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Use the Dummy Mesh Current Analysis to set up the matrix equation necessary for solving for the unknown mesh currents. R₁ w R₂ W R3. M1 VS1 R4 ☐ M2 R8 R5 V82. R6 M4 M3 R W R9 Set up the matrix equation: (R₁ + R3 + R4) -RA 0 0 -RA (R4 + R5 + R8) 0 IMI VS2 -R5 0 IM2 +Vs2 == -R5 (R2 + R5 + R6 + R7) -(R6 + R7) IMз 0 0 0 -(R6 + R7) (R6 R7 Rg). IMA -VS1 0 IMI -V$1 [ (R₁ + R3 + R4 + V51) -R4 -R4 (R4 + R5 + R8) 0 0 IM2 +VS1 -R5 = 0 0 -R5 0 (R₂+ R5 + R6 + R7 - Vs1) -(R6 + R7) IM3 0 -(R6 + R7) (R6 R7 R9 +Vs2). IMA -VS2 0 (R₁ + R3 + R4) -RA -RA (R4 + R5 + R8) 0 -VS1 IM -R5 0 +VS1 IM2 - 0 0 -R5 0 (R2 + R5 + R6 + R7) -(R6 + R7) -(R6 + R7) (R6 R7 Rg) -VS2 0 (R₁ + R3 + R4) -RA -RA (R4 R5 + R8) 0 -R5 IMI 0 IM2 = 0 -R5 (R₂ + R5 + R6 + R7) -(R6 + R7) Iм3 IMз IM4 Vsi +VS₁ 0 0 0 -(R6 + R7) (R6 + R7 + Rg) IMA 0 (R₁ + R3 + R4) -RA -R4 -(R4 + R5) 0 (R4 + R5 + R8) 0 -R5 IMI -VS1 -(R4 + R$) IM2 = -R5 0 (R2 + R5 + R6 + R7) -(R6 + R7) IM3 -(R6 + R7) (R6 + R7 + Rg) IMA +Vsi 0 -VS2 0 [(R₁ + R3 + R4) -R4 -(R4 + R5) 0 -RA (R4 + R5 + R8) 0 -R5 IMI -VS1 -(R4 + R5) IM2 0 = -R5 (R2 + R5 + R6 + R7) -(R6 + R7) IMз 0 -(R6 + R7) (R6 + R7 + Rg) IMA 0 0

Use the Dummy Mesh Current Analysis to set up the matrix equation necessary for solving for the unknown mesh currents. R₁ w R₂ W R3. M1 VS1 R4 ☐ M2 R8 R5 V82. R6 M4 M3 R W R9 Set up the matrix equation: (R₁ + R3 + R4) -RA 0 0 -RA (R4 + R5 + R8) 0 IMI VS2 -R5 0 IM2 +Vs2 == -R5 (R2 + R5 + R6 + R7) -(R6 + R7) IMз 0 0 0 -(R6 + R7) (R6 R7 Rg). IMA -VS1 0 IMI -V$1 [ (R₁ + R3 + R4 + V51) -R4 -R4 (R4 + R5 + R8) 0 0 IM2 +VS1 -R5 = 0 0 -R5 0 (R₂+ R5 + R6 + R7 - Vs1) -(R6 + R7) IM3 0 -(R6 + R7) (R6 R7 R9 +Vs2). IMA -VS2 0 (R₁ + R3 + R4) -RA -RA (R4 + R5 + R8) 0 -VS1 IM -R5 0 +VS1 IM2 - 0 0 -R5 0 (R2 + R5 + R6 + R7) -(R6 + R7) -(R6 + R7) (R6 R7 Rg) -VS2 0 (R₁ + R3 + R4) -RA -RA (R4 R5 + R8) 0 -R5 IMI 0 IM2 = 0 -R5 (R₂ + R5 + R6 + R7) -(R6 + R7) Iм3 IMз IM4 Vsi +VS₁ 0 0 0 -(R6 + R7) (R6 + R7 + Rg) IMA 0 (R₁ + R3 + R4) -RA -R4 -(R4 + R5) 0 (R4 + R5 + R8) 0 -R5 IMI -VS1 -(R4 + R$) IM2 = -R5 0 (R2 + R5 + R6 + R7) -(R6 + R7) IM3 -(R6 + R7) (R6 + R7 + Rg) IMA +Vsi 0 -VS2 0 [(R₁ + R3 + R4) -R4 -(R4 + R5) 0 -RA (R4 + R5 + R8) 0 -R5 IMI -VS1 -(R4 + R5) IM2 0 = -R5 (R2 + R5 + R6 + R7) -(R6 + R7) IMз 0 -(R6 + R7) (R6 + R7 + Rg) IMA 0 0

Power System Analysis and Design (MindTap Course List)
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 6.55P
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Use the Dummy Mesh Current Analysis to set up the matrix equation necessary for solving for the unknown mesh currents. R₁ w R₂ W R3. M1 VS1 R4 ☐ M2 R8 R5 V82. R6 M4 M3 R W R9 Set up the matrix equation: (R₁ + R3 + R4) -RA 0 0 -RA (R4 + R5 + R8) 0 IMI VS2 -R5 0 IM2 +Vs2 == -R5 (R2 + R5 + R6 + R7) -(R6 + R7) IMз 0 0 0 -(R6 + R7) (R6 R7 Rg). IMA -VS1 0 IMI -V$1 [ (R₁ + R3 + R4 + V51) -R4 -R4 (R4 + R5 + R8) 0 0 IM2 +VS1 -R5 = 0 0 -R5 0 (R₂+ R5 + R6 + R7 - Vs1) -(R6 + R7) IM3 0 -(R6 + R7) (R6 R7 R9 +Vs2). IMA -VS2 0 (R₁ + R3 + R4) -RA -RA (R4 + R5 + R8) 0 -VS1 IM -R5 0 +VS1 IM2 - 0 0 -R5 0 (R2 + R5 + R6 + R7) -(R6 + R7) -(R6 + R7) (R6 R7 Rg) -VS2 0 (R₁ + R3 + R4) -RA -RA (R4 R5 + R8) 0 -R5 IMI 0 IM2 = 0 -R5 (R₂ + R5 + R6 + R7) -(R6 + R7) Iм3 IMз IM4 Vsi +VS₁ 0 0 0 -(R6 + R7) (R6 + R7 + Rg) IMA 0 (R₁ + R3 + R4) -RA -R4 -(R4 + R5) 0 (R4 + R5 + R8) 0 -R5 IMI -VS1 -(R4 + R$) IM2 = -R5 0 (R2 + R5 + R6 + R7) -(R6 + R7) IM3 -(R6 + R7) (R6 + R7 + Rg) IMA +Vsi 0 -VS2 0 [(R₁ + R3 + R4) -R4 -(R4 + R5) 0 -RA (R4 + R5 + R8) 0 -R5 IMI -VS1 -(R4 + R5) IM2 0 = -R5 (R2 + R5 + R6 + R7) -(R6 + R7) IMз 0 -(R6 + R7) (R6 + R7 + Rg) IMA 0 0
Transcribed Image Text:Use the Dummy Mesh Current Analysis to set up the matrix equation necessary for solving for the unknown mesh currents. R₁ w R₂ W R3. M1 VS1 R4 ☐ M2 R8 R5 V82. R6 M4 M3 R W R9 Set up the matrix equation: (R₁ + R3 + R4) -RA 0 0 -RA (R4 + R5 + R8) 0 IMI VS2 -R5 0 IM2 +Vs2 == -R5 (R2 + R5 + R6 + R7) -(R6 + R7) IMз 0 0 0 -(R6 + R7) (R6 R7 Rg). IMA -VS1 0 IMI -V$1 [ (R₁ + R3 + R4 + V51) -R4 -R4 (R4 + R5 + R8) 0 0 IM2 +VS1 -R5 = 0 0 -R5 0 (R₂+ R5 + R6 + R7 - Vs1) -(R6 + R7) IM3 0 -(R6 + R7) (R6 R7 R9 +Vs2). IMA -VS2 0 (R₁ + R3 + R4) -RA -RA (R4 + R5 + R8) 0 -VS1 IM -R5 0 +VS1 IM2 - 0 0 -R5 0 (R2 + R5 + R6 + R7) -(R6 + R7) -(R6 + R7) (R6 R7 Rg) -VS2 0 (R₁ + R3 + R4) -RA -RA (R4 R5 + R8) 0 -R5 IMI 0 IM2 = 0 -R5 (R₂ + R5 + R6 + R7) -(R6 + R7) Iм3 IMз IM4 Vsi +VS₁ 0 0 0 -(R6 + R7) (R6 + R7 + Rg) IMA 0 (R₁ + R3 + R4) -RA -R4 -(R4 + R5) 0 (R4 + R5 + R8) 0 -R5 IMI -VS1 -(R4 + R$) IM2 = -R5 0 (R2 + R5 + R6 + R7) -(R6 + R7) IM3 -(R6 + R7) (R6 + R7 + Rg) IMA +Vsi 0 -VS2 0 [(R₁ + R3 + R4) -R4 -(R4 + R5) 0 -RA (R4 + R5 + R8) 0 -R5 IMI -VS1 -(R4 + R5) IM2 0 = -R5 (R2 + R5 + R6 + R7) -(R6 + R7) IMз 0 -(R6 + R7) (R6 + R7 + Rg) IMA 0 0
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