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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Chapter 2, Problem 2.36P
To determine
(a)
The
To determine
(b)
Convert the voltage source to current sources and determine the
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Q2. Figure Q2 shows the single-line diagram. The scheduled loads at buses 2 and 3 are as
marked on the diagram. Line impedances are marked in per unit on 100 MVA base and the line
charging susceptances are neglected.
a) Using Gauss-Seidel Method, determine the phasor values of the voltage at load bus 2
and 3 according to second iteration results.
b) Find slack bus real and reactive power according to second iteration results.
c) Determine line flows and line losses according to second iteration results.
d) Construct a power flow according to second iteration results.
Slack Bus
= 1.04.20°
0.025+j0.045
0.015+j0.035
0.012+j0,03
3
|2
134.8 MW
251.9 MW
42.5 MVAR
108.6 MVAR
Q2) In the network in the figure below Y-Y connected transformers, each with
grounded neutrals, are at the ends of each transmission line that is not
terminating at bus 3. The transformers connecting the lines to bus 3 are Y-A, with
the neutral of the Y solidly grounded and the A sides connected to bus 3. All the
line reactances shown in the figure between busses include the reactances of the
transformers. Zero sequence values for these lines including transformers are 2.0
times those shown in the figure.
Both generators are Y-Connected. Zero-sequence reactances of the
generators connected to bus 1 and bus 3 are 0.04 and 0.08 per unit, respectively.
The neutral of the generator at bus 1 is connected to ground through a reactor
of 0.02 per unit; the generator at bus 3 has a solidly ground neutral.
Find the bus impedance matrices (¹), (²), z for the given network and
'bus' 'bus' bus
then compute the Subtransient current in per unit for a single line-to-ground fault
on bus 2 and the fault…
In a string of suspension insulator with three units, the line unit has 20kV and k=0.35. The voltage across tower unit is........ and across middle unit is.......
Chapter 2 Solutions
Power System Analysis and Design (MindTap Course List)
Ch. 2 - The rms value of v(t)=Vmaxcos(t+) is given by a....Ch. 2 - If the rms phasor of a voltage is given by V=12060...Ch. 2 - If a phasor representation of a current is given...Ch. 2 - Prob. 2.4MCQCh. 2 - Prob. 2.5MCQCh. 2 - Prob. 2.6MCQCh. 2 - Prob. 2.7MCQCh. 2 - Prob. 2.8MCQCh. 2 - Prob. 2.9MCQCh. 2 - The average value of a double-frequency sinusoid,...
Ch. 2 - The power factor for an inductive circuit (R-L...Ch. 2 - The power factor for a capacitive circuit (R-C...Ch. 2 - Prob. 2.13MCQCh. 2 - The instantaneous power absorbed by the load in a...Ch. 2 - Prob. 2.15MCQCh. 2 - With generator conyention, where the current...Ch. 2 - Consider the load convention that is used for the...Ch. 2 - Prob. 2.18MCQCh. 2 - The admittance of the impedance j12 is given by...Ch. 2 - Consider Figure 2.9 of the text, Let the nodal...Ch. 2 - The three-phase source line-to-neutral voltages...Ch. 2 - In a balanced three-phase Y-connected system with...Ch. 2 - In a balanced system, the phasor sum of the...Ch. 2 - Consider a three-phase Y-connected source feeding...Ch. 2 - For a balanced- load supplied by a balanced...Ch. 2 - A balanced -load can be converted to an...Ch. 2 - When working with balanced three-phase circuits,...Ch. 2 - The total instantaneous power delivered by a...Ch. 2 - The total instantaneous power absorbed by a...Ch. 2 - Under balanced operating conditions, consider the...Ch. 2 - One advantage of balanced three-phase systems over...Ch. 2 - While the instantaneous electric power delivered...Ch. 2 - Given the complex numbers A1=630 and A2=4+j5, (a)...Ch. 2 - Convert the following instantaneous currents to...Ch. 2 - The instantaneous voltage across a circuit element...Ch. 2 - For the single-phase circuit shown in Figure...Ch. 2 - A 60Hz, single-phase source with V=27730 volts is...Ch. 2 - (a) Transform v(t)=75cos(377t15) to phasor form....Ch. 2 - Let a 100V sinusoidal source be connected to a...Ch. 2 - Consider the circuit shown in Figure 2.23 in time...Ch. 2 - For the circuit shown in Figure 2.24, compute the...Ch. 2 - For the circuit element of Problem 2.3, calculate...Ch. 2 - Prob. 2.11PCh. 2 - The voltage v(t)=359.3cos(t)volts is applied to a...Ch. 2 - Prob. 2.13PCh. 2 - A single-phase source is applied to a...Ch. 2 - Let a voltage source v(t)=4cos(t+60) be connected...Ch. 2 - A single-phase, 120V(rms),60Hz source supplies...Ch. 2 - Consider a load impedance of Z=jwL connected to a...Ch. 2 - Let a series RLC network be connected to a source...Ch. 2 - Consider a single-phase load with an applied...Ch. 2 - A circuit consists of two impedances, Z1=2030 and...Ch. 2 - An industrial plant consisting primarily of...Ch. 2 - The real power delivered by a source to two...Ch. 2 - A single-phase source has a terminal voltage...Ch. 2 - A source supplies power to the following three...Ch. 2 - Consider the series RLC circuit of Problem 2.7 and...Ch. 2 - A small manufacturing plant is located 2 km down a...Ch. 2 - An industrial load consisting of a bank of...Ch. 2 - Three loads are connected in parallel across a...Ch. 2 - Prob. 2.29PCh. 2 - Figure 2.26 shows three loads connected in...Ch. 2 - Consider two interconnected voltage sources...Ch. 2 - Prob. 2.35PCh. 2 - Prob. 2.36PCh. 2 - Prob. 2.37PCh. 2 - Prob. 2.38PCh. 2 - Prob. 2.39PCh. 2 - A balanced three-phase 240-V source supplies a...Ch. 2 - Prob. 2.41PCh. 2 - A balanced -connected impedance load with (12+j9)...Ch. 2 - A three-phase line, which has an impedance of...Ch. 2 - Two balanced three-phase loads that are connected...Ch. 2 - Two balanced Y-connected loads, one drawing 10 kW...Ch. 2 - Three identical impedances Z=3030 are connected in...Ch. 2 - Two three-phase generators supply a three-phase...Ch. 2 - Prob. 2.48PCh. 2 - Figure 2.33 gives the general -Y transformation....Ch. 2 - Consider the balanced three-phase system shown in...Ch. 2 - A three-phase line with an impedance of...Ch. 2 - A balanced three-phase load is connected to a...Ch. 2 - What is a microgrid?Ch. 2 - What are the benefits of microgrids?Ch. 2 - Prob. CCSQCh. 2 - Prob. DCSQ
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- Consider three ideal single-phase transformers (with a voltage gain of ) put together as three-phase bank as shown in Figure 3.35. Assuming positive-sequence voltages for Va,Vb, and Vc find Va,Vb, and VC. in terms of Va,Vb, and Vc, respectively. (a) Would such relationships hold for the line voltages as well? (b) Looking into the current relationships, express IaIb and Ic in terms of IaIb and Ic respectively. (C) Let S and S be the per-phase complex power output and input. respectively. Find S in terms of S.arrow_forwardConsider the oneline diagram shown in Figure 3.40. The three-phase transformer bank is made up of three identical single-phase transformers, each specified by X1=0.24 (on the low-voltage side), negligible resistance and magnetizing current, and turns ratio =N2/N1=10. The transformer bank is delivering 100 MW at 0.8 p.f. lagging to a substation bus whose voltage is 230 kV. (a) Determine the primary current magnitude, primary voltage (line-to-line) magnitude, and the three-phase complex power supplied by the generator. Choose the line-to-neutral voltage at the bus, Va as the reference Account for the phase shift, and assume positive-sequence operation. (b) Find the phase shift between the primary and secondary voltages.arrow_forwardThe per-unit equivalent circuit of two transformers Ta and Tb connected in parallel, with the same nominal voltage ratio and the same reactan of 0.1 per unit on the same base, is shown in Figure 3.43. Transformer Tb has a voltage-magnitude step-up toward the load of 1.05 times that of Ta (that is, the tap on the secondary winding of Tb is set to 1.05). The load is represented by 0.8+j0.6 per unit at a voltage V2=1.0/0 per unit. Determine the complex power in per unit transmitted to the load through each transformer, comment on how the transformers share the real and reactive powers.arrow_forward
- please solve for nodal stress method. (if it is possible to apply supernodes)arrow_forwardThree zones of a single-phase circuit are identified in the figure. The zones are connected by transformers T₁ and T2, whose ratings are also shown. Using base values of 100 kVA and 240 volts in zone 1, draw the per-unit circuit and determine the per-unit impedances and the per-unit source voltage. Then calculate the load current both in per-unit and in amperes. Transformer winding resistances and shunt admittance branches are neglected. Zone 1 Zone 2 Vs = 220/0° volts 3---38 T, 30 KVA 240/480 volts M 0.10 p.u. Xoa Xune = 2 fl T T₂ 20 kVA 460/115 volts Xeg = 0.10 p.u. Zone 3 ww Zload = 0.9 - 10.20arrow_forwardThe single line diagram of a power system is shown in Figure Q2.1 includinggenerator and transformer winding connection and earthing details. The parametersfor this system have been calculated on a common 100 MVA base and are given inTable Q2.1. All resistances and shunt susceptances are neglected. This systemexperiences a single line to ground fault at a point F on line L1. The point F is at adistance d from Bus 4 along the line L1. The total length l of the line L1 is 50 km.Note that the location of d is not drawn to scale in Figure Q2.1. The fault current atthe fault point F is measured to be 6.106 kA. i) Determine the zero, positive, and negative sequence Thevenin equivalentimpedances as seen at the fault point F. These should be evaluated in per unitand shown as a function of d.ii) Use the sequence impedances calculated in part (i) to determine the distance dof the fault (in km) from Bus 4. It's different from the answer, please don't send itarrow_forward
- The single line diagram of a power system is shown in Figure Q2.1 including generator and transformer winding connection and earthing details. The parameters for this system have been calculated on a common 100 MVA base and are given in Table Q2.1. All resistances and shunt susceptances are neglected. This system experiences a single line to ground fault at a point F on line L1. The point F is at a distance d from Bus 4 along the line L1. The total length ?? of the line L1 is 50 km. Note that the location of ?? is not drawn to scale in Figure Q2.1. The fault current at the fault point F is measured to be 6.106 kA. i) Determine the zero, positive, and negative sequence Thevenin equivalent impedances as seen at the fault point F. These should be evaluated in per unit and shown as a function of d.ii) Use the sequence impedances calculated in part (i) to determine the distance d of the fault (in km) from Bus 4.arrow_forwardb) The single line diagram of a power system is shown in Figure Q2.1 including generator and transformer winding connection and earthing details. The parameters for this system have been calculated on a common 100 MVA base and are given in Table Q2.1. All resistances and shunt susceptances are neglected. This system experiences a single line to ground fault at a point F on line L1. The point F is at a distance d from Bus 4 along the line LI. The total length of the line L1 is 50 km. Note that the location of d is not drawn to scale in Figure Q2.1. The fault current at the fault point F is measured to be 6.106 kA. G1 G1 G2 i) G2 T1 T2 T3 L1 11) 2 Rated voltage (kV) 20 20 20/33 20/33 33/11 11 T1 ΔΕ T2 T3 Figure Q2.1 Table Q2.1 Zero sequence reactance Xo (p.u.) 0.20 0.15 0.12 0.20 0.20 1.20 Positive sequence reactance X₁ (p.u.) 0.30 0.25 0.12 0.20 0.20 0.50 UNIVERSITY OF LIVERPOOL L1 (l-d) 5 Negative sequence reactance X₂ (p.u.) 0.35 0.30 0.12 0.20 0.20 0.50 Determine the zero, positive,…arrow_forward400Ω A k=0.9 600Ω B k=0.8 66Ω 600Ωarrow_forward
- Three zones of a single-phase circuit are identified shown in Figure below. The zones are connected by transformers T1 and T2, whose ratings are also shown. Using base values of 33 kVA and 232 volts in zone 1, Find: 1- Draw the per-unit circuit including the per-unit impedances and the per-unit source voltage. 2- Calculate the load current both in per-unit and in amperes (actual or original value). Vs Zone 1 232.940° Vs G. 38 T₁ 30 KVA 240/480 volts Xeq = 0.10 p.u. Zone 2 Xiine = 4 Ω T₂ 20 KVA 460/115 volts Zload = Xea = 0.10 p.u. Zone 3 u 1+j2.2 Ω 2arrow_forward1. FIGURE 52 shows the one-line diagram of a simple three-bus power system with generation at bus I. The voltage at bus l is V1 = 1.0L0° per unit. The scheduled loads on buses 2 and 3 are marked on the diagram. Line impedances are marked in per unit on a 100 MVA base. For the purpose of hand calculations, line resistances and line charging susceptances are neglected a) Using Gauss-Seidel method and initial estimates of Va 0)-1.0+)0 and V o)- ( 1.0 +j0, determine V2 and V3. Perform two iterations (b) If after several iterations the bus voltages converge to V20.90-j0.10 pu 0.95-70.05 pu determine the line flows and line losses and the slack bus real and reactive power. 2 400 MW 320 Mvar Slack 0.0125 0.05 300 MW 270 Mvar FIGURE 52arrow_forwardFollowing figure shows the one-line diagram of a two bus system. Take bus 1 as slack bus, bus 2 as load (PQ) bus. Neglect the shunt charging admittance. Obtain the bus admittance matrixYBUs and find V₂ and 62, power flows and line losses using FDLF method. All the values are given in per unit on 100MVA base. Use a tolerance of 0.001 for power mismatch. 1 Z12= 0.12+10.16 Slack bus V₁ 1.0/0⁰ pu 2 PL2=1.0pu Q12=0.5puarrow_forward
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