# Power Electronics and FACTS

College of Engineering, Design and Physical
Sciences
Department of Electronic and Computer Engineering

Examinations Cover Sheet

SUBJECT AREA: ECE

Module Code: EE5519 – EE5119

Module Title:
Power Electronics and FACTS

Date-Month:
May Year: 2018

Time allowed – Hours:
2 – Hours

Answer-questions: Full marks can be obtained by answering 3 questions out of 5 questions. If more than 3 questions are attempted all attempts will be marked but only the marks for the 3 highest marked questions will be counted.

Only College approved calculators are allowed.

Examiner(s):

Dr M Darwish Dr B Rawn

Special Stationery Requirements:

Formulae sheet attached
Data sheet attached

1.
Design an active power filter to eliminate the 11th, 13th, 23rd and 25th current harmonics at the input of a 12-pulse 11 kV HVDC link converter. In your design you should cover the following points:

a) Principles of active power filter configuration.
b) Steps for evaluating the active power filter control pulses.
c) Effect of the active filter on the Total Harmonic Distortion (THD).
d) You also need to, critically, discuss the limitations of active power filters.
[20 marks]

2.
The 3-phase A.C. voltage controller shown in Figure Q2 is used to control the power to balanced resistive loads of 1 kΩ each. The input phase voltage is 240V rms, 50 Hz and the switches used are IGBT with a single PWM in the middle of each half cycle.
a) Work out the duration of conduction, in degrees, of each of the IGBT switches in order to deliver an output power of 1000 W per phase.
b) If the IGBTs are replaced by thyristors, work out the thyristor triggering angle to deliver the same power (as in part ‘a’) to the load.
c) Critically comment on both control methods used in ‘a’ and ‘b’.

Fig. Q2
[20 marks]
3. Design a switched mode power supply with the following specifications:
Vin (DC) = 2 V
Vout (DC) = 5 V
Output Power = 50 W
Output ripple voltage: ≤0.5%
Efficiency (η) ≥ 97%

In your design you should cover the following points: a) A sketch and explanation of your design.
b) Calculation of the range of the switch duty cycle and justification of any switching frequency used.
c) A sketch of the gain of the power supply against the duty cycle for ideal and non-ideal inductor.
d) Calculation of the value of any inductor used in your design.
e) Calculation of the value of any capacitor used in your design.
Comment on your calculated value of ‘C’.
f) Describe how you can protect any used switching devices against any transient voltage and current stress.
[20 marks]

4. A buck-boost converter is used to control the voltage to a highly inductive load.

a) Explain the operation of the converter with reference to its circuit diagram, the modes, the action table, the current and voltage waveforms, and the related switching functions.
b) Derive the Unifying Equation from the action table and hence derive an expression for the output dc voltage as a function of the input dc voltage and the duty cycle of the switch (D or Ko).
c) Explain why the output voltage cannot rise indefinitely with the duty cycle.
[20 marks]

5. The SVC in Figure Q5 contains multiple legs with different functions. The reactances of L2b, C5 and C3 have the same magnitude.

Fig. Q5

a) Suppose the firing delay of Q2a and Q2b is zero, and S5 is closed. S1 is open; Q3a and Q3b are not firing. Sketch on a single plot versus time the fundamental component of the current flowing through Leg 2, Leg 5, and the total current, including the fundamental component of the voltage.
[8 marks]

b) For the situation described in part (a), comment on the level of current harmonics produced, and explain how the design of the SVC accounts for this.
[2 marks]

c) Design a switching strategy to cause the SVC to shift from its operating point in part (a) to an operating point where the highest possible capacitive current is drawn. Include a scaled sketch in the
VB – ||ISVC|| plane, indicating which legs are active during the shift as current increases.
[6 marks]

d) Design a switching strategy to operate the SVC so that the highest possible inductive current is drawn. What design choice would you make to give the SVC equal capability to absorb and deliver reactive power?
[4 marks]
Power Electronics Formulae Sheets

DC/AC Inverter Circuits:
M f
1
rms(n) 2 2 2
% sin n (1 M A) sin n(2k 1) 100
Vdc n M f k 0 M f
rms(Total)
% 100 (1 MA
Vdc
M

AC/AC Voltage Controller Circuits (Phase control):

Vout(rms) Vin(rms)
Vm 2 (cos((1 n) ) 1) 2 (cos((1 n) ) 1)
an
2 1 n 1 n
Vm 2 (sin((1 n) )) 2 (sin((1 n) ))
bn
2 1 n 1 n

Three-Phase Rectifiers with source inductance:
3𝑉𝑚 𝐿−𝐿 3 × 2𝜋𝜋𝜋
𝑉𝐴 = cos 𝑎− 𝐼𝑑
𝜋 𝜋

Snubber Circuits:
The power dissipated in the turn-on snubber resistor ‘R’:
LI 2
PR
2T
The energy dissipated in the turn-off snubber switch:

I2 t2f
W
24C
Buck Converter:
Vout DVin
L out (1 D) V
iL f
(1 D)R
Lmin
2 f
1 D
C Buck-Boost Converter:
D
Vout Vin 1 D
(1 D)2 R
Lmin
2 f
D
C
Vout

8L f 2 Vout
Vout

Boost Converter:
Vin
Vout
1 D
L Vin D iL f
D(1 D)2 R
Lmin

2 f
D
C
Vout

Exam Question Paper
College/ Institute College of Engineering, Design and Physical Sciences

Department
Electronic and Computer Engineering

Exam Author(s) Dr M Darwish
Dr A. Zobaa

Module Code
EE5519 – EE5119

Module Title
Power Electronics and FACTS

Month
May
Year 2019

Paper Type
End of Year

Duration
2 Hours

Question Instructions

This paper consists of 5 questions. All questions carry equal marks.

Are Calculators Permitted? Yes
Make/Model number of permitted calculators. Standard

Permitted Reference
Materials
None

Required Stationery /
Equipment
Formulae sheet attached Data sheet attached

1.
a) Explain briefly five means by which power and current flow can be controlled in power transmission.
[10 marks]

b) An uncompensated lossless transmission line with voltage of 220 V at each end, reactance of 1 : and line current of 140 A.

i) Find the phase angle, active power and reactive power.
[6 marks]

ii) If an ideal shunt compensation is used at the midpoint of this line, find the reactive power supplied by the shunt compensation if the transmitted active for shunt compensation is 55 kW.
[4 marks]

2.
a) Outline and explain the benefits that voltage source converters can offer over line-commutated converters when controlling power flow in the transmission system.
[8 marks]

b) A fully controlled three-phase bridge converter A is connected to a 3300 V, 60 Hz system that has an inductance of 2 mH/phase. A dc link, of resistance 0.7 : go and return, connects converter A to a converter B. Converter B is also of the fully controlled three-phase bridge type and is connected to a 3800 V, 50 Hz system that has an inductance of 2.5 mH/phase. Power flow is from the 60 Hz to the 50 Hz system.
Calculate the firing delay angle of Converter B for a dc link current of 200 A, if the firing delay angle of converter A is 20q. Support the calculations with an equivalent circuit diagram of the transmission system.
[12 marks]

3. Design a switched mode power supply with the following specifications:
Vin (DC) = 220-240 V
Vout (DC) = 24 V
Output Power = 100 W
Output ripple voltage: ≤1%
Efficiency (η) ≥ 95%

In your design you should cover the following points: a) A sketch and explanation of your design.
b) Calculation of the range of the switch duty cycle and justification of any switching frequency used.
c) Calculation of the value of any inductor used in your design.
d) Calculation of the value of any capacitor used in your design.
Comment on your calculated value of ‘C’.
e) Describe how a closed loop system can be implemented in such power supply in order to maintain a constant output voltage.
[20 marks]

4.
a) A sinusoidal PWM technique is used to control the switches in a fullbridge MOSFET inverter. Explain the effects that a change in the modulation index has on the performance of the inverter.
[8 marks]

b) It is required that the inverter output has a fundamental frequency of
50 Hz with 3 pulses per half cycle (R=3) and a d.c. input (V) of 100 V. The graph in Figure Q4 shows the switching angle/modulation index curves for the inverter. If the modulation index is set at 0.3 then determine:

(i) The rms value of the fundamental component of the output voltage (V1).
[4 marks]

(ii) The total harmonic distortion (Vhar / V1).
[4 marks]

(iii) Discuss what performance improvements may be made if R is increased.
[4 marks]

Modulation Index
Figure Q4
5.
a) Give the block diagram of a Grid Connected System and briefly explain its operation with regards to the flow of power from the PV modules to the Grid via the various sub systems and the role of the control parameters of each subsystem.
[8 marks]

b) The PV panel used in such a system has its maximum power point at
Vmpp = 183 V and Ιmpp = 16.28 Α at a specific time during the day. Calculate the values of the control parameters of the system for the transfer of power to the Grid at unity power factor and state any assumptions made.
[6 marks]

c) The dc voltage at the input of the inverter is 400 V, the decoupling inductance is 0.5 mH and the switching frequency is 5 kHz. Explain the role of a filter at the output of the inverter and calculate the d.c. current at the input. Explain why a 100Hz current flows at the d.c. side of the inverter. Derive an approximate mathematical expression for this dc current based on the parameters of the PWM signal and calculate a value of this current with the available data. Explain carefully any assumptions made and assume that the grid voltage is
230V.
[6 marks]

Power Electronics Formulae Sheets

DC/AC Inverter Circuits:
ª M f 1 º

Vdc « nS
«
¬
¨ M f A ¸¹ k¦ 0 ¨© M f ¸¹»u
»
¼
% rms(n) ««2 2 sin §¨n S (1 M )¸· 2 sin ¨§n(2k 1) S ·¸»» 100

rms(Total)
% 100 u (1M A
Vdc
M f

AC/AC Voltage Controller Circuits (Phase control):

Vout(rms) Vin(rms) 1D sin 2D
S 2S
V2m ª 2 (cos((1n)D)1) 2 (cos((1n)D)1)º» an «1n 1n ¼

V2Sm ª 2 (sin ((1n)D)) 2 (sin ((1n)D))º» bn «1n 1n ¼
¬

Three-Phase Rectifiers with source inductance:

3𝑉𝑚 𝐿−𝐿 3 × 2𝜋𝑓𝐿
𝑉𝐴 = cos 𝑎 − 𝐼𝑑
𝜋 𝜋

M f is odd

Snubber Circuits:
The power dissipated in the turn-on snubber resistor ‘R’:
LI 2
PR
2T

The energy dissipated in the turn-off snubber switch:

I2 t2f
W
24C

Buck Converter:

Vout DVin

L Vout (1D) ‘iL f

R
Lmin
2 f

C 1 D

Boost Converter:

Vin
Vout
1D
L Vin D
‘iL f
Lmin D(1 D)2 R
2 f
D
C
§’Vout ·¸
R f ¨

Buck-Boost Converter:
Vout Vin §¨ D ·¸
(1 D)2 R
Lmin
2 f
D
C

EXAM QUESTION PAPER
College/ Institute Engineering, Design and Physical Sciences
Department Department Electronic and Computer Engineering
Exam Author(s) M Darwish
Module Code EE5519
Module Title Power Electronics and FACTS
Month August Year 2020
Exam Type Full Format Take home exam

Duration
3 Hours and 15 minutes plus 45 minutes to allow for upload of your work and hand in.

Please ensure you click the green hand in button to submit your work (a single pdf file) as shown below

Number of questions 5 Questions
Question Instructions Answer ALL questions in WiseFlow
Can students include drawings/ diagrams? YES (optional)
Permitted reference materials (including external websites) Open book: all resources used must be fully referenced
Contact for Academic Queries: 1st Mohamed.darwish@brunel.ac.uk
2nd Ahmed.Zobaa@brunel.ac.uk
Contact for technical issues: Email WISEflowhelp@brunel.ac.uk or use the Chat tool that is embedded in WISEflow.
Contact once Flow has ended: for example if you have missed out/failed to upload pages or missed the deadline due to technical issue examinations@brunel.ac.uk

By continuing beyond this point, you confirm that you have read the information and instructions above, and understand the conditions of this examination.

1.
a) Critically discuss, with the aid of the phasor diagrams, the capacitive and the inductive modes of operation of STATCOM.

b) Figure Q1 shows the equivalent circuit of a STATCOM connected to a load bus.

Figure Q1

The bus voltage Vbus = 0.97<-10° p.u. The coupling transformer reactance Xsh = 0.2 p.u.

i. Assuming a lossless STATCOM, find the fundamental magnitude of the STATCOM output voltage Vsh, if the STATCOM delivers a reactive power of 0.1 p.u to the load bus.

ii. If the STATCOM has losses and it receives an active power of 0.02
p.u. from the load bus, find the reactive power delivered by the STATCOM, if the magnitude of the STATCOM output voltage Vsh =1.02 p.u.

2.
Design Thyristors based AC voltage controller with the following specifications:

Input voltage: Three-phase 415 V, 50 Hz.
Output voltage: Three-phase 0 – 200 V, 50 Hz.
Power: 5 kW delivered to a purely resistive load.
Fifth current harmonic: <3%.

In your design you should cover the following points:
a) A sketch of your design (circuit and waveforms).
b) Calculation of your control pulses.
c) Your calculation of the 5th current harmonic before and after any filtering effect.

3.
a) A combined load consists of a linear part (20 Ω resistor in series with 50 mH inductor) and a non-linear part (single-phase diode bridge rectifier). The load is connected in series to a 240 V, 50 Hz supply. Calculate the value of the shunt capacitor required to improve the displacement factor to 0.95 (lagging).

b) An inverter-based active filter is used to correct the distortion factor in the combined load in Q3 a). Work out the switching pattern used in the inverter-based active filter in order to eliminate the 3rd, 5th, 7th and 9th harmonics. You may use the following equation in your calculations.

M
4 k1 cos(niDk ) 0 fi(D) niSk¦ 1(1)

c) Show how the inverter-based active filter can be used to improve the power factor (distortion and displacement) of the combined load in Q3 a).

4.
a) The waveforms in Fig. Q4 are examples of waveform distortions which affect the power quality. Critically discuss these types of distortion their causes and impacts.

Fig. Q4

b) A DC/DC buck converter is used to step down the voltage from 12 V to 5 V, delivering 100 W power to a highly inductive load. Design a turn-on snubber circuit for this buck converter. In your design you should cover the following points:

i. Functions of snubber ciurcuits.
ii. Sketch of the buck converter with the snubber circuit
iii. Sketch of the switch current and voltage waveforms. iv. The calculations of any parameters you use in your design.
v. The effect of increasing or decreasing your calculated values on the efficiency of the buck converter.

5.
a) Explain briefly the role and the operation of the STACOM and show by the aid of phasor diagrams the conditions under which either leading or lagging reactive power is produced. State the control parameter.

b) The voltage at the dc side of the STACOM is 500V and the inductance connecting the STACOM to the mains is 0.0005H. The mains voltage is 230V at 50Hz.

Calculate
(i) The reactive power to the grid and state if it is capacitive or inductive at modulation index of 0.6.

(ii) The modulation index for the production of 15ΚVAr capacitive reactive power.

(iii) The lowest order harmonic current at the dc side.

(iv) State the magnitude of the dc current and comment.

Power Electronics Formulae Sheets

DC/AC Inverter Circuits:
ª M f 1 º
% rmsV (n) ««2n 2 sin§¨¨n S (1M A)·¸¸ 2¦ sin¨§¨n(2k1) MSf ¸¹¸·»»»u 100
« »
¬ ¼

rms(Total)
% 100 u (1M A
Vdc
M

AC/AC Voltage Controller Circuits (Phase control):

Vout(rms) Vin(rms) 1Dsin2D
S 2S
V2m ª 2 (cos((1n)D)1) 2 (cos((1n)D)1)º» an «1n 1n ¼

V2Sm ª¬ 2 (sin((1n)D)) 2 (sin((1n)D))º» bn «1n 1n ¼

Three-Phase Rectifiers with source inductance:

3𝑉𝑚 𝐿−𝐿 3 × 2𝜋𝑓𝐿
𝑉𝐴 = cos 𝑎 − 𝐼𝑑
𝜋 𝜋

M f is odd

Snubber Circuits:
The power dissipated in the turn-on snubber resistor ‘R’:
LI 2
PR
2T

The energy dissipated in the turn-off snubber switch:
I2 t2f
W
24C

Buck Converter:

Vout DVin

L Vout (1 D) ‘iL f

R
Lmin
2 f

C 1 D

Boost Converter:

Vin
Vout
1D
L Vin D
‘iL f
D(1 D)2 R
Lmin
2 f
D
C
§’Vout ·¸
R f ¨

Buck-Boost Converter:
Vout Vin §¨ D ·¸
(1 D)2 R
Lmin
2 f
D
C

Some Practice Questions
1)
Design Thyristors based AC voltage controller with the following specifications:
Input voltage: Three-phase 415 V, 50 Hz.
Output voltage: Three-phase 0 – 200 V, 50 Hz.
Power: 5 kW delivered to a purely resistive load.
Fifth current harmonic: <3%.
In your design you should cover the following points:
– A sketch of your design (circuit and waveforms).
– Calculation of your control pulses.
– Your calculation of the 5th current harmonic before and after any filtering effect.

2)
A combined load consists of a linear part (20 Ω resistor in series with 50 mH inductor) and a non-linear part (single-phase diode bridge rectifier). The load is connected in series to a 240 V, 50 Hz supply. Calculate the value of the shunt capacitor required to improve the displacement factor to 0.95 (lagging).

3)
An inverter-based active filter is used to correct the distortion factor in the combined load in question 2 above. Work out the switching pattern used in the inverter-based active filter in order to eliminate the 3rd, 5th, 7th and 9th harmonics. You may use the following equation in your calculations.
ni4 kM=1 k+1cos(ni k ) = 0 fi( ) = (−1)
Show how the inverter-based active filter can be used to improve the power factor (distortion and displacement) of the combined load in question 3 above.

4)
Outline the operation and explain the benefits that voltage source converters can offer over line-commutated converters when controlling power flow in the transmission system.

5)
A fully controlled three-phase bridge converter A is connected to a 3300 V, 60 Hz system that has an inductance of 2 mH/phase. A dc link, of resistance 0.7 go and return, connects converter A to a converter B. Converter B is also of the fully controlled three-phase bridge type and is connected to a 3800 V, 50 Hz system that has an inductance of 2.5 mH/phase. Power flow is from the 60 Hz to the 50 Hz system.
Calculate the firing delay angle of Converter B for a dc link current of 200 A, if the firing delay angle of converter A is 20 . Support the calculations with an equivalent circuit diagram of the transmission system.

6)
Design a switched mode power supply with the following specifications:
Vin (DC) = 220-240 V
Vout (DC) = 24 V
Output Power = 100 W
Output ripple voltage: ≤1%
Efficiency (η) ≥ 95%

In your design you should cover the following points:
– A sketch and explanation of your design.
– Calculation of the range of the switch duty cycle and justification of any switching frequency used.
– Calculation of the value of any inductor used in your design.
– Calculation of the value of any capacitor used in your design. Comment on your calculated value of ‘C’.
– Describe how a closed loop system can be implemented in such power supply in order to maintain a constant output voltage.

7)
A sinusoidal PWM technique is used to control the switches in a full-bridge MOSFET inverter. Explain the effects that a change in the modulation index has on the performance of the inverter.

8)
It is required that the inverter output has a fundamental frequency of 50 Hz with 3 pulses per half cycle (R=3) and a d.c. input (V) of 100 V. The graph in the figure below shows the switching angle/modulation index curves for the inverter.
If the modulation index is set at 0.3 then determine:
– The rms value of the fundamental component of the output voltage (V1).
– The total harmonic distortion (Vhar / V1).
– Discuss what performance improvements may be made if R is increased.

Power Electronics Formulae Sheets DC/AC Inverter Circuits:
M f −1
rms(n) 2 2 2
% = sin n (1−M A) sin n(2k+1) 100
Vdc n M f k=0 M f
rms(Total)
% = 100 (1−MA
Vdc
M

AC/AC Voltage Controller Circuits (Phase control):

Vout(rms) =Vin(rms)
Vm 2 (cos((1+n) )−1) + 2 (cos((1−n) )−1)
an=
2 1+n 1−n
Vm 2 (sin((1+n) )) − 2 (sin((1−n) ))
bn=
2 1+n 1−n
Three-Phase Rectifiers with source inductance:

𝑉𝐴 = 3 𝑉𝑚 𝐿−𝐿 cos 𝑎 − 3 × 2𝜋𝑓𝐿 𝐼𝑑
𝜋 𝜋
Snubber Circuits:
The power dissipated in the turn-on snubber resistor ‘R’:
LI2
PR=
2T
The energy dissipated in the turn-off snubber switch:

I2 t2f
W =
24C
Buck Converter:

Vout =DVin
L= Vout (1− D)
iL f
Lmin = (1− D)R
2 f
C= 1− D
8L f 2 Vout
Vout

Boost Converter:
Vin
Vout =
1−D
L= Vin D iL f
D(1− D)2 R
Lmin =
Buck-Boost Converter:
D Vout =−Vin
1−D
Lmin = (1− D)2 R
2 f
D
C =
Vout

2 f
D
C=
Vout