Parallel transformers with unequal impedance and a tap mismatch
An 11 kV/433 V industrial substation has two Dyn11 transformers operating in parallel on the same LV bus: T1 is 1000 kVA with 5.0% impedance and T2 is 750 kVA with 6.0% impedance. The site load is 1600 kVA at 0.9 power factor. Both transformers are on the same off-load tap, but to raise the far-end voltage an operator has moved T2 to the -2.5% tap while T1 remains on nominal. The LV bus voltage is 433 V. T1 current is close to its rating and T2 is lightly loaded; the transformers are noticeably warmer than at the same load last week. The protection is a single LV breaker per transformer with no circulating-current relay. The operator wants to increase the load to 1800 kVA because T2 still has spare capacity.
1. Ignoring the tap mismatch, calculate the approximate load sharing at 1600 kVA and determine whether either transformer is overloaded. What is the maximum total load that can be supplied without overloading either unit?
Read the worked answer
For parallel transformers of the same voltage ratio, load sharing is proportional to rated kVA divided by per-unit impedance. Use the loading factors:
- T1: 1000/5 = 200
- T2: 750/6 = 125
- Total = 325
At 1600 kVA:
- S1 = 1600 × 200/325 = 984.6 kVA, or 98.5% of 1000 kVA
- S2 = 1600 × 125/325 = 615.4 kVA, or 82.1% of 750 kVA
Neither unit is overloaded, but T1 is almost full while T2 has apparent spare capacity. That spare capacity is not freely available because the 6% impedance of T2 makes it take less load. The maximum total load without overloading either unit is set by T1 reaching 1000 kVA:
Smax = 1000 × 325/200 = 1625 kVA.
At 1800 kVA, T1 would be about 1108 kVA (110.8%) and T2 about 692 kVA (92.3%). The proposed 1800 kVA is therefore not acceptable on impedance grounds alone, even before the tap problem is considered.
2. Explain the effect of the -2.5% tap on T2. Estimate the no-load circulating current between the transformers at 433 V, given the impedance values, and state why the transformers are warmer.
Read the worked answer
The -2.5% tap reduces the turns ratio of T2, so its secondary open-circuit voltage is about 2.5% above T1: ΔV ≈ 0.025 × 433 ≈ 10.8 V. That voltage difference drives a circulating current through the two transformer impedances even with no site load.
Refer the impedances to the LV side:
- Z1 = 0.05 × 433²/1,000,000 = 0.0094 Ω
- Z2 = 0.06 × 433²/750,000 = 0.0150 Ω
- Sum ≈ 0.0244 Ω
Circulating current ≈ 10.8/0.0244 ≈ 443 A. T1 rated LV current is about 1333 A and T2 about 1000 A, so this is roughly 33% of T1 rating and 44% of T2 rating. The actual value depends on impedance angles and the exact tap step, but the order of magnitude is hundreds of amps. This current adds to one machine and subtracts from the other, produces extra copper and stray losses, and heats both transformers without contributing to useful load. It also distorts the apparent load sharing, so T2 having nameplate spare capacity does not mean it can be loaded to 750 kVA while the taps are mismatched.
3. What operating limit and corrective actions would you recommend before supplying 1800 kVA?
Read the worked answer
First, do not treat 1800 kVA as available. Take both transformers off load, set identical taps, confirm phase sequence and voltage, then re-energise and measure circulating current with a clamp meter or relay record. With matched taps, the impedance-based limit remains about 1625 kVA; 1800 kVA exceeds T1 rating. Operate at or below 1600 kVA until additional capacity is provided, and check ambient temperature and cooling because the units are already warmer than normal.
Corrective actions: match the taps, ideally with a master-follower OLTC scheme if automatic voltage control is needed; add a circulating-current relay or at least a regular clamp check; and rebalance the LV load. To reach 1800 kVA, add transformer capacity, split the bus into two sections, or replace T2 with a unit whose impedance matches T1 more closely. Increasing the LV breaker setting is not a solution - it removes protection without increasing transformer capacity.