Symmetrical angle control for power factor

Symmetrical angle control is a power factor improvement method in which a forced-commutated switch is turned ON at $\alpha = (\pi-\beta)/2$ and turned OFF at $(\pi+\beta)/2$, so that the conduction interval $\beta$ is placed symmetrically about the peak of the supply voltage ($\omega t = \pi/2$). As a result, the fundamental input current is in phase with the supply voltage and the displacement factor is unity.

Why it is needed

In a phase-controlled (thyristor) converter the input current always lags the voltage by $\alpha$ (or $\alpha/2$ in a semiconverter). At large $\alpha$ the input power factor becomes very poor. Thyristors cannot be turned off at will, but GTOs, IGBTs or power transistors can, so the position of the current pulse can be chosen freely.

Circuit

              P (+)
        +-------+-------+-------+
        |       |       |       |
       S1      S2       |       |
        |       |      Dm     Load
 a o----+       +--o b  |    (Ia)
        |       |       |       |
       D1      D2       |       |
        |       |       |       |
        +-------+-------+-------+
              N (-)
 S1, S2: forced-commutated switches (GTO/IGBT)
 Dm: freewheeling diode

Operation (highly inductive load, current $I_a$ constant)

1. Positive half cycle: S1 is turned ON at $\omega t = (\pi-\beta)/2$. Current flows $a \to$ S1 $\to$ load $\to$ D2 $\to b$; $v_o = v_s$, $i_s = +I_a$.
2. S1 is turned OFF at $(\pi+\beta)/2$ by a gate signal. The load current transfers to the freewheeling diode Dm; $v_o = 0$, $i_s = 0$.
3. Negative half cycle: S2 is turned ON at $(3\pi-\beta)/2$ and OFF at $(3\pi+\beta)/2$; current flows $b \to$ S2 $\to$ load $\to$ D1 $\to a$; $v_o = -v_s$ (positive), $i_s = -I_a$.
4. For the rest of the time the load current freewheels through Dm.

 is
 +Ia       +-----+
           |     |
  0  ------+     +-------+     +------
                         |     |
 -Ia                     +-----+
     (90-b/2)(90+b/2) (270-b/2)(270+b/2)
 b = beta; vs is positive 0-180, negative 180-360

Output voltage

$$V_{dc} = \frac{2}{2\pi}\int_{(\pi-\beta)/2}^{(\pi+\beta)/2} V_m\sin\omega t\, d(\omega t) = \frac{2V_m}{\pi}\sin\frac{\beta}{2}$$ $$V_{rms} = \frac{V_m}{\sqrt2}\left[\frac{1}{\pi}(\beta + \sin\beta)\right]^{1/2}$$

Input current and power factor

• Input current: quasi-square wave of $\pm I_a$, width $\beta$, centred on the voltage peaks.
• RMS input current: $I_s = I_a\sqrt{\beta/\pi}$
• Fundamental (rms): $I_{s1} = \frac{2\sqrt2 I_a}{\pi}\sin\frac{\beta}{2}$, with displacement angle $\phi_1 = 0$.
• Displacement factor $= \cos 0 = 1$.
• Power factor:

$$PF = \frac{I_{s1}}{I_s}\cos\phi_1 = \frac{2\sqrt2\,\sin(\beta/2)}{\sqrt{\pi\beta}}$$

Merits and demerits

• Unity displacement factor at all output levels; only the harmonic (distortion) factor reduces the PF.
• Less reactive power is drawn from the supply.
• Demerit: it needs self-commutated devices and gate turn-off circuitry, so the cost is higher.