Abstract—In distribution systems, shunt capacitors are added in order to reduce the total active power loss and improve the power factor. However, the installation of shunt capacitors in distorted distribution systems will amplify the harmonics distortion level, if it is not placed in a proper location with harmonics consideration. Therefore, to take into account the presence of harmonic distortion, this paper proposes a simplified direct search algorithm to determine capacitors placement and sizing in distorted distribution systems. This algorithm is connected to harmonic power flow to search the proper location and size of shunt capacitors, which can decrease the total active power loss and increase the power factor, while the total harmonic distortion does not exceed the maximum allowable harmonic distortion level at each bus. To validate the method proposed, this algorithm is tested on 13-bus radial distribution system and 34-bus radial distribution system with harmonic current injection in order of 5, 7, 11, 13, and 17. Index Terms—Shunt capacitors, active power loss, harmonic power flow, simplified direct search algorithm. I. INTRODUCTION In distribution systems, shunt capacitors are installed to compensate reactive power, reduce active power loss, adjust power factor, and improve voltage profile [1]. However, in radial distribution systems, the presence of harmonic distortion have to be considered for compensating reactive power by adding shunt capacitors. Because the installation of shunt capacitors in the distorted distribution systems can cause resonances, increase active power loss, extensive reactive power demand, and overvoltage, if determining the location and size of capacitors without considering the presence of harmonics in the systems [2]. Many research have taken into account the presence of harmonic current and voltage to optimize the placement and size of shunt capacitors using different methods, such as Genetic Algorithm(GA) [1], Genetic Algorithm with Fuzzy Logic (GA-FL) [2] and Fuzzy Set Theory (FST) [3] in a balanced three-phase systems. Moreover, in unbalanced three-phase system, Particle Swarm Optimization (PSO) [4] and Harmony Search Approach (HSA) [5] have been applied to find the optimal location and size of shunt capacitors in the distorted distribution systems. Manuscript received August 20, 2013; revised December 16, 2013. This work was supported by Brawijaya University and Power Systems Simulation Laboratory, Department of Electrical Engineering, Sepuluh Nopember Institute of Technology (ITS). Fitriana Suhartati is with Department of Electrical Engineering, Brawijaya University, Malang 65145 Indonesia (e-mail: fitrianas@ub.ac.id). Dimas Fajar U. P., Ontoseno Penangsang, and Adi Soeprijanto are with the Power Systems Simulation Laboratory, Department of Electrical Engineering, Sepuluh Nopember Institute of Technology (ITS), Surabaya 60111 Indonesia. (e-mail: dimasfup@gmail.com). This paper proposes a simplified direct search algorithm to determine the efficient location and size of capacitors [6] in distorted radial distribution systems, in order to minimize active power loss, improve power factor, and suppress the harmonic distortion level. The previous paper [6] applied a direct search algorithm for capacitive compensation in radial distribution systems, but the system does not contain any harmonics. In this paper, to consider harmonic distortion, a harmonic power flow algorithm based on backward-forward sweep technique [7] is implemented simultaneously with radial distribution power flow for the fundamental component [8]. II. PROBLEM FORMULATION A. Objective Function The objective function(1) is minimized to determine the efficient location and size of capacitors [9]: P l =P l 1 +  P l h h max h=h 0 (1) where   : total active power loss (kW);   1 : fundamental component of total active power loss (kW);   ℎ : harmonic component of total active power loss (kW); h : the harmonic order; h 0 : the smallest harmonic order; h max : the highest harmonic order; B. Constraints In order to find the best location and size of shunt capacitors which not amplify the harmonic distortion, it is need to limit the power factor, The Total Harmonic Distortion (THD), and the number of compensators by the following constraints: 1) The power factor of each bus is not allowed less than 0.8. 2) THD of each bus is kept less or equal to 5% as recommended by the IEEE standard 519-1992 [7]. The THD of the ith bus is defined by [7]: max 0 2 () 2 (1) (%) h h h h i i i V THD V    (2) where THD i : the total harmonic distortion of the ith bus(%);   1  : the magnitude of bus voltage at the fundamental frequency; ( ) h i V : the magnitude of bus voltage at the harmonic frequency; h 0 , h max : the minimum and the maximum harmonic Capacitor Placement and Sizing in Distorted Distribution Systems Using Simplified Direct Search Algorithm Fitriana Suhartati, Dimas Fajar U. P., Ontoseno Penangsang, and Adi Soeprijanto Journal of Clean Energy Technologies, Vol. 2, No. 4, October 2014 317 DOI: 10.7763/JOCET.2014.V2.147