The maximum load that a power transformer can carry is limited by its

he maximum load that a power transformer can carry is limited by its thermal capacity. The key factors that determine a transformer's thermal capacity and therefore its maximum load are:

Winding temperature rise: Transformers have a maximum allowable winding temperature above the ambient temperature, typically around 65°C. Exceeding this temperature can degrade the insulation and shorten the transformer's lifespan.
Core temperature rise: The transformer core also has a maximum allowable temperature rise, usually around 55°C above ambient. Excessive core heating can lead to increased core losses and reduced efficiency.
Oil temperature rise: The temperature of the transformer oil, which acts as a coolant, is also limited to prevent degradation of the oil and other insulating materials.
Cooling capacity: The transformer's cooling system, whether natural air cooling or forced oil/air circulation, must be able to dissipate the heat generated at the maximum load without exceeding the temperature limits.
The transformer is typically designed with a safety margin below these thermal limits to account for variations in load, ambient conditions, and aging effects over the lifetime of the transformer. Exceeding the maximum load can therefore lead to overheating and potential failure of the transformer.