IMPLEMENTATION OF BACTERIAL FORAGING ALGORITHM AND GRAVITATIONAL SEARCH ALGORITHM FOR VOLTAGE PROFILE ENHANCEMENT WITH LOSS MINIMIZATION

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1 Volume 115 No , ISSN: (printed version); ISSN: (on-line version) url: ijpam.eu IMPLEMENTATION OF BACTERIAL FORAGING ALGORITHM AND GRAVITATIONAL SEARCH ALGORITHM FOR VOLTAGE PROFILE ENHANCEMENT WITH LOSS MINIMIZATION Prabhakaran.K 1, Jaisiva.S 2, Harshavardhan Naidu.S 3, Sugavanam.K.R 4*, Senthil Kumar.R 5 1,3,4,5 Dept of Electrical & Electronics Engineering, VelTech HighTech Dr.Rangarajan Dr.Sakunthala Engineering College, TamilNadu, India 2 Dept of Electrical & Electronics Engineering,IFET Engineering College, Tamilnadu, India * Corresponding Author: sugavanamkr@gmail.com Abstract: Optimal Reactive Power Dispatch (ORPD) for voltage profile enhancement and loss minimization is attained by implementation of two different algorithm in power systems. The many objective of reactive power optimization problems are minimization of the losses and minimization of bus voltage deviation. By employing various artificial intelligence techniques helps in attaining Optimal Reactive Power Dispatch in the Optimal Reactive Power Flow (ORPF). The artificial intelligent techniques includes differential evolution, artificial bee colony, particle swarm optimization, ant colony algorithm,, evolutionary programming. In this paper the objective functions were optimized by two newly proposed algorithm like the newly proposed algorithms Gravitational Search Algorithm (GSA) and Bacterial Foraging Algorithm (BFA) IEEE 30 bus system is employed to attain objective function and the control variable are transformer tap position, generator bus voltage and static switchable shunt VAR compensators. Keywords: Bacterial Foraging Algorithm (BFA), Gravitational Search Algorithm (GSA), Optimal Reactive Power Dispatch (ORPD), Loss Minimization. 1. Introduction The major difficult task is Voltage profile enhancement in power system operation and control. Bus voltage deviation and real power loss minimization in power system or network helps in an improvement of voltage profile. Optimal placing of reactive power source such as shunt VAR compensator in an optimum manner reduces circulating VAR (volt ampere reactive), thereby providing a uniform voltage profile which leads to appreciable power saving on account of reduced system transmission losses. By adjusting transformer taps, generator voltage and VAR sources reactive power generations in the system is altered, the problem can be solved to a far extent and the objective function can be attained easily. 2. Objective Function The reactive power control is the main objective function of this work. The reactive power control variables including the rate of shunt VAR compensator is helps to find reactive power at optimal setting values. By tuning the reactive power of shunt VAR compensator leads to the minimization of voltage deviation and real power loss. The total real power loss and voltage deviation of the system can be calculated as follows V dev = 2 } (1) Where, N and NL are total number of buses and no. of transmission lines in the system respectively, the conductance of the line is G k where k is line number. The magnitude of sending and receiving end voltage are V i and V j and are angles of the end voltages 2.1 Constraints The equality and inequality constraints subjected to minimization of objective. The minimization problem is subject to the following equality and inequality constraints Equality Constraints Load Flow Constraints: The equality constraints represent the load flow equations, which are given below for i th bus: (2) (3) where Pgi active power and Qgi are reactive power of i th generator bus. Similarly P Di, Q Di are load active and reactive power of i th bus Inequality Constraints Generator Constraints Upper and lower limits of Generator voltage and reactive power of i th bus are i= 1,2,...NG (4) i= 1,2,...NG (5) 331

2 Where, are the minimum and maximum voltage of i th generating unit and Qmingi, Qmaxgi are the minimum and maximum reactive power of i t generating unit. Load bus constraints i= 1,2,...NL (6) Where, are the minimum and maximum load voltage of i t unit. Transmission line constraints i= 1,2,...,NTL (7) Where S L1 is the apparent power flow of i th branch and is the maximum apparent power flow limit of i th branch. Transformer tap constraints Transformer tap settings are bounded between upper and lower limit as given below: i= 1,2,...,NT (8) Where, are the minimum and the minimum and maximum tap setting limits of i th transformer. Shunt compensator constraints Shunt compensation are restricted by their limits as follows:, i=1,2...,nc (9) Where, are the minimum and maximum VAR injection limits of i th shunt capacitor. 3. Bacterial foraging algorithm Generally Foraging algorithm is developed on the natural behaviour of animals, since their attitude of finding food for their energy nutrient which provide maximum energy for foraging nature [10]. This algorithm is coined by the natural searching behaviour of E.coil bacteria for their energy. It is a microorganism origin which has a tendency of quick searching food by nature..it is gained by having natural behaviour of chemical substance Chemo taxis, which helps in quick search and also provide required nutrient for their survival. Step by step implementation of searching behaviour of E.coil deploys as Bacterial Foraging Algorithm (BFA).Initially the stepping rate of chemotaxix is j, the reproductive step rate is k and index elimination l in the dispersal event. The total count of chemotaxix steps N c helps in providing the states of length of life span of bacteria Ns maximum number of steps in free space boundary made bacteria swims freely and reduces losses. Later reproduction of chemo taxis is adopted. Bacteria population is sorted out by no.of population of reproduction Nre. which helps in increment of bacteria population. This method maintain bacteria size as constant with sustainable nutrients. While initialization, you must choose p, S, Nc, Ns, Nre, Ned, ped, and the C( i), i = 1,2,K, S. The additional parameter as like cell to cell attraction also needed for making swarming functions. ; Also, initial values for the θi, i = 1,2,K, S, must be chosen. The optimal value is obtained by choosing within limits is attaining a good choice. Otherwise they need to move in random manner in their desire path within the specified boundary domain in order to obtain optimal solution. The algorithm allow bacteria to populate chemo taxis, volatility, reproductively, elimination and dispersal is stated by initializing the parameters like j,k,l. By updating the parameter θi result in auto update of P. The sophistic termination leads to advantages of attaining maximum number of iteration for a specified constraints. 3.1 Implementation of Bacteria Foraging Algorithm STEP 1: Eliminating -the existing dispersal loop: l = l + 1 STEP 2: Creating Reproductive loop: k = k + 1 STEP 3: Increment Chemo taxis loop: j = j + 1 For i = 1,2,K,S, take bacterium i to a chemotactic step and follow First compute J(i,j,k,l). Let J(i,j,k,l) = J(i, j,k,l)+ J cc(θi(j,k,l), p( j,k,l )) (i.e., cell to cell add on attraction effect to concentrate more nutrients.). Let J last = j(i,j,k,l) to find for better cost function save it and proceed it for further iteration.. Tumble: Create a randomly vector like ( i) _p with each element involved with m(i),m = 1,2,K,p, and a random number lies between [ 1,1]. Move: Let For each and every bacterium i, resulted with step size C(i) during tumble functioning. Obtain J( i, j + 1,k,l), and then J( i, j + 1,k,l) = J(i,j+1,k,l)+Jcc(θi(j+ 1,k,l),P(j+1,k,l)). Swim (here we did an approximation in swimming behaviour of bacteria, bacteria is allowed to swan from each cell within the bacterial limits numbers {1,2,K,i} and had movement to {i+1, i+2, K, S} if not; this sort method is simpler to simulate than simultaneous swimming and tumbling by all bacteria at the same instant time. Let m=0 (swim length count). While m<ns (if not it is too long) Let m=m+ 1. If J(i,j+1,k,l) <Jlast (if doing better), let Jlast= J(i,j+1,k,l) and let 332

3 Else, let m= Ns. End of the while command. Move to next bacterium (i + 1) if i S (i.e., go to b) to process the next Bacterium). If j < Nc, go to step 3. In this case, life of bacteria is not fed up process with chemo taxis, until it lasting. Reproduction: a) For the given value of k and l, and for every i = 1,2,K, S, let i be the bacterium health ( it measure the consumption of nutrients for its survival throughout life span and also counting the avoiding noxious substances) Arrange the bacteria in ascending order of cost function Health(Low health by higher cost) with the parameters of chemo taxis. b) The bacteria with highest Health ranges will die often and the rest of bacteria Sr with best value split in to two equal half ( leads to copy their parental behaviour at the same point of exist) STEP 4: If k < Nre, go to step 2. The specified reproductive step is not yet obtained then continued with next generation to carried out in chemotixis loop. STEP 5: Elimination-dispersal: For i = 1,2,K, S, elimination and disperse of each bacterium is done by probability ped, (by doing so, it helps in maintaining population as constant ). While by eliminating a bacterium simply disperse it in random location in optimization range.. STEP 6: If l<ned, then go to step 1; otherwise terminate, end. Table 1. Control Parameter of the BFA S.No Parameter Values 1 Total no. of bacteria, S 20 2 No. of Chemo tactics steps, 20 Nc 3 Maximum no. of steps, Ns 4 4 Probability constant Ped No. of. reproduction steps, 4 Nre 6 No. of elimination- disperse steps, Ned 2 4. Gravitational search algorithm Gravitational Search Algorithm is a population based search algorithm based on the law of gravity and mass interaction. The algorithm considers agents as objects consisting of different masses. The entire agents move due to the gravitational attraction force acting between them and the progress of the algorithm directs the movements of all agents globally towards the agents with heavier masses. Each agent in GSA is specified by four parameters. Position of the mass in d th dimension, inertia mass, active gravitational mass and passive gravitational mass. The positions of the mass of an agent at specified dimensions represent a solution of the problem and the inertia mass of an agent reflect its resistance to make its movement slow. Both the gravitational mass and the inertial mass, which control the velocity of an agent in specified dimension, are computed by fitness evolution of the problem. The positions of the agents in specified dimensions (solutions) are updated in every iteration and the best fitness along with its corresponding agent is recorded. The termination condition of the algorithm is defined by a fixed amount of iterations, reaching which the algorithm automatically terminates. After termination of the algorithm, the recorded best fitness at final iteration becomes the global fitness for a particular problem and the positions of the mass at specified dimensions of the corresponding agent becomes the global solution of that problem. The algorithm can be summarized as below: Step 1: Initialization of the agents: Initialize the positions of the N number of agents randomly within the given search interval as below: Where, N is the space dimension of the problem and x i d defines the position of the i th agent in the d th dimension. Initially, the agents of the solution are defined randomly and according to Newton gravitation theory. Step 2: Fitness evolution and best fitness computation for each agents: Perform the fitness evolution for all agents at each iteration and also compute the best and worst fitness at each iteration defined as below: For a minimization problem: For a maximization problem: Step 3: Computation of gravitational constant G: Compute gravitational constant G at iteration t using the following equation: In this problem, G 0 is set to 200, is set to 10 and T is the total number of iterations. Step 4: Calculate the mass of the agents: Calculate gravitational and inertia masses for each agents at iteration t by the following equations: 333

4 where, M ai is the active gravitational mass of the i th agent, M pi is the passive gravitational mass of the i th agent, M ii is the inertia mass of the i th agent. Step 5: Calculate accelerations of the agents: Compute the acceleration of the i th agents at iteration t as below: Where is the force on i th agent in d th dimension as given in the following equation. The control variables are generator s voltages, tap settings of the regulating transformers and var injection of shunt capacitors. The upper and lower bounds of the different control variables are given in Table 2. Table 2. Control variable limits S. Control Variable Limit No 1 Generator voltage (V G ) ( ) p.u. 2 Tap setting (T P ) ( ) p.u. 3 MVAR by static compensators (Q svc ) (0-10) k best is the set of first k agents with the best fitness value and biggest mass. k best is computed in such a manner that it decreases linearly with time and at last iteration the value of k best becomes 2% of the initial number of agents. is the force acting on agent `i' from agent `j' at d th dimension and t th iteration is computed as below: where, is the Euclidian distance between two agents `i' and `j' at iteration t and G(t) is the computed gravitational constant at the same iteration. is a small constant. Step 6: Update velocity and positions of the agents: Compute velocity and the position of the agents at next iteration (t + 1) using the following equations: 5. Result and Discussion The performance of the BFA and GSA algorithm based real power loss minimization and voltage profile enhancement is tested in IEEE 30 bus system. The algorithm is coded in MATLAB environment and a Core 2 Duo, 2.8 MHz, 2GB RAM based PC is for the simulation purpose. The test system taken has six generating units connected to buses 1,2,5,8,11 and 13. There are 4 regulating transformers connected between bus numbers 6-9, 6-10, 4-12 and Two static shunt VAR compensators are connected in bus numbers 10 and 24. The system is interconnected by 41 transmission lines. Single line diagram of standard IEEE 30 bus system is shown in figure Step 7: Repeat from Steps 2-6 until iterations reaches their maximum limit. Return the best fitness computed at final iteration as a global fitness of the problem and the positions of the corresponding agent at specified dimensions as the global solution of that problem. 4.1 Implementation of Gravitational Search Algorithm to the OPF problem Step 1: Form an initial generation of N candidates in a random manner respecting the limits of search space as [V Gi, T Pi, Q SVCi ]. Step 2: Calculate the fitness function values of all candidate solution by running the NR load flow. Step 3: Update G(t), best(t), worst(t) and M i (t) for i = 1, 2,..., N. Step 4: Calculation of the total force in different directions, acceleration and velocity. Step 5: Return to step 2 until stopping criteria has been achieved. Figure.1. Single line diagram of standard IEEE - 30 bus system. 6. Minimization of Objective function The objective function of the paper is to optimize the real power loss minimization using the two different algorithms i.e BFA and GSA. Real power transmission loss minimization is the major component of reactive power optimization and it needs more attention. It shows that the real power loss is about MW is minimized using BFA. Though, GSA shows the adequate real power loss minimization up to

5 MW. From the result it is observed that GSA shows effectual real power loss minimization in the network. For clear understanding of the improvement in voltage profile, the p.u. voltage magnitude of all the buses in the system with BFA and GSA algorithm are compared in figure 2. It is clear that from the figure most of the load bus voltages are equal to about 1.0 p.u. Figure.2. Voltage profile improvement 6.1. Enhancement of Voltage Profile Values Table 3. Voltage profile values at different load buses using the two different algorithms S.No Bus Voltage profile values No. With BFA With GSA Conclusion In this paper, voltage profile improvement and loss minimization are demonstrated through two different algorithms. Bacterial Foraging Algorithm (BFA) and Gravitational Search Algorithm (GSA) are the two different algorithms used for solving the objective functions such as real power loss minimization and voltage profile improvement in IEEE 30 bus system network. It is clear from the numerical results that voltage profile improvement is attained both in BFA and GSA but real power loss minimization are highly encouraging in GSA Algorithm. References [1]P.K. Roy, S.P. Ghoshal, S.S. Thakur, Optimal VAR Control for Improvements in Voltage Profiles and for Real Power Loss Minimization using Biogeography Based Optimization, Electrical Power and Energy Systems, Vol. 43, No.1, pp , December [2]Serhat Duman, Ugur Guvenc, Yusuf Sonmez, Nuran Yorukeren, Optimal Power Flow Using Gravitational Search Algorithm, Energy Conversion and Management, Vol. 59, pp.86 95, July [3]Abbas Rabiee, Maziar Vanouni, Mostafa Parniani, Optimal Reactive Power Dispatch for Improving Voltage Stability Margin Using a Local Voltage Stability Index, Energy Conversion and Management, Vol. 59, pp , July [4]Kursat Ayan, Ulas kilic, Artificial Bee Colony Algorithm Solution for Optimal Reactive Power Flow, Applied Soft Computing, Vol.12, No. 5, pp , May [5]M. Varadarajan, K.S. Swarup, Differential Evolutionary Algorithm for Optimal Reactive Power Dispatch, Electrical Power & Energy Systems, Vol. 30, No. 8, pp , October [6]Amit Saraswat, Ashish Saini, Multi-Objective Optimal Reactive Power Dispatch Considering Voltage Stability in Power Systems using HFMOEA, Engineering Applications of Artificial Intelligence, Available online 18 July [7]Altaf Q.H. Badar, B.S. Umre, A.S. Junghare, Reactive Power Control Using Dynamic Particle Swarm Optimization for Real Power Loss Minimization, Electrical Power & Energy Systems, Vol. 41, No. 1, pp , October

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