# Phase Controlled Rectifiers

 Question 1
A single-phase, full-bridge, fully controlled thyristor rectifier feeds a load comprising a 10$\Omega$ resistance in series with a very large inductance. The rectifier is fed from an ideal 230 V, 50 Hz sinusoidal source through cables which have negligible internal resistance and a total inductance of 2.28 mH. If the thyristors are triggered at an angle $\alpha = 45^{\circ}$, the commutation overlap angle in degree (rounded off to 2 decimal places) is_____.
 A 2.4 B 4.8 C 6.4 D 8.2
GATE EE 2020   Power Electronics
Question 1 Explanation:
\begin{aligned}&1-\phi\text{ SCR bridge rectifier} \\ \alpha &=45^{\circ},\; \; R=10\, \Omega\\ &\text{supply 230 V, 50 Hz}\\ L_{s}&=2.28\, mH \\ \mu &=? \\ \Delta V_{d}&=\frac{V_{m}}{\pi }[\cos \alpha -\cos (\alpha +\mu )]\\ &= 4fL_{s}I_{0} \\ V_{0}&=\frac{2V_{m}}{\pi }\cos \alpha -4fL_{s}I_{0} \\ I_{0}R&=\frac{2V_{m}}{\pi}\cos \alpha -4fL_{s}I_{0} \\ &\text{Find }I_{0} \\ I_{0}\times 10&=\frac{2\times 230\sqrt{2}}{\pi } \cos 45 \\&-4\times 50\times 2.28\times 10^{-3}I_{0} \\ I_{0}(10+0.456)&=146.42 \\ I_{0}&=\frac{146.49}{10.456}=14.0036\: A \\ \Delta V_{d0 }&=\frac{230\sqrt{2}}{\pi }[\cos 45-\cos (45+\mu)] \\ &=4\times 50\times 2.28\times 10^{-3}\times 14 \\ &=6.384 \\ \cos 45^{\circ}-\cos (45^{\circ}+\mu )&=0.061659 \\ 45+\mu &=49.80 \\ \therefore \, \, \mu =4.80^{\circ}\end{aligned}
 Question 2
Consider the diode circuit shown below. The diode, D, obeys the current-voltage characteristic $I_D=I_S\left ( exp\left ( \frac{V_D}{nV_T} \right )-1 \right )$, where $n \gt 1, V_T \gt 0, V_D$ is the voltage across the diode and $I_D$ is the current through it. The circuit is biased so that voltage, $V \gt 0$ and current, $I \lt 0$. If you had to design this circuit to transfer maximum power from the current source ($I_1$) to a resistive load (not shown) at the output, what values $R_1 \; and \; R_2$ would you choose?
 A Large $R_1$ and large $R_2$. B Small $R_1$ and small $R_2$. C Large $R_1$ and small $R_2$. D Small $R_1$ and large $R_2$.
GATE EE 2020   Power Electronics
Question 2 Explanation:
$R_{1}$-low, $R_{2}$- high
$V_{D}=V\times \frac{R_{2}}{R_{1}+R_{2}}$
If $R_{2}$ is large $V_{D}$ becomes high
If $R_{1}$ is less $V_{D}=V$
So for maximum power, $R_{1}$ is small and $R_{2}$ is large.
 Question 3
Thyristor $T_1$ is triggered at an angle $\alpha$ (in degree), and $T_2$ at angle $180^{\circ} + \alpha$, in each cycle of the sinusoidal input voltage. Assume both thyristors to be ideal. To control the load power over the range 0 to 2 kW, the minimum range of variation in $\alpha$ is:
 A $0^{\circ} \; to \; 60^{\circ}$ B $0^{\circ} \; to \; 120^{\circ}$ C $60^{\circ} \; to \; 120^{\circ}$ D $60^{\circ} \; to \; 180^{\circ}$
GATE EE 2020   Power Electronics
Question 3 Explanation:
As per GATE official answer key, MTA (Marks to All)

As load is capacitive, for any $\alpha$ :

\begin{aligned} V_{or}&=\frac{V_m}{\sqrt{2\pi}}\left [ \pi - \alpha +\frac{1}{2} \sin 2\alpha \right ]^{1/2}\\ P_0&=\left ( \frac{V_{or}}{z} \right )^2 \times R\\ &=\frac{V_{or}^2}{100} \times 5=\frac{V_{or}^2}{20}\\ \text{For }\alpha &=0^{\circ}\\ V_{or}&=\frac{V_m}{\sqrt{2}}=200\\ P_0&=\frac{200}{20}=2KW \end{aligned}
For $\alpha =120^{\circ}$, as current distinguishes, so $P=0.$
So, $\alpha$ should be $0^{\circ} \text{ to } 120^{\circ}.$
 Question 4
A single-phase, full-bridge diode rectifier fed from a 230 V, 50 Hz sinusoidal source supplies a series combination of finite resistance. R, and a very large inductance, L, The two most dominant frequency components in the source current are:
 A 50 Hz, 0 Hz B 50 Hz, 100 Hz C 50 Hz, 150 Hz D 50 Hz, 250 Hz
GATE EE 2020   Power Electronics
Question 4 Explanation:
For full bridge rectifier, High inductive load

\begin{aligned} I_{source}&=\sum_{n=1,3,5}^{\infty }\frac{4I_0}{n \pi} \sin nd \sin \frac{n \pi}{2} \sin (n\omega t+\phi _n) \\ 2d &=\pi , \;\; d=\frac{\pi}{2}\\ I_{source}&= \frac{4I_0}{n \pi} \sum_{n=1,3,5}^{\infty } \sin ^2 n\left ( \frac{\pi}{2} \right ) \sin (n\omega t+\phi _n)\\ I_{source}&\neq 0 \end{aligned} For $n=1,3,5,...$
Since the most dominant frequency component will be $f, 3f, f = 50$
So dominant frequency $= 50 Hz, 150 Hz.$
 Question 5
A single-phase fully-controlled thyristor converter is used to obtain an average voltage of 180 V with 10 A constant current to feed a DC load. It is fed from single-phase AC supply of 230 V, 50 Hz. Neglect the source impedance. The power factor (round off to two decimal places) of AC mains is________
 A 0.25 B 0.55 C 0.78 D 0.95
GATE EE 2019   Power Electronics
Question 5 Explanation:
$V_{sr}I_{sr} \cos \phi =V_0I_0$
For single-phase fully controlled converter,
$I_0=I_{sr}=10A$
$\cos \phi =\frac{V_0}{V_{sr}}=\frac{180}{230}=0.78$
 Question 6
A fully-controlled three-phase bridge converter is working from a 415V, 50 Hz AC supply. It is supplying constant current of 100 A at 400 V to a DC load. Assume large inductive smoothing and neglect overlap. The rms value of the AC line currentin amperes (round off to two decimal places) is ________.
 A 81.65 B 41.25 C 66.45 D 69.85
GATE EE 2019   Power Electronics
Question 6 Explanation:
AC line current rms $=(I_s)_{rms}=I_0\sqrt{\frac{2}{3}}=100 \times \sqrt{\frac{2}{3}}=81.65A$
 Question 7
A six-pulse thyristor bridge rectifier is connected to a balanced three-phase, 50Hz AC source. Assuming that the DC output current of the rectifier is constant, the lowest harmonic component in the AC input current is
 A 100Hz B 150Hz C 250Hz D 300Hz
GATE EE 2019   Power Electronics
Question 7 Explanation:
For 6 pulse converter harmonics present in AC current are $6k\pm 1$
Lowest order harmonic =5
Lowest harmonic frequency = 5 x 50 =250Hz
 Question 8
A phase controlled single phase rectifier, supplied by an AC source, feeds power to an R-L-E load as shown in the figure. The rectifier output voltage has an average value given by
$V_{0}=\frac{V_{m}}{2 \pi}(3+ \cos \alpha),$ where $V_{m}=80\pi$ volts and $\alpha$ is the firing angle. If the power delivered to the lossless battery is 1600 W, $\alpha$ in degree is________ (up to 2 decimal places).
 A 45 B 90 C 60 D 30
GATE EE 2018   Power Electronics
Question 8 Explanation:
\begin{aligned} V_0&=\frac{V_m}{2 \pi}(3+\cos \alpha )\\ E_bI_0&=1600W\\ I_0&=\frac{1600}{80}=20A\\ V_0&=E_b+I_0R_a\\ \frac{V_m}{2 \pi}(3+\cos \alpha )&=80+(20 \times 2)\\ \frac{80 \pi}{2 \pi}(3+\cos \alpha )&=80+40\\ \alpha &=90^{\circ} \end{aligned}
 Question 9
The waveform of the current drawn by a semi-converter from a sinusoidal AC voltage source is shown in the figure. If $I_0$=20 A, the rms value of fundamental component of the current is ___________A (up to 2 decimal places).
 A 17.39 B 18.92 C 24.67 D 14.86
GATE EE 2018   Power Electronics
Question 9 Explanation:
\begin{aligned} i_{s1}&=\frac{4I_0}{\pi}\cos \frac{\alpha }{2}\\ I_{s1(rms)}&=\frac{2\sqrt{2}}{\pi}I_0\cdot \cos \frac{\alpha }{2}\\ &=\frac{2\sqrt{2}}{\pi} \times 20 \times \cos \left ( \frac{30^{\circ}}{2} \right )\\ &=17.39A \end{aligned}
 Question 10
A single phase fully controlled rectifier is supplying a load with an anti-parallel diode as shown in the figure. All switches and diodes are ideal. Which one of the following is true for instantaneous load voltage and current?
 A $v_{0}\geq 0 \text{ and } i_{0} \lt 0$ B $v_{0} \lt 0 \text{ and } i_{0}\lt 0$ C $v_{0}\geq 0 \text{ and } i_{0}\geq 0$ D $v_{0} \lt 0 \text{ and } i_{0}\geq 0$
GATE EE 2018   Power Electronics
There are 10 questions to complete.