Cooling system for a transformer and a method of cooling a transformer

An electrical generation system comprising:

• a heat exchanger;
• a pump fluidically connected to the heat exchanger;
• a generator including a cooling circuit fluidically connected to the pump;
• and
• a transformer electrically connected to the generator and fluidically connected to the pump, the transformer comprising:
• a housing having a base wall, a first side wall, a second side opposing wall, a third side wall extending between and joining the first side wall and the second side wall at a first end, and a fourth side wall extending between and joining the first side wall and the second side wall at a second end, the first, second, third, and fourth side walls collectively defining an interior portion;
• a cover extending across each of the first side wall the second side wall, the third side wall, and the fourth side wall;
• and
• a cooling system including a first cooling channel disposed in the third side wall, a second cooling channel disposed in the fourth side wall, and a third cooling channel disposed in the cover, the third cooling channel being directly fluidically connected to at least one of the first cooling channel and the second cooling channel.