This paper presents an optimization problem formulation for allocation and sizing of single tuned passive filters in power distribution systems with the objective of minimizing total harmonic distortion. Inequality constraints are considered to determine upper and lower bounds for power factor correction, tuned frequency, voltage unbalance factor, voltage magnitudes and harmonic distortion based on power quality standard limits. The optimization problem is solved using genetic algorithm in which the filters locations, their connection types and parameters for each phase of the system are determined. Simulations are carried out using three-phase unbalanced 33-bus and 69-bus distribution test feeders to demonstrate the viability and efficiency of the proposed formulation to obtain results with total harmonic distortion lower than 5%, voltage unbalance factor lower than 1%, power factor greater than 0.92 and voltage magnitudes between acceptable limits. The main contributions of this paper are the formulation considering multiple power quality indexes in three-phase unbalanced distribution systems, the possibility of the filters to be connected in Y or Δ to satisfy the objective function and the constraints of the optimization problem. Additionally, security constraints related to the operation of the capacitor banks of the filters are considered in this paper.

Introduction

The main consequence of using loads with non linear characteristics and power electronic based devices is the generation of harmonic components in electric power systems [1]. Their proliferation causes several problems such as malfunction of machines, electronic equipment, protection relays, telecommunication conflicts, increasing of power losses, temperature rise in cables and overhead lines [2]. It is extremely important to mitigate and reduce harmonic levels in power grids for power quality improvement. There are many different solutions for harmonic mitigation, including passive, active and hybrid filters. Passive filters are often used for bigger installations due to lower cost when compared to other alternatives [3] and simplicity of implementation and maintenance [2]. They are basically shunt devices, which consist of the connection of inductors, capacitors and resistors that in a specified tuned frequency act as a resonant element with low impedance, forcing the current at that specified frequency to be absorbed, flowing to the earth. Harmonic filters are generally installed in sensitive parts of the networks with large non linear loads and higher harmonic distortion levels for mitigation purpose. However, their allocation is not a trivial task when the objective is to provide a global benefit to a power system in which they are allocated, once they can improve not only harmonic distortion but also provide power factor correction in industrial plants [4] and voltage profile improvement of power systems [3]. Depending on the filters location, harmonic distortion can increase at other nodes of the system according to [5]. Consequently, it is necessary to analyze the filters allocation and sizing with adequate methodologies.