Power rectifiers
With a 30° delay, a three-phase thyristor bridge connected to 400 V delivers 468 V instead of 540, and its power factor drops from 0.95 to 0.83. Regulating the voltage with the firing angle consumes reactive power.
01Uncontrolled rectifiers
A diode rectifier delivers a fixed DC voltage, which depends only on the line. With a highly inductive load, the output current is nearly constant and each diode conducts for a portion of the cycle:
| Configuration | Average voltage | Pulses per cycle |
|---|---|---|
| Single-phase bridge | \( \frac{2\sqrt2}{\pi} V \approx 0.90\,V \) | 2 |
| Three-phase bridge (six-pulse) | \( \frac{3\sqrt2}{\pi} V_{LL} \approx 1.35\,V_{LL} \) | 6 |
| Two bridges with a wye-delta transformer | Twice as much, with less ripple | 12 |
With a capacitor at the output, on the other hand, the line current is a series of narrow peaks near the voltage maximum: this is how the rectifiers of nearly all electronic equipment work, and how they pollute the grid with harmonics, a topic of power quality. Active power factor correction is covered in switching power supplies.
02Controlled rectifiers
By replacing the diodes with thyristors, each one is triggered with a delay \( \alpha \) relative to the instant at which a diode would start to conduct. In a three-phase bridge with an inductive load:
The current of each phase is a nearly rectangular 120° wave, shifted by \( \alpha \) relative to its voltage. It contains the harmonics of order \( 6k \pm 1 \) —5, 7, 11, 13…— with amplitudes close to \( 1/h \) of the fundamental, and its power factor is approximately \( 0.955 \cos\alpha \).
A six-thyristor bridge connected to a 400 V, 50 Hz line, with a highly inductive load of constant current Id. Top, the output voltage (blue) and its average value (yellow); bottom, the current of phase a (orange) along with the shape of its voltage, in gray.
03Applications
Controlled rectifiers feed DC motors (DC machines), electrolysis plants, furnaces and high-power battery chargers, and are the basis of high-voltage direct-current transmission, where one bridge rectifies at one end and another, with α close to 150°, inverts at the other. For small and medium powers they were replaced by diode rectifiers followed by a switching converter, or by active rectifiers with transistors, which draw sinusoidal current with unity power factor.
04In the laboratory
With a half-controlled bridge on a resistive and an inductive load, measure the average voltage as a function of the firing angle and compare it with the formula.
With a power quality analyzer, measure the current spectrum of a three-phase bridge and verify orders 5, 7, 11 and 13.
Add inductances in series with the line and observe the notches in the output voltage.
05Common mistakes
- Forgetting the commutation drop. With a weak grid, the average voltage is considerably lower than the ideal one.
- Pushing the firing angle close to 180° in inverter mode. The outgoing thyristor does not manage to turn off and the bridge fails.
- Confusing the displacement factor with the power factor. Harmonics lower the power factor even if cos φ is high.
- Applying the inductive-load formulas to a resistive load. With a resistive load and α greater than 60° the current becomes discontinuous and the average voltage is different.
06Self-assessment
What average voltage does a three-phase diode bridge give on 400 V?
\( 1.35 \cdot 400 \approx 540 \) V.
What firing angle gives 270 V, with no line inductance?
60°, because cos 60° = 0.5.
What harmonics does the current of a six-pulse bridge have?
Those of order 6k ± 1: 5, 7, 11, 13, 17, 19…
What is needed for the bridge to work as an inverter?
An energy source on the DC side that sustains the current, and α between 90° and about 150°.
07Further reading
- Ned Mohan, Tore M. Undeland and William P. Robbins. Power Electronics: Converters, Applications, and Design. 3rd ed., Wiley, 2003. Diode and thyristor rectifiers, including commutation.
- Muhammad H. Rashid. Power Electronics: Devices, Circuits, and Applications. 4th ed., Pearson. (Spanish edition: “Electrónica de potencia”.) Controlled rectifiers with their performance parameters.
- Jos Arrillaga and Neville R. Watson. Power System Harmonics. 2nd ed., Wiley, 2003. The harmonics of converters and their effect on the grid.