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.

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 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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(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.