--- title: "20 kVA 2200/220 V, LV-side circuit" subject: "Electrical Machine" chapter: 2 key: "semester_4/electrical_machine:transformer-20kva-2200-220-lv-side" source: https://www.bctengineer.com/q/semester_4/electrical_machine/transformer-20kva-2200-220-lv-side site: BCT Engineering --- # 20 kVA 2200/220 V, LV-side circuit Electrical Machine · Chapter 2: Transformer - Asked in: 2070 Magh, 8 marks - Video: [35. OPEN CIRCUIT TEST, SHORT CIRCUIT TEST NUMERICAL PROBLEM, FIND TRANSFORMER CIRCUIT CONSTANT](https://www.youtube.com/watch?v=PCpJF99BoZs) — Electrical Tutorial - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/electrical_machine/transformer-20kva-2200-220-lv-side - Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machine/chapter-2 ## Question 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. ## 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). ## Answer **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) ```text 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) ```text 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 ```text 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.** ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Why are Ro = 387.2 Ω and Xo = 233.6 Ω used directly for the LV-side circuit? A. Because the OC test was done on the LV side B. Because they are small C. Because K = 1 D. Because they are series parameters Answer: A. OC test on LV side gives LV-side values. (Key point: Shunt branch no transfer) 2. How is the HV-side SC impedance referred to the LV side when K = 10? A. Divide by 10 B. Multiply by 100 C. Multiply by 10 D. Divide by 100 Answer: D. Z01 = Z02/K² = Z02/100. (Key point: Referring series to LV) 3. What is R01 referred to LV? A. 4.067 Ω B. 0.4067 Ω C. 0.00407 Ω D. 0.0407 Ω Answer: D. R02 = 4.067 Ω divided by 100 gives 0.0407 Ω. 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