# Three-phase Rectifiers

Jan 04, 2018

### Three-phase rectifiers

Single-phase rectifiers are commonly used for power supplies for domestic equipment. However, for most industrial and high-power applications, three-phase rectifier circuits are the norm. As with single-phase rectifiers, three-phase rectifiers can take the form of a half-wave circuit, a full-wave circuit using a center-tapped transformer, or a full-wave bridge circuit.

Thyristors are commonly used in place of diodes to create a circuit that can regulate the output voltage. Many devices that provide direct current actually generate three-phase AC. For example, an automobile alternator contains six diodes, which function as a full-wave rectifier for battery charging.

#### Three-phase, half-wave circuit

Controlled three-phase half-wave rectifier circuit using thyristors as the switching elements, ignoring supply inductance

An uncontrolled three-phase, half-wave midpoint circuit requires three diodes, one connected to each phase. This is the simplest type of three-phase rectifier but suffers from relatively high harmonic distortion on both the AC and DC connections. This type of rectifier is said to have a pulse-number of three, since the output voltage on the DC side contains three distinct pulses per cycle of the grid frequency:

The peak values of this three-pulse DC voltage are calculated from the RMS value {\displaystyle V_{\mathrm {LN} }} of the input phase voltage (line to neutral voltage, 120 V in North America, 230 V within Europe at mains operation): {\displaystyle V_{\mathrm {peak} }={\sqrt {2}}\cdot V_{\mathrm {LN} }}. The average no-load output voltage results from the integral under the graph of a positive half-wave with the period duration of (from 30° to 150°):

#### Three-phase, full-wave circuit using center-tapped transformer

Controlled three-phase full-wave rectifier circuit using thyristors as the switching elements, with a center-tapped transformer, ignoring supply inductance

If the AC supply is fed via a transformer with a center tap, a rectifier circuit with improved harmonic performance can be obtained. This rectifier now requires six diodes, one connected to each end of each transformer secondary winding. This circuit has a pulse-number of six, and in effect, can be thought of as a six-phase, half-wave circuit.

Before solid state devices became available, the half-wave circuit, and the full-wave circuit using a center-tapped transformer, were very commonly used in industrial rectifiers using mercury-arc valves.[4] This was because the three or six AC supply inputs could be fed to a corresponding number of anode electrodes on a single tank, sharing a common cathode.

With the advent of diodes and thyristors, these circuits have become less popular and the three-phase bridge circuit has become the most common circuit.

#### Three-phase bridge rectifier uncontrolled

Disassembled automobile alternator, showing the six diodes that comprise a full-wave three-phase bridge rectifier.

For an uncontrolled three-phase bridge rectifier, six diodes are used, and the circuit again has a pulse number of six. For this reason, it is also commonly referred to as a six-pulse bridge. The B6 circuit can be seen simplified as a series connection of two three-pulse center circuits.

For low-power applications, double diodes in series, with the anode of the first diode connected to the cathode of the second, are manufactured as a single component for this purpose. Some commercially available double diodes have all four terminals available so the user can configure them for single-phase split supply use, half a bridge, or three-phase rectifier.

For higher-power applications, a single discrete device is usually used for each of the six arms of the bridge. For the very highest powers, each arm of the bridge may consist of tens or hundreds of separate devices in parallel (where very high current is needed, for example in aluminium smelting) or in series (where very high voltages are needed, for example in high-voltage direct current power transmission).

Controlled three-phase full-wave bridge rectifier circuit (B6C) using thyristors as the switching elements, ignoring supply inductance

The pulsating DC voltage results from the differences of the instantaneous positive and negative phase voltages {\displaystyle V_{\mathrm {LN} }}, phase-shifted by 30°:

The ideal, no-load average output voltage of the B6 circuit results from the integral under the graph of a DC voltage pulse with the period duration of  (from 60° to 120°) with the peak value {\displaystyle {\hat {v}}_{\mathrm {DC} }={\sqrt {3}}\cdot V_{\mathrm {peak} }}:

3-phase AC input, half-wave and full-wave rectified DC output waveforms

If the three-phase bridge rectifier is operated symmetrically (as positive and negative supply voltage), the center point of the rectifier on the output side (or the so-called isolated reference potential) opposite the center point of the transformer (or the neutral conductor) has a potential difference in form of a triangular common-mode voltage. For this reason, the two centers must never be connected to each other, otherwise short-circuit currents would flow. The ground of the three-phase bridge rectifier in symmetrical operation is thus decoupled from the neutral conductor or the earth of the mains voltage. Powered by a transformer, earthing of the center point of the bridge is possible, provided that the secondary winding of the transformer is electrically isolated from the mains voltage and the star point of the secondary winding is not on earth. In this case, however, (negligible) leakage currents are flowing over the transformer windings.

The common-mode voltage is formed out of the respective average values of the differences between the positive and negative phase voltages, which form the pulsating DC voltage. The peak value of the delta voltage amounts ¼ of the peak value of the phase input voltage  and is calculated with  minus half of the DC voltage at 60° of the period:

The RMS value of the common-mode voltage is calculated from the form factor for triangular oscillations:

• If the circuit is operated asymmetrically (as a simple supply voltage with just one positive pole), both the positive and negative poles (or the isolated reference potential) are pulsating opposite the center (or the ground) of the input voltage analogously to the positive and negative waveforms of the phase voltages. However, the differences in the phase voltages result in the six-pulse DC voltage (over the duration of a period). The strict separation of the transformer center from the negative pole (otherwise short-circuit currents will flow) or a possible grounding of the negative pole when powered by an isolating transformer apply correspondingly to the symmetrical operation.

#### Three-phase bridge rectifier controlled

The controlled three-phase bridge rectifier uses thyristors in place of diodes. The output voltage is reduced by the factor cos(α):

• Or, expressed in terms of the line to line input voltage:[5]

Where:

• VLLpeak, the peak value of the line to line input voltages,

• Vpeak, the peak value of the phase (line to neutral) input voltages,

• α, firing angle of the thyristor (0 if diodes are used to perform rectification)

The above equations are only valid when no current is drawn from the AC supply or in the theoretical case when the AC supply connections have no inductance. In practice, the supply inductance causes a reduction of DC output voltage with increasing load, typically in the range 10–20% at full load.

The effect of supply inductance is to slow down the transfer process (called commutation) from one phase to the next. As result of this is that at each transition between a pair of devices, there is a period of overlap during which three (rather than two) devices in the bridge are conducting simultaneously. The overlap angle is usually referred to by the symbol μ (or u), and may be 20 30° at full load.

With supply inductance taken into account, the output voltage of the rectifier is reduced to:

Where:

• Lc, the commutating inductance per phase

• Id, the direct current

 Three-phase Graetz bridge rectifier at alpha=0° without overlap Three-phase Graetz bridge rectifier at alpha=0° with overlap angle of 20°
 Three-phase controlled Graetz bridge rectifier at alpha=20° with overlap angle of 20° Three-phase controlled Graetz bridge rectifier at alpha=40° with overlap angle of 20°

#### Twelve-pulse bridge

Twelve pulse bridge rectifier using thyristors as the switching elements

Although better than single-phase rectifiers or three-phase half-wave rectifiers, six-pulse rectifier circuits still produce considerable harmonic distortion on both the AC and DC connections. For very high-power rectifiers the twelve-pulse bridge connection is usually used. A twelve-pulse bridge consists of two six-pulse bridge circuits connected in series, with their AC connections fed from a supply transformer that produces a 30° phase shift between the two bridges. This cancels many of the characteristic harmonics the six-pulse bridges produce.

The 30 degree phase shift is usually achieved by using a transformer with two sets of secondary windings, one in star (wye) connection and one in delta connection.