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Journal of Automation and Control Engineering Vol. 3, No. 3, June 2015 Controlling Voltages and Reduction of Real Power Loss in Power System by Using Crossbreed Spiral Dynamics Bacterial Chemotaxis Algorithm K. Lenin and B. Ravindranath Reddy, Jawaharlal Nehru Technological University Kukatpally, Hyderabad 500 085, India Email: gklenin@gmail.com  evolutionary and heuristic algorithms such as Genetic Algorithm (GA) [2], Differential Evolution (DE) [8] and Particle Swarm Optimization (PSO) [9]. In [10] developed a hybrid optimization algorithm - combining bacterial foraging optimisation algorithm (BFA) with BBO, and referred to it as intellectual biogeography based optimization. In [11] introduced a hybrid description of BFA with differential evolution (DE) algorithm called chemotaxis differential evolution. In [12] introduced a hybrid algorithm BPSO-DE synergizing BFA, particle swarm optimization (PSO), and DE to solve dynamic economic dispatch problem with valvepoints effect. Bacterial. This paper presents hybrid version [13]-[14] of bacterial foraging algorithm (BFA) chemotaxis strategy and spiral dynamics algorithm (SDA).The proposed Algorithm is tested on IEEE30-bus system for evolution of effectiveness of it. Results obtained from CSDBCA are powerful than other algorithms in solution of ORPD problem. Abstract—In this paper a new hybrid optimization algorithm, referred to as Crossbreed spiral dynamics bacterial chemotaxis algorithm (CSDBCA) is proposed to solve the optimal reactive power dispatch (ORPD) Problem. CSDBCA synergizes bacterial foraging algorithm (BFA) chemotaxis approach and spiral dynamics algorithm (SDA). The original BFA has higher convergence speed while SDA has better accuracy and stable convergence when approaching the optimum value. This crossbreed approach conserves the strengths of BFA and SDA. So the CSDBCA has the capability of producing superior results. In order to evaluate the proposed algorithm, it has been tested on IEEE 30 bus system consisting 6 generators and compared other algorithms and simulation results show that CSDBCA is more efficient than others in solving the reactive power dispatch problem. Index Terms—spiral dynamics, bacterial chemotaxis, optimization algorithm, optimal reactive power dispatch, power system. II. FORMULATION OF ORPD PROBLEM I. INTRODUCTION The objective of the ORPD problem is to minimize the objective functions by satisfying a number of constraints such as load flow, generator bus voltages, load bus voltages, switchable reactive power compensations, reactive power generation, transformer tap setting and transmission line flow. In modern years the optimal reactive power dispatch (ORPD) problem has established a huge attention as a result of the development on economy and security of power system operation. Solutions of ORPD problem plan to minimize real power loss by satisfying number of constraints like limits of bus voltages, tap settings of transformers, reactive and active power of power resources and transmission lines and controllable Variables [1], [2].At the beginning, a number of classical methods such as gradient based [3], interior point [4], linear programming [5] and quadratic programming [6] have been effectively used in order to solve the ORPD problem. However, these methods had some disadvantages in the method of solving the complex ORPD problem. Drawbacks of these algorithms can be confirmed by their insecure convergence properties, long execution time, and algorithmic complexity and can be trapped in local minima [1], [7]. In order to prevail over these disadvantages, researches had successfully applied A. Minimization of Real Power Loss Minimization of 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. B. Minimization of Voltage Deviation Minimization of the Deviations in voltage magnitudes (VD) at load buses is mathematically stated as follows. Minimize VD = ∑ Manuscript received May 5, 2014; revised August 1, 2014. ©2015 Engineering and Technology Publishing doi: 10.12720/joace.3.3.233-236 (1) 233 | | (2) Journal of Automation and Control Engineering Vol. 3, No. 3, June 2015 where nl is the number of load busses and V k is the voltage magnitude at bus k. C. System Constraints In the minimization process of objective functions, some problem constraints which one is equality and others are inequality had to be met. Objective functions are subjected to these constraints shown below. Load flow equality constraints: ∑ ] [ (3) ∑ ] [ (4) IV. SPIRAL DYNAMICS INSPIRED OPTIMIZATION ALGORITHM where, nb is the number of buses, PG and QG are the real and reactive power of the generator, P D 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: The SDA is a different metaheuristic algorithm adopted from spiral phenomena in nature [13].Furthermore; comparisons with other optimization algorithms [13] such as PSO and DE have shown that SDA performance is better. This simple and effectual approach retains the diversification and amplification at the early phase and later phase of the trajectory as diversification and amplification are important characteristics of the optimization algorithm. At the initial stage, the spiral trajectory explores a wider search space and it incessantly converges with a smaller radius providing dynamics step size when close to the final point, which is the best solution, situated at the centre. The distance between a point in a path trajectory and the centre point is varied regularly. The radius of the trajectory is altering at steady rate thus making the radius an important converging parameter for the algorithm. The strength of SDA lies in its spiral dynamics model. An n-dimensional spiral mathematical model that is derived using composition of rotational matrix based on combination of all 2 axes is given as: (18) Load bus voltage (VLi) inequality constraint: (19) Switchable reactive inequality constraint: power compensations sail and it happens when the E. Coli navigates in the search area and once the food source is found, and it swims like ambushing a objective area with enormous speed, up to 20μm/s or faster in a rich nutrient medium. This exclusive movement is called chemotaxis. Reproduction, elimination and dispersal events then happen to bacteria with high fitness that has capability to reach food source precisely and rapidly. The details of the original algorithm and pseudo code of BFA can be found in [20]. In this paper, number of bacteria, number of chemotaxis, chemotactic step size, number of swims, number of reproduction, number of elimination & dispersal are represented as S, Nc, C, Ns, Nre and Ned respectively. The probability that each bacterium will be eliminated and dispersed is defined as ped and its value 0.25 for our problem. (QCi) (20) Reactive power generation (QGi) inequality constraint: (21) Transformers tap setting (Ti) inequality constraint: (22) Transmission line flow (SLi) inequality constraint: (23) (24) where, nc, ng and nt are numbers of the switchable reactive power sources, generators and transformers. where ( III. BACTERIAL FORAGING OPTIMIZATION ALGORITHM and The BFA is a biologically inspired algorithm introduced in [15]. It is based on adaptation technique of Escherichia Coli (E. Coli) bacteria to find out nutrient or food source throughout their lifetime and the method is called bacterial foraging strategy. One of the outstanding characteristics of E. Coli is that it has very high augmentation rate, which is normally exponential. Bacterial foraging strategy consists of three fundamental sequences namely chemotaxis, reproduction and elimination & dispersal. These sequences are rolling processes and are effective for optimization purposes [16].When searching for food or nutrient, plummeting and swimming will take place. Plummeting is similar to ©2015 Engineering and Technology Publishing ( ) ) [ [ where - Bacteria angular displacement on around the origin. - Spiral radius ] ] plane V. CROSSBREED SPIRAL DYNAMICS BACTERIAL CHEMOTAXIS ALGORITHM 234 Journal of Automation and Control Engineering Vol. 3, No. 3, June 2015  -Maximum iteration number  m – Number of search points  Ns - Maximum number of swim  xi (k)- Bacteria position n  R - n x n matrix In this planned approach, bacterial chemotaxis strategy is employed in step 3 to balance and augment exploration and exploitation of the search space. The bacteria move from low nutrient location in the direction of higher nutrient location, located at the centre of a spiral. The most significant feature of CSDBCA algorithm is the particular diversification and amplification at the early phase and later phase of the spiral motion. In the diversification phase, bacteria are located at low nutrient location and move about with larger step size thus producing quicker convergence. On the other hand, in the amplification phase, bacteria are approaching rich nutrient location and move about with smaller step size hence avoiding fluctuation around the optimum point. Another factor contributing to superior performance of the algorithm is the swimming action in bacterial chemotaxis. Bacteria continuously swim towards optimum point if the next location has superior nutrient value compared to previous location until the maximum number of swim is reached. The CSDBCA is a mixture of bacterial chemotaxis approach used in BFA and SDA. BFA has quicker convergence speed due to the chemotaxis approach, but suffers from fluctuation problem towards the end of its search method. On the other hand, SDA provides superior stability when approaching optimum point due to dynamic spiral pace in its trajectory motion but has sluggish convergence speed. CSDBCA algorithm conserves the strengths possessed by both BFA and SDA. CSDBCA for solving optimal reactive power problem. Step 1: Training choose the number of search points (bacteria) m ≥ 2 , parameters0 ≤θ < 2π , 0

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