Question 1 |

A double pulse measurement for an inductively loaded circuit controlled by the IGBT
switch is carried out to evaluate the reverse recovery characteristics of the diode. D,
represented approximately as a piecewise linear plot of current vs time at diode turn-off.
L_{par} is a parasitic inductance due to the wiring of the circuit, and is in series with the
diode. The point on the plot (indicate your choice by entering 1. 2, 3 or 4) at which the
IGBT experiences the highest current stress is ______.

1 | |

2 | |

3 | |

4 |

Question 1 Explanation:

Using KCL, I_s=I_L-I_D

For inductively loaded circuits, load can be assumed to be constant.

\therefore \; I_s is maximum when, I_D is minimum, i.e. at point 3.

Therefore, IGBT experiences highest current stress at point 3.

Question 2 |

For the circuit shown in the figure below, assume that diodes D_1,D_2 and D_3 are ideal.

The DC components of voltages v_1 \; and \; v_2, respectively are

The DC components of voltages v_1 \; and \; v_2, respectively are

0 V and 1 V | |

-0.5 V and 0.5 V | |

1 V and 0.5 V | |

1 V and 1 V |

Question 2 Explanation:

\begin{aligned} V_{2\; avg}&=\frac{V_m}{\pi}=\frac{\pi/2}{\pi}=\frac{1}{2}=0.5V \\ V_{1\; avg} &=\frac{1}{2 \pi}[ \int_{0}^{\pi}\frac{\pi}{2}\sin 100 \pi t\cdot d(\omega t)\\ &+\int_{\pi}^{2\pi} \pi \sin 100 \pi t\cdot d(\omega t) ]\\ &= -0.5V \end{aligned}

Question 3 |

Consider a HVDC link which uses thyristor based line-commutated converters as shown in the figure. For a power flow of 750 MW from System 1 to System 2, the voltages at the two ends, and the current, are given by: V_{1}=500 kV, V_{2}=485 kV and V_{3}=1.5 kA. If the direction of power flow is to be reversed (that is, from System 2 to System 1) without changing the electrical connections, then which one of the following combinations is feasible?

V_{1}=-500 kV,V_{2}=-485 kV and latex]I=1.5kA[/latex] | |

V_{1}=-485 kV,V_{2}=500 kV and latex]I=1.5kA[/latex] | |

V_{1}=500 kV,V_{2}=-485 kV and latex]I=-1.5kA[/latex] | |

V_{1}=-500 kV,V_{2}=-485 kV and latex]I=-1.5kA[/latex] |

Question 3 Explanation:

To maintain the direction of power flow from system 2 to system 1, the voltage V_1=-485kV and voltage V_2=500kV and I=1.5kA.

Since, current cannot flow in reverse direction. Option (B) is correct answer.

Since, current cannot flow in reverse direction. Option (B) is correct answer.

Question 4 |

The SCR in the circuit shown has a latching current of 40 mA. A gate pulse of
50 \mus is applied to the SCR. The maximum value of R in \Omega to ensure successful
firing of the SCR is ______.

4050 | |

5560 | |

6060 | |

8015 |

Question 4 Explanation:

Let us assume the SCR is conducting,

\begin{aligned} &I_{ss}=\frac{100}{500}=0.2A\\ &[\because \text{inductor will be dhort circuited in DC}]\\ &i(t)=I_{ss}(1-e^{-t/\tau })\\ &\tau =\frac{L}{R}=\frac{200 \times 10^{-3}}{500}\\ &\;\;=4 \times 10^{-4}\; sec\\ &\text{Given }t=50 \times 10^{-6}\; sec\\ &\therefore \; i(t)=0.2\left ( 1-e^{\frac{50 \times 10^{-6}}{4 \times 10^{-4}}} \right )=23.5A \end{aligned}

V=I \times R

R=\frac{V}{I}=\frac{100}{16.5 \times 10^{-3}} =6060 \Omega

\begin{aligned} &I_{ss}=\frac{100}{500}=0.2A\\ &[\because \text{inductor will be dhort circuited in DC}]\\ &i(t)=I_{ss}(1-e^{-t/\tau })\\ &\tau =\frac{L}{R}=\frac{200 \times 10^{-3}}{500}\\ &\;\;=4 \times 10^{-4}\; sec\\ &\text{Given }t=50 \times 10^{-6}\; sec\\ &\therefore \; i(t)=0.2\left ( 1-e^{\frac{50 \times 10^{-6}}{4 \times 10^{-4}}} \right )=23.5A \end{aligned}

V=I \times R

R=\frac{V}{I}=\frac{100}{16.5 \times 10^{-3}} =6060 \Omega

Question 5 |

A single-phase SCR based ac regulator is feeding power to a load consisting of 5 \Omega
resistance and 16 mH inductance. The input supply is 230 V, 50 Hz ac. The maximum firing angle at which the voltage across the device becomes zero all throughout and the rms value of current through SCR, under this operating condition, are

30^{\circ} and 46 A | |

30^{\circ} and 23 A | |

45^{\circ} and 23 A | |

45^{\circ} and 32 A |

Question 5 Explanation:

The maximum firing angle at which the voltage across the device becomes '\phi ' = load angle.

\begin{aligned} \phi &= \tan ^{-1} \left ( \frac{\omega L}{R} \right )\\ &= \tan^{-1}\left ( \frac{2 \pi \times 50 \times 16 \times 10^{-3}}{5} \right ) \\ \phi &=45.15\simeq 45^{\circ} \end{aligned}

Rms value of current through SCR is

\begin{aligned} I_{T_{rms}} &=\sqrt{\left [ \frac{1}{2 \pi}\int_{\alpha }^{\pi+\alpha }\left ( \frac{V_m}{z}\sin (\omega t-\phi ) \right )^2 d(\omega t) \right ]}\\ &=\sqrt{\frac{V_m^2}{2 \pi z^2} \int_{\alpha }^{\pi+\alpha } \left [ \frac{1-\cos 2(\omega t-\phi )}{2} \right ] d(\omega t)}\\ &=\sqrt{\frac{V_m^2}{2 \times 2 \pi z^2} \left [\pi- \left.\begin{matrix} \frac{\sin 2(\omega t-\phi )}{2} \end{matrix}\right|_\alpha ^{(\pi+\alpha )} \right ] }\\ &=\frac{V_m}{2z \sqrt{\pi} } \sqrt{\left [ \pi+\frac{-\sin 2(\pi+\alpha -\alpha )+\sin 2(\alpha -\alpha )}{2} \right ] }\\ &=\frac{V_m}{2z \sqrt{\pi} }\sqrt{\pi}=\frac{V_m}{2z}\\ I_{T_{rms}}&=\frac{230\sqrt{2}}{2 \times \sqrt{5^2(2 \pi \times 50 \times 16 \times 10^{-3})^2}}\\ &=22.93\simeq 23A\\ I_{T_{rms}}&=23A \end{aligned}

\begin{aligned} \phi &= \tan ^{-1} \left ( \frac{\omega L}{R} \right )\\ &= \tan^{-1}\left ( \frac{2 \pi \times 50 \times 16 \times 10^{-3}}{5} \right ) \\ \phi &=45.15\simeq 45^{\circ} \end{aligned}

Rms value of current through SCR is

\begin{aligned} I_{T_{rms}} &=\sqrt{\left [ \frac{1}{2 \pi}\int_{\alpha }^{\pi+\alpha }\left ( \frac{V_m}{z}\sin (\omega t-\phi ) \right )^2 d(\omega t) \right ]}\\ &=\sqrt{\frac{V_m^2}{2 \pi z^2} \int_{\alpha }^{\pi+\alpha } \left [ \frac{1-\cos 2(\omega t-\phi )}{2} \right ] d(\omega t)}\\ &=\sqrt{\frac{V_m^2}{2 \times 2 \pi z^2} \left [\pi- \left.\begin{matrix} \frac{\sin 2(\omega t-\phi )}{2} \end{matrix}\right|_\alpha ^{(\pi+\alpha )} \right ] }\\ &=\frac{V_m}{2z \sqrt{\pi} } \sqrt{\left [ \pi+\frac{-\sin 2(\pi+\alpha -\alpha )+\sin 2(\alpha -\alpha )}{2} \right ] }\\ &=\frac{V_m}{2z \sqrt{\pi} }\sqrt{\pi}=\frac{V_m}{2z}\\ I_{T_{rms}}&=\frac{230\sqrt{2}}{2 \times \sqrt{5^2(2 \pi \times 50 \times 16 \times 10^{-3})^2}}\\ &=22.93\simeq 23A\\ I_{T_{rms}}&=23A \end{aligned}

Question 6 |

A solar energy installation utilize a three-phase bridge converter to feed energy
into power system through a transformer of 400V/400 V, as shown below.

The energy is collected in a bank of 400 V battery and is connected to converter through a large filter choke of resistance10\Omega.

The kVA rating of the input transformer is

The energy is collected in a bank of 400 V battery and is connected to converter through a large filter choke of resistance10\Omega.

The kVA rating of the input transformer is

53.2 kVA | |

46.0 kVA | |

22.6 kVA | |

7.5 kVA |

Question 6 Explanation:

RMS value of supply current in case of 3-\phi bridge converter

I_s=I_0\sqrt{\frac{2}{3}}=40\sqrt{\frac{2}{3}}=32.66A

KVA rating of the input transformrer

\begin{aligned} &=\sqrt{3}V_sI_s \\ &= \sqrt{3} \times 400 \times 32.66 \times 10^{-3}\; kVA\\ &=22.62\; kVA \end{aligned}

I_s=I_0\sqrt{\frac{2}{3}}=40\sqrt{\frac{2}{3}}=32.66A

KVA rating of the input transformrer

\begin{aligned} &=\sqrt{3}V_sI_s \\ &= \sqrt{3} \times 400 \times 32.66 \times 10^{-3}\; kVA\\ &=22.62\; kVA \end{aligned}

Question 7 |

A solar energy installation utilize a three-phase bridge converter to feed energy
into power system through a transformer of 400V/400 V, as shown below.

The energy is collected in a bank of 400 V battery and is connected to converter through a large filter choke of resistance10\Omega.

The maximum current through the battery will be

The energy is collected in a bank of 400 V battery and is connected to converter through a large filter choke of resistance10\Omega.

The maximum current through the battery will be

14A | |

40A | |

80A | |

94A |

Question 7 Explanation:

Average output voltage of the converter

V_0=\frac{3 V_{ml}}{\pi} \cos \alpha

The converter acts as line commutated inverter and for such mode \alpha \gt 90^{\circ} and V_0 is negative.THerefore, battery supplies energy to AC system. So, current through battery

I_0=\frac{400-V_0}{R}

For V_0=0 \text{ or }\alpha =90^{\circ},

Maximum current flow through battery

(I_0)_{max}=\frac{400}{10}=40A

Question 8 |

The input voltage given to a converter is

v_i=100\sqrt{2}\sin (100 \pi t) V

The current drawn by the converter is

i_i=10\sqrt{2}\sin (100\pi t-\pi/3) + 5\sqrt{2}\sin (300\pi t+\pi/4) + 2\sqrt{2}\sin (500\pi t-\pi/6)A

The active power drawn by the converter is

v_i=100\sqrt{2}\sin (100 \pi t) V

The current drawn by the converter is

i_i=10\sqrt{2}\sin (100\pi t-\pi/3) + 5\sqrt{2}\sin (300\pi t+\pi/4) + 2\sqrt{2}\sin (500\pi t-\pi/6)A

The active power drawn by the converter is

181W | |

500W | |

707W | |

887W |

Question 8 Explanation:

Rms value of input voltag,

V_{rms}=\frac{100\sqrt{2}}{\sqrt{2}}=100V

Rms value of current,

I_{rms}=\sqrt{\left (\frac{10\sqrt{2}}{\sqrt{2}} \right )^2+\left (\frac{5\sqrt{2}}{\sqrt{2}} \right )^2+\left (\frac{2\sqrt{2}}{\sqrt{2}} \right )^2}=11.358A

Let input power factor \cos \phi

V_{rms}I_{rms} \cos \phi = active power drawn by the coverter

\Rightarrow \;100 \times 11.358 \times \cos \phi =500W

\Rightarrow \; \cos \phi =0.44

V_{rms}=\frac{100\sqrt{2}}{\sqrt{2}}=100V

Rms value of current,

I_{rms}=\sqrt{\left (\frac{10\sqrt{2}}{\sqrt{2}} \right )^2+\left (\frac{5\sqrt{2}}{\sqrt{2}} \right )^2+\left (\frac{2\sqrt{2}}{\sqrt{2}} \right )^2}=11.358A

Let input power factor \cos \phi

V_{rms}I_{rms} \cos \phi = active power drawn by the coverter

\Rightarrow \;100 \times 11.358 \times \cos \phi =500W

\Rightarrow \; \cos \phi =0.44

Question 9 |

The input voltage given to a converter is

v_i=100\sqrt{2}\sin (100 \pi t) V

The current drawn by the converter is

i_i=10\sqrt{2}\sin (100\pi t-\pi/3) + 5\sqrt{2}\sin (300\pi t+\pi/4) + 2\sqrt{2}\sin (500\pi t-\pi/6)A

The input power factor of the converter is

v_i=100\sqrt{2}\sin (100 \pi t) V

The current drawn by the converter is

i_i=10\sqrt{2}\sin (100\pi t-\pi/3) + 5\sqrt{2}\sin (300\pi t+\pi/4) + 2\sqrt{2}\sin (500\pi t-\pi/6)A

The input power factor of the converter is

0.31 | |

0.44 | |

0.5 | |

0.71 |

Question 9 Explanation:

\begin{aligned} V_i&=100\sqrt{2}\sin (100 \pi t)\\ i_i&=10\sqrt{2} \sin \left ( 100 \pi t -\frac{\pi}{3} \right )\\ &+5\sqrt{2} \sin \left ( 300 \pi t +\frac{\pi}{4} \right )\\ &+2\sqrt{2} \sin \left ( 500 \pi t -\frac{\pi}{4} \right )A \end{aligned}

Fundamental component of input voltage

\begin{aligned} (V_i)_1&=100\sqrt{2} \sin (100 \pi t)\\ (V_i)_{1,rms}&=\frac{100\sqrt{2}}{\sqrt{2}}=100V \end{aligned}

Fundamental component of current

\begin{aligned} (i_L)_1&=10\sqrt{2} \sin (100 \pi t-\frac{\pi}{3})\\ (i_L)_{1,rms}&=\frac{10\sqrt{2}}{\sqrt{2}}=10 \end{aligned}

Phase difference between these two components

\phi _1=\frac{\pi}{3}, \cos \phi _1= \cos \frac{\pi}{3}=0.5

Active power due to fundamental components

P_1=(V_i)_{1,rms} \times (i_i)_{1,rms} \cos \phi =100 \times 10 \times 0.5=500W

Since 3^{rd} \text{ and } 5^{th} harmonic are absent in input voltage, there is no active power due to the these components.

Hence, active power drawn by the converter

P_0= Active power due to fundamental components =500 W

Fundamental component of input voltage

\begin{aligned} (V_i)_1&=100\sqrt{2} \sin (100 \pi t)\\ (V_i)_{1,rms}&=\frac{100\sqrt{2}}{\sqrt{2}}=100V \end{aligned}

Fundamental component of current

\begin{aligned} (i_L)_1&=10\sqrt{2} \sin (100 \pi t-\frac{\pi}{3})\\ (i_L)_{1,rms}&=\frac{10\sqrt{2}}{\sqrt{2}}=10 \end{aligned}

Phase difference between these two components

\phi _1=\frac{\pi}{3}, \cos \phi _1= \cos \frac{\pi}{3}=0.5

Active power due to fundamental components

P_1=(V_i)_{1,rms} \times (i_i)_{1,rms} \cos \phi =100 \times 10 \times 0.5=500W

Since 3^{rd} \text{ and } 5^{th} harmonic are absent in input voltage, there is no active power due to the these components.

Hence, active power drawn by the converter

P_0= Active power due to fundamental components =500 W

Question 10 |

The power electronic converter shown in the figure has a single-pole double-throw switch. The pole P of the switch is connected alternately to throws A and B. The converter shown is a

step down chopper (buck converter) | |

half-wave rectifier | |

step-up chopper (boost converter) | |

full-wave rectifier |

Question 10 Explanation:

When switch is connected to A for time duration T_1

V_{out}=V_{in}

When switch is connected to B for time duration T_2

Average output voltage =\frac{V_{in}T_1}{T_1+T_2}=\alpha V_{in}

where, \alpha =\text{duty cycle}=\frac{T_1}{T_1+T_2}

Therefore, the converter shown is a step down chooper.

V_{out}=V_{in}

When switch is connected to B for time duration T_2

Average output voltage =\frac{V_{in}T_1}{T_1+T_2}=\alpha V_{in}

where, \alpha =\text{duty cycle}=\frac{T_1}{T_1+T_2}

Therefore, the converter shown is a step down chooper.

There are 10 questions to complete.