MODELLING AND ANALYSIS OF THREE PHASE CONTROLLED RECTIFIERS USING PIVOTAL FUNCTION TECHNIQUE

Abstract

This paper describes the extension of pivotal function approach to deriving the mathematical representation of the input current of a controlled three phase bridge rectifier circuit. The basis is that a single thyristor and its associated rectifier circuits could be modelled as a pivotal function which relates the input voltage and current with load resistance. In the conduction region the thyristor behaves as a double P-N junction diode, which implies that it could be modelled as a pivotal function with the conduction interval controlled by a gate firing pulse. On this projection is based the development of a thyristor controlled rectifier model in this paper beginning with the mathematical expression of a thyristor current. The model equation was derived in a manner as to include or exclude the effect of source inductance for flexible applications. Considering the effect of source inductance resulted in a non-linear second order ordinary differential equation with the inverse pivotal function as the second coefficient. The model was also modified to cater for cases involving unbalanced three phase supply voltages.  Simulation result on the studied circuit based on the derived model expression compared with its counterpart from Simpower simulation has established that the pivotal function technique reflects properly the regulating behavior of a thyristor. The derived model was deployed in analyzing the waveforms and harmonic profile of the distorted input current of the studied circuit at different firing angles. The result has established that the derived model will further enhance the analysis of controlled rectifiers in resonance studies.