# Does low frequency PWM create reactive power in a transformer?

I got a 350VA transformer (230V~/24V~) which is directly connected to a heating unit at it's 24 V ends. The 230V end of the transformer are connected to 230 V~ mains over a solid state relay (SSR).

The scenario is that a controller triggers the SSR to switch through, the heating unit heats up to the target temperature and then a controller with a temperature sensor sends a 5 Hz pulse width modulation (PWM) signal to the SSR to keep the heating unit at a constant temperature.

The heating unit has a impedance of 1.0 Ω, the transformer 0.3 Ω (idle). The PWM frequency is as low as 5Hz and the solid state relay has a response time of 10ms (using zero-crossing, still 20 times faster than the PWM). I measured the actual voltage on the transformer with a RMS multimeter and measured 20 V (idle)

From what I understand the expected current would be

I = U / R = 20 V / (1.0 + 0.3 Ω) = 15.4 A

and the power user would be

P = U * I = 15.4 A * 20 V = 308 VA

That all worked well for a while, with a perfectly costant temperature on the heating unit, until the transformer started smoking and eventually failed.

Is there any reactive power generated in the transformer due to the PWM that actually causes a much larger current that the expected 15.4 A? What could I do to avoid this? Does it help if I put the SSR between the heating unit and the transformer instead of between mains and the transformer?

I need the PWM control since constant temperature is crucial in my application, the choice for AC power in combination with a SSR is simply because AC transformers are cheaper than DC power supplys in that range (15+ A).