Oil-filled transformers can be cooled in three ways:
- ONAN: Oil Natural, Air Natural. The transformer is filled with oil, which circulates naturally by the "thermosiphon" effect. Air circulates naturally, by convection, over the tank and cooling fins.
- ONAF: Oil Natural, Air Forced. The transformer oil circulates naturally, and a fan is provided to blow air over the radiator fins. The fan is controlled by a thermostat, and the fan turns on when the oil/winding temperature rises above some threshold, probably around 70C. This typically extends the transformer's thermal capacity about 20%.
- ODAF: Oil Driven, Air Forced. The transformer oil is circulated by a pump - again, controlled by a thermostat. A radiator fan is also provided, again, controlled by a thermostat.
(The codes ONAN, ONAF, ODAF have standard meanings given in IEC / AS 60076.2.)
Small transformers, such as those found on pole-tops and in kiosk substations, tend to be ONAN. The transformer has no active cooling equipment, which means there's no fans or pumps to maintain out in the field.
Medium transformers in the 1 MVA - 20 MVA range tend to have cooling fans. A typical rating is 10/12.5 MVA, ONAN/ONAF - you get an extra 2.5 MVA capacity if the fans are turned on. The extra maintenance is no problem, because these are located at substations, which are convenient to work at.
Larger transformers in the 25 MVA+ range tend to have both fans and oil pumps. A typical rating is 36/48/60 MVA ONAN/ONAF/ODAF - you get an extra 12 MVA capacity if the fans are turned on (ONAF), and an additional 12 MVA if both the fans and oil pumps are on (ODAF).
The reason for the difference in weight is at least partly due to the extra weight of the fans and pumps themselves.
I'd also hazard a guess that the iron cores have to be bigger to handle the increased magnetic flux required to transfer the additional MVA's of power. The size of the iron core is dictated by the required power capacity, not cooling considerations.