Need Help: Power percentage calculation in phase firing angle

[Don_dody]

Let say we have firing delay for 5 ms after zero crossing point as shown by the picture below. (220V 50Hz)

That means the firing angle is 90 degree right?

My problem now is, by knowing the firing delay (5 ms) and the firing angle (90) how do I calculate the percentage of power that is delivered to the load?
Is there any specific formula for my question?

 

[mtwieg]

Assuming a resistive load, you just need to calculate the RMS value of the phase chopped waveform. It should be equal to Vrms_load=Vrms_source*√[θ/(2π)-sin(2θ)/(4π)], where θ is the phase conduction angle ranging from 0 to π. For a non-resistive load, the expression is much more complicated.

 

[Don_dody]

yes resistive load.

is there any links or sources that give more explanation?

Thank you.

 

[mtwieg]

I just derived that equation by hand using some calculus. There's really nothing else to it.