Figure 11.1 Basic three-phase rectifier bridge in .NET

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Figure 11.1 Basic three-phase rectifier bridge
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independent of the current and should therefore play an insignificant part in the commutation process since all ,valvescommutating on the same side of the bridge suffer similar drops. Such a voltage drop is taken into account by adding it to the d.c. line resistance. The transformer windings resistance is also ignored in the development of the equations, though it should also be included to calculate the power loss.
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(ii) The converter transformer leakage reactances as viewed from the secondary terminals are identical for the three phases, and variations of leakage reactance caused by on-load tap-changing are ignored.
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(iii) The direct current ripple is ignored, i.e. sufficient smoothing inductance is assumed on the d.c. side.
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Rectifier loads can use diode and thyristor elements in full or half-bridge configurations. In some cases the diode bridges are complemented by transformer on-load tap-changer and saturable reactor control. Saturable reactors produce the same effect as thyristor control over a limited range of delay angles. Referring to the voltage waveforms in Fig. 11.2. and using as time reference the
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Figure 11.2 Diode rectifier waveforms: (a) alternating current in phase '& (b) common anode (ca) and cathode (cc) voltage waveform; (c) rectified voltage
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instant when the phase to neutral voltage in phase b is a maximum, the commutating voltage of valve 3 can be expressed as:
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eb - e, = f i a
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where a is the off-nominal tap-change position of the converter transformer. The shaded area in Fig. II.2(b) indicates the potential difference between the common cathode (cc) and common anode (ca) bridge poles for the case of uncontrolled rectification. The maximum average rectified voltage is therefore (11.2.1) 4 3 However, uncontrolled rectification is rarely used in large power conversion. Controlled rectification is achieved by phase-shifting the valve conducting periods with respect to their corresponding phase voltage waveforms. With delay angle control the average rectified voltage (shown in Fig. 11.3) is thus (11.2.2) In practice the voltage waveform is that of Fig. 11.4, where a voltage area (6A) is lost due to the reactance (X,) the a.c. system (as seen from the converter), referred of to as commutation reactance. The energy stored in this reactance has to be transferred from the outgoing to the incoming phase, and this process results in a commutation or conduction overlap angle (u). Referring to Fig. 11.4, and ignoring the effect of resistance in the commutation circuit, area 6 A can be determined as follows:
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eb - e, = 2-
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Figure I13 Thyristor-controlledwaveform:(a)alternatingcurrent in phase & (b)rectified d.c. voltage waveforms
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Figure 11.4 Effect of commutation reactance: (a) alternating current; (b) d.c. voltage waveforms
where e,, eb are the instantaneous voltages of phases a and b respectively, and i, is the incoming valve (commutating) current. Hence
Finally, by combining equations (11.2.1), (11.2.2) (11.2.4) following a.c.-d.c. and the voltage relationship is obtained:
It must be emphasised that the commutating voltage (V,,,,) is the a.c. voltage at the closest point to the converter bridge where sinusoidal waveforms can be assumed. The commutation reactance (X,) the reactance between the point at which V,,,, is exists and the bridge. Where filters are installed the filter busbar voltage can be used as V,,,. In the absence of filters, V,,,, must be established at some remote point and X, must be modified to include the system impedance from the remote point to the converter. With perfect filtering, only the fundamental component of the current waveform will appear in the a.c. system. This component is obtained from the Fourier analysis of the current waveform in Fig. 11.4,and requires information of i, and I(. Taking as a reference the instant when the line voltage (eb- e,) is zero, equation (11.2.3) be written as can fiaV,,,,sinot
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