--- title: "OC and SC tests, efficiency and regulation" subject: "Electrical Machine" chapter: 2 key: "semester_4/electrical_machine:oc-sc-test-efficiency-regulation" source: https://www.bctengineer.com/q/semester_4/electrical_machine/oc-sc-test-efficiency-regulation site: BCT Engineering --- # OC and SC tests, efficiency and regulation Electrical Machine · Chapter 2: Transformer - Asked in: 2074 Bhadra, 6 marks - Video: [Transformer OC test and SC test problems | effeciency, voltage regulation calculations](https://www.youtube.com/watch?v=aB2j_Fqd4zo) — The PiSquare Academy - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/electrical_machine/oc-sc-test-efficiency-regulation - Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machine/chapter-2 ## Question Discuss how to conduct open-circuit and short-circuit tests on a single phase transformer. From the test results how the efficiency and voltage regulation of the transformer is determined? ## Short answer OC test on LV side with HV open gives iron loss Pi and parameters Ro, Xo. SC test on HV side with LV shorted gives full-load copper loss Pcu and R₀₁, X₀₁. Efficiency η = x S cos φ / (x S cos φ + Pi + x² Pcu). % regulation ≈ (I₂ R₀₂ cos φ ± I₂ X₀₂ sin φ)/V₂ × 100. ## Answer Open-circuit (OC) and short-circuit (SC) tests give the core-loss and copper-loss data without loading the transformer. #### Open-circuit test (no-load test) ```text W A o──[W]─[A]──+───────+ o AC V (HV winding supply (LV side) open) ``` - The meters (wattmeter, ammeter, voltmeter) are connected on the **low-voltage** side with rated voltage V0 applied; the HV side is left open. - Readings: V0, I0, W0. Since I0 is only 2–5 % of rated, copper loss is negligible, so **W0 = iron loss Pi**. ```text cos φ0 = W0/(V0 I0) Iw = I0 cos φ0 , Iμ = I0 sin φ0 Ro = V0/Iw , Xo = V0/Iμ ``` #### Short-circuit test - The **HV** side is supplied through a variable-voltage source (e.g. autotransformer); the LV side is short-circuited with an ammeter. - The voltage is raised slowly until the rated current flows. This voltage is only 5–10 % of the rated voltage, so flux and iron loss are very small. Readings: Vsc, Isc, Wsc. - **Wsc = full-load copper loss Pcu**. ```text Z01 = Vsc/Isc , R01 = Wsc/Isc² , X01 = √(Z01² − R01²) ``` Referring to the other side uses the factor K². #### Efficiency For a fraction *x* of full load at power factor cos φ: ```text η = x S cos φ / ( x S cos φ + Pi + x² Pcu ) × 100 % ``` Pi from the OC test, Pcu (at rated current) from the SC test. The load at which η is maximum is x = √(Pi/Pcu). #### Regulation Regulation = (E2 − V2)/E2 × 100 %. Using R02, X02 from the SC test and the rated secondary current I2: ```text % regulation ≈ (I2 R02 cos φ ± I2 X02 sin φ) / V2 × 100 ``` "+" for lagging loads, "−" for leading loads. Maximum regulation occurs at power factor cos φ = R02/Z02. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. On which side is the open-circuit test normally performed and what does the wattmeter read? A. HV side; copper loss B. LV side; iron loss C. LV side; copper loss D. HV side; total loss at full load Answer: B. Rated voltage is applied on the LV side with HV open; W0 is practically the iron loss. (Key point: OC test side) 2. In the short-circuit test, what does the wattmeter reading Wsc give? A. Iron loss B. No-load loss C. Full-load copper loss D. Stray loss only Answer: C. At rated current with low voltage, Wsc equals the full-load copper loss Pcu. (Key point: SC test) 3. Which formulas give R01 and X01 from the SC test? A. R01 = Wsc/Isc², X01 = sqrt(Z01² − R01²) B. R01 = Vsc/Isc, X01 = Wsc/Isc C. R01 = Wsc/Isc, X01 = Vsc/Isc² D. R01 = Wsc/Vsc, X01 = Z01 + R01 Answer: A. Z01 = Vsc/Isc, R01 = Wsc/Isc², and X01 follows from Z01² = R01² + X01². (Key point: SC test parameter formula) 4. In the approximate regulation formula, the X sin φ term is subtracted for which load? A. Lagging loads B. Unity power factor loads C. Leading loads D. Resistive loads only Answer: C. The '+' sign is for lagging loads and the '−' sign for leading loads. 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