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Application of Fruit Fly Algorithm for Security Constrained Optimal Power Flow Problem

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Application of Fruit Fly Algorithm for Security Constrained Optimal Power Flow Problem International Journal of Computer Applications (0975 – 8887) Volume 162 – No 12, March 2017 Application of Fruit Fly Algorithm for Security Constrained Optimal Power Flow Problem S. Sakthivel K. Kavipriya, P. Poovarasi B. Prema Professor, UG students UG students V.R.S. College of Engineering and V.R.S. College of Engineering and V.R.S. College of Engineering and Technology, Technology, Technology, Arasur-607 107, Arasur-607 107, Arasur-607 107, Villupuram Dt, Tamil Nadu, India. Villupuram Dt, Tamil Nadu, India. Villupuram Dt, Tamil Nadu, India. ABSTRACT (ISEA) etc. These techniques have been increasingly applied Optimal power flow (OPF) is a major task in power system for solving power system optimization problems such as economics and operation. In OPF power real power outputs economic dispatch, optimal reactive power flow and OPF for from the generators of a power system are so adjusted that the decades. total production cost is minimum. Security constraint OPF R.Gnanadass et al. [3] discuss the evolutionary programming (SC-OPF) is minimizing the cost keeping line flows within algorithm to solve the OPF problem with non-smooth fuel their respective limits for security reasons. Real power output cost function. M.R.Al Rashidi and M.E.EI.Hawary [4] have from generators, generator bus voltage magnitudes, var reported a hybrid particle swarm optimization algorithm to outputs from shunt compensators and transformer tap settings solve the discrete OPF problem with valve loading effect. M. are controlled for optimizing the total fuel cost in this OPF Varadarajan and K.S Swarup [5] proposed differential problem. This proposed work considers the bio inspired fruit evolution approach to solve OPF problem with multiple fly algorithm (FFA) for optimally selecting the values for objectives. A.V.Naresh Babu and S.Sivanagaraju [6] proposed control variables. The proposed algorithm is simple, with less a new approach based on two step initialization to solve the number of parameters and easy to implement. The OPF problem. performance of this algorithm in OPF task is tested on IEEE 30 bus test system. Numerical results are compared to All search intelligence techniques are population based and literature results and found to be improved. stochastic in nature and are applied to obtain quality solutions [7] to optimization problems. big-bang and big-crunch (BB- Keywords BC) developed by Erol and Eksin [8] from the concept of Optimal power flow, security constraint optimal power flow, universal evolution, fire fly optimization (FFO) also a bio inspired algorithm, line flow limit. heuristic algorithm developed by Dr. Xin-she yang [9] and cuckoo optimization algorithm [10] proposed by X.S. Yang 1. INTRODUCTION are also a population based search technique used to solve OPF control in power systems has a direct impact on system OPF problem. security and economic dispatch. It has become one of the most important problems and the main objective of the problem is In this proposed work, optimal power flow problem is handled to optimize a chosen objective function through optimal by the recently introduced bio inspired fruit fly algorithm [11]. adjustments of power system control variables while at the This simple and efficient algorithm is tested on the standard same time satisfying system operating conditions with power IEEE-30 bus system. flow equations and inequality constraints. The equality 2. PROBLEM FORMULATION constraints are the nodal power balance equations, while the The main objective this work is to minimize the total inequality constraints are the limits of all control or state production cost of real power for reasons of economics. This variables. The control variables involve the tap ratios of can be mathematically written as follows [12]. transformers, the generator real power, the generator bus voltages and reactive power of sources. In general, the OPF 푀푖푛푓 푥, 푢 1 problem is a large-scale, highly constrained, nonlinear and non-convex optimization problem. s.t. H.W. Dommel and W.F.Tinney [1] firstly presented the solution of optimal power flow. In the past, conventional 푔 푥, 푢 = 2 methods such as interior point method, linear programming and nonlinear programming have been discussed by K. Deb 푕 푥, 푢 ≤ 0 3 [2] for optimizing engineering problems. The disadvantage of these techniques is that it is not possible to use as an efficient 푢휖 ∪ 4 tool in practical systems because of nonlinearity of the 푇 푇 푇 problem. Recently many population-based methods have been 푤푕푒푟푒 푥 = [훿 , 푉퐿 ] proposed for solving the OPF problem successfully. Examples of such methods are genetic algorithm (GA), particle swarm x is the state vector of the system with bus voltage angles δ optimization (PSO), differential evolution (DE), simulated and load bus voltages VL. Control variables to optimize the annealing (SA), Intelligent search evolutionary algorithm equation 1 are real power generation of generator ( 푃푔 ), 16 International Journal of Computer Applications (0975 – 8887) Volume 162 – No 12, March 2017 terminal voltages of generators ( 푉 ), tap-setting of violations, generator reactive power limit violations and 푔 violations for thermal limits of lies respectively. transformers (푡푡푎푝 ) and switchable shunts (푄푠푕 ). 3. FRUIT FLY OPTIMIZATION 푇 푇 푇 푇 푢 = 푃푔 , 푉푔 , 푡푡푎푝 , 푄푠푕 5 ALGORITHM Fruit Fly Optimization Algorithm is put forward by Equation (1) is considered as sum of quadratic cost functions Taiwanese scholar Pan [11]. It is a new optimization method based on fruit fly’s foraging behaviors and most researchers of thermal generating units with usual 푎푖, 푏푖, 푐푖 cost coefficients. used this algorithm for many optimization problems. Fruit flies are superior to other species in terms of visual senses. 푁푔 They can successfully pick up various odors floating in the air 퐹 푃 = 푎 + 푏 푃 + 푐 푃2 $ 푕푟 6 with their olfactory organ, some can even smell food sources 푇 푔 푖 푖 푔푖 푖 푔푖 40 kilometers away. Then, they would fly to the food. They 푖=1 may also spot with their sharp vision food or a place where This objective is subjected to the following constraints. their companions gather. Fruit fly’s foraging characteristics have been summarized and 2.1 Equality constraints programmed into the following steps, which are: (i) Active power balance at all the buses 1: Randomly generate initial position for the swarm of fruit 푃푖 − 푃푔푖 + 푃푑푖 = 0 (7) fly. 푖 = 1,2,3, . 푁퐵 Init X axis; Init Y axis 14 (ii) Reactive power balance at all the nodes 2: Randomly assign each fruit fly a direction and distance for their movement to look for food with their olfactory organ. 푄푖 − 푄푔푖 + 푄푑푖 = 0 8 푋푖 = 푋푎푥푖푠 + 푅푎푛푑표푚푉푎푙푢푒 15 푖 = 푁퐺 + 1, . 푁퐵 푌푖 = 푌푎푥푖푠 + 푅푎푛푑표푚푉푎푙푢푒 16 2.2 Inequality constraints Since food position is unknown, the distance (Dist ) to the (i) Limits on active power generation i origin is estimated first, and the judged value of smell 푚푖푛 푚푎푥 concentration (S ), which is the inverse of distance, is then 푃푔푖 ≤ 푃푔푖 ≤ 푃푔푖 9 i calculated. 푖 = 1,2, . 푁퐺 2 2 (ii) Limits on reactive power generation 퐷푖푠푡푖 = 푋푖 + 푌푖 ; 푆푖 = 1 퐷푖푠푡푖 17 푚푖푛 푚푎푥 푉푔푖 ≤ 푉푔푖 ≤ 푉푔푖 10 3: Substitute the judged values of smell concentration (Si) into the smell concentration judge function (also called fitness 푖 = 1,2, . 푁퐺 function) to get the smell concentrations (Smelli) of at (iii) Limits on switchable shunt compensators positions of each and every fruit flies. 푚푖푛 푚푎푥 Smelli = Function Si 18 푄푠푕푖 ≤ 푄푠푕푖 ≤ 푄푠푕푖 11 4: Identify the fruit fly whose position has the best smell 푖 = 1, . 푁 푆퐻 concentration (maximum value) (iv) Limits on tap setting of transformers bestSmellbestIndex = max Smell 19 푡푚푖푛 ≤ 푡 ≤ 푡푚푎푥 12 푡푎푝 푡푎푝 푡푎푝 5: Keep the best smell concentration value and x, y 푖 = 1, . 푁푇 coordinate; the fruit fly swarm will see the place and fly towards the position. The limits on the control variables of real power generations, voltage magnitudes of generators, transformer tap settings and Smellbest = bestSmell 20 switchable shunt devices are implicitly handled while X axis = X bestIndex 21 generating the parameters randomly. Due to inclusion of penalty terms, equation (6) transforms to a pseudo objective Y axis = Y bestIndex 22 function (F) 6: Enter iterative optimization, repeat steps 2-5 and judge min 퐹 = 퐹푇 푃푔 + 푃푠 whether the smell concentration is higher than that in the 푁푃푄 previous iteration; if so carry out step 6. + 푃푉푖 4. IMPLEMENTATION OF FOA 푖=1 푁퐺 푁퐿 ALGORITHM + 푃푄푖 + 푃퐿푖 13 Form an initial generation of NP flies in a random manner 푖=1 푖=1 respecting the limits of search space. Each fly is a vector of all control variables, i.e. [Pg, Vg, Ttap, Qsh]. There are 5 Pg’s, 6 Here are penalty terms for slack 푃푠 , 푃푉푖 , 푃푄푖 , 푃퐿푖 Vg’s, 9 Qsh’s and 4 Ttap’s in the IEEE-30 system and hence a bus generator MW limit violation, Load bus voltage limit fly is a vector of size 1x15. Calculate the smell concentration function values of all flies solution by running the NR load 17 International Journal of Computer Applications (0975 – 8887) Volume 162 – No 12, March 2017 flow. The control variable values taken by different flies are transformers tap settings and 2 static var compensators. The incorporated in the system data and load flow is run. The total first bus is the slack bus and its real power generation is not line loss corresponding to different flies are calculated. The controlled for OPF. System total load considered is the base steps followed in this algorithm is given below. load (2.834 p.u.+j1.2620 p.u.) on 100 MVA base. Step 1: Form an initial generation of NP flies in a random manner respecting the limits of search space.
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