Power Electronics Question Bank

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POWER ELECTRONICS Question Bank by

Shankar Version: PEQBTNC06

Conventional, Objective and Interview questions in Power Electronics for GATE |IES | All PSUs

Version Code: PEQBTNC06


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Copyright © Reserved 2014

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PREFACE I would like to present this Question bank on Power electronics to my student community at free of cost. I have prepared both conventional and objective questions in the subject of Power Electronics from various sources and knowledge gained from my teaching experience over a span of 7 years. The content of this Question bank is mainly useful for GATE and Engineering Service (ESE) aspirants to gain in depth analysis into the subject. As previous GATE and ESE papers are available in various modes, I have not repeated those questions here. It is expected that the reader must have basic knowledge in the area of Power Electronics and its applications at under graduate level before solving this booklet. This booklet contains the following sections: Conventional Questions: By solving these questions, the reader can enhance his/her basic concepts in Power electronics and can establish the link between other branches of electrical engineering. By solving these types of questions, I am sure your confidence levels in the subject will increase which is the key thing for success in any competitive exam and in career as well. I have provided answers for around 90% of questions and remaining 10% is left as open for the readers so that they can sharpen their knowledge. I will address these questions in the next release of this booklet based on response and will provide some more open questions in subsequent releases Objective Questions: In the present trend, every exam is based on Objective questions. After solving the conventional questions, the reader can test his/her understanding in the concepts by taking 4 practice tests based on objective questions Interview Questions: These questions are collected from various interviews like M.Tech admissions in IITs, OCES & DGFS interviews in BARC etc from student community itself. In fact, these questions are not my creation and collected from various students. If you attend any interview, you can also share your experience for the benefit of your next generation And then I have given practical approach for compensator design for PE converter After solving this booklet, I am expecting you can face any exam, or interview very confidently especially in the field of Power Electronics. With initial thoughts in my mind, this booklet came out. I am planning to update this booklet based on feedback received and will revise in regular intervals and need basis Finally I would like to express my sincere thanks to Mr Saida (my student) for his valuable suggestions and efforts in the drafting corrections If you have any suggestions for further development of this booklet, if you find any mistakes or corrections required, please feel free to write an email to [email protected] by referring version code



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INDEX Sl. No 0 1 2 3 4 5 6 7 8 10 11 12

Description Preface Conventional Questions Objective Questions - Practice Test 1 Objective Questions - Practice Test 2 Objective Questions - Practice Test 3 Objective Questions - Practice Test 4 Interview Questions Answers for Conventional Questions Answers for Objective Questions Compensator Design Useful units for Electrical Engineering Useful Mathematical Formulae


Page No 3 5 35 47 60 68 76 89 92 93 114 116


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Power Electronics Conventional Questions Q1. In a power electronics laboratory, an experiment is conducted to find circuit component value and its circuit diagram is shown in Fig. The voltage and current waveforms for periodic time of 20 ms are captured from oscilloscope are also shown below. Find out what could be the circuit element and its value vi 10V i1(t)

ii

1A t

Vi(t) −10V Ts 2

Fig for Q1 Q2. In a power electronics laboratory, an experiment is conducted to find circuit component value and its circuit diagram is shown in Fig. The voltage and current waveforms for periodic time of 10 ms are captured from oscilloscope are also shown below. Find out what could be the circuit element and its value Ii v(t)

10A

vi

1V Ii(t)

t

Ts 2

Fig for Q2 Q3. In a power electronics laboratory, the impedance Z(s) diagram (bode plot) for a pure inductor is captured using network analyzer as shown in Fig



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dBΩ Z(s)

6 dB 0 dB

ω1

−6 dB

ω2

log10(ω)

ω0

Fig for Q3 (a) If ω0 = 100 rad/s, find the value of inductance (b) If ω1 = 50 rad/s and ω2 = 200 rad/s then find the value of Z (s) in dB and Ω at ω = 1000 rad/s Q4. In a power electronics laboratory, the impedance Z (s) diagram (bode plot) for a pure capacitor is captured using network analyzer as shown in Fig dBΩ Z(s)

20 dB 0 dB ω1

ω0

ω2

log10(ω)

−20 dB

Fig for Q4 (a) If C = 10µF then find the values of ω0, ω1 and ω2 in rad/s (These frequencies are in decade fashion) (b) Find the frequency in rad/s when Z (s) = 2 Ω Q5. The current through and the voltage across a power semi conductor switch is shown in Fig.



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20A

Fig for Q5 Evaluate, (a) The average current and the RMS current rating of the device. (b) The conduction loss in the device Q6. The approximate wave shape of a capacitor current in a commutation circuit is shown in Fig. The capacitor has an equivalent series resistance (ESR) of 20 mΩ.

Fig for Q6 Evaluate the power dissipation in the capacitor Q7. In an inverter, the current through the active device is measured and found to be as shown in Fig. The switching frequency may be considered very high compared to the fundamental frequency of the output current.

Fig for Q7



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Determine, (a) The average and RMS current rating of the switch. (b) If the power device is a power transistor with a Vce drop of 1.2 V, evaluate the conduction loss Q8. The SCR is used in an application carrying half sinusoidal current of period 1 ms and a peak of 100 A as shown in Fig. The SCR may be modeled during conduction to have a constant voltage drop of 1.1 V and a dynamic resistance of 8 mΩ. Calculate the average conduction loss in the device for this application

Fig for Q8 Q9. The periodic current through a power-switching device in a switching converter application is shown in Fig.

Fig for Q9 (a) Evaluate the average current through the device. (b) Evaluate the RMS current through the device. (c) A BJT with a device drop of 1.2 V and a MOSFET with an of 150 mΩ are considered for this application. Evaluate the conduction loss in the device in either case. Q10. A power diode (ideal in blocking and switching) shown in Fig, is capable of dissipating 75 W. For square wave operation, it is rated for peak current of 100 A and 135 A at duty ratios 0.5 and 0.33 respectively.



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Fig for Q10 (a) Evaluate the ON state model of the diode (This procedure is known as piecewise modeling of semiconductor device). (b) The above diode while dissipating 40W at an ambient temperature of 350 C, is running with a case temperature of 750 C and 1250 C respectively. Evaluate the thermal resistances of the device Q11. The diode (20ETS08) is a 20 A, 800 V rectifier diode. It has a voltage drop of 0.8 V at 2 A and 1.2 V at 30 A. (a) Find a piece-wise linear model for this diode consisting of a cut-in voltage and dynamic resistance. (b) With this piece-wise model evaluate its conduction loss for a 30 A peak half sine wave of current. Q12. A power-switching device is rated for 600 V and 30 A. The device has an on state voltage drop of 1.5 V to 2.4 V for conduction current in the range of 15 to 30 A. The device has a leakage current of 5 mA while blocking 600 V. Evaluate (a) The maximum conduction loss, (b) The maximum blocking loss, and (c) The ratio of the conduction and blocking loss with maximum possible power that may be controlled by this switch and make your comment on the result. Q13. A composite switch used in a power converter is shown in Fig. The periodic current through the switch is also shown.



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Fig for Q13 Evaluate, (a) The average current and RMS current through the composite switch. (b) The power loss in the MOSFET and the diode of the composite switch. Q14. A power MOSFET has an Rds(on) of 50 mΩ. The device carries a current as shown in Fig. Consider the switching process to be ideal and evaluate the conduction loss in the device. (Explore if you can simplify the evaluation of RMS value by applying superposition).

Fig for Q14 Q15. A power-switching device is ideal in conduction and blocking (0 V during conduction and 0 A in blocking). It is used in a circuit with switching voltages and currents as shown. The switching waveforms under resistive loading and inductive loading are shown in Fig. The switching times tr and tf are 100 ns and 200 ns respectively. Evaluate, (a) The switch-on and switch-off energy loss (in joule) for resistive loading (b) The switch-on and switch-off energy loss (in joule) for inductive loading (c) The resistive and inductive switching losses in watt for a switching frequency of 100 kHz.



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Fig for Q15 Q16. The current through and the voltage across a switching device is given in Fig. Evaluate the approximate switch-off and switch-on energy loss in the device.

Fig for Q16 Q17. A disc type Thyristor is shown with its cooling arrangement in Fig. The device is operating with a steady power dissipation of 200 W.

Fig for Q17



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Various thermal resistances are defined as below: = 0.3 C/W; = 0.3 C/W; = 0.05 C/W; = 0.05 C/W; = 0.5 C/W; = 0.4 C/W; Evaluate the steady state temperature rise of the junction

Q18. A composite switch (Q1 and Q2 in parallel) carrying a load current of 10 A is shown in Fig. The switches may be considered ideal in switching. The on-state resistances of the devices Q1 and Q2 are respectively 0.8 Ω and 0.2 Ω. The devices are mounted on a common heat sink held at a temperature of 800 C.

Fig for Q18 Evaluate, (a) RMS values of I1 and I2 (b) The average power dissipation (P1 and P2) in Q1 and Q2. (c) The junction temperatures of Q1 and Q2 (Note: RJC1 and RJC2 is thermal resistances from Junction to case of Q1 and Q2). Q19.

Fig for Q19



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The voltage across a capacitor used for a power electronic application is shown in Fig. The capacitance value is 2.5 µF. The capacitor has an equivalent series resistance (ESR) of 10 mΩ. The dielectric of the capacitor has a thermal resistance of 0.2 0C/W to the ambient. (a) Sketch the current waveform through the capacitor for one cycle (b) Evaluate the losses in the capacitor (c) Evaluate the temperature rise in the dielectric of the capacitor Q20. A power electronic capacitor is specified to have the following values. Capacitance = 10 µF; ESR = 30 mΩ; ESL = 75 nH; Sketch the impedance of the capacitor as a function of frequency in the dBΩ vs log ω. Determine the range of frequency for which the capacitor may be idealized to be a pure capacitance of 10 µF

Q21. The current through a diode is shown in Fig. Consider the following data for waveform analysis. t1 = 100 µs, t2 = 350 µs, t3 = 500 µs, f = 250 Hz, fs = 5 kHz, Im = 450 A and Ia = 150 A Determine, (a) Average diode current and (b) RMS diode current

Im Ia

i1=Imsinωst i2 t1 T=

t2

t3

T

t

1 f

Fig for Q21 *Q22. Visit a manufacturer's website, identify a controlled power switching device (BJT, or MOSFET, or IGBT etc) of rating > 10A and > 600V. Download the datasheet and fill in the following. (a) Manufacturer (b) Device and Type No (c) On-state voltage (V) (d) ON-state current (A) (e) Transient switching times (s) (f) Maximum junction temperature (K) (g) Recommended drive conditions (?) (h) Conduction loss at rated current (W) (i) Blocking loss at rated voltage (W) (j) Switching energy loss (J).



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Q23. The magnetic circuit of a coupled inductor is shown in Fig. The magnetic material of the core may be assumed to be ideal. N1= 100 T; N2 = 200 T; Ag1= Ag2 = 40mm2; Ag = 80mm2; lg1 = 1mm; lg2 = 2mm; lg = 1.5mm

Fig for Q23 Evaluate the inductances L1; L2; L12; L21 *Q24. The following figures (a, b, and c) show three magnetic circuits with an exciting winding on each having 100 turns. The core in (c) is obtained by assembling together one each of cores shown in (a) and (b). The magnetic material for the core may be considered to have very large permeability with saturation flux density of 0.2 T. (a) Evaluate the expression for flux linkages (Nϕ) for cores (a) and (b) as a function of the exciting current ia and ib. (b) Plot the characteristics Nϕ vs i for the cores (a) and (b). (c) From the above plot Nϕ vs i for the composite core (c). (d) Comment on the inductance of the circuit (c).

Fig for Q24



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*Q25. 0

A 0

(a) π

A

2π

0

(b) 0

µ µ 2 2

µ µ 2 2

0

A

(c)

A µ µ 2 2

0

0

µ µ 2 2

(d)

A 0

A

ωt

(e) A

A

0

ωt

(f) t DT T

Fig for Q25

(a) For the waveforms shown in Fig, calculate their average value, RMS values of the fundamental and the harmonic frequency components (b) For the waveforms shown in Fig, consider A = 100 and µ = 600 where applicable. Calculate their total RMS values (c) For the waveforms shown from a to d in Fig shown, calculate the ratio of (i) the fundamental frequency component to the total RMS value and (ii) the distortion component to the total RMS value (d) For the waveforms shown from e to f in Fig shown, calculate the ratio of the average value to the total RMS value (form factor)



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(e) For some common rectifiers, the line currents may be like the waveforms shown in a to b of Fig 2 with µ = 600. The need for power per phase is the same in the two cases i.e, the RMS value of the fundamental component the line currents are 100 A in both cases. (i) Calculate the amplitude and the RMS value for waveform a in Fig shown (ii) Calculate the amplitude and the RMS value for waveform b in Fig shown (iii) Comment on the above answers Q26. An inductive load connected to a 120 V, 60 Hz ac source draws 1 kW at a power factor of 0.8. Calculate the capacitance required in parallel with the load in order to bring the combined pf to be 0.95 lag Q27. A 110 V/220 V, 60 Hz single phase 1 kVA transformer has a leakage reactance of 4 %. Calculate its total leakage inductance referred to (a) the 110 V side and (b) 220 V side *Q28. An input voltage of a repetitive waveform is filtered and the applied across the load resistance as shown in Fig. Consider the system to be in steady state. It is given that L = 5 µH and Pload = 250 W

vi iload

+

+

+

iL vi

v0 ic

−

15V

R −

(load)

(Fig 3)

t

0 4 µs 6 µs

Fig for Q28 (a) Calculate the average output voltage V0 (b) Assume that C ∞ so that vo (t) = V0. Calculate Iload and the RMS value of the capacitor current ic (c) In part (b), plot vo and iL *Q29. The voltage v across load and current i into the positive polarity are as follows (ω1 ≠ ω3 ) = + √2 !"# + √2 "$%# + √2& !"#& 'V http://electrical-mentor.blogspot.in/


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$ = ) + √2) !"# + √2)& !"#& − +& 'A Calculate the following: (a) The average power P supplied to the load (b) The RMS value of $and (c) The power factor at which the load is operating Q30. A single phase half wave diode rectifier is designed to supply dc output voltage of 200 V and load resistance of 10 Ω. Calculate the average and RMS current ratings of diode, PIV of diode and transformer for this circuit arrangement Q31. (a) In the circuit shown in Fig, The PMMC ammeter reads 10 A. Find the inductance value. Also find volt meters reading if they are PMMC type

V1 A 220V

∼

V2

L

50Hz

Fig for Q31 (b) If all the meters in part (a) are replaced with MI type instruments, then find the meter readings Q32. (a) In the circuit shown in Fig, Ideal PMMC instruments are placed. Find voltmeter readings V1 A 220V

∼

1µF

C

V2

50Hz

Fig for Q32




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(b) In case voltmeter 2 in part (a) is replaced by MI type, then find its reading Q33. A battery is to be charged by a single phase half wave diode rectifier. The supply voltage is 30 V, 50 Hz and the battery emf is constant at 6 V. Determine, (a) The resistance to be inserted in series with the battery to limit the charging current to 4 A. Take a voltage drop of 1 V across the diode when it is ON (b) PIV of diode (c) In case battery capacity is 100 W.h, find the charging time in hours Q34. Find the time required to deliver a charge of 200 A.h through a single phase half wave diode rectifier with an output current of 100 A (RMS) and with sinusoidal input voltage. Assume diode conduction over a half cycle. *Q35. (a) A dc battery is to be charged through a resistor R from a single phase half wave uncontrolled rectifier. For an ac source voltage of 230 V 50 Hz, find the value of average charging current and supply power factor for R = 8 Ω and E = 150 V (b) In case, if diode is replaced by SCR and fired continuously through a constant dc signal, the repeat part (a) (c) In case, SCR in part (b) is triggered after 1 ms from its forward bias point. Then repeat part (b) (d) Comment on all the calculations Q36.

Fig for Q36 (a) For the single phase half wave rectifier shown find out the PIV rating of diode



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(b) Will the required PIV rating change if a inductor is placed between the diode and capacitor (c) What will be the required VRRM rating if the capacitor is removed? Assume a resistive load. (d) The source of the single phase rectifier circuit has an internal resistance of 2 Ω. Find out the required Non repetitive peak surge current rating of the diode. Also 2

find the i t rating of the protective fuse to be connected in series with the diode. *Q37.

A single phase midpoint converter is shown in Fig, where we assume the transformer is to be ideal and the dc side load to be represented by a current stiff load. Calculate the VA rating of the transformer as a ratio of the average power supplied to the load. n:1:1

D1

Id Vp=Vmsinωt

∼

D2

Fig for Q37 Q38. A single bridge consists of one SCR and three diodes operating with a firing angle of 450. Find the average load current and power delivered to the load in case the load consists of R = 8.356 Ω, L = 8 mH and E = 100 V. Assume the load current is constant in the entire working range Q39. A single phase full converter feeds power to RLE load with R = 10 Ω, L = 6 mH and E = 60 V. The ac source voltage is 220 V, 50 Hz. In case one of the four SCRs gets open circuited due to fault, find the average value of load current by assuming the load current as continuous and firing angle is 450. Q40. A three phase half wave phase controlled rectifier delivers power to a resistive load of 10 Ω. Input to the rectifier is 400 V, 50 Hz three phase ac supply. Find power delivered to the load for a firing angle of (a) 150 and (b) 600




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Q41. A three phase half wave phase controlled rectifier is operated from a 3-ph 230 V, 50 Hz supply with load resistance of 10 Ω. An average output voltage of 50 % of the maximum possible output voltage is required. Determine, (a) Firing angle of the converter (b) Average and RMS values of load current Q42. A three phase half wave phase controlled rectifier is fed from a 3-ph, 400 V 50 Hz source and is connected to load taking a constant current of 30 A. SCRs are having a voltage drop of 1.9 V during their conduction. Calculate, (a) Average value of load voltage for a firing angle of 300 and 600 (b) Average and RMS current ratings of SCRs as well as PIV of SCRs (c) Power loss in each SCR (d) In case, if freewheeling diode (FD) is connected across load, find the average value of output voltage, average and RMS value of FD current for firing angles of 300 and 600 Q43. A three phase half wave phase controlled rectifier is operating from a 3-ph, 400 V 50 Hz and delivers power to the armature of a dc motor with negligible resistance and large inductor in the dc bus. The source transformer has DY-11 connection with unity phase turns ratio. Back emf of the motor is 300 V. Find the firing angle of the rectifier Q44. A three phase fully controlled rectifier is delivers a ripple free load current of 10 A with a firing angle of 300. The average output voltage is 400 V. Find active and reactive power input to the bridge and input power factor of the converter Q45. A battery consists of R = 5 Ω and E = 150 V is charging through a three phase half wave phase controlled rectifier. Input voltage to the converter is 230 V (RMS) from any line to neutral and firing angle for SCRs is 300. Find average current flowing through the battery Q46. A three phase full converter is fed from 230 V, 50 Hz supply having source inductance of 4 mH per phase. The load current is 10 A and ripple free (a) Calculate the voltage drop in dc output voltage due to source inductance (b) If dc output voltage is 210 V, find firing angle and overlap period (c) In case, the bridge is made to operate as a line commutated inverter with dc voltage of 210 V, find firing angle for the same load current



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Q47. A three phase half wave diode rectifier delivers power to an inductive load which takes ripple free current of 100 A. The source voltage to the bridge is 3-ph 440 V, 50 Hz. Determine, (a) The average and RMS current ratings of diode (b) PIV of diode (c) RMS value of source current *Q48. A battery with a nominal voltage of 200 V and internal resistance of 10 mΩ has to be charged at constant current of 20 A from a 3-phase 220 V, 50 Hz AC power supply. Which of the following converter circuit will give better performance in terms of Distortion factor in source current, fundamental power factor, and total input power factor? (i) 3-ϕ Full converter (ii) 3-ϕ Semi converter Q49. (a) For the same average DC output voltage of 100 V, calculate the PIV of SCR for the following configurations (Consider α = 00) (i) 1-ϕ full wave center tap converter (midpoint converter) (ii) 1-ϕ full converter (iii) 1-ϕ semi converter (iv) 3-ϕ half wave converter (v) 3-ϕ full converter (vi) 3-ϕ semi converter (b) From the above calculations, which configuration is having maximum and minimum PIV rating for SCR Q50.

Fig for Q50



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Two six pulse converters, used for a bipolar HVDC transmission system (shown in figure) are rated at 1000 MW, ±200 kV. Evaluate, the RMS current and peak reverse voltage ratings for each of the SCRs Q51. A buck converter has an input voltage of 16 V. The required average output voltage is 8 V and peak to peak ripple in output voltage is 10 mV. The switching frequency of the converter is 25 kHz. If the peak to peak ripple in inductor current is limited to 0.7 A. Determine, (a) Duty cycle ratio (b) Filter inductance (c) Filter capacitance Q52. The input voltage to a boost converter is 8 V. The required average output voltage is 16 V and the average output load current is 0.5 A. The switching frequency of the converter is 30 kHz. If L = 160 µH and C = 380 µF, calculate, (a) Duty cycle ratio (b) The peak to peak ripple in inductor current (c) The peak current of the switch (d) The ripple voltage in capacitor Q53. The input voltage to a buck- boost converter is 10 V. The switch is operating with a duty ratio of 0.3 and the switching frequency is 25 kHz. The filter inductance is 150 µH and filter capacitance is 220 µF. The average load current is 1.2 A. Determine, (a) The average output voltage (b) The peak to peak ripple in output voltage (c) The peak to peak ripple in inductor current (d) The peak and average current of the switch *Q54. A switched mode power converter is shown in Fig. The switches S are ON during DTs and the switches S´ are ON during (1-D)Ts S Ig + Vg

L

S′

V0+∆V0

IL+∆IL S′

I0 S

C

R

Fig for Q54 (a) Evaluate the steady state performance of the circuit. Assume the switches, inductors and capacitors are to be ideal (b) Indicate how the voltage conversion ratio will be modified if the inductor has a resistance of RL



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*Q55. Consider the circuit given in Fig. Carry out the steady state analysis for the same and evaluate the following

Fig for Q55 (a) Output voltage (b) Average input current (c) Output power (d) Efficiency (e) Power dissipation in the MOSFET and the diode *Q56. Figure P13 shows a boost converter cascaded by a buck converter. The switches S −

and S are ON during DTS and (1-D)TS respectively.

Fig for Q56 (a) Evaluate the steady state currents in L1 and L2 in terms of I0 and D. (b) Evaluate the steady state voltages across C1 and C2 in terms of Vg and D (c) Evaluate the current ripples in L1 and L2 (d) Evaluate the voltage ripple in C1 and C2 Q57. A DC-DC converter circuit is shown in Fig. It consists of on active switch (S1) and three passive switches D1, D2 and D3. It has four energy storage elements - two inductors (L1, L2) and two capacitors (C1, C2). Consider that the currents through the inductor and voltage across the capacitors are all continuous. The switch S1 is on during Ton and off during Toff . The duty ratio of S1 may be designated as D. The switch drops may be taken to be zero during conduction.



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Fig for Q57 (a) Indicate the duty ratios of the three diodes D1, D2 and D3. (b) Evaluate the steady-state inductor currents (I1, I2) and the steady state capacitor voltages (VC1, VC2). (c) Evaluate the voltage conversion ratio Vo/Vg. (d) Sketch the steady-state waveforms of (I1, I2; VC1, and VC2). (e) Evaluate the ripple currents ∆I1 and ∆I2 in terms of Vg, D, L1, L2 and R. (f) Evaluate the ripple voltages ∆VC1 and ∆VC2 in terms of Vg, D, L1, L2, C1, C2, and R. (g) Calculate L1, L2, C1 and C2 by considering the circuit data as Vg = 100 V, D = 0.6, R = 12 Ω and Ts = 20 µs. Assume ripple in capacitor voltage is 1% of its average value and ripple in inductor current is 10 % of its average value Q58. In the buck converter shown the diode D has a lead inductance of 0.2µH and a reverse recovery change of 10 µC at iD =10A.

Fig for Q58 Find peak current through active switch. Q59. The following Figure shows a PI controller and its asymptotic magnitude bode plot. Select R1, R2, and C. make any suitable assumptions if necessary



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Fig for Q59 *Q60. A fly back converter operating at a duty ratio of 0.3 is shown in the following Fig. The transistor ON state drop is 1 V. The diode ON state drop is 0.7 V. The resistance of the inductor windings is 0.5 and 0.25 for the primary and secondary respectively.

Fig for Q60 Evaluate the voltage conversion ratio and efficiency of the converter Q61 In a flyback converter, the required output voltage is 100 V for a nominal input voltage of 12 V. If the switch is operating at D = 0.5 (a) Find the turns ratio of flyback transformer. Assume voltage drop across switch is 0.8 V and diode is 0.8 V (b) Find minimum and maximum values of D, if input voltage varies from 10 to 14 V, by maintaining V0 be constant. Assume the switching frequency of 2 kHz (c) Find the value of Ls on secondary winding so that secondary current is just continuous at the minimum value of D calculated in part (b). Consider load resistance of 100 Ω



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Q62. A fly-back converter is to be designed to operate in just-continuous conduction mode when the input dc is at its minimum expected voltage of 200 volt and when the load draws maximum power. The load voltage is regulated at 16 volts. What should be the primary to secondary turns ratio (N1/N2) of the transformer if the switch duty ratio is limited to 80 %. Neglect ON-state voltage drop across switch and diodes Q63. The average output voltage flyback converter is 24 V at a resistive load of 0.8 Ω. The duty cycle ratio is 0.5 and switching frequency is 1 kHz. The ON state voltage drops of BJT and Diode are VT = 1.2 V and VD = 0.7 V. The turns ratio of transformer is => = 0.25. Find the efficiency of the converter = ?

Q64. Find maximum voltage stress of the switch in the primary winding and diode in the tertiary winding if the forward converter-transformer has 10 primary turns and 15 tertiary turns and the maximum input dc voltage is 300 V Q65. If the turns ratio of the primary and tertiary windings of the forward transformer are in the ratio of 1:2, what is the maximum duty ratio at which the converter can be operated? Corresponding to this duty ratio, what should be the minimum ratio of secondary to primary turns if the input dc supply is 400 V and the required output voltage is 15 V. Neglect switch and diode conduction voltage drops. Q66.

Fig for Q66



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A forward converter is operating at the boundary of continuous and discontinuous conduction. The switch is operating at 100 kHz. Assume µ = ∞ for the core so that energy recovery winding is ignored. A load of 10 A at 20 V is being supplied. ∆AB

(a) Find the inductance value

(b) Find peak to peak ripple in output voltage as % of average output voltage (

AB

)

*Q67. A forward converter operating at a duty ratio of 0.3 is shown in the following Fig. The transistor while ON drops a voltage of 1.0 V, and the diode while ON drops a voltage of 0.7 V.

Fig for Q67 Evaluate the output voltage and efficiency of the converter. *Q68. A forward converter operating at a duty ratio of 0.4 is shown in the following Fig. Assume the components to be ideal.

Fig for Q68




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Sketch the following waveforms under steady state. (a) Inductor current. (b) Secondary current. (c) Primary current. (d) Output voltage. Q69. A single phase full bridge VSI is fed from 230 V dc. In the output voltage waveform, only fundamental component of voltage is considered. (a) Determine the RMS current ratings of switches and diode of the bridge for the following types of loads: (i) R = 2 Ω (ii) ωL = 2 Ω (b) Find also the repetitive peak voltage that may appear across switches in part (a) Q70.

A single phase full bridge VSI delivers power to RLC load with R = 3 Ω and XL = 12 Ω. The bridge operates with periodicity of 0.2 ms. Calculate the value of C so that load commutation is achieved for the SCRs. Turn off time for thyristors is 12 µs and consider factor of safety 2. Assume that load current contains only fundamental component. Q71. A single phase full bridge VSI delivers power at 50 Hz to RLC load with R = 5 Ω, L = 0.3 H and C = 50 µF. The dc input voltage is 220 V. Evaluate, (a) Expression for load current up to 5th harmonic (b) Power delivered to load and fundamental power (c) The RMS and peak currents of each switch (d) Conduction time of switches and diodes by considering only fundamental components Q72. A single phase full bridge VSI delivers power to a load of R = 12 Ω and L = 0.04 H from a 400 V DC source. If the inverter operates at a frequency of 50 Hz, determine the power delivered to the load for (a) Square wave operation (b) Quasi square wave operation with an on period of 0.6 of a cycle (c) Two symmetrically spaced pulses per half cycle with an on period of 0.6 of a cycle Q73. A single phase current source inverter (CSI) with ideal switches has the following data: Source current = 30 A, frequency = 500 Hz, and pure capacitive load = 20 µF For this inverter, Evaluate: http://electrical-mentor.blogspot.in/


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(a) The circuit turn off time (b) The maximum value of reverse voltage that appears across switches Q74. A single phase capacitor commutated CSI connected to the load R has the following data: R = 40 Ω, C = 50 µF, Source current = 40 A, frequency = 500 Hz. Evaluate, (a) Express the load current as function of time and its value at t = 0 and t = T/2 (b) The circuit turn off time Q75. A 3-phase 1200 mode inverter feeds a star connected load of R = 5 Ω. DC source voltage is 230 V and output frequency is 50 Hz. (a) Express the line to line output voltage, line to neutral output voltage and line current in fourier series up to 11th harmonic components. (b) RMS values of line to line and line to neutral voltages (c) RMS values of line to line and line to neutral voltages at fundamental frequency (d) THD for line current (e) Load power and average value of source current (f) Average and RMS value of switch currents Q76. SCR T in the figure below is initially OFF and is triggered with a single pulse of EE EE width 10 s. It is given that C = D F G μH and K = D F G μF. Assume latching and

holding currents are zero and initial conditions L and C are zero. (a) Evaluate the conduction time of SCR T (b) Voltage across device and capacitor after SCR is turned OFF

Fig for Q76 Q77. A circuit employing current commutation as shown below has C = 20 µF and L = 3 µH. Initially capacitor is charged towards the source voltage (=230 V dc).



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Fig for Q77 Determine the conduction time for auxiliary SCR (TA) and circuit turn off time for main SCR (TM) in case constant load current is (a) 300 A and (b) 60 A Q78. In the circuit shown in the Figure below, has commutating elements L = 20 µH and C = 40 µF are connected in series with the load resistance of R = 1 Ω.

Fig for Q78 Check whether self commutation or load commutation, would occur or not. Find also conduction time of SCR Q79. For the circuit shown in Fig, (dv/dt) rating of thysristor T is 400 V/µs. and its junction capacitance is 25 pF. Switch S is closed at t = 0.



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Fig for Q79 (a) Calculate the value of Cs so that thyristor T is not turned on due to dv/dt (b) In case maximum current through thyristor in above circuit is limited to 40 A, determine the value of Rs Q80. For illustrating complementary commutation, the following circuit is employed where Vdc = 200 V and R1 = 10 Ω.

Fig for Q80 (a) Find the value of capacitor so that T1 is commutated in 50 µs. (b) It is required that SCR T2 is turned off naturally when current through it falls below holding current of 4 mA. Find the value of R2. Q81. In the complementary scheme of commutation, Source voltage is 200 V dc, R1 = 10 Ω and R2 = 100 Ω. Evaluate, (a) Peak value of current through SCRs T1 and T2 (b) Capacitance value C if each SCR has turn off time of 40 µs. Take a factor of safety 2. Justify if you make any assumptions http://electrical-mentor.blogspot.in/


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*Q82. (a) A separately excited dc motor is represented in block diagram form as show in Fig. Fill all the blocks with usual and your convenient notation

TWL Vt(s)

?

Te(s)

Ia(s)

?

?

Q(s)

-Ea(s) ?

Fig for Q82-a

(b) From the block diagram given in part (a), find G1 (s) and G2 (s) as per the definitions given below #O " #O " M " = N Q V%W M " = N Q P " XYZ " RST UE

A[ UE

(c) Now, express G1 (s) in terms of machine mechanical and electrical time constants which are defined as below: ]^ _ C^ \O = V%W \b = `R `a ]^ Where, KT and KE are torque and electrical constant (d) The dc motor under consideration is having the following data. T rated = 10 N-m ; Nrated = 3700 rpm KT = 0.5 N-m/A ; KE = 53V/1000 rpm; Ra = 0.37 Ω, 6e = 4.05ms, 6m = 11.7 ms If this motor is controlled from a power electronic converter, Evaluate the terminal voltage required (in steady state) if motor is required to deliver a torque of 5 Nm at a speed of 1500 rpm (e)

If G1(s) in the given statement is expressed as M " =

/cd

efD

gh kg Ge g ij ij

Then find the values of D and ωn by using data given in part (d). Now, plot the asymptotic magnitude and phase plot of G1 (s) by means of bode plot. Then find out Phase margin and Gain margin with approximate hand calculations or using MATLAB http://electrical-mentor.blogspot.in/


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(f) A PI controller is used in the speed control loop (shown in Fig) to obtain the transfer function of the following form:

*

Q (s)

*

Σ

Kp

ω (s)

Fw(s)

−

1 2o " 1 + " D# G + #p p Where D = 0.5 and ωn = 300 rad/s

lY " =

#" = # ∗ "

ω(s)

1 s

Q(s)

Fig for Q82-f

(g) Draw the bode plot of closed loop transfer function lq " = q∗ f if the gain KP = qf

60 is used for the proportional position regulator.

(h) What is the bandwidth of the above closed loop systems (Hint: This is indication of speed of the response) Q83. A 200 V, 1450 rpm, 100 A separately excited dc motor has an armature resistance of 0.04 Ω. The machine is driven by a 3-ϕ half controlled rectifier operating from a 3-ϕ 220 V, 50 Hz supply. The motor operates at rated speed and rated load torque. Assuming continuous conduction to evaluate (a) Firing angle of the converter (b) RMS value of fundamental input current (c) Fundamental power factor (d) THD in source current Q84. A 3-ϕ full converter is feeding a 100 HP, 400 V, 1500 rpm separately excited dc motor having armature resistance of 0.1 Ω and filter choke which is connected in series with armature to maintain constant current of 175 A. The bridge is connected to a 3-ϕ, 400 V, 50 Hz supply. The source has an inductance of 0.5 mH and back emf constant of the machine is 0.25 V/rpm. Evaluate (a) Firing angle (b) Overlap angle




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Q85. A 200 V, 875 rpm, 150 A separately excited dc motor has an armature resistance of 0.06 Ω. It is fed from a single phase fully controlled rectifier with an ac source voltage of 220 V, 50 Hz. Assuming continuous conduction calculate, (a) Firing angle for rated motor torque and at 750 rpm (b) Firing angle for rated motor torque and at (-500) rpm (c) Motor speed for α = 1600 and rated torque Q86. A 220 V, 1500 rpm, 50 A separately excited dc motor with armature resistance of 0.5 Ω is fed from a 3-ϕ full converter. Available ac source has a line voltage of 440 V, 50 Hz. A Y-∆ connected transformer is used to feed the full converter so that motor rated terminal voltage equals the rated voltage when converter firing angle is zero. (a) Calculate the turns ratio of transformer (between phase windings of primary and secondary) (b) Determine the firing angle of the converter when (i) motor is running at 1200 rpm and rated torque (ii) motor is running at -800 rpm and twice the rated torque Q87. A 230V, 960 rpm and 200 A separately excited dc motor with armature resistance of

0.02 Ω. The motor is fed from basic chopper circuit which provides both motoring and baking operation. The source has a voltage of 230 V. Assuming continuous conduction (a) Calculate the duty ratio of the chopper for motoring operation at rated torque and 350 rpm (b) Calculate the duty ratio of the chopper for braking operation at rated torque and 350 rpm (c) If maximum duty ratio of chopper is limited to 0.95 and maximum permissible motor current is twice the rated. Calculate maximum permissible motor speed obtainable without field weakening and power fed to the source (d)If motor field is also controlled in part (c), calculate filed current as a fraction of its rated value for a speed of 1200 rpm Q88. A four pole, 10 HP, 460 V Induction motor is supplying its rated power to a centrifugal pump type of load at a 60 Hz frequency. Its rated speed is 1746 rpm (a) Calculate its speed, slip frequency, and slip when it is supplied by a 230 V, 30 Hz source (b) If the starting torque is required to be 150 % of the rated torque for a constant air gap flux, find the starting frequency that need to apply to the motor



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Objective Questions Practice Test - 1 Q1. Which of the following power semi conductor device is popularly using in wind and solar power converters? (A) SCR (B) GTO (C) IGBT (D) BJT Q2. Which of the following MOSFET is most suitable as power electronic switch? (A) N – channel depletion MOSFET (B) P – channel depletion MOSFET (C) N – channel enhancement MOSFET (D) P – channel enhancement MOSFET Q3. Consider the following statements and choose the correct option. Statements about ideal switches: 1. In OFF state, current flowing through ideal switch is zero. 2. In ON state, voltage across ideal switch is zero. 3. The ideal switch need finite energy to switch ON/OFF or OFF/ON. 4. The switch can be turned ON and OFF instantaneously (A) All statements are true (B) Only 1, 2 and 4 true (C) Only 1, 2 and 3 are true (D) None 04. Match List – I (Transfer characteristics) and List – II (Devices) and select the correct option. List – I List – II ID

(1)

(2)

ID

(P)

(Q)

D G

G VGs

ID

(3)

(4)

S

S

VGs

D

(R)

ID

(S)

G

G S

VGs

(A) (C)

P 1 4

Q 3 1

R 2 3

S

VGs

S 4 2

(B) (D)

P 2 1

Q 1 2

D

R 4 3

S 3 4

Q5. A BJT with a device drop of 1.2 V is carrying a current which is shown below. i

10A

http://electrical-mentor.blogspot.in/ 0

Copyright © Reserved 2014 (µs) 5

15 20

30

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(A) 5 W

(B) 5.5 W

(C) 6 W

(D) 8 W

Q6. Which of the following device (s) will be considered as bipolar and unidirectional switch. 1. SCR 2. Symmetrical GTO 3. Asymmetrical GTO 4. BJT in series with diode (A) Only 1, 2, 3

(B) 1, 3 and 4 (C) 1, 2, 3, 4

(D) 1, 2 and 4

Q7. During forward conduction, a thyristor has static V – I characteristic as shown by a straight line in given figure. Find the average power loss in the thyristor in case thyristor is carrying a constant current of 80 A for one half cycle. Ia

(A) 70.4 W (B) 11.6 W (C) 40 W (D) 50 W

100A

Va

0.8V 2.0V

Q8. The switching waveform for a power transistor are shown in below figure In case, Ics=80A, Vcc=220V, ton=1.5 µs and toff=4 µs then power loss in the transistor during turn ON is ic (A) 8.8 W (B) 23.46 W (C) 32.6 W (D) None

ICs t υCE VCC t ton

tof T

Q9. For a power diode, the reverse recovery time is 3.9 µs and the rate of diode current decay is 50 A/µs. For a softness factor of 0.3, Find the storage charge. (A) 350 µC (B) 292.5 µC (C) 150 µC (D) 200 µC Q10. Turn on time of an SCR in series with RL circuit can be reduced by (A) Increasing R (B) Decreasing R (C) Increasing L (D) Decreasing L



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Q11. For dynamic equalizing circuit used for series connected SCRs, the selection of C is based on (A) Reverse recovery characteristics (B) Turn – on characteristics (C) Turn – off characteristics (D) Rise time characteristics The circuit symbol for GTO is

Q12.

A

A

A

A

G

G

G

G K (Q)

(P)

K (R)

G

(A) P, Q and S are correct (C) Only Q & S are correct

K (S)

(B) Only P & Q are correct (D) All are symbols are GTO

Q13. Input power factor of any rectifier circuit can be defined as below: (A) IPF =

Actual power input to the rectifier Apparent power input to the rectifier

(B) IPF = (distortion factor) × (displacement factor) (C) IPF =

DPF 1 + (THD )

2

(D) All the above Q14. A single phase semi converter is operated from 230 V, 50 Hz AC supply and operated with a firing angle of

π . The load on the converter is highly inductive with a resistance of 15.53 Ω 3

and load current is ripple free. RMS value of the fundamental source current will be. (A) 10A (B) 9A (C) 5A (D) 7.8A Q15. A single phase fully controlled rectifier is supplying power to a purely resistive load of 100 Ω and the bridge is triggered with α= 90°. The source voltage is 200 V, 50 Hz. The power delivered to the load is given by (A) 1 kW (B) 2 kW (C) 3 kW (D) 4 kW Q16. The DC equivalent circuit of a single phase full converter is shown below. The net average output voltage is available across terminals X and Y. Find the source inductance by assuming input frequency of 50 Hz. x I0


2Vm cosα π = 220V

V0=200V yCopyright © Reserved 2014

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(A) 1 H

(B) 0.2 H

(C) 0.01 H

(D) none

Q17. Match List – I (1-φ bridge configuration) with list – II (Average output voltage) and choose the correct option. (Assume I0 is constant) List – I (1-φ φ bridge) (P) with 4 SCRs

List – II [Average output voltage]

2Vm π 2Vm 2. V0 = cosα π V 3. V0 = m [3 + cos α ] 2π V 4. V0 = m [1 + cos α ] 1. V0 =

(Q) with 2 SCRs + 2 diodes (R) with 1 SCR + 3 Diodes (S) with 4 diodes

π

(A) (C)

P 2 4

Q 4 2

R 1 3

S 3 1

(B) (D)

P 2 4

Q 4 2

R 3 1

S 1 3

Q18. Which of the following PE converter circuits can be used to operate the DC machine in regenerative braking mode? Select your choices from the given options. 1. 1-φ full converter 2. 1-φ semi converter 3. 3-φ full converter 4. 3-φ semi converter 5. Type E chopper 6. 1-φ full bridge VSI Options: (A) 1, 3, 5 and 6 only (B) 1, 2, 3, 4 only (C) 1, 3 and 5 only (D) All can be used Q19. In controlled rectifiers the nature of load current i.e. whether load current is continuous or discontinuous (A) does not depend on type of load and firing angle delay (B) depends on type of load and firing angle delay (C) depends only on the type of load (D) depends only on the firing angle delay Q20. If α=90o in the following circuit, the RMS value of the output voltage is (A) 230 V

(B) 230 2 V


(C) 115 V

(D) 115 2 V



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T1

230V ∼

D3

D1

R

T2

+ υ0 −

50Hz D4

D2

Q21. A 230 V, 50 Hz one-pulse SCR controlled converter is triggered at a firing angle of 40o and load current extinguishes at an angle of 210o. Find the circuit turn off time (in second) if load R=5 Ω and L=2 mH (A) 120

(B) (1/120)

(C) 60

(D) (1/60)

Q22. A four quadrant operation of the DC machine requires (A) Two full converters is series (B) Two full converters connected back to back (C) Two full converters connected in parallel (D) Two semi converters connected back to back. Q23. The output ripple frequency of 3-φ semi converter depends on (A) Input frequency (B) firing angle (C) source inductance (D) both A&B Q24. A 3-φ full converter feeds power to a resistive load of 10 Ω. For a firing angle of 45o, the load takes 1 kW. Find the magnitude of the line Voltage (A) 100 2 V

(B) 100 3 V

(C) 200 V

(D) 200 3 V

Q25. A 3-φ half wave controlled rectifier is delivering power to highly inductive load with continuous load current. Which of the following equation can be used to find average output voltage when firing angle is 450? (A) V0 =

3 3Vmp

[1 + cos α]

2π 3Vmp  π   (C) V0 = 1 + cos α +   2π  6  

(B) V0 =

3 3Vmp

cos α 2π 3 3Vmp  π   (D) V0 = 1 + cos α +   2π  6  

Q26. A 3-φ full converter is supplying power to an inductive load and current of 31.42 A. The RMS value of fundamental input current will be (A) 24.5 A (B) 31.42A (C) 25.65A (D) None



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Q27. In 12 pulse rectifier, the lowest harmonic in the input current will be (A) 3rd (B) 5th (C) 7th (D) 11th Q28. Which of following rectifier can only be used as both 3-pulse and 6-pulse rectifier? (A) 1-φ full converter (B) 3-φ full converter (C) 3-φ half wave converter (D) 3-φ half controlled converter Q29. In step up chopper (boost converter), the average output voltage when duty cycle ratio=1. (A) infinity (B) zero (C) equal to source voltage (D) less than infinity but greater than source voltage Q30. In which of the following DC-DC converter, the nature of power conversion will be of current to voltage type (A) Buck converter (B) Boost converter (C) Buck-Boost converter (D) fly back converter (Isolated type) Q31. A chopper circuit shown in the figure is operating at a switching frequency of 25 kHz with a duty cycle ratio of 0.25 The peak to peak ripple in the inductor current will be sw +

12V (A) 1 A

(B) 1.8 A

120µH

V0 −

(C) 0.5 A

(D)0.8 A

Q32. The fundamental difference between transformer and inductor used in power conversion circuits is (A) both have same purpose (B) Inductor is used to smoothen energy flow where as transformer will provide electrical isolation and voltage levels matching. (C) Inductor will store energy whereas transformer will not store energy (D) both B & C are correct Q33. A type – A chopper is operating at 2 kHz from a 100 V dc source has a load time constant of 5 ms and load resistance of 10 Ω. Find the max value of inductor current for a mean load voltage of 50V. (A) 5.25A (B) 5.025A (C) 5.125A (D) 4.875A



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Q34. A diode is connected in series with LC circuit as shown in fig. Assume the capacitor is initially charged to a voltage of -50 V. sw

D

L=0.2mH

C=10µF

230V

The voltage across capacitor at the time diode turns off is (A) 230 V (B) -280 V (C) -220 V

(D) 510 V

Q35. Find the conduction time of SCR in the following circuit. Assume L and C are initially relaxed 100Ω 5mH

1µF

300V

(A) 0.314 ms

(B) 0.314 µs

(C) 3.14 ms

(D) none

Q36. A complementary commutation scheme is shown in fig. R1

R2

T1

T2

Vdc

If Vdc = 200V, R1 = 10Ω and R2 = 100Ω determine peak value of current through T2. (A) 24A (B) 42A (C) 21A (D) 12A Q37. In the circuit shown in figure, if Vdc = 200 V, C = 4 µF and L = 16 µH and R = 20 Ω. The peak value of current through T1 and D can respectively be T1

Vdc D



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(A) 110 A, 100 A

(B) 110 A, 10 A

(C) 10 A, 110 A

(D) 100 A, 110 A

Q38. In 3-φ full bridge VSI, which of the following voltage will have 3rd harmonic in 180° operation (A) line voltage (B) phase voltage (C) pole voltage (D) none Q39. A single phase full bridge VSI is feeding power to a resistive load of 5 Ω. The fundamental output voltage is found to be 200 V (rms). Find the rms value of switch and diode currents at fundamental frequency (A) Isw,1 = 20 2A and ID,1 = 10 2A (B) Isw,1 = 20 2A and ID,1 = 0A (C) Isw,1 = 10 2A and ID,1 = 0A (D) Isw,1 = 10 2A and ID,1 = 5 2A Q40. The source voltage of a 3 – φ full bridge VSI is 200 V. The rms value of phase voltage in 120° operation will be (A) 40.82V

(B) 20.41V

(C) 81.64V

(D) 141.42V

Q41. A single phase full bridge VSI is operating in 180° square operation. The phase angle between the pole voltages is 45°. The RMS value of the output voltage between two poles is

A B 100V

(A) 100 V

(B) 100 ×

π V 4

(C) 200 V

(D) 50 V

Q42. A single phase full bridge VSI has a source voltage of 200 V. The load consists of RLC in series where R = 1Ω, ωL = 7Ω and

1 = 6Ω . Identify the fundamental component of load ωC

current from the following. (A) 180 sin (ωt + 45°) (B) 180 sin(ωt - 45°) (C) 127.3 sin(ωt-45°) (D) 127.3 sin(ωt+45°)



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Q43. The operating points of three power electronic switches on VI plane is shown below Consider the following statements regarding the switches P, Q, R 1. P is most suitable for VSI 2. P is most suitable for CSI 3. Q is the most suitable for VSI 4. Q is most suitable for CSI 5. P, Q and R can be used in either VSI or CSI

Now, select the correct option from the following (A) only 2 & 3 are correct (B) only 1 & 4 are correct (C) 2, 3 and 5 are correct (D) All are correct Q44. In single pulse modulation used in PWM inverters, Vdc is the input dc voltage. For eliminating third harmonic, the magnitudes of rms value of fundamental component of output voltage and pulse width are respectively

4Vdc ,60 o π 2 2 (C) Vdc , 60 o π

(A)

(B) (D)

6

π

Vdc ,120 o

4 Vdc ,120 o π

Q45. A PWM inverter is capable of producing the following type of output voltage (A) variable in magnitude and frequency



Page 44 of 120


(B) (C) (D)

variable voltage, fixed frequency Fixed voltage, variable frequency Fixed voltage, fixed frequency (2)

Q46. Consider the following circuits

Load (1)

Load

SCR ∼

∼

(3)

TRIAC

(4)

Load

Load ∼

MOSFET/ ∼

BJT/ IGBT

From the above circuits which one can be considered as AC voltage regulator (A) only 1 & 3 (B) only 1, 2 and 3 (C) only 1 (D) All circuits Q47. An induction motor is required to run at a very low speed around 25 to 40 rpm from 50 Hz source. Which of the following circuit is most suitable for this application (A) step up cycloconverter (B) inverter (C) step down cycloconverter (D) All the above Q48. A load consisting of R = 10 Ω and ωL = 10 Ω is being fed from 230 V, 50 Hz source through a 1-φ AC voltage controller. For a firing angle delay of 45°, the rms value of load current will be (A) 23A

(B)

23 2

A

(C) >

23 2

A

(D) <

23 2

A

Q49. A dc motor is driven from a 3-φ full converter draws a dc line current of 10A with negligible ripple. The rms value of thyristor current will be (A) 10 A (B) 7.07 A (C) 5.77 A (D) 17.32 A Q50. Which of the following chopper circuit can be used to drive the dc motor in regenerative braking is 1. Type – A 2. Type – B 3. Type – C 4. Type – D 5. Type - E



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(A) only 2

(B) only 2, 3 and 4

(C) all except 1

(D) all circuits

Q51. A separately excited dc motor fed through a single phase semi converter runs at a speed of 1200 rpm. when ac supply voltage is 220 V, 50 Hz and the motor counter emf is 90 V. The firing angle is 90° and armature resistance is 1 Ω. Find the average armature current (A) 7A (B) 8A (C) 9A (D) 10A Q52. In the speed control of dc motors in servo applications, where response time is very critical, which of the following PE converter circuit is most preferable (A) DC-DC converter (switched mode) (B) phase controlled rectifiers (C) Dual converters (D) Any one is suitable Q53. A separately excited dc motor is driven from a 3-φ full converter. The armature current is ripple free. Find 3rd and 5th harmonic components of line currents as a % of the fundamental component respectively (A) 0% and 20% (B) 0% and -20% (C) 20% and 0% (D) 0% and -40% Directions: the following items consist of two statements; one labeled as Assertion (A) and the other as Reason (R). You are to examine these two statements carefully and select the correct answers to these items using the codes given below. (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true but R is not the correct explanation of A. (C) A is true but R is false (D) A is false but R is true Q54. Assertion (A): In SCR, latching current corresponds to turn ON process. Reason (R): In SCR, holding current corresponds to turn OFF process. Q55. Assertion (A): Semi converters are not suitable for braking applications. Reason (R): V0 is always +ve for all values ‘α’ in semi converters. Q56. Assertion (A): In rectifiers, input power factor can be improved by using freewheeling diode across load. Reason (R): With freewheeling, some power can fed back to the source. Q57. Assertion (A): The output ripple frequency in 3-φ rectifiers is less than 1-φ rectifier. Reason (R): Output voltage of 3-φ rectifier will have more number of pulses than 1-φ rectifier. Q58. Assertion (A): MOSFET is most suitable switch in DC – DC converters than SCR. Reason (R): Ripple content is less when tsw is high in DC-DC converters. Q59. Assertion (A): MOSFET is most preferable switch CSI.




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Reason (R): Switches with anti parallel diodes should not be used in CSI. Q60. Assertion (A): 1 - φ triac can be used in fan regulators. Reason (R): Voltage control method is effective in low power 1-φ induction motors.



Page 47 of 120


Objective Questions Practice Test - 2 Q1. Consider the following statements (1) The ON state voltage drop of GTO is higher than that of SCR. (2) GTO can be used for more switching frequency than that of SCR. (3) SCR can handle large currents than GTO. (4) GTO can turn ON and OFF from same gate. Choose the appropriate options. (a) Only 1 is true (c) 1,2 and 4 are true

(b) 1,2 and 3 are true (d) all statements are true

Q2.

In the following single-phase diode Rectifier circuit, the average and RMS current rating of the diode will be respectively

(a) IDav = 10.35 A and IDr = 12.68 A (c) IDav = 7.32 A and IDr = 10.35 A

(b) IDav = 14.64 A and IDr = 10.35 A (d) IDav = 10.35 A and IDr = 7.32 A

Q3.

The output voltage of a 3-phase voltage source inverter contains 5th and 7th harmonics. Assume the output is balanced. If Va = V1m sin (ωt) +V5m sin (5ωt) +V7msin(ωt) then Vb can be expressed as 2π   (a) Vb = V1msin  ωt −  +V5msin(5ωt)+V7msin(7ωt) 3   2π  2π  2π     (b) Vb = V1m sin  ωt −  +V5msin  5ωt +  + V7 m sin  7ωt −  3  3  3     2π  2π  2π     (c) Vb = V1m sin  ωt −  + V5 m sin  5ωt −  + V7 m sin  7ωt +  3  3  3     (d) None of these



Page 48 of 120


Q4. In a single phase semi converter, THD in source current is found to be 31%. Then firing angle could be (a) 30° (b) 40° (c) 45° (d) 60° Q5. A three phase half wave phase controlled rectifier is operated from a 3-phase star connected 400 V, 50 Hz supply and the load resistance is R = 10 Ω If it is required to obtain an average output voltage of 50% of maximum possible output voltage then the converter circuit need to operate at α = (a) 135° (b) 67.7° (c) 60° (d) 30° 06. A boost converter is shown in the figure. The DC source voltage is 100 V and load resistance is 10 Ω. Assume that the inductor has an internal resistance of 0.5 Ω. The range of duty cycle which can give the stable operation of the converter circuit is

(a) 0< D< 0.78

(b) 0.78
(c) 0.8
(d) 0
Q7. A single phase full bridge VSI has a source voltage of 200 V DC. The load consists 1 of RLC in series where R = 1Ω, ωL = 6Ω and = 7Ω . Identify the fundamental ωC component of the load current from the following. (a) 180 sin (ωt+45°) (b) 180 sin(ωt−45°) (c) 127.3 sin (ωt−45°) (d) 127.3 sin (ωt+45°) Q8. A separately excited DC Motor is driven from a 3 phase full converter. The armature current is ripple free. Find 3rd and 5th harmonic components of line currents as a percentage of the fundamental component respectively (a) 0% and 20% (b) 0% and -20% (c) 20% and 0% (d) 0% and −40% Q9. A buck converter circuit is shown in the figure Vdc is input voltage and v0 is the output voltage. Consider iL and v0 as state variables. If R = 1Ω, L = 1H and C = 0.1 F then the nature of the response will be



Page 49 of 120


(a) Under damped (c) Over damped

(b) Critically damped (d) Undamped

Common Data for Questions 10 & 11

A single phase semi converter is operated from 230 V, 50 Hz AC supply and with a firing angle of (π/4). The load on the converter is highly inductive with a resistance of 17.765 ohm and load current is ripple free Q10. The RMS value of the freewheeling current is (a) 10 A (b) 3.33A (c) 5 A Q11. RMS value of fundamental source current will be (a) 10 A (b) 9 A (c) 5 A

(d) None

(d) 8.315 A

Q12. A single phase full bridge inverter has RLC load of R = 4Ω, L = 35 mH and C = 155 µF. The DC input voltage is 230 V and the fundamental output frequency is 50 Hz. The conduction time of the diodes is (consider only fundamental components) (a) 6.264 ms (b) 2.5 ms (c) 3.736 ms (d) None Q13. In the following rectifier circuit, the load current will be maximum at ωt =



Page 50 of 120


(a) 90°

(b) 135°

(c) 45°

(d) Load current does not have max

Q14. Regarding Buck-Boost converter, which of the statement is true 1. It will operate as Buck converter when 0Dmax. Select the options as below: (a) only 1 & 3 are true (b) all are true (c) only 1&2 are true (d) None of these Q15. In the given circuit a thyristor converter is feeding a resistor R, The power consumed by R in the absence of SCR is P. In the presence of SCR, the power consumed by R at α = 90° would be reduced by a factor of

(a) 1/2 (b) 1/4 (c) 1/6 (d) 1/12 Q16. A 3-φ full converter feeds power to a resistive load of 10 Ω. For a firing angle of 30° the load takes 5 kW. Find the magnitude of per phase input supply voltage (a) 230 V (b) 188 V (c) 108 V (d) 335.5V



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Q17. A 1−φ fully controlled rectifier is supplying power to a resistive load of 35 Ω as shown in figure. If the bridge is triggered at 90°, the average current drawn by the load is given by

(a) 0 A

(b)

2A

(c) 2 2A

(d)

1 2

A

Q18. A 3−φ Fully controlled rectifier is operated from a 3−φ star connected 400 V, 50 Hz AC supply and the load resistance is R = 10 Ω. A large inductance is connected in series with the load to maintain ripple free load current. If it is required to obtain an average output voltage of 86.66 % of the maximum possible output voltage. Find the firing angle (a) 30° (b) 60° (c) 45° (d) 90° Q19. A Power converter is shown in the figure has two power switching devices namely X and Y. The source voltage is 50 V. The inductor current is steady 5 A without any ripple.

On the V-I plane, identify the correct operating points of switches from the given options.




Page 52 of 120

(d) None Q20.

A single phase AC voltage Regulator has a load resistance of 10 Ω. Input voltage is 200 V, 50 Hz. If SCRs are triggered at π/2 with symmetrical triggering scheme, find the RMS value of SCR current. (a) 0A (b) 20 A (c) 4.5 A (d) 10 A Q21. The following chopper circuit is operating at a switching frequency of 1 kHz with a duty cycle ratio of 50%. Assume a voltage drop of 2 V across the switch when it is ON. Find the converter circuit efficiency.




Page 53 of 120

(a) 95% (b) 98% (c) 100% (d) 99% Q22. A buck converter is shown in the figure. The switch is operating at 25 kHz. From an experiment, it is observed that ∆V0 = 20 mV and ∆IL = 0.8 A.

For an average output voltage of 5V, find the value of capacitance (b) 145. 8 µF (c) 150 µF (d) None (a) 200 µF Q23. A single phase full bridge VSI is feeding power to a resistive load of 2 Ω. The fundamental output voltage is found to be 230 V (rms). Find the RMS value of switch and diode currents at fundamental frequency (a) Isw1 = 81.33 A ID1 = 0A (b) Isw1 = 54.818 A ID1 = 0A ID1 = 17.328 A (c) Isw1 = 54.818 A (d) None of these Q24. The reverse recovery time of a diode is 3 µs and the rate of fall of the diode current is 3 A/µs. The peak value of reverse current of the diode is given by (a) 135 A (b) 90 A (c) 100 A (d) 8100 A Q25. In a resonant commutation circuit, supply voltage is 200 V. Load current is 10 A and the device turn off time is 30 µs. The ratio of peak resonant current to load current is 1.5. Find the value of L&C (a) L = 2.66 mH & C = 1.5 µF (b) L = 1.5 mH & C = 0.266 µF http://electrical-mentor.blogspot.in/


Page 54 of 120 120


(c) L = 0.266 mH & C = 1.5 µF

(d) None of these

Common Data for Questions 26 & 27

Two 3-phase bridge rectifiers are connected as shown below.

Q26. The total number of pulses in the output voltage at the terminals A & B is (a) 6 (b) 12 (c) 3 (d) 24 Q27. The lowest harmonic in the input current is (a) 3 (b) 5 (c) 11 (d) 13 Q28. A 220 V, 60 A DC series motor having a combined resistance of armature and field of 0.15 Ω is controlled in regenerative braking mode through a DC-DC converter. The DC source voltage is 220 V. Motor constant is 0.05 V-s/rad. The average motor armature current is rated and ripple free. Find the speed during regenerative braking (a) 32.33 rad/s (b) 47 rad/s (c) 74 rad/s (d) None Q29. A 3-phase full bridge VSI delivers power to a resistive load from a 450 V DC source. For a star connected balance load of 10 Ω/ph. Find the RMS value of the load current under 180° conduction mode (a) 18.708 A (b) 13.23 A (c) 18.371 A (d) 21.213 A




Page 55 of 120

Q30. A thyristor is used in an application carrying half sinusoidal current of period of 1 msec and a peak of 100 A as shown in fig. The thyristor may modeled during conduction to have a constant voltage drop of 1.1 V and a dynamic resistance of 8 mΩ. Evaluate the average conduction loss in the device

(a) 35 W (b) 0.4 W (c) 55 W (d) 20 W Q31. The wave form in the following figure shows the periodic current thorugh a powerswitching device in a switching converter application.

A BJT with a device drop of 1.2 V and MOSFET with an ON state resistance of 150 mΩ are considered for this application. The conduction loss in BJT and MOSFET are respectively (a) 6W & 3.75 W (b) 6 W & 6.67 W (c) 3.75w & 6 W (d) 6.67 W&6 W Q32. In the following circuit, MOSFET Q is switched at 100 kHz with a duty ratio of 0.5. MOSFET is having an ON state resistance of 1 Ω when it is ON. Find average conduction losses in MOSFET



Page 56 of 120


(a) 20.41 W

(b) 41.67 W

(c) 12.5 W

(d) 4.1667 W

Q33. A 3-phase full converter supplying power to inductive load with ripple free current is shown in fig. All positive group devices are represented with P1P2,P3 and all negative group devices are represented with N1, N2, N3 as shown below.

By assuming υYB = Vml sinωt and α = 60° the following load voltage is obtained.

Which of the following statement is true as per the given output voltage waveform (a) x1 = v RB , x 2 = vYR & x3 = vYB (b) x 1 = v RY , x 2 = v YB & x 3 = v BY (c) x1 = vRB , x2 = vYR & x3 = vBY (d) x 1 = v RY . x 2 = v YB & x 3 = v BR Q34. A forward converter is operating at boundary of continuous & discontinuous conduction. The switch is operating at 100 kHz. Assume µr of core is ∞ so that energy recovery in winding can be neglected. A load of 10 A at 20V is being supplied as shown is fig. Find peak to peak ripple in output voltage




Page 57 of 120

(a) 0.25 V (b) 2.5V (c) 0.025 V (d) 1.25 V Q35. Which of the following converter circuit representation is equivalent to Buck-Boost converter?

Q36. A power electronic switch is realized by SCR and diode as shown below. Identify the static operating points on V-I plane




Page 58 of 120

Q37. Which of the following switch can be used as four quadrant switch [used in matrix converter]

Q38. The center-tap full-wave single-phase rectifier circuit uses 2 diodes as shown in the given figure. The rms voltage across each diode is



Page 59 of 120


(a) 790.7 V (b) 395.3 V (c) 280 V (d) 201.3 V Q39. In the following resonant pulse communication scheme, find the voltage across main SCR when it gets turned off.

(a) 460 V

(b) 177 V

(c) 174.37 V

(d) 230 V

Q40. An RL load is connected to DC voltage source of 220 V through a diode as shown below. A free wheeling diode is connected a cross the load to recover the trapped energy. Assume that switch is closed for 100 µs and then opened. Find the final energy stored in the inductor by assuming negligible load resistance

(a) 1 J

(b) 0.5 J


(c) 1.5 J

(d) 1.1 J


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Objective Questions Practice Test – 3 Q1. A single phase full converter charges a battery which offers a constant value of E = 12V. A resistor R is inserted to limit the battery charging current. The supply voltage to the bridge is 40 V, 50 Hz, Ac. Consider a voltage drop of 1 V conducting SCRs. Assume that pair of SCRs fired continuously. Find the value of R in case battery charging current is 10 A. (a) 2 Ω (b) 2.4 Ω (c) 4 Ω (d) 8 Ω Q2. In the circuit shown in Fig. switch S is open and a current of 20 A is flowing through FD, R & L. If switch S is closed at t = 0, the expression for current flowing through the switch is given by sw + R

10Ω

L

10mH

FD

220V

20A −

Fig.

(a) i( t ) = 22 + 2e −1000 t

(b) i( t ) = 2 − 22e −1000 t

(c) i( t ) = 22 − 2e −1000 t

(d) i( t ) = 0

Q3. The switching waveform for a power electronic switch is shown in fig. Find the energy loss during turn ON and turn OFF transistors isw 80A t

vsw 220V t tON

tOFF

1.5µs

4µs

(a) E ON = 4.4 mJ : E OFF = 13.2 mJ

(b) E ON = 4.4 mJ : E OFF = 11.73 mJ

(c) E ON = 13.2 mJ : E OFF = 4.4 mJ

(d) E ON = 11.73 mJ : E OFF = 4.4 mJ



Page 61 of 120


Q4. A power diode is modeled in ON state as shown in figure. Consider it is ideal in blocking and switching durations A

K

⇒

A

K Rd

Vd

The above diode is capable of dissipating 75W in ON state. For square wave operation, it is rated for peak current of 100A and 135 A at duty ratios of 0.5 and 0.33 respectively. Find the diode parameters Rd and Vd (a) R d = 5mΩ : Vd = 0.98V

(b) R d = 0.98Ω : Vd = 5mV

(c) R d = 3mΩ : Vd = 0.5V

(d) Not a valid model.

Hint: Diode current waveforms are shown below

i

i I=100A

I

I=135A

I

D=0.5

D=0.33

Q5. A composite switch used in a power converter is shown in figure. The periodic current through the switch is also shown. Evaluate the total power loss in the composite switch. i 12A t 5

10

(µs) 20

25

Rds=0.1Ω B

A VON=0.8V

(a) 4.8 W

(b) 3.6 W

(c) 8.4 W

(d) None

Q6. A battery is to be charged from single phase un controlled bridge rectifier. On full discharge, the battery voltage is 10.2 V and on full charge it is 12.7 V. The battery internal resistance is 0.1 Ω. Find the input voltage to the rectifier so that the battery charging current under full charging condition is 10% (a) 14.415 V (b) 41.41 V (c) 24.41 V (d) 48 V



Page 62 of 120


Q7. A 3 - φ full converter bridge is supplying power to a purely resistive load of 10 Ω. The input to the bridge is 400 V, 50 Hz, 3 - φ AC. If the bridge is triggered at α = 900. Find power delivered to the load. (a) 0 W (b) 1384 W (c) 1117.6 W (d) 524 W Q8. A single phase diode bridge is delivering power to purely resistive load of 10 Ω. The input to the bridge is 230 V, 50 Hz, 1 - φ AC. Find the rms value of second harmonic component of load current. (a) 0A (b) 8.76 A (c) 9.76 A (d) 10.76 A Q9. A single phase full converter feeds power to RL load with R = 6Ω, L = 6mH. The AC source voltage is 230 V, 50 Hz. In case one of the 4 SCRs gets open circuited due to a fault, find the average load current on the assumption of load current is continuous by taking α = 600 (a) 12.94 A (b) 8.62 A (c) 17.25 A (d) None Q10. Consider the following circuits (P)

(R)

(Q)

MOSFET/

∼ ∼

BJT/

∼

From the above circuits, which one will operate as AC voltage regulator (a) only P (b) only P & Q (c) P, Q and R (d) None

Common Data for Questions 11 & 12 An AC voltage regulator and diode bridge rectifier are connected together as shown below. T1

D1

D3

i0 +

A R 230V

∼

50Hz

B

T2 D4

V0 −

D2

Q11. Find power delivered to load in case α = 600 and R = 10 Ω (a) 4251.8 W (b) 2125.8 W (c) 1062.75 W


(d) 8502 W


Page 63 of 120


Q12. In case, if D3 in above circuit is open circuited then find power delivered to load. (a) 4251.8 W (b) 2125.8 W (c) 1062.75 W (d) 8502 W Q13. The input voltage given to a converter and current drawn by converter are expresses as r = 300 "$%100s + 100 "$%300s s s s )r = 10 "$% D100s − G + 5 "$% D300s + G + 2 "$% D500s − G 3 4 6 Find input power factor of the converter (a) 0.44 lag (b) 0.6 lag

(c) 0.707 lag

(d) 0.522 lag

Q14. A separately excited DC motor is driven from a 3-phase full converter. The armature current is ripple free. Find 3rd and 5th harmonic components of line currents as a % of the fundamental component respectively. (a) 0% and 20% (b) 20% and 0% (c) 0% and −20% (d) 0% and 40% Q15. A pure inductance of

2 Henry is connected to a single phase full bridge and bridge is π

operated with firing angle of 1200. Input supply to the bridge is 200V, 1φ, 50 Hz AC. Find the peak current flowing through load. (a) 1A (b) 0.5 A (c) 2A (d) unstable system Q16. In the flowing DC – DC converter circuit, if the switch is operated at 20 KHz with duty ratio of 0.5. Find the energy transferred from V1 to V2 V1

(a) 940 J (b) 94 J (c) 0.47 J (d) 0.047 J

+100V L=100µH V2

sw

D

+300V

Q17. A 3 - φ full converter supplying power to an inductive load with ripple free load current is sown in the figure. P1

P2

P3

I0 + V0 −

R Y B N1


N2

N3


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By assuming VYB = Vm sin ωt and with α = 600. The following output voltage is obtained. V0

x2

x1

60

x3

ωt

0

0

360

180

0

Which of the following statements are true as per the given output voltage waveform. (b) x1 = VRB , x2 = VYR , x3 = VBR (a) x1 = V RY , x 2 = VYB , x3 = V RB (d) x1 = V RB , x 2 = VYR , x3 = V BY

(c) x1 = VRY , x 2 = VYB , x3 = VBR

Q18. In single phase semi converter, THD in source current is found to be 31%. Then firing angle could be (a) 300 (b) 400 (c) 450 (d) 600 Q19. In the following DC – DC converter circuit the switch is operating at frequency 10 kHz. When the switch is at position 1, the inductor stores energy for a period of 50 µs and release energy is 20 µs when the switch is moved to position 2. Find ratio of V1 to V2. 1

V1

(a)

2 5

(b)

5 2

2

V2

L

(c)

7 2

(d)

2 7

Q20. A 3 - φ voltage source inverter has a star connected load of R = 5Ω, and L = 23 mH. The inverter fundamental frequency is 60Hz. And DC input voltage is 220 V consider that inverter output voltage is free form 11th and higher harmonics. Find the rms value of line current in load (a) 9.91 A (b) 13.02A (c) 7.75 A (d) None

Q21. Consider the following DC – DC converter circuit. 100mH

220V

D

sw

+ 10µF

1KΩ

V0 −



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Switch is operating at a duty cycle ratio of 0.5. Find the settling time for the response to



reach within 2% tolerance band H int : t s =



(a) 50 ms

4 ξω n

 s 

(b) 79 ms

(c) 100 ms

(d) 10 ms

Statement for Linked Answer Questions 22 & 23 (Numerical Type) A DC Motor transfer function defined as follows:

G 1 (s) =

ω(s ) Vt (s ) T

=

L =0

1 K E s .Tm .Te + sTm + 1

[

2

]

Where Tm = mechanical time constant = Te = electrical time constant =

RaJ KTE

La Ra

KT & KE = are torque and emf constants respectively Machine data is as follows: T rated = 10 N-m ; nrated = 3700 rpm KT = 0.5 N-m/A ; KE = 53V/1000 rpm Ra = 0.37 Ω, Te = 4.05ms, Tm = 11.7 ms Q22. This motor is controlling from a power electronic converter. Determine the terminal voltage in steady state if the motor is required to deliver a torque of 5 N-m at a speed of 1500 rpm ………… Q23. If G1(s) in the given statement is expressed as

G 1 (s ) =

1/ K E 2sD s 2 1+ + ω n ω 2n

Then D and ωn will be respectively Q24. A single phase full bridge converter is used to regulate DC output voltage. The rms value of AC input is 230V, 50Hz. And load current I0 = 10A. In below figure Y-axis represents active and reactive powers with and without free wheeling diode and X-axis represents firing angle.



2500 Version Code: PEQBTNC06 2000

Page 66 of 120

1500 1000 500 0 0

-500

30

45

60

75

90

105 120 135 150 165 180

-1000 -1500 -2000 -2500 W

Match the following List – I 1. W 2. X 3. Y 4. Z Codes: 1 (a) A (b) D (c) B (d) A

X

Y

Z

List - II A. Active power with freewheeling diode B. Reactive power without freewheeling diode C. Active power without freewheeling diode D. Reactive power with freewheeling diode

2 B C C B

3 C B A D

4 D A D C

Q25. A single phase full bridge VSI has an RLC load with R = 10 Ω, L = 31.5 mH and C =112 µF.The inverter fundamental output frequency is 50 Hz and DC input voltage is 220V. This VSI is controlling with sine triangular PWM technique with 5 pulses per half cycle and harmonics of order higher than 9 and above are negligible effect. Find power delivered to the load (consider harmonic power if present). (a) 1639.55 W (b) 885.45 W (c) 1770.9 W (d) 3279.1 W Q26. A commutation circuit for a thyristor is shown in fig. Determine the available turn off time of the circuit if Vdc = 100 V, R = 10 Ω and C = 10 µF voltage across capacitor before SCR T2 is fired, is Vdc with polarity as shown. T1 C

− +

VCO R

Vdc

T2



Page 67 of 120


(a) 69.3 µs

(b) 69.3 ms

(c) 0.693 µs

(d) 0 s

Common Data for Questions 27 & 28 A 220 V, 1450 rpm, 100 A separately excited DC motor has am armature resistance of 0.04 Ω. the motor is driven by a 3 - φ half controlled converter operating from a 3 - φ, 220 V, 50 Hz AC supply. The motor operates at rated speed and rated load torque. Assume continuous conduction. Q27. RMS value of fundamental component of input current (a) 70 A (b) 63.87A (c) 26.67 A Q28. Total harmonic distortion in the input current is (a) 60% (b) 31% (c) 48.43%

(d) None

(d) 65.5%

Statement for Linked Answer Questions 29 & 30 A single phase full bridge VSI is operating in 1800 square operation mode with source voltage 100 V – 0 – 100 V. The phase angle between the pole voltages is 450. Q29. RMS value of the output voltage between two poles at fundamental frequency (a) 34.44 V (b) 50 V (c) 68.9 V (d) 127.28 V Q30. RMS value of switch current at fundamental frequency for a resistive load of 10 Ω (a) 4.87 A (b) 6.89 A (c) 9.74 A (d) 2.445 A



Page 68 of 120


Objective Questions Practice Test - 4 Q1. In which of the following devices, conductivity modulation phenomenon is absent (A) Power diode (B) SCR (C) Power MOSFET (D) Power BJT Q2. A power MOSFET rated for 25 A, carries a periodic current of 20 A as shown in figure. The ON-state resistance of the MOSFET is 0.1 Ω. What is the average ONstate loss in the MOSFET? i

20 A

π

(A) 15 W

2π

(B) 20 W

3π

4π

5π

ωt

(C) 25 W

(D) 10 W

Q3. In the following circuit, the ammeter reads 12.68 A when it is of MI type. What would be the ammeter reading if it is of MC type D A

230 V,

∼

0.1 H

50 Hz

(A) 12.68 A

(B) 10 A

(C) 10.35 A

(D) Ammeter will damage

Q4. The average input and output voltages of chopper circuit are 100 V and 50 V respectively. The inductor current wave form is as shown in figure. iL

IL max 100 50 L L

Ton


t T


Page 69 of 120


What could be the chopper circuit? (A) step down chopper (C) step up/down chopper

(B) step down/up chopper (D) step up chopper

Q5. Which of the following converter circuit operation will be unstable for large duty cycle ratios? (A) Buck converter (B) Boost converter (C) Buck-Boost converter (D) Both (B) & (C) Q6. A diode in anti parallel with the controlled switch like IGBT is used in VSI to (A) prevent reversal of dc link current (B) control a non-unity power factor load at the output. (C) protect the circuit against accidental reversal of dc bus polarity. (D) None of the above Q7. A single phase full bridge VSI is fed from DC source such that fundamental component of output voltage is 200 V. Find average value of source current when load is R = 10 Ω. Assume all harmonics absent. (A) 10A (B) 20 A (C) 40 A (D) None Q8. A 3-phase induction motor operates under constant volt/hertz control. At 50 Hz supply, the motor current and its pf are 30 A and 0.3 lag at the time of starting. These values at the time of starting at 25 Hz supply would be (A) Motor current > 30 A and pf >0.3 (B) Motor current < 30 A and pf < 0.3 (C) Motor current < 30 A and pf > 0.3 (D) Motor current > 30 A and pf < 0.3 Q9. A single phase ACVR feeds a pure resistive load. Each SCR conducts for angle of γ when operating at firing angle α > 90o. If the load is replaced by a pure inductance keeping the firing angle same as before. The conduction angle of each SCR would be γ γ (A) 2 γ (B) γ (C) (D) 2 3 Q10. The fundamental input power factor of single phase full converter is

1

when it is 2 operating with a firing angle of 40o. Assume the load current is constant and ripple free. What is the overlap angle in degree ________



Page 70 of 120


Q11. The fourier series for voltage and current of a power electronic circuit in pu are given below: υ(t) = 1.2 sin(ωt)+0.33sin(3ωt) +0.2sin(5ωt) i(t) = 0.6 sin(ωt+30o)+0.1sin(5ωt+45o)+0.1sin(7ωt+60o) The average power is given by (in p.u) (A) 0.312 (B) 0.007 (C) 0.32 (D) Voltage equation is wrong. Q12. Two six pulse converters, used for a bipolar HVDC transmission system (shown in figure) are rated at 1000 MW, ±200 kV +

+ υ01 – +

υ0 υ02

–

–

The RMS current rating of each thyristor will be (A) 2500 A (B) 1443.4 A (C) 2041.2 A

(D) 0 A

Q13. In the following chopper circuit, The IGBT Q is switched at 10 kHz. The circuit is operated in steady state at the boundary of continuous and discontinuous inductor current. If IGBT has a constant voltage drop of 0.5 V when it is ON, Find the conduction loss in IGBT. Q

100 V

(A) 853 W

(B) 16 W

iL

100 µH

(C) 32 W

400 V

(D) None

Q14. In a boost converter, the duty ratio is adjust to regulate the output voltage V0 at 48 V. the input voltage varies in a wide range from 12 to 36 V. the maximum output



Page 71 of 120


power is 120 W. For stability reasons, it is required that the converter always operate in a discontinuous current conduction mode. The switching frequency is 50 kHz. Assuming ideal components and C as very large, calculate the maximum value of L that can be used. (B) 12 µH (C) 20 µH (D) < 9 µH (A) 9 µH Q15. In the circuit shown in fig, capacitor C is initially charged to Vdc = 200 V with polarity as indicated. Find the circuit turn off time for main SCR (T1) after it is voltage commutated by SCR (TA) load current is constant at 40 A and C = 10 µF. T1 – C + 200 V

(A) 20 µs

(B) 50 µs

Load TA

(C) 25 µs

(D) Insufficient data

Q16. A separately excited dc motor is fed from 220 V dc source through a step down chopper operating at 400 Hz. The load torque is 30 N-m at a speed of 1000 rpm. The motor has ra = 0, La = 20 mH. Machine constant is 1.5 V-s/rad. Calculate minimum and maximum values of armature current. (A) Ia,max = 22.8 A and Ia min = 17.2 A (B) Ia,max = 22.8 A and Ia min = 18.48 A (C) Ia,max = 17.2 A and Ia min = 11.57A (D) None Q17. A 220 V, 1450 rpm, 100 A separately excited dc motor has an armature resistance of 0.05 Ω.the machine is driven by a 3–φ half controlled converter operating from a 3– φ, 220 V, 50 Hz supply. The motor operates at rated speed and rated load torque. Assume continuous conduction. % THD in source current at AC mains is given by (A) 70.5 % (B) 68.2 % (C) 31 % (D) None Q18. A single phase full bridge VSI delivers power to a series RLC load with R = 2 Ω and ωL = 10 Ω. The periodic time T = 0.1 ms. What value of C should be used to has load commutation consider tq = 10µ s and factor of safety 1.5. (A) 12.48 µF (B) 1.248 µF (C0 12.48 mF (D) None Q19. A 3-ph square wave inverter feeds a balanced 3-phase inductance type of load. The worst case load phase current (peak magnitude) is expected to be 100 A and the



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worst case dc input voltage is expected to be 600 V. The diodes of inverter will be subjected the following peak voltage and current stresses. (A) 600 V, 100 A (B) 600 V, 70.7 A (C) 424 V, 70.7 A (D) 424 V, 100 A Q20. A PWM inverter is operated from a dc link voltage of 600 V. the maximum rms line to line voltage (fundamental component) will be less than or equal to (A) 600 V (B) 490 V (C) 467 V (D) 405 V Q21. A single phase full bridge VSI, fed from 230 V dc is connected to load of R = 10 Ω and L = 0.03 H. fundamental frequency of inverter output is 50 Hz. Inverter is operating with a quasi-square wave output with an on-period of 0.5 of a cycle. Find the rms value of load current at fundamental frequency. (A) 15.07 A (B) 10.65 A (C) 9.15 A (D) None Q22. A single phase force commutated CSI is shown in the figure. T3

T1 50 µ F A

40 A

B T4 40 Ω

T2

Output frequency of the inverter is 500 Hz. Find circuit turn off time (B) 750.25 µs (C) 200 µs (A) 438.14 µs (D) None Q23. dV rating of SCR is 350 V/µs and its junction dt capacitance, is 20 pF. Switch S is closed at t = 0. Calculate to value of Cs so that dV SCR T is not turn ON due to dt 20 Ω

For the circuit shown in figure,

S

D 250 V

Rs Cj T

Cs



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(A) 0.0357 µF

(B) 0.025 µF

(C) 2.5 µF

(D) 3.5 µF

Q24. A 3-ph fully controlled rectifier is supplying power to a purely resistive load of 10 Ω. Input to the bridge is 230 V, 50 Hz. The power delivered to the load in watts when α = 90o is _______ (in W) Q25. A single phase CSI (with ideal switches) has the following data: I = 30 A, f = 500 Hz and load of pure capacitance = 20 µF. Find the peak value of reverse voltage that appears across thyristors in volts ______ Q26. In the following circuit. The RMS value of load current in amps by assuming α= 90o is ______ (in amp) D1

T1

D3

A 200 V ∼

Io

 10   Ω  2

T2 B

50 Hz

D4

D5

Common Data for Questions 27 & 28 A three phase fully controlled converter operates from a 3-phase 230 V, 50 Hz supply through a Y- ∆ transformer to supply a 220 V, 600 rpm, 500 A separately excited DC Motor. The motor has an armature resistance of 0.02 Ω. Q27. What should be the transformer turns ratio (from primary to secondary) such that the converter produces rated motor terminal voltage at 0o firing angle. (A) 1:1.2267 (B) 1:1.5 (C) 1:1.789 (D) 1:0.8152 28. The above converter is now used to brake the motor regeneratively in the reverse direction. If thyristors are to be provided with a minimum turn off time of 100 µs, what is the maximum reverse speed at which rated braking torque can be produced? (A) 600 rpm (B) 657 rpm (C) 700 rpm (D) 625 rpm



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Statement for Linked Answer Questions 29 & 30 The chopper below controls a dc machine with an armature inductance La = 0.2 mH. The armature resistance can be neglected. The armature current is 5 A. fs = 30 kHz and D = 0.8. id

ia

La

i0 +

Vdc +–

υ0 =V0

+ ea –

–

Q29. The average output voltage V0, equals to 200 V. Calculate the ripple in armature current. (A) 8.332 A (B) 2.5 A (C) 6.667 A (D) 1.6675 A Q30. The load on the dc machine is now reduced and Ia,max = 2 A. The current is now discontinuous. What is the back emf voltage Ea,? (A) 250 V (B) 200 V (C) 175 V (D) 235 V Q31. A single phase asymmetrical semi-converter feeds an RL load with R = 10 Ω and large L so that load current is current stiff. The source voltage to the bridge is 200 V, 50 Hz. For a firing angle of 30° , the RMS value of diode current will be _______ A. Q32. Consider a current stiff load with free wheeling diode across it. Which of the following rectifier circuit will have 3 pulses in the output voltage? (B) 3-φ full converter with α = 90° (A) 1-φ full converter with α = 90° (C) 3-φ semi converter with α = 90° (D) Both (B) & (C)



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Q33. In the 3-φ inverter circuit shown, the load is balanced and gating scheme is 120° conduction mode. All the switches are ideal. If the dc source voltage is 200 V, the power consumed by 3-φ load is

S1

S3

S5

S4

S6

S2

15 Ω

15 Ω

Vdc = 200V 15 Ω

3-ph Balanced load

A) 5.33 kW

(B) 3 kW

(C) 4 kW

(D) 1.33 kW

Q34. The source voltage to the AC voltage regulator shown in the figure is 220 V, 50 Hz. If SCRs are triggered at 120° symmetrically in every half cycle, then RMS value of the fundamental component of source current (is) will be T1 is

220 V

∼

i0

j 1.2284 Ω

T2

50 Hz

(A) 57 A

(B) 70 A

(C) 40 A

(D) 0 A

Q35. In a Buck-Boost converter operating at 20 kHz, L = 0.05 mH. The output capacitor C is sufficiently large and Vdc = 15 V. The output is to be regulated at 10 V and the converter is supplying a load of 10 W. Calculate the duty ratio D (A) 0.4 (B) 0.2 (C) 0.3 (D) None



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Interview questions ELECTRICAL ENGINEERING Note: The following interview questions have been collected from so many students from my previous batches and consolidated as below. Try to get answers from yourself by referring standard text books, have a group discussion among your friends. Do not directly go to teacher without some home work as you may not get the same questions. It is recommended the reader to get answers on your own by applying fundamentals so that you can expose deeper into the subject and you can increase your confidence levels. Cracking these exams is very simple if you have confidence with subject knowledge

IIT Kanpur Power & Control • Questions on control circuits & stability issues. • Basics of VSI (Voltage source inverter) in details, its wave form for various types of loads, its analysis for different modes of conduction. • Devices (power electronic), their characteristics eg. Difference between a signal and power devices, Bundle conductors, corona losses, surge impedance • Induction motor T-S characteristics, Synchronous motors and generators, applications of dc motors. • They gave different references & inputs to comparator and ask about the output. • They asked circuit diagram of buck, buck-boost and various wave forms. • They gave some circuit in which there was freewheeling diode and asked about its operation in detail • Equivalent diagram of induction motor and significance of different elements in equivalent diagram. • On stability analysis (power system)…. They gave a circuit in which a single line to ground fault had occurred. They asked to draw the swing curve, indicate accelerating and decelerating areas, asked how rotor angle is increased physically, what is the physical meaning of accelerating and decelerating areas. • Explain Ferranti effect. They asked in very details about Ferranti effect. • Why hydro power generators rotate at slower speed than thermal (steam) generators? • Questions on load-flow studies & electric drives, from the basics but tricky. • One of the Profs drew a circuit of dc-dc converter and asked to identify that. Be very clear about buck, buck-boost, boost converters, inverters.




•

•

•

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In control system they asked very basic questions of bode plot, nyquist, polar plot and asked to draw them with a given transfer function (not very tough). They’ll first ask your area of interest. Depending on that they’ll ask questions on that field and related fields. Nevertheless, prepare for the whole syllabus. They’ll ask you to answer each question by drawing circuit, writing equations...etc……on the black board.

IIT Delhi Power Electronics, Electrical Machines & Drives • Questions on Induction motor principles & BE/B.Tech project • Draw four quadrant chopper circuit without SCR? • Why more than six pulse is used in HVDC converters? • Torque-slip characteristics of Induction Motor • Questions about switching devices for PE circuits • How to select switch based on application? • V & inverted V curve of SM. • Inverters and Devices in much detail, they used to ask the typical rating of the devices. • First they asked about B.Tech project in very much details, • They asked about linear system, linear equations……then asked whether Swing equation is linear or not and asked each and every question out of it. • Asked other very basic questions from transmission line, distribution system etc. • If you hold a good GATE score (/rank) and fairly good SGPA, they will primarily focus on your B.Tech project. If it is not the case, they will ask everything you have read in B.Tech (that was the case with one of my friend). Control & Automation • What are advanced controllers?? (they intended to ask about fuzzy and ANN) • Comment on stability of a given Nyquist plot. • Parameters in root locus • Something about bode plot • Basic control system & Lead controller • Define stability, and stable system • What is impulse response? • Linear and nonlinear systems, causal and anti-causal systems • Different stability criteria • Transfer function definition and why initial conditions are zero while defining transfer function



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•

Derive the transfer function for DC motor and draw its block diagram. While answering this question, they will mostly observe your approach

IIT Bombay Microelectronics (RA) • Working of NMOS. • Some questions on OP-AMP. • Questions mostly on B Tech project Power Electronics & Power Systems (RA) • Some Questions in Mathematics. • Draw the full bridge rectifier diagram. • Explain commutation process. • Questions on basic circuit theory. • Questions based on operation and speed control of induction motor, transformer OC and SC test. Control & Computing (RA) • Questions were not from the B.Tech syllabus. • Majority were on Computer & its peripherals. ( for a Network Admin in electrical dept) IIT Madras Communication Systems (M.S. RA) • Basic questions on DFT, DTFT. • Purpose of transforms like DFT, DTFT etc. Power Electronics • They will start with basic concepts of Inductor and capacitor. • Most of the questions will be on DC-DC converters and their various quadrants of operation. • Explain the basic difference between 4-Q chopper and single phase VSI • If we give 3-ph AC supply to IM and TF. Rotation magnetic field will not produce in TF but in IM, it will produce. Explain with phasor diagrams • IIT Kharagpur Power Electronics • Draw torque-slip characteristics of IM and locate the normal stable operating point. Now if the two of the supply terminals suddenly reversed, then where it will shift after t=0+ • Draw the buck converter circuit diagram and derive output voltage equation from energy conversion principles. If resistor is removed and capacitor is ideal, then what is the output voltage



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•

•

•

Draw separately exciter DC motor circuit. Now, connect the motor in such a way that it should rotate at half the rated speed at no load. Do not touch field winding as it is constant What is the time constant of 1/(s+1) and give any physical example for such system. Obtain the step response and what is the physical meaning of the response plot Draw series RLC circuit and by taking I as reference, draw phasor diagram for VR, VL, VC, Vtotal IIT Roorkee

Written exam Imp point: No negative marking. • Electrical Drives: Questions on constant power and constant torque drives ...e.g they changed the armature voltage and were asking about the dynamics of the machine. • Instrumentation: Questions on Increasing the range of Ammeter/Voltmeter. • Questions on Laplace transform. • Control Systems: Bode plot , Stability...(easy questions, just refer Nagarath Gopal and Ogatta books of Control Systems). • Application of KCL in a circuit containing inductor and/or capacitor. • Switching circuits (capacitor and Inductor transient and steady state concepts). • Result was a combination of GATE score & the exam conducted. • Direct counseling thereafter. IISc Bangalore Electrical Communication Engineering [M.S.] • Basic questions on mathematics, signals and system, communication and probability theory • Only basic fundamentals and no questions from advanced technology. ( Very strict on fundamentals) • Panel often asks to explain things in a physical sense rather than putting some equations and solving them. For example: Physically how will you interpret the process of convolution? • Syllabus of the interview will be clearly mentioned before the interview. • There will be some 5 topics mentioned and out of those one has to select 3 topics and questions will be asked from these topics only. Electrical Engineering • Questions on B Tech project & electronics.



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Interview questions from IIT Madras (Dec-2013) (Note: The following questions are collected from Madhuri Depuru, while she attending for MS interview in IIT Madras during the winter session for 2013-14 academic year) 1. If you are given a pure sinusoidal wave and a perfect DC is required from it. What is the circuit you will employ? 2. Draw the most simple rectifier circuit you know 3. Derive Load current equation for RL load in rectifier circuits using both Laplace transform and differential equations 4. What is the most advanced PE equipment employed in motor drives as per your knowledge? 5. Can a full wave bridge rectifier be used as an inverter? Can you use it without changing the source? 6. How can you justify pulsating DC output you are getting out of rectifier can serve the purpose of rectification? 7. What is the physical form inverter we are using in homes? 8. What happens if an inductor of small value if connected to the source given in VSI? 9. Even though DC motors have efficient speed control capabilities, we are using Induction motors for most of the applications. Why? 10. Why supply frequency is only 50 or 60 HZ? 11. Why not diode bridge circuit cannot be used as an inverter? 12. Draw the waveforms for RL load in VSI circuits? 13. Draw the waveform for RC load? Will you use RC load parallel combination or series combination? Explain in detail 14. What happens if 10A rms, current source is given to LC parallel circuit where initial stored energies in L and C are zero? 15. What are the practical applications of KCL, KVL and ohms laws? 16. Is there any particular situation in circuit, ohm’s law cannot be applicable? 17. What is the need of cyclo converters? 18. Explain everything you know about three phase cyclo converter by drawing as much as waveforms you can draw. (Note: Professor in the panel asked her to draw waveforms on board…She realized the pain I am having daily in my class….I am kidding… I am enjoying daily in work) 19. If we are happy with half wave rectifier circuits, why full wave rectifier circuits are invented? 20. What are the typical ratings of SCR? 21. Do you know about Matrix converter? 22. Tell me the practical applications of PE you have seen? (My 3 hours introduction class is the answer for this question) 23. What is DC transformer? 24. Will PE equipment affect the stability of any machine employed in electric drives? 25. What is the resistance between primary and secondary windings of the transformer? http://electrical-mentor.blogspot.in/



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26. Why only semiconductor devices in PE circuits will operate as switches? 27. Do you know anything about secondary breakdown of BJT? 28. What happened if mechanical switches are used in place of SCRs in converters? 29. Finally why do you want to join in power electronics why not in power systems in M.S/M.Tech?

Written test questions: 1. Explain SCR characteristics as bipolar and unidirectional switch? 2. A single phase full converter input is sinusoidal voltage. And load current is 4 A of constant. Find ripple factor in output voltage, fundamental rms source current, fundamental power factor, THD. Derive all the equations used 3. Explain with derivations, how to find active power, pf when voltage and current are having harmonics 4. A constant DC voltage source is connected to and RL draw load through a diode. Draw current and voltage across all components. Derive all the equations One important question: Finally, one of the professors in panel asked her “Who is your PE faculty and where did you learn power electronics” As the candidate answered all the questions, interview panel appreciated her understanding in the subject




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One more student (Anvesh Reddy) interview experience during M.Tech admission in IIT KGP and BARC in 2013 I am giving here directly in his hand writing to motivate you





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Some more standard interview questions in Electrical Engineering: 1. What is the basic difference between Transformer and Inductor? What are the applications of these two in power electronic converter circuits? 2. What do you understand by step down and step up transformers? 3. Draw the flux waveform in a transformer when its primary is excited by voltage waveform of (a) Sinusoidal (b) Square (c) Trapezoidal 4. How can you measure the losses in a transformer? How can you minimize these losses?



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5. Is it possible to operate a single phase 110 V, 50 Hz transformer satisfactorily at 200 Hz? If yes, explain how? 6. How are the transformer losses affected if pf of a given load is varied? 7. How is voltage regulation of transformer affected by a change in its operating frequency? 8. Two mutually coupled coils act as an ideal transformer. Find the nature of its reluctance. 9. What happens in a transformer if its core is made from high permeability ferromagnetic material? 10. What are the basic difference between hot rolled and CRGO laminations used in a transformer? 11. What are the three basic principles for the electromechanical energy conversion? 12. For an electromechanical energy conversion process, reaction of coupling magnetic field on electrical or mechanical system is essential. Explain in simple words. 13. How is the reluctance torque produced in a rotating machine? 14. Salient pole alternators are more suitable for low speed operation. Explain? 15. Non salient pole alternators are more suitable for high speed operation. Explain? 16. Can a dc generator be converted into alternator? Justify your answer with reasons 17. What is the meaning of “electrical angle”? How is it different from mechanical angle? 18. What are the methods of reducing space harmonics in a machine? 19. How is a sinusoidal voltage developed in a synchronous machine? 20. Why should the output voltage from a poly phase alternator be sinusoidal?



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21. What is the magnetization curve in reference to a dc shunt generator? Explain the procedure to get it 22. What do you mean by GNA and MNA in a dc machine? 23. What is the motor best suitable for traction applications? Any other alternative you can suggest 24. Draw the block diagram for a DC motor and then explain speed control of dc motor 25. Explain armature reaction in (a) DC machine (b) Synchronous machine 26. What is meant by alternator on infinite bus bars? 27. Does a change in the excitation of a synchronous motor affect its speed and power factor? 28. What is meant by synchronizing power? 29. What are different methods to find out voltage regulation of an alternator? Which one is the best one? 30. What is the purpose of damper winding used in salient pole type synchronous machine? 31. Name three important characteristics of a three phase synchronous motor not found in induction motor? 32. What is synchronous condenser? Do you know any equipment which will do the same job without rotating parts? 33. It is desirable that the incoming machine should be little fast at the time of synchronization. Explain with phasor diagrams? 34. With 3 ph balanced sinusoidal voltages, a rotating magnetic field will produce in 3-phase induction motor but not in 3 phase transformer. Explain mathematically with neat diagrams 35. Name the two types of three phase induction motors. What are the differences in construction between the two? 36. How can the direction of the following machines can reverse (a) dc motor (b) Induction motor (c) Synchronous motor



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37. How does the change in supply voltage and frequency affect the performance of three phase induction motor? 38. Explain why the starting currents are very high in reference to (a) dc motor (b) Induction motor 39. What is induction generator? Name any one popular application in present days 40. Where do we prefer the use of lap windings and wave windings? 41. What is meant by balanced system and phase sequence in three phase systems? 42. Explain two watt meter method in the measurement of power in a three phase system. What is the nature of pf when, (a) one wattmeter reads zero (b) two wattmeter readings are equal but opposite sign 43. What is the basic definition of power system stability? Explain various terms you are familiar in stability? 44. What is per unit system? What is the use of it? 45. Explain the synchronous machine behavior when three phase short circuit is created at the terminals 46. What is swing equation and inertia constant? 47. Explain the following terms: (a) Synchronous reactance (b) Transient reactance (c) Sub transient reactance 48. What is meant by capability curve in synchronous machine? 49. What is meant by surge impedance loading in a transmission line? 50. What is operating frequency in India? How many regional grids in India. Do you know any country in the world is operating with two different frequencies? 51. Explain mathematically, the transfer of power (active and reactive) between two active sources shown below:



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52. What is load flow problem and explain various buses used in load flow study 53. What is the simple algorithm used in load flow study 54. Explain the following concepts with neat sketches (a) Transient stability (b) Small signal stability (c) Voltage stability 55. What will happen if excitation system in a synchronous generator fails? How can you detect and protect the systems from excitation failures 56. What will happen if prime mover to a synchronous generator fails when it is connected to infinite bus? 57. When HVDC transmission system is preferable. Do you know any HVDC links in India? (Note: to get the answer, visit www.powergridindia.com) 58. Explain various components of HVDC transmission system 59. What do you meant by FACTs? Name any FACTs controllers that you are familiar with 60. Explain the function of SVC and draw simple schematic




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Answers for Conventional Questions

L = 0.1 H C = 0.05 F (a) 10 mH (b) 20 dB and 10 Ω (a) 100 krad/s, 10 krad/s and 1000 krad/s (b) 50 krad/s (a) 5 A and 8.165 A (b) 5 W 25 W (a) 23.75 A and 1.2 A (b) 28.5 W 55 W (a) 5 A (b) 6.67 A (c) 6 W with BJT and 6.67 W with MOSFET (a)Vt = 0.98 V; Rd = 0.005 Ω (b) θJC = 1.25 0C/W; θCA = 1 0C/W (a) Vt = 0.771 V and Rd = (1/70) Ω (b) 10.577 W (a) 72 W (b) 3 W (c) 0.4167% (a) 4.5 A and 6.93 A (b) 4.8 W, 3.6 W and total loss is 8.4 W 2.8 W (a) Eon= 133.33 µJ; Eoff = 266.67 µJ (b) Eon= 400 µJ; Eoff = 800 µJ (c) 40 W and 120 W Q16. Eon = 60 mJ and Eoff = 60 mJ Q17. 79.69 0C Q18. (a) 2A and 8 A (b) 3.2 W and 12.8 W (c) 118.4 0C Q19. (b) 107.8 W (c) 21.6 0C Q20. C is ideal upto a frequency of 18.4 kHz Q21. (a) 12.79 A (b) 58.1 A

Q1. Q2. Q3. Q4. Q5. Q6. Q7. Q8. Q9. Q10. Q11. Q12. Q13. Q14. Q15.

Q22. Q23. Q24. Q25. Q26. Q27.

***

L1 = 325.25 µH, L2 = 827.9 µH, L12 = L21 = 177.41 µH *** ***

77.6 µF (a) 1.28 mH (b) 5.14 mH Q28. (a) 10 V (b) Iload = 25 A Q29. **** Q30. 20A, 31.416 A, 628.32 V and 13.96 kVA Q31. (a) L =70√2 mH; V1 = 0 V and V2 = 0 V (b) V1 = 0 V; V2 = 220 V and A = 12.25

A

Q32. Q33. Q34. Q35. Q36. Q37. Q38. Q39.

(a) V1 = √2 V ; V2 =200√2 V (b) V2 =200√3 V (a) 2.5467 Ω (b) 49.42 V (c) 4.167 3.1416 hr ***

(a) 650 V (b) PIV rating will increase (c) 325 V (d) 41.55 X 103A2s ***

10A and 1835.6 W 1A



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Q40. (a) 7243 W (b) 4 kW Q41. (a) 67.70 (b) 7.765 A and 10.477 A Q42. (a) 232 V and 133.15 V (b) 10A & 17.32 A; 565.68 V (c) 19 W (d) 232 V, 154 V;

0 A, 0 A and 7.5 A, 15 A Q43. 50.110 Q44. 4 kW, 2.31 kVAR and 0.827 lag Q45. 19.95 A Q46. (a) 12 V (b) 44.370 and 0.3344 ms (c) 129.60 Q47. (a) 33.33 A & 57.735 A (b) 622.25 V (c) 81.65 A Q48. Q49. Q50. Q51. Q52. Q53. Q54. Q55. Q56. Q57. Q58. Q59. Q60. Q61. Q62. Q63. Q64. Q65. Q66. Q67. Q68. Q69. Q70. Q71. Q72. Q73. Q74. Q75.

***

(a) (i) 341.16 V (ii) 157.1 V (iii) 157.1 V (iv) 209.44 V (v) 104.72 V (vi)104.72 V 1443.4 A and 104.7 kV (a) 50% (b) 228.57 µH (c) 350 µF (a) 50% (b) 0.833 A (c) 1.416 A (d) 21.93 mV (a) 4.29 V (b) 65.45 mV (c) 0.8 A (d) 2.11 A and 0.514 A *** *** ***

(g) L1 = 2.67 mH, L2 = 960 µH, C1 = 24 µF and C2 = 2 µF 24.14 A

vw vg

=4;

***

vw

= 25

(a) N2/N1 = 9 (b) 0.46 < D < 0.55 (c) 7.35 mH 50:1 96% Vsw = 500 V and Vd = 750 V 1/3 and 1/9 (a) 6 µH (b) 1.25 % *** ***

(a) {i} 73.211 A and 0 A; {ii} 51.776 A & 51.776 A (b) {i} 230 V {ii} 230 V 2.148 µF (b) 204.54 W & 204.12 W (c) 9.044 A & 4.522 A (d) 5.513 ms & 4.487 ms (a) 5285.56 W (b) 3400.96 W (c) 2706.34 W (a) 500 µs (b) 750 V (a) 40x1 − 1.245yz{|EE} ~, -9.8 A and 9.8 A; (b) 438.14 µs (b) 162.635 V and 93.897 V (c) 155.304 V and 89.665 V (d) 28.15 % (e) 5154.86 W and 22.412 A (f) 7.667 A and 13.28 A Q76. (a) 100 µs (b) VT = -15 V and VC = 30 V Q77. (a) 24.335 µs and tc = 13.23 µs (b) 24.335 µs and tc = 76.273 µs Q78. Yes and 125.664 µs Q79. (a) 0.025 µF (b) 10 Ω Q80. (a) 7.2135 µF (b) 50 kΩ Q81. (a) IT1,max = 24 A and IT2,max = 42 A (b) C = 11.542 µF Q82. ***




Q83. Q84. Q85. Q86. Q87. Q88.

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(a) 69.70 (b) 63.98 A (c) 0.821 lag (d) 70.3 % (a) 39.20 (b) 8.30 (a) 29.30 (b) 1200 (c) -893.2 rpm (a) 1.559: 1 (b) (i) 34.650 (ii) 104.20 (a) 0.376 (b) 0.34 (c) 962 rpm and 87.4 kW (c) 0.8 (a) 900 rpm, 0.45 Hz, 1.5 % (b) 2.7 Hz



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Answers for Objective Questions Test -1 1-C

2-C

3-B

4-B

5-C

6-D

7-A

8-A

9-B

10 - D

11 - A

12 - C

13 - D

14 -D

15 - B

16 - B

17 -B

18 -C

19 -B

20 -D

21 -B

22 -B

23 -D

24 -A

25 -B

26 -A

27 -D

28 -D

29 -B

30 -B

31 -A

32 -D

33 -C

34 -D

35 -A

36 -B

37 -A

38 -C

39 -B

40- C

41 - D

42 - B

43 - A

44 -B

45 -A

46 - D

47 - C

48 - B

49 - C

50 - C

51 - C

52 - A

53 - B

54 - B

55 - A

56 - C

57 - D

58 - A

59 - D

60 -A

Test -2 1-C

2-A

3-B

4-D

5-B

6-A

7-A

8-B

9-C

10 - C

11 - D

12 - C

13 - C

14 -A

15 - B

16 - C

17 -C

18 -A

19 -B

20 -D

21 -D

22 -A

23 -A

24 -B

25 -C

26 -B

27 -C

28 -B

29 -D

30 -C

31 -B

32 -D

33 -D

34 -A

35 -C

36 -B

37 -D

38 -B

39 -C

40- D

Test -3 1-B

2-C

3-B

4-A

5-C

6-A

7-B

8-C

9-B

10 - C

11 - A

12 - B

13 - D

14 -C

15 - A

16 - D

17 -D

18 -D

19 -B

20 -A

21 -B

24 - B

25 - B

26 -A

27 -B

28 -D

29 -C

30 -A

22

83.2 V

23

D = 0.85 and 145 rad/s

7–B 17 – B 27 - A

8–C 18 – B 28 – B

9–A 19 – A 29 – C

41922 20 - C 30 - D

1–C 11 – C 21 – B 31:12.8

2–B 12 – B 22 – A 32 - C

3–C 13 – B 23 – A 33 - C

4–B 14 – D

Test-4 5–D 6–B 15 – B 16 – A

24 : 457.6

25 - 750

34 - B

35 - C


26 – 20


Page 93 of 120


How to design a closed control system for power electronic converters In this document, the control requirements of the dc-dc converter are stated and are related to the frequency domain performance indices such as the loop gain, crossover frequency, dc loop-gain, and phase margin of the loop gain and so on. The closed loop controller design is briefly outlined and then demonstrated through the example of a buck and boost converter. Control requirements of closed loop system: The control specification of the converter will be in two parts. • •

Steady state accuracy Settling time and allowed transient overshoot in the event of disturbances or command changes.

The steady state error is related to the dc loop gain [G(0)H(0)] of the closed loop system. The steady state error is approximately 1/ G(0)H(0). For example, a dc loop gain of 100 will result in a steady state error of about 1%. The settling time and transient overshoot are related to the 0 dB crossover frequency of the loop gain and the phase margin (PM). If ωc is 0 dB crossover frequency of the loop gain then the settling time (for a stable system) will be about to 3/ωc to 4/ωc The approximate transient overshoot is related to the phase margin (PM) of the loop gain according to the following table. PM (deg) Overshoot (%)

300 37%

350 30%

400 25%

450 16%

500 9%

550 5%

600 1%

For acceptable transient overshoot, the phase margin may be taken as 450. The first design step in closed loop controller design is to convert the control specification to the following: 1. Desired DC loop gain (to meet the steady state error) 2. Desired ωc(to meet the settling time) 3. Desired phase margin (to meet the transient overshoot) Compensator structure is shown in the following figure



Page 94 of 120


The first stage H1(s) of the compensator achieves the desired bandwidth ωc and the desired phase margin and the second stage is designed to meet the desired steady state error. The following steps will make the design procedure to be simple: The important rule that is used here is that, if the loop gain crosses 0 dB (unity gain) with a single slope (-20dB/decade), then the closed loop system will be stable. The reason is that the phase gain of a function crossing 0 dB with a single slope at a frequency of ωc is approximately the same as the function K=1/ωc(s) and is equal to 900. This argument is valid only when the loop gain is a minimum phase function. The actual phase angle will depend on the poles and zeroes nearest to the crossover frequency. With the above simple rule in mind, the compensator function H1(s) is selected to be simple lead-lag compensator. " = `

" 1 + D# G

" 1 + #

The purpose of is to make the slope of crossover section of the loop gain to -20 dB/decade near the desired crossover frequency, and to improve the phase margin • • •

•

If G(s) is a first order system in the vicinity of ωc, then H1 may be just K1 If G(s) is a second order system in the vicinity of ωc, then select ωz1 and ωp1 such that ωz1 < ωc < ωp1 If G(s) is a second order system with pole pair ω0, then ωz1 may be taken as ω0 and ωp1 is usually several times higher than ωz1 (about ωp1 = 10 to 100 times ωz1) Now K1 may be selected to meet the requirements of ωc and PM

The structure of second system can be considered as follows: M" =


` " " 1 + # + #E E


Page 95 of 120


The next part of the compensator H2(s) is needed to meet the steady state error specification. If G(0)H1(0) is already compatible with the steady state error, then H2(s) is 1. However, if G(0)H1(0) is not compatible with the desired steady state error, H2(s) is different from unity. The conditions on H2(s) are • •

•

G(0)H1(0)H2(0) = dc loop gain H2(s) must not affect the gain & phase margin already designed. Or in the other words, phase and magnitude gain of H2(s) in the vicinity of ωc must be 00 and 0dB respectively. A PI controller H2 (s) of the following form will satisfies the above requirements. " 1+ # " = " # Then the overall compensator is " # " = ` " " 1 + # # " 1 + D# G

1+

And this H(s) can be realized using either operational amplifier circuits or DSP controller or FPGA controller The control transfer functions for three basic DC-DC converters are giving here for quick reference: Buck: E " = W Boost:

1 C 1 + " ] + " CK

E " = 1 − o W

1 + "

Buck-Boost:

E " = 1 − o W

1 + "

1−"

C ]1 − o

C CK + " 1 − o ]1 − o 1 − "o

C ]1 − o

C CK + " 1 − o ]1 − o



Page 96 of 120


Compensator design example 1 (For buck converter)

A buck converter transfer function is given as follows: M" =

1 +

40

" 2" + 100s 100s

Q: Design a compensator with acceptable transient and steady state response parameters as follows: a) Phase Margin and Gain Margin of loop gain should be greater than 450 and 20 dB respectively b) Steady state error should not be more than 5% c) Settling time should not be more than 1 s d) Peak overshoot should not be more 5 % Justify all the design requirements with suitable response plots

Note: Derivation of transfer function G(s) is out of scope of this document. You can refer any standard text book in PE



Page 97 of 120


Compensator Design procedure with bode plot approach: Step1. Let us draw the asymptotic gain bode plot of G(s)

Fig 1 Observations from Fig 1: M" =

40

" 100s 0dB cross over frequency of open loop plant transfer function is around 2000 rad/s and phase margin is around 18.20. The consequence of this is peak overshoot in the response will be very high. That can be observed in the following step response.


2" 1 + 100s +


Page 98 of 120


Step response of G/(1+G) is shown in Fig 2:

Fig 2 From the step response of Fig 2, we can observe that transient response specifications are not satisfied Hence compensator is required As G(s) is a second order system with a complex pole pair ω0 then ωz1 in compensator may be taken as ω0 and ωp1 is usually as several times ωz1 (10 to 50 time) Standard form of H(s) is as follows:

" =


" 1+#

" 1+# Copyright © Reserved 2014

Page 99 of 120


Step2. Let us draw the asymptotic gain bode plot of compensator H(s) " 100s " = " 1+ 40000s 1+

Fig 3 H(s) is basically a lead-lag compensator and it can improve the PM to this plant



Page 100 of 120


Step3. Let us draw the asymptotic gain bode plot of G(s)H(s) Note: Here G(s)H(s) is loop gain

Fig 4 Observations from loop gain bode plot (Fig 4): 1. Closed loop system is stable as loop gain is having PM = 90.50, it is the indication of peak overshoot of CLTF in time response is less than 1% 2. 0 dB cross over frequency is 5 rad/s it means settling will be satisfied which can justified in step response of CLTF as shown below 3. Loop gain is having no issues with GM



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Step4: Verification of response in time domain: Step response of output voltage V(t) with unity feedback is shown inn Fig 5

Fig 5 As settling time and steady state errors specifications are satisfied, there is no need to use PI regulator in the low frequency region

Cross checking other possibilities: Suppose in H(s), if we take pole at 10000π instead of 40000π. Then also stability condition will satisfy but settling time will not satisfy. Let us see these two observations from bode plot of loop and step response with the follow modifications

" = And

k

ewBB k

eBBBB

" =

k

ewBB k

ewBBBB



Page 102 of 120


Fig 6 Step response of V(t) with compensator with two pole locations in the compensator:

Fig 7 http://electrical-mentor.blogspot.in/



Page 103 of 120

From step response shown in Fig 7, we can observe that compensator with poles at 40000π and 10000π are satisfying the stability conditions. But, compensator with pole at 40000π (blue color) is giving settling time of 0.74 s whereas compensator with pole 10000π (green color) is giving settling time of 2.99 s. The same point can be observed from bode plot of loop gain shown in Fig 6; 0dB cross over frequency with H1 is more than H2 that means bandwidth is better with H1 Therefore " =

k wBB k e BBBB

e

will give satisfied response in closed loop operation

If we select suitable circuit components to realize this transfer function or proper controller hardware will satisfy response in closed loop operation Hence compensator design is complete in all aspects.



Page 104 of 120


Compensator design example 2 (For boost converter)

A boost converter has the following transfer function " 1 − 4000s M" = 40 2" " 1+ +D G 80s 80s

Q: Design a compensator with acceptable transient and steady state response parameters as follows: a) Phase Margin and Gain Margin of loop gain should be greater than 450 and 20 dB respectively b) Steady state error should not be more than 5% c) Settling time should not be more than 1 s d) Peak overshoot should not be more 5 % Justify all the design requirements with suitable response plots



Page 105 of 120


Compensator Design procedure with bode plot approach: Step1. Let us draw the asymptotic gain bode plot of G(s)

Fig 8 Note: From the transfer function G(s) of boost converter it can be observed that it has one RHP zero. Due to this compensator design is little difficult. It cannot give stable operation in closed loop for the entire range From the bode plot of G(s) shown in Fig 8, PM and GM are not satisfied values



Page 106 of 120


Step response of G/(1+G) [Unity FB closed loop without compensator] is shown in Fig 9

Fig 9 Observations: From Fig9, it can be observed that even though steady state response is satisfying due to feedback, peak overshoot of 74% is not acceptable. This is because PM of loop gain without controller is 140 which very less (look into Fig 8). Hence compensator is required



Page 107 of 120


Step 2: Bode plot of compensator H(s): Let us consider a compensator has a transfer function of " D1 + 80sG " = " D1 + 4000sG

Fig 10



Page 108 of 120


Step 3: Bode diagram of G(s)H(s) is shown in Fig 11:

Fig 11 This loop gain is not having satisfied PM and GM. Therefore, if we shift the pole to somewhat high value, we can achieve this Let us consider compensator transfer function as below: " D1 + 80s G " = ` " D1 + 40000s G

Where K1 = 0.1 And bode plot of new loop gain is as shown in Fig 12:



Page 109 of 120


Fig 12 Now PM and GM are satisfied. Therefore, BW and peak over shoot conditions will be satisfied. But as low frequency gain is around 12 dB, it will not satisfy the steady state error. Which can understand from the time response of v(t) shown in Fig 13



Page 110 of 120


Fig 13 From the curve shown in Fig 13, we can say that SS error is more than 20%. To reduce this steady state error, let us introduce PI regulator of the following transfer function with pole at very low frequency say 500 rad/sec " 1+ 500 " 500

And bode plot of this PI regulator is shown in Fig 14



Page 111 of 120


Fig 14 Now the final compensator is as follows:

" " D1 + 80s G D1 + G 500 ℎyy ` = 0.1 " = ` " " D1 + 40000s G D G 500

Circuit realization of this compensator is as shown in Fig 15:

Fig 15



Page 112 of 120


Step4: Bode plot of loop gain and step response of output The final bode plot of loop gain [G(s) H(s)] is as shown in Fig 16:

Fig 16 Observations: 1. Loop gain is having reasonable GM of 22 dB. 2. Loop gain is having reasonable PM of 730 which will give satisfied peak overshoot 3. 0 dB cross over frequency is around 1000 rad/s means good BW and hence response will have small settling time 3. Low frequency gain of more than 42 dB will give acceptable steady state error



Page 113 of 120


We can observe all the above conclusions in the step response of the output voltage as shown in Fig 17:

Fig 17 Note: Buck Boost converter will also have similar transfer function that boost converter (with RHP zero) and hence design procedure is same as boost converter. Hence not repeating



Page 114 of 120


Useful units for Electrical Engineering Expression in terms of SI base units

Quantity Time Electrical current Electrical capacitance Electrical charge

Name of Unit/Description second ampere farad coulomb

Symbol s A F C

Electrical conductance Electrical inductance Electrical potential Electrical resistance Force Frequency Magnetic flux

siemens henry volt ohm newton hertz weber

S H V Ω N Hz Wb

Magnetic flux density Power or radiant flux Pressure Work, energy, heat

tesla watt pascal joule

T W Pa J

Wb/m2 J/s

Electrical charge density coulomb per cubic meter

C/m3

m-3 s A

Electric field strength

volt per meter

V/m

m kg s-3 A-1

Electric flux density

coulomb per square meter

C/m2

m-2 s A

Energy density

joule per cubic meter

J/m3

m-1 kg s-2

Moment of inertia

kilogram meter squared

kg.m2

kg.m2

Torque

Newton meter

N .m

m2 kg s-2

Permeability

henry per meter

H/m

m kg s-2 A-2

Permitivity

farad per meter

F/m

m-3 kg-1 s4 A2

kW

10-3 m2 kg s-3

Power kilowatt Permeability of free space E = 4s 10 H/m

C/V A/V W/A V/A

Vs

Nm

Permittivity of free space E = 8.854 10 F/m




Page 115 of 120

Common mistakes in units display – Observe carefully and follow the standard practice* Wrong V = 1000 Vmax 100volts 10 Amps 10 KWs 1 Ohm or 1 Farad or 1 Henry 1 mµF 1milli-gram 1 ampere/meter 10 % (m/m) or 10 % (by weight) 20 mL H2O/kg (or) 20 mL of water/kg 35 × 48 cm 1 MHz – 10 MHz or 1 to 10 MHz 20 ºC – 30 ºC or 20 to 30 ºC 123 ± 2 g 70 ± 5 % 240 V ± 10 % (one cannot add 240 V and 10 %) kilogram/m3, kg/cubic meter, kilogram/cubic meter, kg per m3, or kilogram per meter3 m = five kilograms or m = five kg the current was 15 amperes a 25-kg sphere an angle of 2 º3 '4 " Sin x, Cos x, Tan x It is 75 cm. long l = 10 m 23 cm 4 mm the resistance is 100 Ω/square µr = 1.2 µ

Correct Vmax = 1000 V 100 volt or 100 V 10 A 10 kW (a) 1 ohm or 1 farad or 1 henry (b) 1 Ω or 1 F or 1 H 1 nF 1 milligram or 1 mg 1 ampere per meter or 1 A/m a mass fraction of 10 % the water content is 20 mL/kg 35 cm × 48 cm 1MHz to 10 MHz or (1 to 10) MHz 20 ºC to 30 ºC or (20 to 30) ºC 123 g ± 2 g or (123 ± 2) g 70 % ± 5 % or (70 ± 5) % 240 × (1 ± 10 %) V kg/m3, kg · m−3, or kilogram per cubic meter m = 5 kg the current was 15 A a 25 kg sphere an angle of 2º3'4" sin x, cos x, tan x Its length is 75 cm or It is 75 cm long l = 10.234 m the resistance per square is 100 Ω µr = 1.2 × 10-6

*Note: The above table is prepared by referring Guide for the use of International System of Units (SI) released by NIST (National Institute of Standards and Technology, Department of Commerce USA) as special publication in 2008



Page 116 of 120


Useful Mathematical Formulae 1. Trigonometric functions:

sin ± = sin cos ± cos sin

cos ± = cos cos ∓ sin sin

sin 2 = 2 sin cos

cos 2 = 1 − 2 sin = 2 cos − 1 sin + sin = 2 sin

sin − sin = 2 cos

+ − cos 2 2 + − sin 2 2

cos + cos = 2 cos

− + cos 2 2

cos − cos = −2 sin

− − sin 2 2

sin cos =

1 x sin + + sin − ~ 2

cos cos =

1 xcos + + cos − ~ 2

cos sin =

sin sin =

1 xsin + − sin − ~ 2

1 xcos − − cos + ~ 2

2. Integration functions: y

^

y ^ V sin z − cos z sin z Wz = V +

y ^ cos z Wz =

sin % z Wz =

cos % z Wz =

y ^ V cos z + sin z V +

z sin 2%z − 2 4%

z sin 2%z + 2 4%

sin ¡z . sin %z Wz =

sin¡ − %z sin¡ + %z − ¢! ¡ ≠ % 2¡ − % 2¡ + %



Page 117 of 120


cos ¡z . cos %z Wz =

sin¡ − %z sin¡ + %z + ¢! ¡ ≠ % 2¡ − % 2¡ + %

sin ¡z . cos %z Wz =

cos¡ − %z cos¡ + %z − 2¡ − % 2¡ + %

sin %z sin ¡z . cos %z Wz = 2%

z cos %z Wz =

z sin %z cos %z + % %

z sin %z Wz = −

z cos %z sin %z + % %

Integration by parts: ¤ ¥ W = ¥ − ¤ W¥ 3. Leibnitz’s linear 1st order differential equation: ¦

+ §¨ = Where P, Q are functions of x

). l = y ¤ © , then solution is ¨ ). l = ¤ ). l Wz + K 4. Fourier series: A function f (t) is said to be periodic of time if f (t+T) = f(t), then f (t) can be expanded in Fourier series as under: ¢ = VE + ∑« pUxVp cos %# + p sin %#~, where VE =

R

¤E ¢ W = R R

¬

¤E ¢ # W# ¬

¬

2 1 Vp = ¢ cos %# W = ¢ # cos %# W# X s E

R

E

¬

2 1 p = ¢ sin %# W = ¢ # sin %# W# X s And

E

E



Page 118 of 120


Use of symmetry in Fourier series Symmetry Even

Condition required f(-t) = f(t)

Odd

f(-t) = - f(t)

Half – wave

f(-t) = - f[t+(T/2)]

Even Quarter wave

Even and Half wave

Odd Quarter wave

Odd and Half wave

¬

2 p = 0 and Vp = ¢# cos%# W# s an and bn E

¬

2 Vp = 0 and p = ¢# sin%# W# s E

Vp = p = 0 for even ‘n’ ¬

2 Vp = ¢# cos%# W# s E

p = 0 for all ′n′ ¬⁄

²4 Vp = s ¢# cos%#W# for odd ′n′N ± E °0 for even ′n′ Vp = 0 ¢! V´´ ′%′ ¬⁄

²4 p = s ¢# si %%#W# for odd ′n′N ± E °0 for even ′n′

5. Laplace transforms: ℒx¶~ = 1 ℒx1~ = ℒx~ =

1 "

1 "

ℒx p ~ =

%!

" pe

ℒ xy ±^P ~ =

ℒ xy ^P ~ =

1 "∓V

1 " + V



Page 119 of 120


ℒxsin #~ =

ℒxcos #~ =

# " + #

" " + #

ℒxy ^P sin #~ =

ℒxy ^P cos #~ = P

ℒ 1 − y R =

# " + V + #

"+V " + V + #

1 "" + X

1 y ^P − y ¹P º= ℒ¸ " + V" + −V

ℒ P »¢¼ = ". ½¾ − ¢0

ℒ x¤ ¢ W~ =

½¾ f

+

¿ Àw E f

Where ¢ 0 = N¤ ¢ W |PUE and ½¾ = ℒx¢~

Note: The last two equations can be proved by writing the basic definition of Laplace transform and then apply integration by parts



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