--- title: "Equivalent circuit of 8 kVA 400/120 V transformer" subject: "Electrical Machines I" chapter: 2 key: "semester_4/electrical_machines_i:oc-sc-8kva-400-120-hv" source: https://www.bctengineer.com/q/semester_4/electrical_machines_i/oc-sc-8kva-400-120-hv site: BCT Engineering --- # Equivalent circuit of 8 kVA 400/120 V transformer Electrical Machines I · Chapter 2: Transformer - Asked in: 2078 Chaitra, 8 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_machines_i/oc-sc-8kva-400-120-hv - Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines_i/chapter-2 ## Question A 8 kVA, 400/120 V, 50 Hz single phase transformer on test gives the following results: O.C. test: 120 V, 4 A, 75 W (carried on LV side) S.C. test: 9.5 V, 20 A, 110 W (carried on HV side) Calculate the equivalent circuit parameters referred to HV side. ## Short answer OC test on LV gives R0=2133.3 ohm and X0=337.5 ohm referred to HV. SC test on HV gives R01=0.275 ohm, X01=0.3873 ohm, and Z01=0.475 ohm. ## Answer **Method.** The no-load (OC) test gives the shunt branch: $\cos\phi_0 = \frac{P_0}{V_0 I_0}$, $I_w = I_0\cos\phi_0$, $I_\mu = I_0\sin\phi_0$, $R_0 = \frac{V_0}{I_w}$, $X_0 = \frac{V_0}{I_\mu}$. The SC test gives the series branch: $Z = \frac{V_{sc}}{I_{sc}}$, $R = \frac{P_{sc}}{I_{sc}^2}$, $X = \sqrt{Z^2 - R^2}$. Values found on one side are moved to the other side by multiplying by the square of the voltage ratio. Ratio: HV = 400 V, LV = 120 V, so to refer an LV value to HV multiply by $\left(\frac{400}{120}\right)^2 = 11.11$. #### From OC test (on LV side): 120 V, 4 A, 75 W $$ \begin{aligned} \cos\phi_0 &= \frac{75}{120 \times 4} = 0.1563, \quad \sin\phi_0 = 0.9877 \\ I_w &= 4 \times 0.1563 = 0.625\ \text{A}, \quad I_\mu = 4 \times 0.9877 = 3.951\ \text{A} \\ R_0 (\text{LV}) &= \frac{120}{0.625} = 192\ \Omega, \quad X_0 (\text{LV}) = \frac{120}{3.951} = 30.37\ \Omega \end{aligned} $$ Referred to HV: $$ \begin{aligned} R_0 (\text{HV}) &= 192 \times 11.11 = 2133.3\ \Omega \\ X_0 (\text{HV}) &= 30.37 \times 11.11 = 337.5\ \Omega \end{aligned} $$ #### From SC test (on HV side): 9.5 V, 20 A, 110 W The test is on the HV side, so the results are already referred to HV. (Rated HV current = 8000/400 = 20 A, so this is a full-load test.) $$ \begin{aligned} Z_{01} &= \frac{9.5}{20} = 0.475\ \Omega \\ R_{01} &= \frac{110}{20^2} = 0.275\ \Omega \\ X_{01} &= \sqrt{0.475^2 - 0.275^2} = 0.3873\ \Omega \end{aligned} $$ #### Equivalent circuit referred to HV side ```text I1 -> I0 I2' o-----+--------+---[ R01 ]---[ jX01 ]---o + | | + [ R0 ] [ jX0 ] load V1 | | V2' - | | - o-----+--------+------------------------o All values referred to HV side: R0 = 2133.3 ohm, X0 = 337.5 ohm R01 = 0.275 ohm, X01 = 0.387 ohm ``` **Answer:** $R_0 = 2133.3\ \Omega$, $X_0 = 337.5\ \Omega$, $R_{01} = 0.275\ \Omega$, $X_{01} = 0.387\ \Omega$, $Z_{01} = 0.475\ \Omega$ (all referred to HV). ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. From the OC test, how are R0 and X0 computed? A. R0 = P0/I0, X0 = V0/I0 B. R0 = V0/(I0 cos phi0), X0 = V0/(I0 sin phi0) C. R0 = V0 I0, X0 = P0/I0 D. R0 = V0 sin phi0, X0 = V0 cos phi0 Answer: B. Working current Iw = I0 cos phi0 and magnetising Imu = I0 sin phi0; R0 = V0/Iw and X0 = V0/Imu. (Key point: OC test gives shunt branch) 2. The OC test is on the LV side (120 V). How are R0 and X0 converted to the HV side? A. Leave unchanged B. Multiply by 400/120 C. Divide by 11.11 D. Multiply by (400/120)^2 = 11.11 Answer: D. Impedances scale with the square of the voltage ratio when referred to the higher voltage side. (Key point: Referring to HV) 3. The SC test is made on the HV side. What follows? A. Values must be multiplied by 11.11 B. Z01, R01, X01 are directly referred to HV C. The test gives LV-referred parameters D. Values must be divided by 11.11 Answer: B. Measurements at the HV winding give series parameters already referred to HV. (Key point: SC test side) 4. How is X01 found? A. X01 = Psc/Isc B. X01 = sqrt(Z01^2 - R01^2) = 0.3873 ohm C. X01 = Z01 + R01 D. X01 = Vsc x Isc Answer: B. Z01 = 9.5/20 = 0.475, R01 = 110/400 = 0.275, so X01 = sqrt(0.475^2 - 0.275^2) = 0.3873 ohm. 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