---
title: "Load sharing of 50 kVA and 25 kVA transformers in parallel"
subject: "Electrical Machines I"
chapter: 2
key: "semester_4/electrical_machines_i:parallel-50kva-25kva-60kva-load"
source: https://www.bctengineer.com/q/semester_4/electrical_machines_i/parallel-50kva-25kva-60kva-load
site: BCT Engineering
---

# Load sharing of 50 kVA and 25 kVA transformers in parallel

Electrical Machines I · Chapter 2: Transformer

- Asked in: 2078 Baisakh, 8 marks
- Video: [Parallel Operation of Transformer | Load Sharing Between Two Parallel Transformer |](https://www.youtube.com/watch?v=wj2X1GlHSxA) — Easy Electrical
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/electrical_machines_i/parallel-50kva-25kva-60kva-load
- Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines_i/chapter-2

## Question

A 50 kVA, 4400/220 V transformer with an equivalent impedance of (0.01+j0.02) ohm is to operate in parallel with a 25 kVA, 4400/220 V transformer with an equivalent impedance of (0.02+j0.04) ohm. The two transformers are connected in parallel and made to carry a load of 60 kVA. (i) Find the individual transformer currents. (ii) What percent of the rated capacity is used in each transformer?

## Short answer

The 60 kVA load divides inversely with impedance: A takes 40 kVA and B takes 20 kVA. LV currents are A=181.82 A and B=90.91 A, so each transformer is loaded to 80% of rating.

## Answer

For two transformers with the same voltage ratio in parallel, the load is shared in inverse ratio of their equivalent impedances:
$$
S_A = S\,\frac{Z_B}{Z_A + Z_B}, \qquad S_B = S\,\frac{Z_A}{Z_A + Z_B}
$$
**Assumption:** both impedances are referred to the 220 V (secondary) side; the load power factor is not given, but it is not needed because both impedances have the same angle.

#### Load sharing
$$
\begin{aligned}
Z_A &= 0.01 + j0.02 = 0.02236\angle 63.43^\circ\ \Omega \\
Z_B &= 0.02 + j0.04 = 0.04472\angle 63.43^\circ\ \Omega \\
Z_A + Z_B &= 0.03 + j0.06 = 0.06708\angle 63.43^\circ\ \Omega
\end{aligned}
$$
Since the angles are equal, the ratios are real numbers:
$$
\begin{aligned}
\frac{Z_B}{Z_A+Z_B} &= \frac{0.04472}{0.06708} = \frac{2}{3}, \qquad \frac{Z_A}{Z_A+Z_B} = \frac{1}{3} \\
S_A &= 60 \times \tfrac{2}{3} = 40\ \text{kVA}, \qquad S_B = 60 \times \tfrac{1}{3} = 20\ \text{kVA}
\end{aligned}
$$
Both share the load at the same power factor as the load.

#### (i) Individual transformer currents
Total load current on the 220 V side:
$$
I = \frac{60000}{220} = 272.73\ \text{A}
$$
$$
\begin{aligned}
I_A &= \frac{40000}{220} = 181.82\ \text{A} \quad (\text{primary: } 40000/4400 = 9.09\ \text{A}) \\
I_B &= \frac{20000}{220} = 90.91\ \text{A} \quad (\text{primary: } 20000/4400 = 4.55\ \text{A})
\end{aligned}
$$
Check: $181.82 + 90.91 = 272.73$ A.

#### (ii) Percentage of rated capacity used
$$
\begin{aligned}
\text{Transformer A} &: \frac{40}{50} \times 100 = 80\% \\
\text{Transformer B} &: \frac{20}{25} \times 100 = 80\%
\end{aligned}
$$

Both are loaded to the same fraction of their rating because the 25 kVA unit has exactly twice the ohmic impedance of the 50 kVA unit, i.e. both have the **same per-unit impedance**:

| Quantity | 50 kVA (A) | 25 kVA (B) |
|---|---|---|
| Impedance | 0.0224 Ω | 0.0447 Ω |
| Load shared | 40 kVA | 20 kVA |
| Secondary current | 181.82 A | 90.91 A |
| Loading | 80% | 80% |

**Answer:** $I_A = 181.82$ A, $I_B = 90.91$ A (LV side); each transformer runs at **80%** of its rated capacity.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. How do two transformers with equal voltage ratio share a load?
   A. In proportion to their impedances
   B. Equally
   C. In inverse proportion to their equivalent impedances
   D. In proportion to their resistances only
   Answer: C. Both have the same impedance drop, so I_A Z_A = I_B Z_B and current is inversely proportional to Z. (Key point: Load sharing rule)

2. Why is the load pf not needed in this problem?
   A. Because kVA is conserved
   B. Power factor is always unity
   C. Because the transformers have equal ratings
   D. Both impedances have the same angle (63.43 deg), so sharing ratios are real
   Answer: D. Equal X/R ratio means the ratios Z_B/(Z_A+Z_B) are real, and kVA shares do not depend on pf. (Key point: Why power factor is not needed)

3. What are the loads on the 50 kVA and 25 kVA units for a 60 kVA load?
   A. 30 kVA and 30 kVA
   B. 40 kVA and 20 kVA
   C. 20 kVA and 40 kVA
   D. 50 kVA and 10 kVA
   Answer: B. Z_B is twice Z_A, so A takes 2/3 (40 kVA) and B takes 1/3 (20 kVA). (Key point: kVA shares)

4. What percent of rated capacity does each transformer carry?
   A. 80% each, because both have equal per-unit impedance
   B. 100% for A, 40% for B
   C. 66.7% each
   D. 80% for A, 100% for B
   Answer: A. 40/50 = 80% and 20/25 = 80%; same per-unit impedance gives the same fractional loading. (Key point: Percent loading)

## Related in Electrical Machines I

- [Equivalent impedance and copper loss of 50 kVA transformer](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3A50kva-4400-220-equivalent-copper-loss) — Electrical Machines I, chapter 2
- [Parallel transformers and per-unit impedance load sharing](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Aparallel-operation-per-unit-impedance) — Electrical Machines I, chapter 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
- [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
- [Efficiency of 25 kVA transformer at half load and overload](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3A25kva-2200-220-efficiency-half-overload) — 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×

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