Performance Parameters for Converters

The role of a rectifier circuit is to produce a dc output voltage from an ac sinusoidal source. The rectifier's output is not pure d.c. and it contains ripple superimposed on its d.c. content and the current drawn from the ac source is not sinusoidal either. It contains some fundamental component and harmonics. For the output voltage, its ripple content is the performance criterion. It would be desirable to obtain the amplitude frequency spectrum of the output of the rectifier in order to design a suitable filter circuit. However there is no mention of how to design a filter in this page.

As far as the ac source is concerned, the distortion in the source current is the performance criterion. The total harmonic distortion(THD) or the harmonic factor, the amplitude frequency spectrum of the source current, the apparent power factor and the displacement power factor have also to be computed. In addition, the crest factor is also to be computed, to facilitate the selection of the proper SCR.

Given a periodic function f(t) with a period of T, f(t) can be described by a trigonometric Fourier series, as shown in equation (4). The coefficients are defined as shown in equations (5), (6) and (7).

In the equations above, * is used to in place of the product sign and it should not be confused with the same symbol used for indicating convolution integrals. The source frequency, f, is taken as the fundamental and hence w_o = 2pf. It is preferable to express the above equation in terms of angle q, where q = w_ot. If T is the cycle period, w_oT = 2p fT = 2p, since f = 1/T. Then the equations for the Fourier coefficients can be expressed as shown in equations (8), (9) and (10).

In the case of the full-wave bridge rectifier circuit, the period of the output is only half that of the input sinusoidal source and hence the output contains a dc component and even harmonics only. The source current has half-wave symmetry. A waveform defined as f(t) over a cycle is said to have half-wave symmetry if it satisfies equation (11). A waveform with half-wave symmetry contains a fundamental component and odd harmonics only.

Let the Fourier coefficients for the output voltage be av₀(a), av_2n(a) and bv_2n(a) , where a is the firing angle and these coefficients are evaluated as shown in equations (12), (13) and (14). Since the output repeats itself twice for every cycle of source voltage, it contains only even harmonics. Then we obtain the amplitude of the harmonic as shown in equation (16).

Let the Fourier coefficients for the source current be acur₀(a), acur_2n(a) and bcur_2n(a) . The line current waveform has half-wave symmetry and contains only odd harmonics. When the SCRs are assumed to be ideal, load current i_Line(q) is defined by equation (17).

For the case where the load is purely resistive, the r.m.s. source current can be computed from the value obtained for the output voltage, as shown in equation (22). Then the total harmonic distortion is defined by equation (23). Let the r.m.s current when the firing angle is 0^o be I_rms,max. Since the waveform of the source current is purely sinusoidal when the firing angle is 0^o, the crest factor can be taken to be square root of 2. The program that simulates the operation of this circuit computes the various values for a given firing angle and displays them in a suitable manner.

The displacement power factor, DPF, is the cosine of the angle by which the fundamental component of the line current lags the source voltage. Then apparent power factor can be estimated as shown in equation (24).

 
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