Explanation Concept used: Write the expression for 4 × 4 admittance matrix. Y b u s = ( 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 ) ...... (1) Here, Y b u s is 4 × 4 admittance matrix. Calculation: The admittance is the reciprocal value of impedance. The admittance circuit diagram is redrawn as shown in Figure 1. Y 11 is the value of sum of admittance connected to node 1 . So Y 11 = 1 S Y 12 is the negative of value of sum of admittance connected between node 1 and node 2 . So Y 12 = − 1 S Y 13 is the negative of value of sum of admittance connected between node 1 and node 3 . So Y 13 = 0 S Y 14 is the negative of value of sum of admittance connected between node 1 and node 4 . So Y 14 = 0 S Y 21 is the negative of value of sum of admittance connected between node 2 and node 1 . So Y 21 = − 1 S Y 22 is the value of sum of admittance connected to node 2 . So Y 22 = 1 S + 0 .5 S + 0 .33 S − j1 S = ( 1 .83 − j1 ) S Y 23 is the negative of value of sum of admittance connected between node 2 and node 3 . So Y 23 = − ( 0 .33 S − j1 ) S Y 24 is the negative of value of sum of admittance connected between node 2 and node 4 . So Y 24 = − 0.25 S Y 31 is the negative of value of sum of admittance connected between node 3 and node 1 . So Y 31 = 0 S Y 32 is the negative of value of sum of admittance connected between node 3 and node 2 . So Y 32 = − ( 0 .33 S − j1 ) S Y 33 is the value of sum of admittance connected to node 3 . So Y 33 = j 0.25 S + j 0 .5 S + 0 .33 S − j1 S = ( 0 .33 − j0 .25 ) S Y 34 is the negative of value of sum of admittance connected between node 3 and node 4 . So Y 34 = − j 0.25 S Y 41 is the negative of value of sum of admittance connected between node 4 and node 1 . So Y 41 = 0 S Y 42 is the negative of value of sum of admittance connected between node 4 and node 2 . So Y 42 = − 0.25 S Y 43 is the negative of value of sum of admittance connected between node 4 and node 3 . So Y 43 = − j 0.25 S Y 44 is the value of sum of admittance connected to node 4 . So Y 44 = 0.25 S + j 0 .25 S − j0 .33 S = ( 0 .25 − j0 .08 ) S Substitute 1 S for Y 11 , − 1 S for Y 12 , 0 S for Y 13 , 0 S for Y 14 , − 1 S for Y 21 , ( 1 .83 − j1 ) S for Y 22 , − ( 0 .33 S − j1 ) S for Y 23 , − 0.25 S for Y 24 , 0 S for Y 31 , − ( 0 .33 S − j1 ) S for Y 32 , ( 0 .33 − j0 .25 ) S for Y 33 , − j 0.25 S for Y 34 , 0 S for Y 41 , − 0.25 S for Y 42 , − j 0.25 S for Y 43 and ( 0 .25 − j0 .08 ) S for Y 44 in equation (1). Y b u s = ( 1 − 1 0 0 − 1 ( 1 .83 − j1 ) − ( 0

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

See similar textbooks

Concept explainers

Load flow analysis

Load flow analysis is a study or numerical calculation of the power flow of power in steady-state conditions in any electrical system. It is used to determine the flow of power (real and reactive), voltage, or current in a system under any load condition…

Nodal Matrix

The nodal matrix or simply known as admittance matrix, generally in engineering term it is called Y Matrix or Y bus, since it involve matrices so it is also referred as a n into n order matrix that represents a power system with n number of buses. It sho…

Types of Buses

A bus is a type of system of communication that transfers data between the components inside a computer or between two or more computers. With multiple hardware connections, the earlier buses were parallel electrical wires but the term "bus" is now used …

Question

Chapter 2, Problem 2.37P

To determine

Admittance bus matrix and nodal equation in matrix form.

Expert Solution & Answer

Chapter 2 Solutions

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

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

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.