Explanation Concept used: Write the expression for nodal equation in matrix form for 4 bus system. ( Y 11 Y 12 Y 13 Y 14 Y 21 Y 22 Y 23 Y 24 Y 31 Y 32 Y 33 Y 34 Y 41 Y 42 Y 43 Y 44 ) ( V 1 V 2 V 3 V 4 ) = ( I 1 I 2 I 3 I 4 ) ...... (1) Here, V 1 is voltage at node 1 , V 2 is voltage at node 2 , V 3 is voltage at node 3 , V 4 is voltage at node 4 , I 1 is current at node 1 , I 2 is current at node 2 , I 3 is current at node 3 , I 4 is current at node 4 . Calculation: The admittance circuit diagram is redrawn as shown in Figure 1. Here Y 11 is the value of sum of admittance connected to node 1 . So Y 11 = Y c + Y d + Y f Here Y 12 is the negative of value of sum of admittance connected between node 1 and node 2 . So Y 12 = − Y d Here Y 13 is the negative of value of sum of admittance connected between node 1 and node 3 . So Y 13 = − Y c Here Y 14 is the negative of value of sum of admittance connected between node 1 and node 4 . So Y 14 = − Y f Here Y 21 is the negative of value of sum of admittance connected between node 2 and node 1 . So Y 21 = − Y d Here Y 22 is the value of sum of admittance connected to node 2 . So Y 22 = Y b + Y d + Y e Here Y 23 is the negative of value of sum of admittance connected between node 2 and node 3 . So Y 23 = − Y b Here Y 24 is the negative of value of sum of admittance connected between node 2 and node 4 . So Y 24 = − Y e Here Y 31 is the negative of value of sum of admittance connected between node 3 and node 1 . So Y 31 = − Y c Here Y 32 is the negative of value of sum of admittance connected between node 3 and node 2 . So Y 32 = − Y b Here Y 33 is the value of sum of admittance connected to node 3 . So Y 33 = Y a + Y b + Y c Here Y 34 is the negative of value of sum of admittance connected between node 3 and node 4 . So Y 34 = 0 Here Y 41 is the negative of value of sum of admittance connected between node 4 and node 1 . So Y 41 = − Y f Here Y 42 is the negative of value of sum of admittance connected between node 4 and node 2 . So Y 42 = − Y e Here Y 43 is the negative of value of sum of admittance connected between node 4 and node 3 . So Y 43 = 0 Here Y 44 is the value of sum of admittance connected to node 4 To determine (b) The nodal equation in matrix form and suggest method to solve for voltages.

6th Edition

ISBN: 9781337259170

Author: Glover

Publisher: INTER CENG

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Question

Chapter 2, Problem 2.39P

To determine

(a)

The nodal equation in matrix form.

To determine

(b)

The nodal equation in matrix form and suggest method to solve for voltages.

Expert Solution & Answer

Chapter 2 Solutions

POWER SYSTEM ANALYSIS+DESIGN-EBK >I<

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. 2.4MCQ Ch. 2 - Prob. 2.5MCQ Ch. 2 - Prob. 2.6MCQ Ch. 2 - Prob. 2.7MCQ Ch. 2 - Prob. 2.8MCQ Ch. 2 - Prob. 2.9MCQ Ch. 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. 2.13MCQ 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 nodal equation in matrix form.

Concept explainers

(a) The nodal equation in matrix form.

(b) The nodal equation in matrix form and suggest method to solve for voltages.

Chapter 2 Solutions

(a)

The nodal equation in matrix form.

(b)

The nodal equation in matrix form and suggest method to solve for voltages.