MERIT ORDER DISPATCH USING ANT LION OPTIMIZATION ALGORITHM

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1 International Journal of Civil Engineering and Technology (IJCIET) Volume 8, Issue 10, October 2017, pp , Article ID: IJCIET_08_10_173 Available online at ISSN Print: and ISSN Online: IAEME Publication Scopus Indexed MERIT ORDER DISPATCH USING ANT LION OPTIMIZATION ALGORITHM Faseela C.K. Research Scholar, MES College of Engineering & Technology, Kunnukara, Kerala Dr. Vennila Professor, Noorul Islam University, Nagercoil, Tamilnadu ABSTRACT This paper proposes Ant Lion Optimization (ALO) method to come up with solution for any Economic & Emission Dispatch problem. Comparison is done with Particle Swarm Optimization (PSO) method to see the results with respect to already proven optimization methodology. The method is applied to solve IEEE-30 bus system to obtain minimum cost for its generation. Both fuel and emission costs are considered to come up with a result. The analysis shows good convergence property for ALO and provides better results in comparison with PSO. Key words: Particle Swan Optimization (PSO), Ant Lion Optimization (ALO), Economic and Emission Dispatch (ED), Optomization, Methodology, Emission Dispatch. Cite this Article: Faseela C.K and Dr. Vennila, Merit Order Dispatch Using ANT Lion Optimization Algorithm, International Journal of Civil Engineering and Technology, 8(10), 2017, pp INTRODUCTION In the management of power system operation, its highly critical to run generators at optimum cost. This is the primary aim of an Economic dispatch problem. With the growing norms of carbon emissions, its needed to optimize the emission along with the optimization of cost which acts as two major parts of Economic dispatch problem. The economic dispatch prediction should ensure scheduling of generators with respect to minimal cost and minimal emissions. This indirectly makes lower cost for electricity and makes electrical utilities more competitive in the market. As editor@iaeme.com

2 Merit Order Dispatch Using ANT Lion Optimization Algorithm the energy cannot be stored, it requires highly efficient estimation scenarios including transmission and distribution systems to make the same work effectively. Several techniques have been introduced to solve the optimization of Economic Load Dispatch, which is categorized as conventional and stochastic methods. The selection of heuristic optimization algorithm is the core of the problem involving economic dispatch in power system. This throws importance of keeping track of various algorithms involving Evolutionary algorithms [6], physics based algorithms, Swarm based algorithms and human based algorithms come up with the one that provides optimum results with good convergence value. The EDP is developed based on real-valued codification. In modern methodology only the cost function is evaluated and a global minimum solution is computed, independently of the cost function. The use of digital computers for obtaining loading schedules were investigated and used today. The EED problem to be a nonlinear constrained multi objective problem with objectives such as fuel cost, emission and system loss [1] [4]. The future MODE approach acquires an external elitist archive to retain non-dominated a multi-objective differential evolution (MODE) algorithm [2] for economic emission power dispatch (EED) problem. Solutions are found during the evolutionary process. Genetic algorithm [3] and Particle swarm optimization [11] is used for solving the economic dispatch considering the generator constraints. Gaing [14] introduced Particle swarm optimization to solving the economic dispatch considering the generator constraints. This paper compares the result with a particle swarm optimization (PSO) method for solving the economic and emission dispatch (ED) problem in power systems. A newly nature based optimization technique Ant Lion Optimization Algorithm (ALO) is developed based on the hunting mechanism of ant lions. Five main steps of killing, such as the random walk of ants, making trap, trapping ants, catch victims, and re-building traps are implemented [5]. ALO, developed and is used to solve constrained engineering problems. Yet many researches have been carried out to find the closest optimum result in determining the power generation of each generator using. Many nonlinear characteristics of the generator, such as ramp rate limits, prohibited operating zone, and non-smooth cost functions are considered using the proposed method. In this paper, we had studied multiple algorithms to come up with Ant Lion Optimization algorithm for solving Economic dispatch problems. 2. PROBLEM FORMULATION The minimum cost for operation is obtained by economic allocation of loads between different generating units. Objective function that need to be minimized for the economic dispatch considering the valve point effect is given by (1) Where F(P) is total fuel cost, ai, bi, ci, are fuel cost coefficients of i th generator & fi, ei are valve point coefficients. The total emission of various pollutants is expressed as the quadratic equation given below. (2) editor@iaeme.com

3 Faseela C.K and Dr. Vennila A. POWER BALANCE CONSTRAINT The power balance equation [1] is given by Adding loss factor to the equation. (3.i) Power loss PL is calculated as (3.ii) (3.iii) The actual power generation for the generator will be between its maximum and minimum limits which is represented as (3.iv) 3. ANT LION OPTIMIZATION ALGORITHM Now Bio inspired algorithms are commonly used considering its effectiveness in solving the problems when all the constraints are met. Ant Lion optimization algorithm[13] makes use of hunting mechanism of ant lions to capture its prey. A. INSPIRATION Figure 1 Cone-shaped traps and hunting behavior of antlions The antlions belong to the insect family of Myrmeleontid. The larvae of antlions have specific behavior with respect to the predatory characters for catching its prey. Antlion larva digs small cone-shaped pit in sand by throwing out sands with its unique jaw, after moving along circular paths. Fig 1 shows many such cone-shaped pits containing antlion larvae. After digging these pits, the antlion larvae sit hiding underneath the bottom part of the cone and waits for the insects to come as indicated in the figure-1. The edge of the cone is made very sharp to make the insects fall easily to the bottom of the pit and the complete trap is set. However, the insects trapped has its own adaptation to try to escape from the trap. In this case antlions act further intelligently by throwing out sands towards the edge of the pits and making the insects to slip completely and fall into the bottom of the pit. When the insect is caught in its jaw, antlion pulls the same underneath the soil and consumes the same. After consumption, antlion throws the remains of the insect out of the cone and amends the pit to be ready for another hunt editor@iaeme.com

4 Merit Order Dispatch Using ANT Lion Optimization Algorithm Another peculiar behavior of antlions is also to be noted. The size of the cone trap varies on two things 1) Level of hunger & 2) Shape of the moon. If level of hunger is more, antlions are desperate for a catch which make large pit size. When there is enough moon light the insects have better vision, which makes the need for better trap. This way their adaptability for the catch and chances for survival gets improved. Also, its observed by the biologists that antlions does not view the size of the moon or check the light to make this decision, but they have a calculation of internal lunar clock to make these decisions. The ALO algorithm is developed completely taking inspiration from this unique and peculiar behavior of antlion larvae. In the next subsection, these behaviors of antlions are mathematically modelled. An effective optimization algorithm, termed as Ant Lion Optimization [ALO] is then developed based on this mathematical model. This is used for the merit dispatch problem to derive at the optimal solution. B. OPERATORS OF ALO ALGORITHM During optimization, the following conditions of ants and ant lions are applied: Ants move around the observed space making use of different random walks. An indication of the same is given in figure 2. These random walks are applied to all the dimension of ants. Random walks are being affected by the traps of antlions, which makes it to follow different path. Antlions build pits proportional to their fitness function (the higher fitness [more hungry or full moon] the larger pit). Antlions with wider / larger pits have the higher probability to catch ants. Each ant can be caught by an antlion in each iteration and this is treated as the elite (fittest antlion). The range of random walk is decreased adaptively to simulate sliding ants towards antlions. The fitness of ants is measured by its chances of being caught by antlions. I.e. If an ant becomes fitter than an antlion, this means that it is caught and pulled under the sand by the antlion. An antlion reiterates / repositions itself to the latest caught prey and builds another pit to improve its change of catching another prey after each hunt. Figure 2 Random walks ants for modeling Random walks of ants are considered for modeling (Fig 2) editor@iaeme.com

5 Faseela C.K and Dr. Vennila (4) where cumsum calculates the cumulative sum, n is the maximum number of iteration, t shows the step of random walk (iteration in this study), and r(t) is a stochastic function defined as follows (5) The position of ants with respect to antlions are saved and being used during optimization in the following matrix: (6) Fitness of ants are considered as the probability of the same being caught by antlion. For evaluating each ant, a fitness (objective) function is utilized during optimization and the following matrix stores the fitness value of all ants: (7) In addition to the behavior of ants, its assumed that the antlions are also hiding somewhere in the search space (cone shaped pits). In order make use of their positions and fitness values, the following matrices are utilized: (8) A fitness function for antlions are also considered. MOAL is the matrix for saving the fitness of each antlion editor@iaeme.com

6 Merit Order Dispatch Using ANT Lion Optimization Algorithm (9) To keep the random walks within the search space (observed region), they are normalized using the following equation (termed as min max normalization): (10) where ai is the minimum of random walk of i-th variable, bi is the maximum of random walk in i-th variable, c t i is the minimum of i-th variable at t-th iteration, and d t i indicates the maximum of i-th variable at t-th iteration. This equation need to be applied for each iteration. (11) With various methods proposed so far, antlions can create traps according (directly proportional) to their fitness and ants are needed to move randomly. However, when the antlions realize that the ants are being trapped, it throws sands outwards the center of the cone shaped pit, making the ants very little chance to escape. For mathematically modelling this behaviour, the radius of ants random walks hyper-sphere is decreased adaptively. The following equations are being used in this regard: (12) The final stage of hunt is indicated by ants reaching the bottom of the pit and antlion catching the same by its jaw. After this end stage, the antlion pulls the ant inside the sand and consumes its body. For mimicking this process, it is assumed that catching prey occur when ants becomes fitter (goes inside sand) than its corresponding antlion. An antlion is then required to update its position to the latest position of the hunted ant to enhance its chance of catching new prey. The following equation is proposed in this regard: (13) editor@iaeme.com

7 Faseela C.K and Dr. Vennila It shows the current iteration, Antlion t j shows the position of selected j-th antlion at t-th iteration, and Ant t i indicates the position of i-th ant at t-th iteration. Elitism is an important characteristic of evolutionary algorithms that allows them to maintain the best solution(s) obtained at any stage of optimization process. In this study, the best antlion obtained so far in each iteration is saved and considered as an elite. Since the elite is the fittest antlion, it should be able to affect the movements of all the ants during iterations. Therefore, it is assumed that every ant randomly walks around a selected antlion by the roulette wheel and the elite simultaneously as follows: (14) where R t A is the random walk around the antlion selected by the roulette wheel at t-th iteration, R t E is the random walk around the elite at t-th iteration, and Ant t i indicates the position of i-th ant at t-th iteration. C. PSEUDO CODE OF ALO ALGORITHM Initialize the first population of ants and antlions randomly [Np] Calculate the fitness of ants and antlions Find the best antlions and assume it as the elite (determined optimum) [Pelite] while the end criterion is not satisfied [t<ni_max] for every ant [1.. Np] Select an antlion using Roulette wheel [Pselec] Update c and d using equations Eqs. 12 Create a random walk and normalize it using Eqs. 4 and 10 [ RS(t) or RE(t)] Update the position of ant using Eq.14 end Calculate the fitness of all ants Replace an antlion with its corresponding ant if it becomes fitter (Eq.12) Update elite if an antlion becomes fitter than the elite end while Return elite 4. ALO FOR ECONOMIC DISPATCH CASE Merit order dispatch case is implemented using ALO algorithm. The Economic dispatch case implementation is done on standard IEEE 30 bus system. As it s a standard test system, various parameters had already been recorded. This system was used in many comparable studies in the merit order dispatch. A. IEEE-30 BUS SYSTEM SAMPLE VALUES This system has 6 generator buses at bus 1, 2, 5, 8, 11 and 13. Each of these generators has their own fuel and emission coefficients. These are represented in per unit values to simplify calculations. The base considered is 100 MVA. The total demand considered is 2.38 p.u. The various generation parameters are tabulated as follows, editor@iaeme.com

8 Merit Order Dispatch Using ANT Lion Optimization Algorithm Generator cost coefficients for IEEE 30 bus system is provided in Table 1 given below. Table 1 Sample Cost Coefficients Unit e f Generator emission coefficients for IEEE-30-bus system is provided in Table-2 given below. Table 2 Sample Emission Coefficients Unit E E E E E E B. IEEE-30 BUS SYSTEM - RESULTS IEEE-30 bus system simulation and implementation of Economic dispatch using ALO is done using MATLAB program. The following are the results obtained in comparison with PSO algorithm. Table 3 Economic Dispatch results using ALO PSO ALO Total Fuel Cost ( ) INR/hr Total Emission ( ) ton/hr Total Emission Cost ( ) INR/hr Total Cost () INR/hr The value is found at each step and results are calculated varying the no of iterations and graph is plotted for the same. The best result is obtained at 125 th iterations and there is no difference afterwards editor@iaeme.com

9 Faseela C.K and Dr. Vennila 5. INFERENCES Ant Lion optimization provides excellent results for an economic dispatch problem in terms of cost optimization and easy convergence. On comparison, the cost optimization of ALO is better than PSO by 1%. There can be further improvements on the algorithm considering the following factors Use combinational algorithms Suggested algorithms are ALO and WOA extracting effective features of both. Include other characteristics of Antlion larvae catching ants especially doing a detailed model on building traps. REFERENCES [1] A.J.WOOD and B.F.Wollenberg, Power Generation, Operation And Control. New York: Wiley,1996 [2] Aniruddha Bhattacharya1,Pranab Kumar Chattopadhyay, Solving economic emission load dispatch problems using hybrid differential evolution 31 October 2010 [3] Chao-Lung Chiang, Improved Genetic algorithm for power economic dispatch of units with valve point effects and multiple fuels,ieee Transactions on power systems,vol 20,no.4,NOV.2005,pp [4] E.Lin, G.L. Viviani, Hierarchical Economic Dispatch for piecewise quadratic cost functions, IEEE Transactions on power apparatus and systems, Vol. PAS-103, No.6, june 1984,pp: [5] Girish Kumar, Rameshwar singh, Economic Dispatch of Power System Optimization with Power Generation Schedule Using Evolutionary Technique,International Journal of Advanced Research in Electrical Electronics and Instrumentation Engineering; Vol. 3, Issue 7, July [6] K. S. Kumar, V. Tamilselvan, N. Murali, R. Rajaram, N. S. Sundaram, and T. Jayabarathi, Economic load dispatch with emission constraints using various PSO algorithms, WSEAS Transactions on Power Systems, vol. 3, no. 9, 2008, pp [7] K.S.Lee and Z.W.Geem, A New Structural Optimization Method Based on Harmony Search Algorithm Computers and structures,82, ,2004 [8] Lin WM,Cheng FS,Tsay MT. Nonconvex economic dispatch by integrated artificial intelligence IEEE Trans power syst 2001;16(2); [9] M.Mahdavi, M.Fesanghary, and E.Damangir, An improved harmony search algorithm for solving optimization problems, applied mathematics and computation,vol. 188,pp.1567{1579,2007. [10] P.Ajay-D-Vimal Raj, et.al, Optimal Power Flow Solution for Combined Economic Emission Dispatch Problem using Particle Swarm Optimization Technique Journal of Electrical System JES ;(2007). [11] P.Subbaraja, R.Rengaraj, S.Salivahanan, Enhancement of self adaptive real coded genetic algorithm using Taguchi method for economic dispatch problem, Applied Soft Computing, pp: [12] Seyedali Mirjalili, The Ant Lion Optimizer, / 2015 Elsevier Ltd, pp , March [13] M. Venkatesh and B. Jagannath Yadav, A Novel Approach to Optimal Design of PI Controller of Doubly Fed Induction Generator using Particle Swarm Optimization. International Journal of Electrical Engineering & Technology, 8(1), 2017, pp editor@iaeme.com

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