Performance of Single-phase, half-wave controlled rectifiers

Performance of Single-phase, half-wave controlled rectifiers with pure resistive load ( For α=π/2)

${V_{dc\left( m \right)}} = \frac{{{V_m}}}{{2\pi }} = 0.1592{V_m}$

${I_{dc}} = \frac{{{V_{dc}}}}{R} = \frac{{0.1592{V_m}}}{R}$

${V_{rms}} = \frac{{{V_m}}}{2}\left( {\frac{1}{{\sqrt 2 }}} \right) = 0.3536{V_m}$

${I_{rms}} = \frac{{{V_{rms}}}}{R} = \frac{{0.3536{V_m}}}{R}$

${P_{dc}} = {V_{dc}}{I_{dc}} = \frac{{{{(0.1592{V_m})}^2}}}{R}$

${P_{ac}} = {V_{rms}}{I_{rms}} = \frac{{{{(0.3536{V_m})}^2}}}{R}$

Half Controlled Rectifier with R Load

Figure a. SCR supplying a passive load. b. Voltage and current waveforms.

Here, we have assumed delay angle (α) of 90 deg. The fundamental component of input current lags behind the input voltage, both P and Q flow from AC side to load or DC side. The displacement PF decreases as we delay the triggering pulse. If SCR is triggered ar 0 deg, no Q is absorbed.

Half Controlled Rectifier with RL Load

Average Load/Output Voltage

${V_0} = \frac{1}{{2\pi }}\int_\alpha ^\beta {\sqrt 2 V\sin \theta d\theta }$
$= \frac{V}{{2\pi }}\left( {\cos \alpha + \cos \beta } \right)$
Average Load/Output Current
${I_0} = \frac{{{V_0}}}{Z}$
Single-phase, half-wave controlled rectifiers with Inductive load
Role of free-wheeling diode
To avoid negative voltage when inductive load involved.

area A = area B
During α < ωt < π:
v_L + v_R = v_o
During π < wt < 2π+α:
v_L + v_R = 0
i ≥ 0 (exp decay)
i(t) is expressed in two separate equations.
Single-phase, half-wave controlled rectifiers with Internal DC Voltage

Thyristor based Rectifiers and Inverters (1-phase)

Fig a. SCR supplying an active load. b. Voltage and current waveforms.