The Overloaded Distribution Transformer
A 500 kVA, 11 kV/400 V distribution transformer serves a mixed residential and small-commercial feeder. During a summer evening peak, the substation operator records a line current of 780 A on the low-voltage side while the voltage at the far end of the feeder falls to 372 V. The transformer's nameplate impedance is 4.5%, and its loading has been climbing for three consecutive evenings. No protective relay has tripped. A consumer complaint about dim lights and a humming refrigerator has reached the subdivision office. The operator must decide whether to shed load, shift load to an adjacent 315 kVA transformer through a normally open tie switch, or simply log the event and wait. Ambient temperature is 38 degrees C, and the transformer is oil-immersed with natural cooling.
1. Using the recorded current and nameplate data, assess whether the transformer is overloaded and explain the reasoning. State any assumptions.
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First compute the rated low-voltage line current. For a three-phase transformer, I_rated = S / (sqrt(3) x V) = 500,000 / (1.732 x 400) = 721.7 A. The measured 780 A is therefore about 108% of rated current, so the transformer is overloaded by roughly 8% on a current basis.
A common mistake is to compare 780 A against the 500 kVA figure directly without converting units. Doing the conversion shows the margin is small but real, and at 38 degrees C ambient the natural-cooling capacity is further reduced because the nameplate rating assumes a standard ambient (often 40 degrees C but with defined temperature-rise limits). The impedance of 4.5% tells us the short-circuit behaviour, not the loading, so it should not be used to judge overload.
The answer should state assumptions: balanced three-phase load, unity or near-unity power factor for current-based comparison, and that the 400 V is nominal rather than measured. Because voltage at the far end has dropped to 372 V (about 7% below nominal), part of the current may be reactive or the feeder drop is significant. The judgement is that the transformer is modestly overloaded and that voltage quality is already unacceptable, so logging and waiting is not defensible.
2. Recommend an operational action and justify it against the alternatives.
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The recommended action is to transfer part of the load through the normally open tie to the adjacent 315 kVA transformer, provided a parallel or short outage transfer is feasible and the receiving transformer has spare capacity. The receiving unit at 315 kVA can absorb roughly 150-200 kVA of load if it is lightly loaded, which would bring the 500 kVA unit back under rating.
Load shedding should be the fallback, not the first step, because it inconveniences consumers and does not fix the underlying imbalance. Waiting is unacceptable: voltage at 372 V is about 7% low, which stresses motors and refrigeration equipment, and the overload is occurring during the hottest part of the day when cooling is least effective. Sustained overload accelerates insulation ageing and shortens transformer life.
The reasoning should weigh: (a) safety and equipment life, (b) continuity of supply, (c) feasibility of the tie transfer including phase rotation and protection coordination, and (d) documentation. A good answer also notes that the tie switch must be operated under the utility's switching procedure with proper authorization, and that the event should be logged for planning purposes so a permanent capacity upgrade is scheduled.