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Exam4Solutions-Spring08

# Exam4Solutions-Spring08 - Test 4 Solutions Spring 2008 R1:=...

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Test 4 Solutions - Spring 2008 R 1 0.2 = R 2 0.05 = X 1 0.4 = X 2 0.4 = X M 10 = s 0.05 = V L 208 = P rated 10000 = P mech 300 = P core 200 = P misc 0 = f e 60 = P 4 = V φ V L 3 = _____________________________________________________________________________ a) Compute I A Z F j X M R 2 s j X 2 + j X M R 2 s + j X 2 + = Z F 0.916 0.473i + = Z F 1.031 = Z in R 1 j X 1 + Z F + = Z in 1.116 0.873i + = Z in 1.417 = I A V φ Z in = I A 84.762 = θ arg I A ( 29 = θ 180 π 38.023 - = _____________________________________________________________________________ b) Stator Copper Loss I A 84 e j - 36 π 180 = θ 36 π 180 = P SCL 3 I A ( 29 2 R 1 = P SCL 4.234 10 3 × = _____________________________________________________________________________ c) Air Gap Power I 2 j X M j X M R 2 s + j X 2 + I A = P AG 3 I 2 ( 29 2 R 2 s = P AG 1.94 10 4 × = The discrepancy in the air gap powers is because I gave you the value of current to use here which is slightly different from the actual current in the motor. Alternatively P in 3 I A V L 3 cos θ ( 29 = P in 2.448 10 4 × = P AG P in P SCL - P core - = P AG 2 10 4 × = _____________________________________________________________________________

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d) Power Converted from Electrical to Mechanical P conv 1 s - ( ) P AG = P conv 1.905 10 4 × = _____________________________________________________________________________ e) Induced Torque P AG 20 10 3 = n sync 120 f e P = ϖ sync n sync 2 π 60 = ϖ sync 188.496 = τ ind P AG ϖ sync = τ ind 106.103 = Newton-Meters _____________________________________________________________________________ f) Load Torque P conv 19.25 10 3 = P OUT P conv P mech - P core - P misc - = n m 1 s - ( ) n sync = ϖ m n m 2 π 60 = n m 1.71 10 3 × = P OUT 1.875 10 4 × = ϖ m 179.071
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Exam4Solutions-Spring08 - Test 4 Solutions Spring 2008 R1:=...

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