Variable inverter output; SCR full-wave average

Variable output voltage in inverter

Yes. The output voltage of an inverter can be varied by:

1. Varying the DC input voltage using a controlled rectifier or chopper before the inverter.
2. Pulse width modulation (PWM) inside the inverter (most common): single-pulse, multiple-pulse or sinusoidal PWM. Changing the pulse width (modulation index) changes the RMS output while the frequency stays fixed.
3. Controlling the AC output with an AC voltage controller or a tapped transformer.
4. Series/phase-shift connection of two inverters, where varying the phase shift between them changes the resultant voltage.

Average output voltage of SCR full-wave rectifier

Consider a centre-tapped full-wave controlled rectifier with resistive load (a bridge gives the same result).

      T1
  +---|>|---+
  )         |
  ) vs      +---[ R ]---+
  )==CT-----------------+
  ) vs      |
  )         |
  +---|>|---+
      T2

• Positive half cycle: T1 is forward biased and fired at ωt = α; it conducts until π.
• Negative half cycle: T2 is fired at π + α and conducts until 2π.
• Load voltage repeats every π.

vo   |  /‾\    /‾\
     | /   \  /   \
     |/  |  \/  |  \
   --+---+--+----+---+--> ωt
     0   α  π  π+α  2π

Derivation:

Vdc = (1/π)∫α^π Vm sin ωt d(ωt)
    = (Vm/π)[−cos ωt]α^π
    = (Vm/π)[−cos π + cos α]
Vdc = (Vm/π)(1 + cos α)

• At α = 0, Vdc = 2Vm/π (same as uncontrolled full-wave rectifier).
• At α = π, Vdc = 0.
• Average load current Idc = Vm(1 + cos α)/(πR).

RMS value for reference:

Vrms = (Vm/√2)·√[ (π − α)/π + sin2α/(2π) ]