ASSESSMENT GUIDELINES
Course code: IRE35017
Course name: Power Electronics and relay protection
Form of examination: Written
Date: 14.12.2018
Lecturer(s): Lucian Mihet, Kamil Dursun
Comments:
Please find enclosed the following documents:
Course description: https://www.hiof.no/english/studies/courses/ir/2018/autumn/ire35017.html Exam
Formula list: https://hiof.instructure.com/courses/1416/files/388199/download?wrap=1 Solution to exam questions
Note also the following:
It is important that the student has understood the philosophy of solving the question. If the thinking and the formulae are correct, the student should not lose more than 5-10% of the points for the relevant question if only the numerical values are wrong.
Do not consider propagating errors - i.e. if the student could not find the right numerical solution at one partial question and needs the value at the next partial question, he should not lose any point at the next question due to the numerical error.
The student should give the answers in English. If the student writes some terms in Norwegian due to language problems this will be accepted. The quality of the language, grammar etc. will not affect the final grade.
EXAM
Course code: IRE35017 Course: Power electronics and relay protection
Date: 14.12.2018 Duration:
5 hours Permitted aids:
Writing utensils, Calculator,
Enclosed formula list
Lecturers:
Lucian Mihet, Kamil Dursun
The exam:
The exam papers consist of 35 pages including this page.
Please check that the examination papers are complete before you start answering the questions.
If you have not managed to solve the numerical values for one question and need the results for the next question, assume a reasonable value and continue. Mark on the answering sheet that you have assumed the values.
Good luck.
Date of announcement of the examination results: 04.01.2019
The exam results will be available on the Studentweb www.hiof.no/studentweb
Question 1 (60% of relay protection part of exam):
Consider the network as shown in Fig. 1
Fig. 1
Q UN = 115 kV; SN = 4000 MVA; cosΦ = 0.008 L1 (ref. 13.8 kV) 0.04 + j0.08 ohm/km ; 10km Z1=Z2=Z0 L2 (ref. 2.4 kV) (1.51+j3.33) milliohm/km; 20km Z1=Z2=Z0
T1 Dyn; UN= 115/13.8kV; SN= 15MVA; Zk = 7%; Rk = 0.5%; Z1=Z2=Z0 T2 Dyn; UN= 13.8/2.4kV; SN= 5MVA; Zk = 5.5%; Rk = 0.46%; Z1=Z2=Z0 M Synchronous motor UGN = 2.4 kV; PN = 1.6 MW; cosΦ = 0.8; xd’’= 14%,
rd=0 Z1=Z2=Z0.
Assume cosΦ = 0.9 for the 6MVA, 3MVA and 2.5 MVA feeders. They all have insulated neutral. Assume Z0=Ꚙ
Assume pick-up/drop-off ratio=0.95 and definite time characteristics for the relays with grading margin Δt = 0.3s
a) Draw the positive, negative and zero sequence circuits for a fault on BB2. Calculate the three pole symmetrical fault current (I’’k3) and single pole earth fault current (I’’k1) at the same busbar. Assume I’’k3 is the maximum and I’’k1 is the minimum short circuit current. What would you use as the constant c?
b) How would you set I> I>> and time selectivity t for R1 and R2? Explain.
Question 2 (40% of relay protection part of exam):
Consider the network in Fig. 2. We have power flowing between A and B. The power may flow in both directions.
Fig. 2
Line1 150 km
Line2 150 km
Line3 300 km
All relays (R1-R8) are distance relays.
All lines have same impedance so you only need to consider the lengths.
a) Which direction is each relay “looking” at? Left or right?
b) Draw zone information for R2. Lengths of Z1, Z2 and Z3 (forwards and backwards).
c) A short circuit occurs at Line1, 10 km to the right of R2. How will all relays react?
Make a table showing pick-up zones, trip and/or reset times for each relay.
d) If you need instantaneous trip for both R2 and R4, how would you achieve this?
e) In the case that R2 does not work, do the same as b) on how each relay will react.
Power Electronics Question 3
For an ideal single-phase single-pulse controlled rectifier with resistive load:
a) Draw the converter topology and the output voltage and current, indicating also in the sketches the firing current pulse, which is applied to the gate terminal;
b) Assuming that we need to provide more power to the load and implicitly to use a single-phase full bridge controlled rectifier, draw the converter topology together with the IN & OUT voltage and current waveforms, and the currents flowing through the switches to highlight how the rectifier works;
c) Assuming that the resistive load is replaced by a large inductive one and considering the voltage source/grid inductance (Ls=5 mH) and knowing that Vs=100 V, f=50 Hz and Id=20 A, calculate the commutation and firing angles and also the average DC Voltage (Vd) and AC and DC power for this case;
d) Highlight the current commutation between switches and the differences which occur in the same waveforms when compare with the previous case from b);
Question 4
For a switch-mode DC/DC converter (Fig. 3) working at a switching frequency fs=50 kHz, the following parameters are given: L=0.05 mH, Vin=15V, Vo=10V, Pload=20W.
a) Define what type of converter is explaining how it works.
b) Calculate the duty cycle (duty ratio) and the output current;
c) Prove in which current conduction operation mode the converter works;
d) Assuming that the load in replaced by a DC machine working in both operation modes (as motor and generator), draw the power electronics equipment for this case.
Fig. 3. A switch mode DC-DC converter.
Question 5
For a three-phase switch-mode DC/AC voltage source inverter (VSI) the following parameters are given: ma=0.95, mf=15, cos(ϕ)=0.866, Io(RMS)=10A. The inverter is driving a three-phase induction machine with the following parameters: Vn=380V, fn=50Hz, Ra=2Ω, La=10mH.
a) Calculate the line-to-line voltage and the frequency of the inverter, which corresponds to the fundamental, and the induced emf voltage of the machine expressed as a phasor;
b) Describe the sinusoidal PWM technique for a VSI.
Power Electronics
Exercise 3.For an ideal single-phase single-pulse controlled rectifier with resistive load:
a) Draw the converter topology and the output voltage and current, indicating also in the sketches the firing current pulse, which is applied to the gate terminal;
b) Assuming that we need to provide more power to the load and implicitly to use a single-phase full bridge controlled rectifier, draw the converter topology together with the IN & OUT voltage and current waveforms, and the currents flowing through the switches to highlight how the rectifier works;
c) Assuming that the resistive load is replaced by a large inductive one and considering the voltage source/grid inductance (Ls=5 mH) and knowing that Vs=100 V, f=50 Hz and Id=20 A, calculate the commutation and firing angles and also the average DC Voltage (Vd) and AC and DC power for this case;
d) Highlight the current commutation between switches and the differences which occur in the same waveforms when compare with the previous case from b);
Exercise 4. For a switch-mode DC/DC converter (Fig. 4.1) working at a switching frequency fs=50 kHz, the following parameters are given: L=0.05 mH, Vin=15V, Vo=10V, Pload=20W.
Fig. 2. A switch mode DC-DC converter.
a) Define what type of converter is explaining how it works.
b) Calculate the duty cycle (duty ratio) and the output current;
V0/Vin=D/(1-D), D=0.4 IoB=IoBmax * (1-D)2 IoBmax=4A, IoB=1.44A
c) Prove in which current conduction operation mode the converter works;
Io=Po/Vo=2A, since Io>IoB the converter works in continuous current conduction mode
d) Assuming that the load in replaced by a DC machine working in both operation modes (as motor and generator), draw the power electronics equipment for this case.
Exercise 5. For a three-phase switch-mode DC/AC voltage source inverter (VSI) the following parameters are given: ma=0.95, mf=15, cos(ϕ)=0.866, Io(RMS)=10A. The inverter is driving a three- phase induction machine with the following parameters: Vn=380V, fn=50Hz, Ra=2Ω, La=10mH.
a) Calculate the line-to-line voltage and the frequency of the inverter, which corresponds to the fundamental, and the induced emf voltage of the machine expressed as a phasor;
b) Describe the sinusoidal PWM technique for a VSI.
