Series operation of two full converters

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.)

Example

With $V_s = 230$ V on each secondary, $V_m = 325.27$ V and the maximum d.c. voltage is $\frac{4 \times 325.27}{\pi} = 414.1$ V, twice that of a single full converter (207.1 V), while each thyristor still blocks only $V_m = 325.3$ V.

Advantages

• High output voltage with devices of half the voltage rating.
• Better input power factor and lower harmonics, because only one converter is phase-controlled at a time.