EXAMPLE 9.1 Power-system sequence networks and their Thévenin equivalents A single-line diagram of the power system considered in Example 7.3 is shown in Figure 9.3, where negative- and zero-sequence reactances are also given. The neutrals of the generator and A-Y transformers are solidly grounded. The motor neutral is grounded through a reactance X, = 0.05 per unit on the motor base. (a) Draw the per-unit zero-, positive-, and negative- sequence networks on a 100-MVA, 13.8-kV base in the zone of the generator. (b) Reduce the sequence networks to their Thévenin equivalents, as viewed from bus 2. Prefault voltage is VF = 1.05/0° per unit. Prefault load current and A-Y transformer phase shift are neglected. FIGURE 9.3 т, 2 M Line Single-line diagram for Example 9.1 X2 - 20 0 X, = 60 N X, 100 MVA 13.8 kV 100 MVA 100 MVA X" - 0.15 13.8-kVA/138-kVY 138-kV Y/13.8-kVA 100 MVA X, = 0.17 X = 0.10 per unit X = 0.10 per unit 13.8 kV Xo = 0.05 per unit X" = 0.20 %3D X2 = 0.21 Xo = 0.10 X, = 0.05 per unit

EXAMPLE 9.1 Power-system sequence networks and their Thévenin equivalents A single-line diagram of the power system considered in Example 7.3 is shown in Figure 9.3, where negative- and zero-sequence reactances are also given. The neutrals of the generator and A-Y transformers are solidly grounded. The motor neutral is grounded through a reactance X, = 0.05 per unit on the motor base. (a) Draw the per-unit zero-, positive-, and negative- sequence networks on a 100-MVA, 13.8-kV base in the zone of the generator. (b) Reduce the sequence networks to their Thévenin equivalents, as viewed from bus 2. Prefault voltage is VF = 1.05/0° per unit. Prefault load current and A-Y transformer phase shift are neglected. FIGURE 9.3 т, 2 M Line Single-line diagram for Example 9.1 X2 - 20 0 X, = 60 N X, 100 MVA 13.8 kV 100 MVA 100 MVA X" - 0.15 13.8-kVA/138-kVY 138-kV Y/13.8-kVA 100 MVA X, = 0.17 X = 0.10 per unit X = 0.10 per unit 13.8 kV Xo = 0.05 per unit X" = 0.20 %3D X2 = 0.21 Xo = 0.10 X, = 0.05 per unit

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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Concept explainers

Fault Analysis

In an electrical engineering system, a fault is an abnormal electric current flowing through the system, and fault analysis is the study of these faults. For instance, a short-circuit is a fault where the live wire touches the ground or neutral wire. If a circuit is interrupted by a failure of a current-carrying wire then an open circuit fault occurs. The open-circuit faults are also called series faults. One or more phases or ground may be involved in a three-phase fault or may occur only between two phases. Current flows into the earth in case of a ground fault or earth fault. For most situations, the prospective short circuit current of a fault that is predictable can be calculated. To limit the loss of service because of a failure, the protective devices can detect fault conditions and operate circuit breakers and also other devices. All phases equally can be affected in a poly-phase system which is known as symmetric electrical fault. The asymmetric fault becomes more complicated to analyze if only some phases are affected. By using methods such as symmetrical components, the power system analysis of these types of faults is often simplified. The main objective of power system protection is to design, detect, and interrupt power system faults.

Question

EXAMPLE 9.1 Power-system sequence networks and their Thévenin equivalents
A single-line diagram of the power system considered in Example 7.3 is
shown in Figure 9.3, where negative- and zero-sequence reactances are also
given. The neutrals of the generator and A-Y transformers are solidly
grounded. The motor neutral is grounded through a reactance X, = 0.05 per
unit on the motor base. (a) Draw the per-unit zero-, positive-, and negative-
sequence networks on a 100-MVA, 13.8-kV base in the zone of the generator.
(b) Reduce the sequence networks to their Thévenin equivalents, as viewed
from bus 2. Prefault voltage is VF = 1.05/0° per unit. Prefault load current
and A-Y transformer phase shift are neglected.
FIGURE 9.3
T,
T2
2.
M
Line
Single-line diagram for
Example 9.1
X, = X2 - 20 n
1 X, = 60 N
%3!
100 MVA
13.8 kV
100 MVA
100 MVA
X" = 0.15
13.8-kVA/138-kVY
138-kV Y/13.8-kV A
100 MVA
X, = 0.17
X = 0.10 per unit
X = 0.10 per unit
%3D
13.8 kV
X" = 0.20
X2 = 0.21
Xo = 0.10
= 0.05 per unit
X.
0.05 per unit
%3D
%3D

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What is the definition of zero sequence impedance in transformer? What is the benefit of zero sequence impedance in transformers?
Describe the process of fault current analysis in power systems and its significance in protecting electrical equipment from damage.
Figure below shows the single-line diagram of three-bus power system with generation at bus 1 and bus 3. The voltage at bus 1 is V₁ = 1.025/0° per unit. The voltage magnitude at bus 3 is fixed at 1.05 per unit with a real power generation of 250 MW. The scheduled load on bus 2 is marked on the diagram. Line impedances are marked in per unit on a 100 MVA base. Line resistances and line charging susceptances are neglected. By using Gauss-Seidel method and initial estimates of V₂(0) = 1.020° and V3(0) = 1.0520°, determine V₂ and V3. Perform calculation for one iteration. V₁ = 1.025/0° j0.1 Slack Bus j0.2 j0.4 j0.2 3 j0.1 250 MW 150 Mvar |V3|=1.05 P3 = 250 MW
A hydro powered 50 MVA generator, with a synchronous reactance 0.33 p.u., delivers 40 MW over a transmission line of 0.15 p.u. reactance to an infinite system. A 3-phase short circuit transient fault occurs on the busbar between the generator and transmission line. Given that the generator emf is 1.4 p.u. prior to and during the fault and all reactances are to a 50 MVA base: Sketch the single line schematic diagram of the system. Determine the maximum load angle the generator can swing to without losing stability. i) ii) iii) iv) Sketch the corresponding power-angle curve for the system showing the accelerating and decelerating areas. Calculate the critical clearing angle of the system to keep its stability.
Q2\ The one-line diagram of a simple power system is shown in figure below. All impedances are expressed in per unit (pu) on a common MVA base. All resistances and shunt capacitances are neglected. The generators are operating on no load at their rated voltage. A three-phase fault occurs at bus 1 through a fault impedance of Zf = 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 of generators during fault. X₁ = = 0.1 XT-0.1 3 1 to ojo XL=0.2 2 040 X₁ = 0.1
Only need answers for the second question(9.16) at bus 1.