Mathematical Analysis

Since the load current tends to be discontinuous, two expressions for the average output voltage can be derived, one for the continuous mode and the other for the discontinuous mode. In the continuous mode, the average output voltage is as shown in equation (1). The conduction becomes discontinuous when the firing angle exceeds 60^o and remains less than 120^o. Then the average voltage is obtained as shown in equation (2).

In equations (1) and (2), the amplitude of phase voltage is designated as E and the amplitude of line voltage is designaed as U.

The rms voltage is computed as follows. When a < 60^o, the conduction is continuous and the expression for the rms voltage is presented in equation (3), whereas equation (4) expresses the rms voltage obtained when firing angle a > 60^o.

The ripple factor can be found out as defined in the previous page.

The line/phase current can be defined as follows. Let R-phase voltage be defined to be

v_R(q) = E*Sin (q).

Then the R-phase current i_R(q) is defined as follows, when the conduction is continuous.

From this definition of phase current, the rms line current, the rms of the fundamental in line current and its THD can be found out.

The applet below displays the average output voltage, the rms output voltage, its ripple factor, the rms line current, the fundamental rms content in line current and its THD as a function of firing angle. The peak average output voltage, (3U/p), is taken to be unity and (3U/pR) is set equal to unity, where R is the load resistor.

 
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