THE UNIVERSITY OF NEW SOUTH WALES. School of Electrical Engineering & Telecommunications FINALEXAMINATION. Session

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1 Name: Student ID: Signature: THE UNIVERSITY OF NEW SOUTH WALES School of Electrical Engineering & Telecommunications FINALEXAMINATION Session 00 ELEC46 Power System Analysis TIME ALLOWED: 3 hours TOTAL MARKS: 00 TOTAL NUMBER OF QUESTIONS: 5 THIS EXAM CONTRIBUTES 65%TO THE TOTAL COURSE ASSESSMENT. Reading Time: 0 minutes. This paper contains 7 pages. Candidates mustattempt ONLY 4questions. Answer each question in a separate answer book. Marks for each question are indicated beside the question. This papermaybe retained by the candidate. Print your name, student ID and question number on the front page of each answer book. Authorised examination materials: Drawing instruments may be brought into the examination room. Candidates should use their own UNSW-approved electronic calculators. This is a closed book examination. Assumptions made in answering the questions should be stated explicitly. All answers must be written in ink. Except where they are expressly required, pencils may only be used for drawing, sketching or graphical work.

2 INFORMATION SHEET Three-phase -connected loads AB, BC, CA can be transformed into equivalent Y- connected loads,, and vice versa: A B C A B B C C A A B B C C A AB ; BC C A A ABCA AB BC CA Round-rotor synchronous generator: AB BC CA ; CA AB BC BC CA ; B ; C AB BC CA AB BC CA B E f + _ jx s I t + V t _ V It It E E 0 t Vt 0 (ref. phasor) f f Power output: VE t f P sin ; x s VE V Q cos x x t f t Given any unbalanced 3-phase sequence X a, Xb, X c, we can find the positive, negative and zero sequences,,,, X, X, X, and it can be shown that: Xa Xb X c, Xa Xb X c, and 0a 0b 0c X X a 0a Xb a a Xa X c a a X a and s X X 0a a Xa a a Xb 3 X a a a X c The zero sequence impedance representations for various transformer connections are shown below: s Winding connection ero sequence impedance representation per phase 0 0

3 QUESTION [5 marks ] Briefly answer the following questions: What are the main objectives of this course on power system analysis? (ii) Explain how the per-unit method is applied in analysing power circuits and the advantages of using such a method (iii) Within the context of power system operation and control, state the operational objectives, operating constraints, and power system control variables. (iv) What is meant by triplen harmonics? Is it possible to have triplen harmonics in line-to-line voltages in a three-phase system? Is it possible to have triplen harmonic current in Y-connected systems? [0 marks] (b) The schematic diagram of a three-phase transmission system is shown in Figure below. Using per-unit normalization with base values of 00 MVA and 3 kv for the transmission line, draw the equivalent circuit of the system, show per-unit values for all the components, and calculate the terminal voltage V S of the generator. Figure [7 marks] (c) A 50-km, 30-kV, three-phase transmission line has a positive-sequence series impedance z 0.06 j0.4 /km and shunt admittance y j S/km. At the load end, the line delivers 50MW at 0.9 power factor lagging and at 95% of rated voltage. (ii) Show the -model equivalent circuit for this transmission line. Derive the formulas for its -port ABCD parameters. Calculate the sending-end voltage. 3

4 QUESTION [5 marks ] Briefly answer the following questions: What is surge impedance loading? Discuss the effect of the termination load on the voltage profile across a lossless transmission line and explain the effect of reactive compensation. (ii) Discuss the power system response to short-circuit faults in relation to different time scales. (iii) Explain the reason behind the use of symmetrical components for analysing unbalanced three-phase faults. (iv) Discuss the stability of synchronous generators in relation to the operating power angle. [0 marks] (b) Consider the -Y connected transformer shown in Figure. Suppose that the transformer is ideal and that the supply phase sequence is ABC. Using sketches of the appropriate phasor diagrams, find the phase difference betweenv AB and V ab (i.e. the difference between the angles of the two phasors). Indicate which quantity leads. a A a A C b b a B C A B B C c c c b Figure [5 marks] (c) A three-phase round-rotor synchronous generator is rated at 3. kv, 00 MW at 0.8 power factor lagging. It has a synchronous reactance of per phase. The stator resistance is negligible. The excitation losses are also negligible. (ii) The generator is connected to an infinite bus and is delivering its rated power at unity power factor. Find the excitation voltage, the power angle, and the reactive power. The field excitation current is maintained as in and the prime mover power into the generator is reduced by 50%. Find the new operating conditions (real and reactive power, power angle, armature current, and power factor). [0 marks] 4

5 QUESTION 3[5 marks ] Bus k is connected to bus i via a transmission line as shown in Figure 3. Derive the expressions for the power flow (real and reactive) from bus k towards bus i in terms of the bus voltages (V k, V i ) and phase angle difference across the line. Bus k Bus i ki k i P ki jq ki jx ki I ki V k V k k V i V i i Figure 3 For the system shown in Figure 4, find Q so that V and for such a case, what is. j0.5 P Q V 0 o V Figure 4 [5 marks] (b) Figure 5 shows a single-line diagram of a four-bus power system. Branch series reactances and busbar loads are given in per-unit on a common base. Branch series resistances and shunt reactances are neglected. Bus is chosen as the slack bus for power flow analysis. V=.0 j0.pu j0.pu 4 j0.4pu P=0. V=.0 Determine the 4 4 j0.5pu j0.pu P=0.5 Q=0. 3 P=0.4 Q=0. Figure 5 Y. per-unit bus admittance matrix (ii) For each bus k,, 3, 4 state which of the variables P, Q, V, are input data and which are unknown. Write the power flow equations for bus 3. [0 marks] 5 ki k k k k

6 QUESTION 4[5 marks ] G T TL T G TL3 TL3 3 Figure 6 Consider the three-phase power system shown in Figure 6. The equipment ratings and perunit reactances are given as follows: Synchronous generator G: 0MVA, 5kV, X 0 = 0.05, X = X = 0. Synchronous generator G: 00MVA, 3.8kV, X 0 = 0.05, X = X = 0. Power transformer T: 00MVA, 5kV Y / 30kV Y, X 0 = X = X = 0.05 Power transformer T: 00MVA, 3.8kV / 30kV Y, X 0 = X = X = 0.05 Tx lines TL, TL3, TL3: 00MVA, 30kV, X = X = 0., X 0 = 0.3 All the generators are Y connected and the star points are grounded through a reactance of 0.03 p.u. All the transformer star points are solidly grounded. (b) (c) Construct the per-unit positive, negative and zero sequence reactance diagrams. Use the 00MVA, 30kV base for the transmission lines. Neglect the -Y transformer phase shifts. A fault occurred at bus 3. Determine the Thevenin equivalent of each sequence network as viewed from the fault bus. Prefault voltage is.0 per unit. Prefault load currents and -Y phase shifts can be neglected. [6 marks] Determine the sub-transient fault current in per-unit and in ka during a bolted threephase fault at bus 3. [5 marks] (d) For a bolted single line-to-ground fault at bus 3, determine the sub-transient fault current in per-unit and in ka, and the (phase) voltages at the fault. [6 marks] 6

7 QUESTION 5[5 marks ] Two generators supply a total load of 700MW. The generator fuel costs are as follows: G: C P 0.0P $/hr (where P G is in MW) G: G G C P 0.003P $/hr (where P G is in MW) G G If there are no constraints on generator outputs, find the power delivered by each generator so that the total fuel cost is minimum. What is the average cost in cents per kwh at this operating condition? (ii) Now suppose that the maximum output power of each generator is 600MW. Taking this constraint into consideration, find the optimal dispatch. (iii) Find the system incremental cost for the two cases above. Comment on the results. [9 marks] (b) Briefly answer the following questions: Provide a functional description of the different types of protection relays. (ii) With the aid of Figure 7, explain how two-zone protection system works. Figure 7 (c) A single phase, 5 MVA, 0/8.66 kv transformer is protected by a differential relay with taps. Standard CT ratios are 5:50, 5:00, 5:50, 5:00, 5:50, 5:300, 5:400, 5:450, 5:500, 5:600, 5:800, 5:900, 5:000, 5:00. Available relay tap settings are 5:5, 5:5.5, 5:6.6, 5:7.3, 5:8, 5:9 and 5:0. Select appropriate CT ratios, and relay tap settings. Also, determine the percentage mismatch for the selected tap setting. END OF EXAMINATION PAPER 7