual of Meleagris Gallopavo population is considered as poultry then as a single Meleagris Gallopavo.

Initialization of Population
Meleagris Gallopavo swarm population are initialized by, With and are lower bound and upper bound of the exploration space. Exploration Step With, , ∈ [1, ] is arbitrarily chosen form Meleagris Gallopavo swarm with ≠ ≠ .
After , ( * )obtained, the objective value (fitness value) compared with the fitness value of , . The solution that has the most excellent fitness value is chosen as an individual of new population & it called as individual of the global population� , ( )�.

Exploitation
Step Through exploration step candidate solution (Meleagris Gallopavo individual) will be obtained & it will be revamped again by exploiting the neighbourhood using the process of reducing poultry and Meleagris Gallopavo formula. Alike with exploration step, this step will also eliminate poultry and Meleagris Gallopavo groups. Local optimum search carried out in two steps, the first step is by using the reduction poultry formula as follows.
The first local optimum solution obtained by exploiting the global optimum population by using the Equation (27). After that the next step is comparing its fitness value with fitness value of previous global optimum solution. The solution which has most excellent fitness value is chosen as individual of the first renewal population that called Local population I � , ( 1 )�.
After new-fangled local population I � , ( 1 )� obtained, subsequently the final step of Meleagris Gallopavo Algorithm (MGA) is to find the more local optimum (the second local optimum) by using the reduced Meleagris Gallopavo formula as follows: ∈ [1, ] is arbitrarily chosen from the local population I with ≠ and � ∈ (0,2)�. After the second local optimum obtained, the next step is compares its fitness value with the previous local optimum solution fitness value. The solution which has most excellent fitness value is chosen as individual of the second renewal population that called local population II� , ( 2 )�. This population is used as the preliminary population for the subsequent iteration until the stopping criteria are met.

With Considering Voltage Stability Evaluation
At first the efficiency of the proposed Meleagris Gallopavo Algorithm (MGA) has been tested it in standard IEEE-30 bus system with voltage stability evaluation.
Standard 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. Table 5 shows Meleagris Gallopavo Algorithm (MGA) reduces real power losses considerably when compared to other standard reported algorithms. In Table 1 optimal values of control variables along with the minimum loss obtained are given & it was found that there are no limit violations in any of the state variables corresponding to this control variables. Table 2 indicates the optimal values of the control variables & there is no limit violations in state variables. Mainly static voltage stability margin (SVSM) has increased from 0.2478 to 0.2489. 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 equivalents to the four critical contingencies are given. Result reveal about the Eigen value has been improved considerably for all contingencies in the second case.   [22] 5.0159 Genetic algorithm [23] 4.665 Real coded GA with Lindex as SVSM [24] 4.568 Real coded genetic algorithm [25] 4.5015 Proposed MGA method 4.2956

Without Considering Voltage Stability Evaluation
Validity of the proposed Meleagris Gallopavo Algorithm (MGA) has been verified by testing in standard IEEE 30-bus without considering Voltage stability evaluation.
Standard IEEE 30-bus has 41 branches, 6 generator-bus, 4 transformer-tap settings, with 2 shunt reactive compensators buses. 2, 5, 8, 11 and 13 are considered as PV generator buses & Bus 1 is taken as slack bus, others are PQ load buses. In Table 6 Control variables limits are given. In Table 7 gives the power limits of generators buses. Table 8 shows the values of control variables. Table 9 narrates the performance of the proposed algorithm. Overall comparison of the results of optimal solution obtained by various methods is given in Table 10. Then Meleagris Gallopavo Algorithm (MGA) has been tested in standard IEEE-57 bus power system. 18, 25 and 53 are reactive power compensation buses. PV buses are 2, 3, 6, 8, 9 and 12 and slack-bus is bus 1. In Table 11 system variable limits are given. IEEE-57 preliminary conditions for the bus power system are given as follows: P load = 12.110 p.u. Q load = 3.050 p.u. Complete sum of initial generations and power losses are attained as follows: ∑ = 12.429 p.u. ∑ = 3.3137 p.u. P loss = 0.25851 p.u. Q loss = -1.2059 p.u.
Control variables values obtained after optimization is given in Table 12. Comparisons of results are shown in Table 13. Then Meleagris Gallopavo Algorithm (MGA) has been tested in standard IEEE 118-bus test system [34].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. In Table 14 the limitations of reactive power source are listed, with the change in step of 0.01.
Comparison results are shown in Table 15 and the results clearly show the better performance of proposed Meleagris Gallopavo Algorithm (MGA) in reducing the real power loss.  Table 16 shows the  optimal control values of practical 191 test system obtained by MGA. And table 17 shows the results about the value of the real power loss by obtained by Meleagris Gallopavo Algorithm (MGA).

CONCLUSION
Meleagris Gallopavo Algorithm (MGA) has been successfully solved reactive power problem. In the Projected Meleagris Gallopavo Algorithm (MGA) additional parameters are eliminated, in order to upsurge the search towards global optimization solution.Proposed Meleagris Gallopavo Algorithm (MGA) has been tested on two modes a. with the voltage stability Evaluation in standard IEEE 30 bus test system, b. Without voltage stability Evaluation in standard IEEE 30, 57,118 bus test systems & practical 191 test system. Simulation results show clearly the better performance of the proposed Meleagris Gallopavo Algorithm (MGA) in reducing the real power loss, enhancement of static voltage stability Index and particularly voltage profiles within the specified limits.