Hi,
The transistions needs to be speedy however, so it has to be driven with eg. 3A..5A to overcome the input capacitance to get a low average dissipation.
You can get MOSFETs handling more than 100A.
The driver is the critical point here.
The MOSFET won't have to handle 1200W. That's the point of using PWM, the transistor is either completely ON, dissipating little power (R*I^2 eg. 0.002*27^2=1.5W), or completely OFF most of the time.You could use a 555 but never with 1 MOSFET. Will need some work to figure out what could handle 1200W and 27A + heavy gauge soldering.
The transistions needs to be speedy however, so it has to be driven with eg. 3A..5A to overcome the input capacitance to get a low average dissipation.
You can get MOSFETs handling more than 100A.
The driver is the critical point here.