##### From The Switching Function: Analysis of Power Electronic Circuits

## 6.1 Introduction

Two cases are examined here: resistive load and inductive load. In the latter case continuous and discontinuous conduction, with and without a free-wheeling diode are considered. Triggering of the thyristor is effected by supplying a positive train of pulses to their gates. Only one thyristor is conducting at a time and it remains conducting until the voltage across it is reversed or the current through it becomes zero. The effect of overlap for the three-phase half-wave phase controlled converter is not examined. Overlap is examined in the next chapter for the full wave system. Its findings can easily be adopted for the half-wave converter.

The delay-firing angle * ?* for the red phase is measured in the usual way from the point of the first crossing of the blue and red phases; hence a fixed delay of 30 always exists for * ?* with reference to the red line. The delay angle for the other two phases is measured in a similar way. The switching function of these circuits is a single pulse, which is repeated for every mains cycle. There are three switching functions, one for each phase, displaced by 120 .

## 6.2 Mathematical Modelling of the Three-phase Half-wave Phase Controlled Converter

The circuit diagram of a half-wave three-phase controlled rectifier with resistive or inductive load is shown in Fig. 6.1. There is one mathematical model valid for continuous and discontinuous conduction including the presence of a free wheeling diode. In each case though the parameters of the...

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