--- title: "Equivalent circuit of 220/440 V transformer" subject: "Electrical Machines I" chapter: 2 key: "semester_4/electrical_machines_i:oc-sc-220-440-lv-params" source: https://www.bctengineer.com/q/semester_4/electrical_machines_i/oc-sc-220-440-lv-params site: BCT Engineering --- # Equivalent circuit of 220/440 V transformer Electrical Machines I · Chapter 2: Transformer - Asked in: 2075 Bhadra, 8 marks - Video: [(E)EM Ex 2.2 || Equivalent Circuit of a Transformer || Refer to Pri & Secy sides ||Open-Short Test](https://www.youtube.com/watch?v=uJP_rFndPtU) — Electrical Engineering 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-220-440-lv-params - Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines_i/chapter-2 ## Question Following test data are obtained in a 220 V/440 V single phase transformer: O/C test: 220 V, 1.3 Amp, 160 watts S/C test: 24 V, 14 Amp, 185 watts Calculate the equivalent circuit parameters referred to low voltage side and draw the equivalent circuit. ## Short answer OC test gives shunt referred to LV: R0 = 302.5 Ω, X0 = 204.2 Ω. SC test referred to LV gives R01 = 0.236 Ω, X01 = 0.358 Ω, Z01 = 0.429 Ω. ## 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. **Assumption:** the OC test (220 V) is on the LV side and the SC test (24 V, about 5% of 440 V) is on the HV side, as is usual. Factor HV to LV: $\left(\frac{220}{440}\right)^2 = 0.25$. #### OC test (LV): 220 V, 1.3 A, 160 W $$ \begin{aligned} \cos\phi_0 &= \frac{160}{220 \times 1.3} = 0.5594, \quad \sin\phi_0 = 0.8289 \\ I_w &= 1.3 \times 0.5594 = 0.727\ \text{A}, \quad I_\mu = 1.3 \times 0.8289 = 1.078\ \text{A} \\ R_0 &= \frac{220}{0.727} = 302.5\ \Omega, \quad X_0 = \frac{220}{1.078} = 204.2\ \Omega \end{aligned} $$ #### SC test (HV): 24 V, 14 A, 185 W $$ \begin{aligned} Z_{02} &= \frac{24}{14} = 1.714\ \Omega, \quad R_{02} = \frac{185}{14^2} = 0.944\ \Omega \\ X_{02} &= \sqrt{1.714^2 - 0.944^2} = 1.431\ \Omega \end{aligned} $$ Referred to LV: $$ \begin{aligned} R_{01} &= 0.944 \times 0.25 = 0.236\ \Omega \\ X_{01} &= 1.431 \times 0.25 = 0.358\ \Omega \\ Z_{01} &= 1.714 \times 0.25 = 0.429\ \Omega \end{aligned} $$ #### Equivalent circuit referred to LV side ```text I1 -> I0 I2' o-----+--------+---[ R01 ]---[ jX01 ]---o + | | + [ R0 ] [ jX0 ] load V1 | | V2' - | | - o-----+--------+------------------------o All values referred to LV side: R0 = 302.5 ohm, X0 = 204.2 ohm R01 = 0.236 ohm, X01 = 0.358 ohm ``` **Answer (LV side):** $R_0 = 302.5\ \Omega$, $X_0 = 204.2\ \Omega$, $R_{01} = 0.236\ \Omega$, $X_{01} = 0.358\ \Omega$, $Z_{01} = 0.429\ \Omega$. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Which test sides are assumed? A. OC on LV (220 V) and SC on HV (440 V side) B. OC on HV, SC on LV C. Both on LV D. Both on HV Answer: A. OC voltage equals LV rated; SC voltage 24 V is about 5% of 440 V so it is on HV. (Key point: Assumption of sides) 2. What are R0 and X0 from the OC test? A. 169 ohm and 275 ohm B. 302.5 ohm and 204.2 ohm C. 204.2 ohm and 302.5 ohm D. 151 ohm and 102 ohm Answer: B. Iw = 0.727 A, Imu = 1.078 A; R0 = 220/0.727, X0 = 220/1.078. (Key point: Shunt branch) 3. How are HV-side R02 and X02 referred to LV? A. Multiply by 0.5 B. Divide by 0.25 C. Multiply by 4 D. Multiply by (220/440)^2 = 0.25 Answer: D. Impedance scales with the square of the voltage ratio. (Key point: Referring factor) 4. What are the LV-referred R01 and X01? A. 0.236 ohm and 1.431 ohm B. 0.236 ohm and 0.358 ohm C. 0.944 ohm and 1.431 ohm D. 0.472 ohm and 0.716 ohm Answer: B. R02 = 185/196 = 0.944 and X02 = 1.431; multiplied by 0.25. (Key point: Series values on LV) ## Related in Electrical Machines I - [Equivalent circuit of 20 kVA 220/2200 V transformer](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Aoc-sc-20kva-220-2200-primary) — Electrical Machines I, chapter 2 - [Equivalent circuit of 100 kVA 2200/220 V transformer](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Aoc-sc-100kva-2200-220-hv) — Electrical Machines I, chapter 2, asked 3× - [Transformer equivalent circuit referred to primary](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Aequivalent-circuit-referred-primary) — Electrical Machines I, chapter 2 - [Equivalent circuit of 10 kVA 250/1000 V transformer](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Aoc-sc-10kva-250-1000-primary) — Electrical Machines I, chapter 2, asked 2× - [Equivalent circuit and half-load efficiency of 50 kVA transformer](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3A50kva-2500-250-test-secondary-half) — Electrical Machines I, chapter 2 - [OC and SC tests to build transformer equivalent circuit](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Aoc-sc-test-10kva-6600-220) — Electrical Machines I, chapter 2 ## Related in other subjects - [20 kVA 2200/220 V tests, equivalent circuit LV side](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Atf-20kva-2200-220-lv-equivalent) — Electrical Machines, chapter 2 - [220/2200 V transformer test parameters](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machine%3Atransformer-220-2200-test-primary) — Electrical Machine, chapter 2, asked 2× - [20 kVA 2200/220 V, LV-side circuit](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machine%3Atransformer-20kva-2200-220-lv-side) — Electrical Machine, chapter 2 - [250/500 V transformer test, equivalent circuit](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Atf-250-500-test-equivalent-primary) — Electrical Machines, chapter 2