Series full converters: rectification and inversion

Two single-phase full converters are fed from two separate transformer secondaries and their d.c. outputs are connected in series. This is used for high-voltage d.c. output (for example traction) and, with sequence control, to improve the input power factor and reduce harmonics.

Circuit

              +------------------+
  ~ ---+  S1  |  Full converter 1|--+ +
       |  ))  |  T1 T3 / T4 T2   |  |  Vo1
  pri  |      +------------------+  |
 (one  |                            +----+
 trans-|      +------------------+  |    | load
 former|  S2  |  Full converter 2|--+    | (RLE)
  two  |  ))  |  T1'T3'/T4'T2'   |  |    |
  sec.)|      +------------------+  |    |
  ~ ---+                            +----+
                                       -

Each secondary has rms voltage $V_s$ and peak $V_m$. The total output is

$$V_o = V_{o1} + V_{o2} = \frac{2V_m}{\pi}(\cos\alpha_1 + \cos\alpha_2)$$

The maximum output is $\frac{4V_m}{\pi}$ (both at $\alpha = 0$).

Rectification mode (power flow a.c. to d.c.)

Converter 1 is kept at $\alpha_1 = 0^\circ$ (output $+\frac{2V_m}{\pi}$) and converter 2 is phase-controlled, $\alpha_2$ from $180^\circ$ down to $0^\circ$:

$$V_o = \frac{2V_m}{\pi}(1 + \cos\alpha_2)$$

At $\alpha_2 = 180^\circ$ the two outputs cancel ($V_o = 0$); at $\alpha_2 = 0^\circ$, $V_o = \frac{4V_m}{\pi}$. So the output is varied smoothly from 0 to $\frac{4V_m}{\pi}$ with power flowing from the a.c. supply to the load.

Inversion mode (power flow d.c. to a.c.)

The load must contain a d.c. source $E$ of reversed polarity (for example a motor in regenerative braking). One converter is held at $\alpha_1 = 180^\circ$ (full negative voltage, $-\frac{2V_m}{\pi}$) and the other is controlled between $0^\circ$ and $180^\circ$:

$$V_o = \frac{2V_m}{\pi}(\cos\alpha_2 - 1)$$

so $V_o$ ranges from 0 to $-\frac{4V_m}{\pi}$; current direction stays the same, so power flows back to the a.c. supply. (In practice the angle is kept below about $165^\circ$ to allow a margin for commutation.)

Waveforms (rectification, $\alpha_1 = 0$, $\alpha_2 = \alpha$, constant load current $I_o$)

 vo1  /\  /\  /\     full-wave, alpha1 = 0
 ----/--\/--\/--\--
 vo2   _    _    _   full converter, alpha2,
 -----|-\-.|-\-.|-\  negative from pi to pi+a
 is1  ____      ____
 ----|    |____|      square, in phase
 is2    ____      __
 ------|    |____|    square, lags by alpha
 is   (sum, on primary):
          ____      level 2Io from a to pi
 ----.___|    |___.   level 0 from 0 to a

• $v_o = v_{o1} + v_{o2}$: during $0$ to $\alpha$ of each half cycle $v_{o2}$ is negative and reduces $v_o$; from $\alpha$ to $\pi$ both add.
• The primary current $i_s = i_{s1} + i_{s2}$ (equal turns) is a stepped wave: zero from $0$ to $\alpha$ and $2I_o$ from $\alpha$ to $\pi$. Its fundamental lags by only $\alpha/2$, so the displacement factor $\cos(\alpha/2)$ is better than $\cos\alpha$ of a single converter.

Advantages

• High output voltage with devices of half the voltage rating.
• Better input power factor and less harmonic content than a single converter of the same rating, because only one converter is phase-controlled at a time (the other runs at $0^\circ$ or $180^\circ$).