Mathematical Analysis

The aim of analysis is to obtain the following values:

1. The average output voltage of the bridge as a function of firing angle.

2. The rms output voltage of the bridge as a function of firing angle.

3. The ripple factor of output voltage of the bridge as a function of firing angle.

4. The rms line current as a function of firing angle and the ratio wL/R.

5. The fundamental rms line current as a function of firing angle and the ratio wL/R.

6. The THD in line current as a function of firing angle and the ratio wL/R.

The Average Output Voltage

The ripple factor is defined then as

Next it is shown how the line current is to be analysed. An expression for load current over half-a-cycle can be obtained first. The load current during a < wt < p can be defined as follows.

where

From the expression for load current,

The load current during p < wt < (p + a) can be defined as follows.

When the load current is repetitive, we have that

That is,

and

Hence we obtain that

Once A is known, the total rms value of line current and the rms value of its fundamental component can be estimated.

Let

and

Then the rms line current given t and a is obtained as follows.

To obtain the rms value of the fundamental component of the line current, we obtain the trigonometric Fourier series coefficients of the fundamental component. The line current has half-wave symmetry and hence these coefficients are obtained as follows.

Then

We obtain the rms value of fundamental component as:

Total harmonic distortion in line current is then

 
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