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20 kVA 250/2500 V test parameters

Short answer

Referred to primary: Ro=595.2 Ω, Xo=187.2 Ω, R01=0.05 Ω, X01=0.141 Ω (Z01=0.15 Ω).

A 20 kVA, 250V/2500V, 50 Hz single phase transformer gave the following test results: No-load test (on L.V. side): 250 V, 1.4 A, 105 watts Short circuit test (on H.V. side): 120 V, 8 A, 320 watts Calculate the equivalent circuit parameters referred to primary side and draw the equivalent circuit.

Given: 20 kVA, 250/2500 V, 50 Hz. No-load test (LV, 250 V side): 250 V, 1.4 A, 105 W. SC test (HV side): 120 V, 8 A, 320 W. Primary = the 250 V side; K = 2500/250 = 10.

Shunt branch (the no-load test is already on the primary)

cos φ0 = 105/(250 × 1.4) = 0.300
Iw = 1.4 × 0.300 = 0.420 A
Iμ = √(1.4² − 0.42²) = 1.336 A
Ro = 250/0.420 = 595.2 Ω
Xo = 250/1.336 = 187.2 Ω

Series branch

On the HV side: Z02 = 120/8 = 15 Ω; R02 = 320/8² = 5 Ω; X02 = √(15² − 5²) = 14.14 Ω.

Refer to the primary (÷ K² = 100):

Z01 = 0.150 Ω ;  R01 = 0.050 Ω ;  X01 = 0.1414 Ω

Equivalent circuit referred to primary

        R01=0.05Ω   X01=0.1414Ω
 o──┬────┬───/\/\/───────(((────────o
    │    │                          
 595.2Ω 187.2Ω                  load
    │    │                       V2'
 o──┴────┴───────────────────────────o

Answer: Ro = 595.2 Ω, Xo = 187.2 Ω, R01 = 0.05 Ω, X01 = 0.141 Ω (Z01 = 0.15 Ω).

✓ Answer checked by Claude Opus 5.5 (high effort)

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