Multiperiod shunt capacitor allocation in radial distribution systems Damanjeet Kaur a,⇑ , Jaydev Sharma b a University Institute of Engineering & Technology, Panjab University, Chandigarh, UT 160 014, India b Indian Institute of Technology, Roorkee 247 667, India article info Article history: Received 3 March 2010 Received in revised form 23 March 2013 Accepted 28 March 2013 Available online 28 April 2013 Keywords: Distribution system Multiperiod PSO ACS abstract In distribution systems, low power factor is a common problem due to inductive nature of the loads. To overcome this problem, generally capacitors are installed on distribution systems. In this paper, to main- tain the voltage profile, a dynamic model considering multiperiod capacitor allocation problem of pri- mary radial distribution system is proposed. The model incorporates the load growth rate, load factor and cost of power and energy losses. This multiperiod optimization problem is solved using a population based swarm method i.e. ACS for minimizing the total cost of the peak power losses and energy losses and cost of capacitor installation from base to horizon year (for the feasible options at each planning year) subject to constraints corresponding to upper and lower bounds of the voltage magnitude at each bus. The feasible set of options for optimal capacitor site and size placement in each single stage problem is obtained using particle swarm optimization To reduce the computational efforts in each stage, the can- didate nodes for placing capacitors in distribution system are determined by calculating change in real power losses with respect to reactive power injection at the buses. The proposed approach has been implemented on 69-bus test system. Ó 2013 Elsevier Ltd. All rights reserved. 1. Introduction In distribution systems, low power factor causes high power losses and thereby degrades the system performance technically (like voltage drop, KVA capacity, losses) as well as economically (e.g. cost of losses). Studies have indicated that approximately 13% of total power generated is consumed as 1 2 R losses at the dis- tribution level [1]. Hence to overcome this problem, it becomes necessary to compensate reactive power in the system. It is a com- mon practice to install capacitors in distribution systems to im- prove power factor and hence to reduce power and energy losses and to improve voltage profile and to release feeder capacity stress/burden. The economical and technical benefits associated with installation of capacitors are influenced by the size, site and time of installation in the distribution system. To achieve these benefits under various operating constraints, distribution planners are required to determine the optimal location, type, size and time of installation of capacitors to be placed. The extent of the benefits from capacitor banks installation depends on electrical network configuration and its load states. The net profit achieved is the amount saved by reducing losses after discounting the investment in equipment acquisition and its installation. Capacitor allocation in distribution networks is a typical optimi- zation problem of great technical and economic importance which has been considered over five decades. In earlier years, different numerical programming methods such as dynamic programming [2,3], local variation method [4], mixed integer [5,6] and integer quadratic programming [7] have been used to solve the capacitor allocation problem. Later on sophisticated methods such as simu- lated annealing [8], heuristic approach [9,10], genetic algorithms [11–15], fuzzy logic [16,17], tabu search [18], MILP [19], ant colony algorithm (ACO), [20,21] and PSO [22,23] based approaches are implemented to solve capacitor allocation problem. The size and location of shunt capacitors are also influenced by load growth factors viz. increase in demand, change in load factor, and escalation in cost of energy [4]. Ponnavaikko and Rao [4] con- sidered growth in load, load factor and cost of energy and solved the problem using direct search technique known as method of lo- cal variations. They solved the developed problem using dynamic programming approach also for comparison purposes. The model developed in [4] considered the load growth factor but the effect of growth factors is not considered in formulations i.e. the model developed is static in nature. This developed model may not give optimum results with increasing load, load factor and cost of energy losses. There is no such model available in the literature which can take into account the load growth in stages and hence there is need to develop a method in which the planning period may be divided into number of stages and load growth is considered stagewise so that total investment required for capaci- tor placement is minimized. In this paper, a dynamic model for capacitor allocation under multiperiod planning is developed. To solve multiperiod problem, 0142-0615/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijepes.2013.03.026 ⇑ Corresponding author. Tel.: +91 9417513030. E-mail addresses: djkb14@rediffmail.com (D. Kaur), jaydsfee@gmail.com (J. Sharma). Electrical Power and Energy Systems 52 (2013) 247–253 Contents lists available at SciVerse ScienceDirect Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes