Explanation Concept used: The 2 × 2 bus admittance matric can be written as Y bus = [ Y 11 − Y 12 − Y 21 Y 22 ] Here, the admittance Y 11 and Y 22 are the self-admittance and, Y 12 and Y 21 are the mutual admittance. Write the expression for the self-admittance. Y = 1 Z ......... (1) Here, Y is the admittance and Z is the impedance. Calculation: The circuit diagram is redrawn as shown in Figure 1 Substitute Y 1 for Y and 0.1 + j 0.5 Ω for Z in equation (1). Y 1 = 1 0.1 + j 0.5 Ω = 0.3845 − j 1.923 ℧ Substitute Y 2 for Y and 0 − j 0.1 Ω for Z in equation (1). Y 2 = 1 0 − j 0.1 Ω = 0 + j 10 ℧ Substitute Y 3 for Y and 0.02 + j 0.2 Ω for Z in equation (1). Y 3 = 1 0.02 + j 0.2 Ω = 0.495 − j 4.95 ℧ Substitute Y 4 for Y and 0 − j 0.1 Ω for Z in equation (1). Y 4 = 1 0 − j 0.1 Ω = 0 + j 10 ℧ Substitute Y 5 for Y and 0.1 + j 0.5 Ω for Z in equation (1). Y 5 = 1 0.1 + j 0.5 Ω = 0.3845 − j 1.923 ℧ The admittance matrix is drawn as shown in the Figure 2. The expression for admittance Y 11 is written as Y 11 = Y 1 + Y 2 + Y 3 Substitute 0.3845 − j 1.923 ℧ for Y 1 , 0 + j 10 for Y 2 and 0.495 − j 4.95 ℧ for Y 3 in the above equation. Y 11 = ( 0.3845 − j 1.923 ℧ ) + ( 0 + j 10 ℧ ) + ( 0.495 − j 4.95 ℧ ) = ( 0.3845 + 0 + 0.495 ) + ( − j 1.923 ℧ + j 10 − j 4.95 ℧ ) = 0.8795 + j 3.127 ℧ The expression for admittance Y 12 is written as Y 12 = Y 3 Substitute 0 To determine (b) Convert the voltage source to current sources and determine the vector of the source currents into buses1 and 2.

MindTap Engineering for Glover/Overbye/Sarma's Power System Analysis and Design, 6th Edition, [Instant Access], 1 term (6 months)

6th Edition

ISBN: 9781305636309

Author: J. Duncan Glover; Thomas Overbye; Mulukutla S. Sarma

Publisher: Cengage Learning US

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Question

Chapter 2, Problem 2.36P

To determine

(a)

The 2×2 bus admittance matric Ybus.

To determine

(b)

Convert the voltage source to current sources and determine the vector of the source currents into buses1 and 2.

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Chapter 2, Problem 2.35P

Chapter 2, Problem 2.37P

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Chapter 2 Solutions

MindTap Engineering for Glover/Overbye/Sarma's Power System Analysis and Design, 6th Edition, [Instant Access], 1 term (6 months)

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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. 2.13MCQ Ch. 2 - The instantaneous power absorbed by the load in a...Ch. 2 - Prob. 2.15MCQ Ch. 2 - With generator conyention, where the current...Ch. 2 - Consider the load convention that is used for the...Ch. 2 - Prob. 2.18MCQ Ch. 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. 2.11P Ch. 2 - The voltage v(t)=359.3cos(t)volts is applied to a...Ch. 2 - Prob. 2.13P Ch. 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. 2.29P Ch. 2 - Figure 2.26 shows three loads connected in...Ch. 2 - Consider two interconnected voltage sources...Ch. 2 - Prob. 2.35P Ch. 2 - Prob. 2.36P Ch. 2 - Prob. 2.37P Ch. 2 - Prob. 2.38P Ch. 2 - Prob. 2.39P Ch. 2 - A balanced three-phase 240-V source supplies a...Ch. 2 - Prob. 2.41P Ch. 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. 2.48P Ch. 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. CCSQ Ch. 2 - Prob. DCSQ

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(a) The 2 × 2 bus admittance matric Y bus .

Solution Summary: The 2times 2 bus admittance matric can be written as Y_bus=left.

Concept explainers

(a)

The 2×2 bus admittance matric Ybus.

(b)

Convert the voltage source to current sources and determine the vector of the source currents into buses1 and 2.

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Chapter 2 Solutions

(a) The 2 × 2 bus admittance matric Y bus .

Solution Summary: The 2times 2 bus admittance matric can be written as Y_bus=left.

Concept explainers

(a) The 2×2 bus admittance matric Ybus.

(b) Convert the voltage source to current sources and determine the vector of the source currents into buses1 and 2.

Want to see the full answer?

Chapter 2 Solutions

(a)

The 2×2 bus admittance matric Ybus.

(b)

Convert the voltage source to current sources and determine the vector of the source currents into buses1 and 2.