Inverters; chopper numerical 220 V, 10 Ω

Inverters

An inverter is a power electronic circuit that converts DC into AC of desired voltage and frequency. Thyristors, MOSFETs or IGBTs are switched in sequence so that the load sees an alternating voltage. Examples: single-phase half-bridge and full-bridge inverters, used in UPS, solar systems and AC motor drives.

Chopper calculation

Given: Vs = 220 V, R = 10 Ω, Vch = 2 V, f = 1 kHz (T = 1 ms), k = 0.5, so kT = 0.5 ms.

Output voltage is (Vs − Vch) during 0 < t < kT and 0 during kT < t < T.

a) Average output voltage

Va = (1/T)∫₀^(kT) (Vs − Vch) dt
   = (kT/T)(Vs − Vch) = k(Vs − Vch)
   = 0.5 × 218
Va = 109 V

b) RMS output voltage

Vo,rms = √[ (1/T)∫₀^(kT) (Vs − Vch)² dt ]
       = √k · (Vs − Vch)
       = 0.7071 × 218
Vo,rms = 154.15 V

c) Chopper efficiency

Po = (1/T)∫₀^(kT) (Vs − Vch)²/R dt = k(Vs − Vch)²/R
   = 0.5 × 218²/10 = 2376.2 W

Pi = (1/T)∫₀^(kT) Vs·i dt,  i = (Vs − Vch)/R
   = k·Vs(Vs − Vch)/R
   = 0.5 × 220 × 218/10 = 2398 W

η = Po/Pi = (Vs − Vch)/Vs = 218/220 = 0.9909

Answer: Va = 109 V, Vo,rms = 154.15 V, η = 99.09 %

The only loss is the 2 V drop across the switch, so the efficiency is very high. This is the main advantage of switching (chopper) control over resistive control.