We have a piece of industrial equipment using a phase angle controller (PAC), and are having some issues calculating the RMS power used by the load.
Personally I am of the opinion that you measure RMS voltage and RMS current on the line side of the PAC. This gives you line RMS * PACed current. Assuming a duty cycle of 50%, this gives you 50% of full power. My reasoning is that this follows Kirchoff's law, and that power in is approximately equal to power out on our PAC (efficiency is >90%).
My colleague suggests that we measure the RMS voltage and RMS current on the load side, after the PAC. Assuming a duty cycle of 50%, this gives 50% current and 50% voltage and we end up measuring 25% of full power. His reasoning is that the load isn't conducting for the off section of the cycle, so the applied RMS voltage is lower.
The former gives us a linear ramp from 0 to 100% duty cycle, the latter gives a non-linear response. Assuming our power factor is 1, our mains supply and PAC signals are clean, and the RMS calculation is correct at the crest factors we're working at (it better be, I designed the sensor), which calculation is correct?