Power System Analysis and Design (MindTap Course List)
6th Edition
ISBN: 9781305632134
Author: J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Publisher: Cengage Learning
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Question
Chapter 9, Problem 9.56P
(a)
To determine
The bus impedance matrix for each of the three sequence networks.
(b)
To determine
The fault current, the current out of phase C of machine 2 and the line-to-ground voltages at the terminals of machine 2during the fault.
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Consider the system shown in the single-line diagram of Figure (3). All reactances are shown in per
unit to the same base. Assume that the voltage at both sources is 1 p.u.
a Find the fault current due to a bolted- three-phase short circuit at bus 3
b- Find the fault current supplied by each generator and the voltage at each of the buses 1 and 2
under fault conditions
0.06 p.u.
0.2 p.u.
0.04 p.u.
0.25 p.u.
0.2 p.u.
0.2 p.. 0.2 p.u.
0.06 p.u.
0.25 p.u.
Figure (3) Single-line diagram
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0.06 p.u.
0.25 p.u.
b) A fault occurs at bus 3 of the network shown in Figure Q4. Pre-fault nodal
voltages throughout the network are of 1 p.u. and the impedance of the electric
arc is neglected. Sequence impedance parameters of the generator,
transmission lines, transformer and load are given in Figure Q4.
V₁ = 120° p.u.
V₂ = 120° p.u. V₂ = 1/0° p.u.
V₂= 120° p.u.
jXj0.1 p.u.
JX2) 0.1 p.u.
jX0j0.15 p.u.
jXn-j0.2 p.u.
1 JX(2)-j0.2 p.u. 2
jX)=j0.25 p.u.
JX20-10.15 p.u.
jXa(z)-j0.2 p.u. 4
jX2(0)=j0.2 p.u.
jXT(1) j0.1 p.u.
jXT(2)=j0.15 p.u.
jXT(0)=j0.1 p.u.
Figure Q4. Circuit for problem 4b).
=
jXj0.1 p.u.
j0.1 p.u.
-
JX(2)
JXL(0) 10.1 p.u.
=
(i) Assuming a balanced excitation, draw the positive, negative and zero
sequence Thévenin equivalent circuits as seen from bus 3.
(ii) Determine the positive sequence fault current for the case when a three-
phase-to-ground fault occurs at bus 3 of the network.
(iii) Determine the short-circuit fault current for the case when a one-phase-
to-ground fault occurs at bus…
b) A fault occurs at bus 4 of the network shown in Figure Q3. Pre-fault nodal voltages throughout the network are of 1 + j0 p.u, and the impedance of the electric arc is neglected (Zf = 0 + j0 p.u.). The positive, negative and zero
sequence impedance parameters of the generator, transmission lines and transformer are given in Figure Q3.
(i) Determine the positive sequence fault current for the case when a three-phase-to-ground fault occurs at bus 4 of the network
(ii) Determine the short-circuit fault current for the case when a one-phase- to-ground fault occurs at bus 4. Recall that phasors can be expressed in terms of their symmetrical components as shown in the picture attached. where F stands for any three-phase quantity (e.g., current, voltage)
(iii) Determine the short-circuit fault current for the case when a phase-to-phase fault occurs at bus 4
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Chapter 9 Solutions
Power System Analysis and Design (MindTap Course List)
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- Consider the oneline diagram of a simple power system shown in Figure 9.20. System data in per-unit on a 100-MVA base are given as follows: The neutral of each generator is grounded through a current-limiting reactor of 0.08333 per unit on a 100-MVA base. All transformer neutrals are solidly grounded. The generators are operating no-load at their rated voltages and rated frequency with their ENIFs in phase. Determine the fault current for a balanced three-phase fault at bus 3 through a fault impedance ZF=0.1 per unit on a 100-MVA base. Neglect -Y phase shifts.arrow_forwardI need the answer as soon as possiblearrow_forwardb) A fault occurs at bus 4 of the network shown in Figure Q3. Pre-fault nodal voltages throughout the network are of 1 p.u. and the impedance of the electric arc is neglected. Sequence impedance parameters of the generator, transmission lines, and transformer are given in Figure Q3, where X and Y are the last two digits of your student number. jX(1) j0.1Y p.u. jX2)= j0.1Y p.u. jXko) = j0.1X p.u. V₁ = 120° p.u. V₂ = 120° p.u. (i) (ii) 0 jX(1) = j0.2 p.u. 1 jx(2) j0.2 p.u. 2 jX1(0) = j0.25 p.u. jXT(1) jXT(2) 종 3 j0.1X p.u. JX3(1) j0.1Y p.u. j0.1X p.u. JX3(2) j0.1Y p.u. jXT(0) j0.1X p.u. JX3(0)=j0.15 p.u. 0 = x = 1, jX2(1) j0.2Y p.u. V₁=1/0° p.u. jX(2(2) = j0.2Y p.u. jX2(0) = j0.3X p.u. = V3 = 120° p.u. Figure Q3. Circuit for problem 3b). For example, if your student number is c1700123, then: y = 7 = = jXa(r) = j0.13 p.u., jXa(z) = j0.13 p. u., and jXa(o) = j0.12 p. u. Assuming a balanced excitation, draw the positive, negative and zero sequence Thévenin equivalent circuits as seen from…arrow_forward
- Please helparrow_forwardb) A fault occurs at bus 4 of the network shown in Figure Q3. Pre-fault nodal voltages throughout the network are of 1 p.u. and the impedance of the electric arc is neglected. Sequence impedance parameters of the generator, transmission lines, and transformer are given in Figure Q3, where X and Y are the last two digits of your student number. V₁ = 120° p.u. V₂ = 120° p.u. jX(1) j0.1Y p.u. jX2)= j0.1Y p.u. jXko) j0.1X p.u. - 0 jX(1) = j0.2 p.u. 1JX(2) = 0.2 p.u. 2 jX1(0) = j0.25 p.u. jX2(1) j0.2 p.u. V₁=1/0° p.u. jX(2(2) = j0.2Y p.u. jX2(0) = j0.3X p.u. = V₂ = 120° p.u. jXT(1) j0.1X p.u. jXT(2) j0.1X p.u. JX3(1) j0.1Y p.u. JX3(2)=j0.1Y p.u. jXT(0) j0.1X p.u. JX3(0)=j0.15 p.u. 0- = 3 = Figure Q3. Circuit for problem 3b). For example, if your student number is c1700123, then: jXa(n) = j0.13 p. u., jXa(z) = j0.13 p. u., and jXa(o) = j0.12 p. u. 4 (i) Assuming a balanced excitation, draw the positive, negative and zero sequence Thévenin equivalent circuits as seen from bus 4. (ii)…arrow_forwardSubtransient fault current in per-unit and in kA, per-unit L-G Voltage at bus 1?arrow_forward
- Quiq plzarrow_forwardThe one-line diagram of a simple power system is shown in Figure 9.20. Each generator is represented by an an emf behind the transient reactance. All impedances are expressed in per unit on a common MVA base. All resistance and shunt capacitances are neglected. The generation are operating on no load at their rated voltage with their emfs in phase. A three-phase fault occurs at bus 1 through a fault impedance of Z_f = j0.08 per unit. Using Thevenin's theorem obtain the impedance to the point of fault and the fault current in per unit. Determine the bus voltages and line currents during fault.arrow_forwardThe one line diagram of a simple three bus power system is shown in figure Each generator is represented by an emf behind the subtraction reactance. All impedances are expressed in per unit on a common MVA base. All resistances and shunt capacitances are neglected. The generators are operating on no load at their rated voltage with their emfs in phase. Athree phase fault occurs at bus 3 through a fault impedance of Zf=j0.19 per unit. a-using thevenin’s theorem obtain the impedance to the point of fault and the fault current in per unit. b-determine the bus voltage and line currents during faultarrow_forward
- Problem 5 Consider the system shown in the single-line diagram of Figure (3). All reactances are shown in per unit to the same base. Assume that the voltage at both sources is 1 p.u. a- Find the fault current due to a bolted- three-phase short circuit at bus 3. b- Find the fault current supplied by each generator and the voltage at each of the buses I and 2 under fault conditions. 0.04 p.u. 0.2 p.u. 0.06 p.u. 0.2 p.u. 0.25 p.u. G, 0.2 p.u. 0.2 p.u. 0.06 p.u. 0.06 р.и. 3 0.25 p.u. 0.25 p.u. G, Figure (3) Single-line diagram for Problem 5 elearrow_forwardQ2. The single-line diagram of a simple three-bus power system is shown in Figure-2. Each generator is represented by an emf behind the sub-transient reactance. All impedances are expressed in per unit on a common MVA base. All resistances and shunt capacitances are neglected. The generators are operating on no load at their rated voltage with their emfs in phase. A three-phase fault occurs at bus 3 through a fault impedance of Zf = j0.19 per unit. (i) Using Th'evenin's theorem, obtain the impedance to the point of fault and the fault current in (ii) Determine the bus voltages per unit. ) j0.05 j0.075 j0.75 2 j0.30 j0.45 Figure-2: Single line diagram of the power system network for Q2 3arrow_forwardFigure shows a sample power system network and Zpus Matrix elements. For a solid three phase fault take place at bus 3. Determine a) Fault current (b) V1 , V21 and Var (c) Post fault current in lines 1-2 and 1-3. The line from bus 1-2 impedance =j1.2p.u The line from bus 2-3 impedance =j0.16p.u The line from bus 3-1 impedance =j1.37p.u The Zbus matrix element values are Zbus Matrix Z13 = 0.4; Zbus Matrix Z23 =1.01; Zbus Matrix Z33 =1.55; Fault Post fault voltage at bus 1 (V1) in p.u Post fault voltage at bus 2 (V21 ) in p.u Post fault voltage at bus 3 (V31 ) in p.u Post fault current( I12) in line between 1-2 in p.u Post fault current (I13) in line between 1-3 in p.uarrow_forward
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