Could you please share steps to calculate effective power applied to a resistive load over time?

[abrilevskiy]

Could you please share steps to calculate effective power applied to a resistive load over time?
Since local power is 50Hz instead of 60 used in the code:

// Time table to set triacs (50us tick)
//   This is the number of ticks after zero crossing that we should wait before activating the
//   triac, where the array index is the applied power from 1 to 100, minus one. This array is
//   calculated based on the equation of the effective power applied to a resistive load over
//   time, assuming a 60HZ sinusoidal wave.

[alexsartin]

To get the desired and exact power timings we've integrated the AC sine wave over time as the power is the area under the sine wave.

You can read more about it here.

Since the wave frequency isn't really a factor for the power calculation, a more practical solution is to divide every value on the table to represent a 50Hz wave OR increase the triac timer tick.

To do the So divide the values by (50 / 60) = 0.083333333. The values will increase (which is correct because the 50 Hz wave is slower) so you will have to look for any impacts on the code.

Maybe a more elegant solution is increasing the 50us timer tick to 60us instead. Again you will have to look If this may impact the code functionality.

I'm not up to date with the code anymore (maybe there is even a define for that) but that's what I can say about the electrical part.

[abrilevskiy]

Thank you for comment, I also comes to integration, but gets stuck at next step since Integration provide RMS value of power over time and we need kind of reverse operation: find time ranges with equal power.

Required timings (let assume we are looking for 100 timings) are timings when Prms :

• timing 1: Prms / 100
• timing 2: 2 x Prms / 100
  ...
• timing 100: 100 x Prms / 100

[alexsartin]

Apply the inverse of cosine in the resulted function. That's the waveform you will see if you plot the uint8_t powerToTicks[] table. You will get the angle/phase THETA from the desired power percentage. Then you can convert it to time.