Answer to Question #184284 in Electrical Engineering for nuri

Question #184284

A balanced Δ (delta) connected source has an internal impedance of 0.018+j0.162 Ω/phase. At no load, the terminal voltage of the source has magnitude of 380 VLL. The source is connected to a Δ (delta) connected load, having an impedance of 7.92+j6.35 Ω/phase through a distribution line having an impedance of 0.074+j0.296 Ω/phase. a) Draw the single phase equivalent circuit of 3-phase system b) Calculate the three line currents c) Calculate the phase currents of the source d) Calculate the magnitude of the line voltage at the terminals of the source


1
Expert's answer
2021-04-23T08:25:20-0400

a) Draw the single-phase equivalent circuit of a 3-phase system

b) Calculate the three line currents

"S_R=\\frac{E_R}{Z_S\/3+Z_d+Z_L\/3}"

"S_R=\\frac{219.39 \\angle{-30}}{0.006+j0.054+0.074+j0.296+2.64-j2.116} =67.56 \\angle 2.99 Amp"

Since loads and source are balanced, all phase current are equal in magnitude but displaced with respect to each other by 1200

"I_Y=I_R= \\angle -120=67.65\\angle2.99-120=67.65\\angle-1770.01 A"

"I_B=I_R= \\angle -120=67.65\\angle122.99"

c) Calculate the phase currents of the source

It is lead line current by 300

"I_R=I_{RY}-I_{BR}=\\sqrt{3}I_{RY} \\angle 30"

"I_{RY}=\\frac{I_R}{\\sqrt{3}} \\angle 30=\\frac{67.65}{\\sqrt{3}} \\angle 2.99+30=39.05+\\angle 32.99 Amp"

"I_{BY}=\\frac{I_Y}{\\sqrt{3}} \\angle 30=\\frac{67.65}{\\sqrt{3}} \\angle -117.01+30=39.05+\\angle -87.01 Amp"

"I_{BR}=\\frac{I_B}{\\sqrt{3}} \\angle 30=\\frac{67.65}{\\sqrt{3}} \\angle 122.99+30=39.05+\\angle 152.99 Amp"

d) Calculate the magnitude of the line voltage at the terminals of the source

"(V_R)_L=E_{RY}-Z_S \\times I_{RY}"

"(V_R)_L=380\\angle0-(0.018+j0.162) \\times (39.05 \\angle 32.99)=382.89 \\angle-0.85 V"

"V_Y=382.89\\angle -0.85-120=382.89 \\angle-120.85 V"

"V_B=382.89\\angle -0.85+120=382.89 \\angle119.15 V"


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS