**An ACO Algorithm for Optimal Capacitor Banks Placement in Power Distribution Networks**

**Dinu Călin SECUI**, **Simona DZIŢAC**, **Gabriel Valentin BENDEA**

University of Oradea

ROMANIA

**Ioan DZIŢAC**

Aurel Vlaicu University of Arad & Cercetare Dezvoltare Agora (R&D Agora)

Oradea, ROMANIA

**Abstract**: This paper aims to present and apply an algorithm based on Ant Colony Optimization (ACO) for optimal allocation of capacitor banks in electric power distribution networks. A nonlinear function based on costs is used as a criterion of the mathematical optimization model. Also the model imposes equality constraints described by the network operating equations and inequality constraints required to maintain within admissible limits the parameters characterizing the system state. The algorithm is applied for a test-network having 35 nodes, the results indicating its validity and efficiency.

**Keywords**: Ant colony optimization algorithm (ACO), capacitor banks placement, power loss reduction.

**Dinu C. Secui** received his M.Sc. in Power Engineering (1993) from Technical University of Timisoara and Ph.D. in Energy Engineering (2003) from University of Oradea. Now he is reader at Energy Engineering Faculty, University of Oradea, Romania. His current research interests include different aspects of Reliability in Power Systems and Optimization Techniques in Power Engineering. He has authored 3 books and more than 60 scientific papers in journals and conferences proceedings. He participated at 11 research grants and projects.

**Simona Dziţac** received B.Sc. (2000) and M. Sc. (2001) in Mathematics-Physics, B.Sc. (2005) and M. Sc. (2007) and Ph.D. (2008) in Energy Engineering from University of Oradea and B.Sc. in Economic Informatics (2007) from University of Craiova, Romania. Her current research interests include Reliability, Applied Mathematics and Computer Science in Engineering fields. She (co-)authored 8 books and 65 scientific papers in journals and conferences proceedings.

**Gabriel V. Bendea** received his M.Sc. in Power Engineering (1992) from Technical University of Timisoara and Ph.D. in Energy Engineering (2001) from University of Oradea. Now he is reader at Energy Engineering Faculty, University of Oradea, Romania. His current research interests include different aspects of Power System Reliability and Power Generation. He has authored 6 books and more than 55 scientific papers in journals and conferences proceedings. He participated at 22 research grants and projects.

**Ioan Dziţac** received his M.Sc. in Mathematics (1977) and Ph. D in Information Sciences (2002) from “Babes-Bolyai” University of Cluj-Napoca. Now he is professor at Mathematics-Informatics Department, Aurel Vlaicu University of Arad, Romania and director of R&D Agora, Oradea, Romania. His current research interests include different aspects of Artificial intelligence and Distributed systems. He has (co-)authored 18 books and more than 70 papers, more than 50 de conferences participation, member in International Program Committee of 40 conference and workshops.

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**CITE THIS PAPER AS**:

Dinu Călin SECUI, Simona DZIŢAC, Gabriel Valentin BENDEA, Ioan DZIŢAC, **An ACO Algorithm for Optimal Capacitor Banks Placement in Power Distribution Networks**, *Studies in Informatics and Control*, ISSN 1220-1766, vol. 18 (4), pp. 305-314, 2009.

**1. Introduction**

Power distribution networks (PDN) are important structures within the power system, and therefore the improvement of their performances is set as main target of electricity companies, in the context of market liberalization. To achieve this goal, the optimal placement of capacitor banks in PDN is one of the possible solutions, having multiple positive effects, such as: voltage level and power factor improvement in the network, feeders’ capacity increment, active power losses reducing [1, 2]. All these effects imply lower operating costs for companies. In order the benefits of capacitor banks placement to be as big, they must be positioned and sized correctly using appropriate mathematical models and methods [3, 4, 5].

Most mathematical models used in literature have as objective function minimizing the costs with technical and economic restrictions of inequality and equality, but the solving techniques have diversified over time following the development of computing techniques and algorithms. Regarding the capacitors placement problem within the PDN, the classic techniques are based upon integer programming [6], nonlinear programming (gradient method) [7], but the solutions obtained do not guarantee achieving the optimum. The problem has been addressed successfully by using the techniques of search and optimization based on simulated annealing [8], genetic algorithm [3,9], immune algorithm [10], Particle Swarm Optimization [11, 12, 13], Ant Colony Search Algorithm [1] or hybrid solutions [14, 15].

Capacitor banks placement in PDN is a complex combinatory problem which can be solved using the ability of ant system algorithms [16, 17, 18] or later developed varieties [19, 20], applied in various fields [21, 22, 23, 24].

In this paper, an algorithm based on Ant Colony Optimization (ACO) is presented in order to solve the problem of optimal capacitor banks placement in PDN, considering their layout on the low voltage nodes of the network. Objective function is based on a nonlinear cost model with equality restrictions, described by the equations of the network functioning, and inequality constraints related to the voltage level, voltage drops and capacitors’ limits.

**5. Conclusions and Future Works**

Metaheuristic techniques allow for high quality solutions in case of problems in real, complex and large electrical distribution networks. An algorithm based on ACO metaheuristic was presented and tested for optimal allocation of capacitor banks in a typical PDN having 35 nodes. The algorithm is relatively easy to implement and runs quickly. The results indicate a significant reduction of active power losses in the network and therefore of the costs, and also an improvement of the voltage level. The very close values of the best and the worst solution (*Best F* and *Worst F*) for the objective function obtained for one hundred runs indicate the efficiency of the presented algorithm and the high quality of the solutions.

In the future, the authors will continue their work by developing algorithms based on ACO for multi-objective optimization of capacitor banks allocation in PDN, considering the issues of continuity in consumers supplying.

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