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20 kVA 2200/220 V, LV-side circuit

Short answer

Referred to LV side: Ro=387.2 Ω, Xo=233.6 Ω, R02=0.0407 Ω, X02=0.0478 Ω (Z02=0.0627 Ω).

The following test results were obtained on a 20 kVA, 2200/220 V, 50 Hz single phase transformer: Open-circuit Test (LV Side): 220 V, 1.1 A, 125 W Short-circuit Test (HV Side): 52.7 V, 8.4 A, 287 W Calculate the equivalent circuit referred to L.V side and draw the equivalent circuit.

Given: 20 kVA, 2200/220 V. OC test on the LV side: 220 V, 1.1 A, 125 W. SC test on the HV side: 52.7 V, 8.4 A, 287 W. The turns ratio is 2200/220 = 10. The HV (2200 V) winding is the primary, so the series values on the HV side are R01, X01 and on the LV side R02, X02.

Shunt branch (the OC test is on the LV side, so no transfer is needed)

cos φ0 = 125/(220 × 1.1) = 0.5165
Iw = 1.1 × 0.5165 = 0.568 A
Iμ = √(1.1² − 0.568²) = 0.942 A
Ro = 220/0.568 = 387.2 Ω
Xo = 220/0.942 = 233.6 Ω

Series branch (the SC test is on the HV side, so refer it to the LV side by dividing by 10² = 100)

On HV:  Z01 = 52.7/8.4 = 6.274 Ω
        R01 = 287/8.4² = 4.067 Ω
        X01 = √(6.274² − 4.067²) = 4.777 Ω
On LV:  Z02 = 0.06274 Ω ; R02 = 0.04067 Ω ; X02 = 0.04777 Ω

Equivalent circuit referred to the LV side

          R02=0.0407Ω  X02=0.0478Ω
 o──┬─────┬────/\/\/────────(((──────o
    │     │                          
 387.2Ω 233.6Ω                  load
    │     │                      V2 (LV)
 o──┴─────┴───────────────────────────o

Answer: Ro = 387.2 Ω, Xo = 233.6 Ω, R02 = 0.0407 Ω, X02 = 0.0478 Ω (Z02 = 0.0627 Ω), all on the LV side.

✓ Answer checked by Claude Opus 5.5 (high effort)

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