find V1, V2, V3, and V4 from these 4 equations: ((5sin(120pi t) - V1) / 470) + ((V2-V1)/ -j3.195*10^3) + ((V3-V4)/-j56.92*10^3) = 0 ((V1-V2)/-j3.195*10^3) + (V2/988) = 0 ((V1-V3)/-j56.92*10^3) + ((V4-V3)/4670) = 0 ((V3-V4)/4670) + (V4 / -j2.947*10^3) = 0

find V1, V2, V3, and V4 from these 4 equations: ((5sin(120pi t) - V1) / 470) + ((V2-V1)/ -j3.19510^3) + ((V3-V4)/-j56.9210^3) = 0 ((V1-V2)/-j3.19510^3) + (V2/988) = 0 ((V1-V3)/-j56.9210^3) + ((V4-V3)/4670) = 0 ((V3-V4)/4670) + (V4 / -j2.947*10^3) = 0

Power System Analysis and Design (MindTap Course List)

6th Edition

ISBN:9781305632134

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

Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Chapter6: Power Flows

Section: Chapter Questions

Problem 6.59P

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Question

find V1, V2, V3, and V4 from these 4 equations:

((5sin(120pi t) - V1) / 470) + ((V2-V1)/ -j3.195*10^3) + ((V3-V4)/-j56.92*10^3) = 0

((V1-V2)/-j3.195*10^3) + (V2/988) = 0

((V1-V3)/-j56.92*10^3) + ((V4-V3)/4670) = 0

((V3-V4)/4670) + (V4 / -j2.947*10^3) = 0

Expert Solution

Step 1

It is given that:

$\frac{5 \sin (120 πt) - V_{1}}{470} + \frac{V_{2} - V_{1}}{- j 3.195 \times 10^{3}} + \frac{V_{3} - V_{4}}{- j 56.92 \times 10^{3}} = 0 . . . . . . . (1) \frac{V_{1} - V_{2}}{- j 3.195 \times 10^{3}} + \frac{V_{2}}{988} = 0 . . . . . . (2) \frac{V_{1} - V_{3}}{- j 56.92 \times 10^{3}} + \frac{V_{4} - V_{3}}{4670} = 0 . . . . . . . (3) \frac{V_{3} - V_{4}}{4670} + \frac{V_{4}}{- j 2.947 \times 10^{3}} = 0 . . . . . . . (4)$

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