Simplified Techniques for Estimation of Compensator Impedances in Power Systems

In this paper, simplified methods for estimation of load compensator impedances for a $3-\phi, 3$ wire balanced AC system with an unbalanced load are discussed. Conventionally, two estimation techniques were proposed in the literature based on instantaneous symmetrical component theory 1) Averaging method 2) Sampling method. The equations for the averaging method consists of three instantaneous voltages and three instantaneous currents, which require at least two voltage sensors, two current sensors and a microcontroller. In this paper, the equations are modified in such a way that two wattmeters are sufficient to estimate the compensator impedance between any two phases. Sampling method in the literature is based on phase voltage, which is difficult to obtain in a 3 wire system. So, a modified Sampling method is proposed here that is based on line voltages. A case study is presented with 3-phase unbalanced load with balanced supply. Matlab/SIMULINK is used to estimate compensator impedances and dynamic behaviour of a simple power system is demonstrated. Further, the performance of a practical compensator is evaluated at two different values of internal resistance of the compensator.

I. Introduction

The reactive power compensators such as capacitive and inductive banks or synchronous condensers at the three-phase load side are being for many years to improve the power factor at the source [1], [2]. These compensators also help in improving the efficiency of transformers and transmission lines connected between the source and the load. However, these compensators give the best performance only when the load is balanced. A generalized approach for load compensation using symmetrical components for a delta connected unbalanced load is presented in [2]. Detailed derivations and mathematical expressions for load compensator impedances in terms of load impedances are given in [2]. Two compensator impedance estimation methods, namely 1) Averaging method 2) Sampling method was described in the above literature [2], [3]. These methods require at least two current sensors, two voltage sensors, and a data acquisition system (DAS) or complex analog circuits for their implementation. Further, programming is necessary to evaluate the expressions for compensator impedances.