� � * �·. THE UNIVERSITY OF HONG KONG Bachelor of Engineering Department of Electrical & Electronic Engineering ELEC4147 Power System Analysis and Control 2019-2020 Semester 2 Online Examination Date: May 27, 2020 Answer ALL questions. Time: 9:30 AM - 12:30 PM This is an open book examination. Candidates may bring to their examination any printed/written materials. Internet access is allowed. If you need to use calculator, please write the calculator model onto the first page of your answer sheet. Use of Electronic Calculators: "Only approved calculators as announced by the Examinations Secretary can be used in this examination. It is candidates' responsibility to ensure that their calculator operates satisfactorily, and candidates must record the name and type of the calculator used on the front page of the examination script." (Use a fresh page for each question) EEE/ ELEC4 l 4 7 /2020 May page 1 of 8 Ql. For a 4-bus system, the admittance matrix is given as follows. 0.245- J0.085 -0.12+0.16} -0.125+0.125} 0 -0.12+0.16} 0.24- 0.2} -0.04+0.08} -0.08+0.06} -0.125+0.125} -0.04+0.08} 0 0 -0.08 + 0.06 j 0.165+0.095} 0 0.08- 0.06} (a) Please determine the connection of the following 4-bus system. 1 2 __ _ 3 __ _ 4 __ _ Figure l(a) (2 marks) (b) Please find the parameters of the pi-equivalent model, i.e., R, X and B, for each line. (8 marks) ( c) Suppose the branch between bus i and bus j is an off-nominal tap transformer, as shown in Figure 1 (b ). Please find the admittances yij, y;o and yjo of the pi-equivalent model, as shown in Figure 1 ( c ). � Figure l(b) Figure l(c) EEE/ ELEC4147 /2020 May page 2 of 8 (5 marks) EEE/ ELEC4147 /2020 May page 3 of 8 Q2. A 4-bus power system is shown in Figure Q2. Bus 1 is the swing bus with I� I= 1.05, B., = 0° . The system bus admittance matrix Y bus is known with its element at ith row and jth column denoted as � = JB iJ , (i = 1- 4, j = 1- 4) . (a) Please determine the dimension of the Jacobian matrix and the variables of power flow equations. (1 marks) (b) Please determine the following elements of Jacobian matrix: 0 � and olQ2 I ae4 a rs (4 marks) ( c) If reactive power load on bus 3 is a function of the voltage. Q L = a IV3' 2 + .BIV3 j + r , where a, /3 and r are known. Please determine the following element of Jacobian matrix: o.6.I Q 3 I a� (3 marks) (d) For a n-bus system, the reactive power flow equation is Q; = Ilv;llv;,i[G;k sin(B; -Bk )-B;k cos(B; -Bk )] k=1 Please show that elements of Jacobian matrix satisfy (7 marks) 1 2 4 3---�- Figure Q2 EEE/ ELEC4147 /2020 May page 4 of 8 Q3. (a) Please write the assumptions to establish the DC power flow equations. (3 marks) (b) For the 4-bus system, as shown in Figure Q2. Under assumptions of the question Q3(a), please show e1 - e2 + B4 - e2 + e3 - e2 = 0 X12 X24 X23 where 61 , 62, 63 and B4 are phase angles of Bus 1 , Bus 2, Bus 3 and Bus 4, respectively. X12 is the reactance of line 1-2, X24 is the reactance of line 2-4, and X23 is the reactance of line 2-3 . ( 12 marks) EEE/ ELEC414 7 /2020 May page 5 of 8 Q4. (a) Assume that we have the following fuel-cost curves for three generators: c1 (PG1 ) = 5 + OAPG1 + o.0025P;1 c2 (PG2 ) = 4 + o.5PG2 + o.ooo5P;2 CiPG3)= 2 + 0. 1PG3 + o.002p;3 If the limits of these three generators are 50MW s PGI s 500MW 50MW s PG2 s 300MW 50MW s PG3 s 400MW Neglecting line losses, please determine the optimal dispatch with the total load PD =700MW. (6 marks) (b) Suppose a power system consisted of two isolated regions: a western region and an eastern region. Five units, as shown in Figure Q4, have been committed to supply 3090 MW. The two regions are separated by transmission tie lines that can together transfer a maximum of 550 MW in either direction. Please fill in the blanks in the Table Q4. I Units l, 2, and 3 l Western region Unit Unit Region Unit Capacity Output (MW) (MW) 1 800 550. Western 2 600 300 3 600 400 Eastern 4 1200 1040 5 600 510 Total 1-5 3800 2800 EEE/ ELEC4147 /2020 May 5SOMW mt>
Figure Q4 Table Q4 Regional Generation (MW) . Units 4.and 5 l Eastern n,gion Spinning Regional Interchange Reserve Load (MW) (MW) (MW) 1800 990 2790 ---- (4 marks) page 6 of 8 Q5. (a) For the following system, please draw the complete positive-sequence, negative sequence and zero-sequence network connection (phase A) for the double line to-ground fault (phases B and C to ground fault) at bus N. M XGJ XTI EGJ Q--+-----{ r XL XL XTJ Figure Q5 (b) Prefault voltage: EGJ = IL0 ° , EG2 = IL0 ° (Per Unit) Parameters (Per Unit): Generators: XG/ = XG1- = XG/ = 0.1, XG/ = XG2- = XGz° = 0.2 Line: X/ =XL- =X/ =0.2 Transformers: Xr/ =Xn- =Xri° =Xr/ =Xr2- =Xrz° =0.4 Xn+ =Xn- =Xn° =0.4 XP2 =Xp3 =0.2 (6 marks) For a single line-ground fault (phase A) at bus N, please find the fault current at phase A. (9 marks) EEE/ ELEC4 l 4 7 /2020 May page 7 of 8 Q6. Assume a round-rotor generator delivering power through two parallel transmission lines and two transformers. The connection of the system is shown as below. M XTI Parameters are as follows: G: XGI = 0.10 Tl: XTI =0.20 T2: Xn = 0.20 Transmission Line: XL = 0.40 Initial state: JE'J = 1.4 ,PM= 1 .5 XL N Xr2 t---+-- V = lL0° ( OCJ -bus) Figure Q6 (a) Assume a three-phase-ground fault via an impedance Xp = 0.4 happens at the beginning (F) of one transmission line, please find the instantaneous generator power PF.ult-on (o) of the fault-on systems. (8 marks) (b) Assume the fault line is tripped at oc = 1 .3 lrad (75 °) , please determine the stability of the system. (7 marks) Q7. For a 2-bus system shown as below, the sending bus voltage Eis given. Suppose for a given load Q = J,,p , where J,, is a given parameter. Please derive the critical X that leads to the voltage stability critical point. EEE/ ELEC414 7 /2020 May ELO VLB 1-1---t•X-l----tl-• P+ JQ Figure Q7 *** END OF PAPER*** ( 15 marks) page 8 of 8 欢迎咨询51作业君
