The voltage at the input of an AC-DC rectifier is given by v(ЁЭСб) = 230√2 sin ЁЭЬФЁЭСб where ЁЭЬФ = 2ЁЭЬЛ × 50 rad/s. The input current drawn by the rectifier is given by \(\rm i(t) = 10 \sin \left( \omega t - \frac{\pi}{3} \right) + 4 \sin \left( 3\omega t - \frac{\pi}{6} \right) + 3 \sin \left( 5\omega t - \frac{\pi}{3} \right)\) The input power factor, (rounded off to two decimal places), is, __________ lag.
Concept:
Sinusoidal supply to Non-linear loads.
Let V(t) = V1 sin (ω1 t + θ1)
i(t) = I0 + I1 sin (ω1 t + ϕ1) + I2 sin (ω2 t + ϕ2) + I3 sin (ω3 t + ϕ3)
Real power, \(\rm P = \frac{V_1}{√2}× \frac{I_1}{√2}\cos(θ_1-ϕ_1)\) watt
Reactive power \(\rm Q = \frac{V_1}{√2}× \frac{I_1}{√2}\sin(θ_1-ϕ_1)\) VAR
Apparent powr S = [VT rms] × [IT Rms]
\(\rm =\frac{V_1}{√2}\left[I_0^2+\left(\frac{I_1}{√2}\right)^2+\left(\frac{I_2}{√2}\right)^2+\left(\frac{I_3}{√2}\right)^2+----\right]^{1/2}\)
Total power factor = \(\rm \frac{P}{S} =\frac{\rm \frac{V_1}{√2}× \frac{I_1}{√2}\cos(θ_1-ϕ_1)}{\frac{V_1}{√2}\left[I_0^2+\left(\frac{I_1}{√2}\right)^2+\left(\frac{I_2}{√2}\right)^2+\left(\frac{I_3}{√2}\right)^2+----\right]^{1/2}} \)
Total power factor = \(\rm \frac{I_{1rms}}{I_{total\ rms}}×\cos (θ_1-ϕ_1)\)
\(\rm \frac{I_{1rms}}{I_{total\ rms}}\)= Distortion factor
cos (θ1 - ϕ1) = Fundamental power factor
Explanation:
Given
V(t) = 230 √2 sin ωt
\(\rm i(t)=10\sin\left(ω t-\frac{π}{3}\right)+4\sin \left(3ω t-\frac{π}{6}\right)+3\sin\left(5ω t-\frac{π}{3}\right)\)
ω = 2 π × 50 rad/sec.
Input power factor or total power factor
\(\rm =\frac{I_{1 rms}}{I_{TRms}}\cos[0^{\circ}-(\pi/3)]\)
Input power factor or total power factor
\(\rm =\frac{I_{1 rms}}{I_{TRms}}\cos[0^{\circ}-(\pi/3)]\)
I1rms = \(\frac{10}{\sqrt2}\)
\(\rm I_{Trms}=\left[\left(\frac{10}{\sqrt2}\right)^2+\left(\frac{4}{\sqrt2}\right)^2+\left(\frac{3}{\sqrt2}\right)^2\right]^{1/2}\)
⇒ \(\rm I_{Trms}=\left[\frac{100}{2}+\frac{16}{2}+\frac{9}{2}\right]^{1/2}\)
\(\rm I_{Trms}=\left[\frac{125}{2}\right]^{1/2}\)
∴ I.P factor = \(\frac{10/\sqrt2}{\frac{(125)^{1/2}}{\sqrt2}}\cos (\pi/3)\)
Input power factor = 0.447 lag.
Important Questions from Phase Controlled Rectifiers
- Which of the following is control element in Silicon Controlled Resistor (SCR)?
A 240 V single-phase AC supply is fed to a load resistor of 100 Ω through a thyristor. If the thyristor is fired at 90°, what is the power consumed by the load?
The maximum firing angle that can be obtained by a pure resistive trigger circuit used in phase control circuit is:
In a 3-phase converter circuit, during commutation when one SCR in one phase is turned on, turning of an SCR in another phase results is:
- Which mode is described when the anode is assigned a positive voltage, the gate is assigned a zero voltage disconnected and the cathode is assigned a negative voltage?
