How to calculate triac angle to set desired RMS voltage

[Urrys]

Hi,

I would like to implement voltage regulator based on microcontroller + triac.
I am able to calculate source RMS voltage by sampling signal using ADC, but don't know how to calculate triac angle to set desired RMS voltage.
For example i have 250v source RMS voltage and i need to calculate triac angle to set output RMS 100v. Desired voltage might be any thirefore i need some formula to make possible recalculate triac angle in runtime.

I have found formula to calculate RMS by using triac angle:
https://www.physicsforums.com/threa...e-from-triac-phase-angle.572668/#post-3737599

But i need to calculate angle by using desired RMS output voltage. The problem that i can not to deduce angle from this formula - angle in sinus argument and also it is outside sinus.

Could you help to make a formula to calculate triac angle by using desired RMS voltage?
Or probably some other method is better to calculate triac angle ?

 

[berkeman]

Welcome to the PF.

What are you going to be driving with this chopped-up waveform? An incandescent light bulb? What is the application?

 

[Svein]

https://www.physicsforums.com/threads/how-to-calculate-rms-voltage-from-triac-phase-angle.572668/

 

[Urrys]

Welcome to the PF.

What are you going to be driving with this chopped-up waveform? An incandescent light bulb? What is the application?

I want to create regulator to make possible set light bulb lighting level in percentage (or in voltage).
E.g. Set 30% of lighting, controller should calculate angle and set correct delay to open triac.

 

[anorlunda]

I want to create regulator to make possible set light bulb lighting level in percentage (or in voltage).
E.g. Set 30% of lighting, controller should calculate angle and set correct delay to open triac.

Light bulb voltage, power, and luminosity are not necessarily linearly related, so 30% of what?

Light dimmer circuits are common, but it is unusual to require advance calibration like this.

 

[Urrys]

Light bulb voltage, power, and luminosity are not necessarily linearly related, so 30% of what?

30% of source voltage.
Original question was to find out triac angle.

 

[anorlunda]

Using the equation linked in #3, I put the following into Wolfram Alpha "solve 0.3=sqrt((2pi-2X+sin(2X))/4pi) for x" and it gives me about 2.7 radians for X. X is triac angle.

 

[berkeman]

Set 30% of lighting,

As @anorlunda says, 30% of Vrms input does not necessarily mean 30% brightness for the lighting. First of all, is this incandescent or LED or CF or some other type of lighting? Some types of lights are not compatible with triac dimming.

Second, the best way to do this is just to use a simple triac dimmer and measure the fire angles that give you the % brightness that you want. Then make a table with those numbers to put into your control microcontroller (uC). You could make the table have 10% increments, and use the uC to interpolate between those entries for the other % settings, for example.

 

[Urrys]

Creating table this is one of the way. But still I am interested to find formula which can be used to calculate angle, just to find common solution which can be applicable not only for light bulb.

 

[berkeman]

Did you read the thread linked to by @Svein in post #3?

 

[Urrys]

Did you read the thread linked to by @Svein in post #3?

Yes i already mentioned this thread in my first post. There is formula to calculate RMS by using triac angle. But i need to deduce triac angle from this formula. It looks like impossible or hard to simplify this formula to make it like TriacAngle= ...

 

[berkeman]

Yes i already mentioned this thread in my first post.

Oops, sorry, I missed that.

It looks like you can rearrange that equation into a form similar to x + sin(x) = <a number>

If so, then there are ways to visualize the solution and also solve for it. See for example this:

http://mathcentral.uregina.ca/QQ/database/QQ.09.99/grover1.html

Others with more math background can probably be of more help.