We first need to know how to relate the firing delay with firing angle. We know that one complete sine wave is 360°. That is 2πradians. We then need to know that the firing angle α = ωt, where ω = 2πf. Since, we’re working with 50Hz here, f=50Hz. Thus, ω = 100π. Just to test this relationship, let’s use t = 0.020 seconds (20ms). Thus α = 100π * 0.020 = 2π, as told before.
So, if we’re firing at a delay of 4ms, that is 4ms after the zero crossing, the firing angle α = 100 π * (4/1000) = 0.4 π (in radians obviously).
The RMS output voltage is found from the relationship:
So, if we are firing after 4ms, (α = 0.4 π), the output RMS voltage is:
Remember, at the beginning, I mentioned that the voltage output is not linearly correlated with the firing angle? This is what I meant. Here, the delay is 4ms. So, the triac is on for 60% of the cycle. But the output RMS voltage is 183.2V – 83% of the input voltage. The lack of direct proportionality is evident here. The reason behind this is the shape of the AC – sinusoidal.
Now, I give you the task of finding the RMS voltage for the other cases mentioned in this tutorial.
If you want to then find power, you can use the relationship P = V2/R to find the power. The assumption here is that the resistance is constant, as was assumed at the beginning of the tutorial. If the resistance is not constant, power will still vary will resistance, just not directly proportionally.
Here in this article, I’ve talked about phase angle control with some background information on triacs. I’ve shown how to implement phase angle control with a PIC and also how to calculate the RMS voltage of the output. I hope I’ve been able to explain this extremely important topic to you clearly and hope that you can now successfully build your own power control circuits using phase angle control with triacs.
Reference Book:
One of the best books for understanding the theory behind phase angle control is “POWER ELECTRONICS – CIRCUITS, DEVICES AND APPLICATIONS” by Muhammad H. Rashid. If you want to learn more about thyristors or phase angle control, I recommend reading this book for more info.
Original article by Tahmid at his blog.
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