Inductive load keep the triac on.

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@Damien Which part of it do you want ? I have enclosed it in a box if you have any questions please ask me and I'll let you know.

What are the nameplate ratings of the compressor? It's a large central air conditioning unit that sits outside on a concrete slab?

I have updated the question with a picture of specifications of the AC unit. Yes it is a split AC unit.

Yes It is; I have checked the cables that are going from the indoor unit to the outdoor unit (compressor) there are two wires and whenever the AC is turned on and it wants to cool it turns the compressor on by simply connecting the two wires to mains in the indoor unit (I think the contactor is in the indoor unit) , so I connected it in the middle.

I also have another bigger AC unit which instead of connecting / disconnecting the Compressor to mains directly it has two signal wires that go from the inside unit to the outside and It turns a contactor on inside the outdoor unit.

@user289266 is probably right. Triacs are not good choice for motor loads. Triacs will 'reset' when the current they are passing goes to zero. This happens 2x per cycle (120 x per second) with a resistive load such as a light bulb. But with a motor, even when the AC voltage goes to zero, the spinning motor acts as a GENERATOR and pushes current even at your 'zero crossing' point. So the triac can never turn off, as the current never goes to zero in sync with the voltage.

BTW, are you sure you can DO a 'soft start' on this???? AC motors spin at a speed determined by the input frequency (60Hz). Also, when a motor first kicks on, it's basically a 'short circuit'. That's why the lights in your kitchen dim momentarily when your refrigerator compressor starts. That surge of current is probably too much for the Triac to handle.

@KyleB What would you suggest to use instead of a TRIAC ? It worked fine on my air compressor; The TRIAC is used to 'soften' the 'short circuit' of the motor when it starts, also it spreads the load over a longer time.

@KyleB I'm uploading a scope view of the air compressor current so you can see the effect.

Does your air-compressor have a capacitor??? That messes with the voltage/current phase relationship. i.e. if your air compressor DOESN"T have one, you may be tricking yourself. The air compressor is also a much smaller motor, so it won't be driving current quite like the AC unit. Maybe use a bigger triac, something grossly overrated for your purpose so it survives the momentary short??? Maybe forget the whole circuit and use an NTC resistor??? i.e. eepower.com/resistor-guide/resistor-types/ntc-thermistor

@KyleB I was going to use an NTC resistor with a relay and a simple RC timer circuit but I couldn't find a big enough NTC. As you can see on the scope, there is no 'short circuit' current on the soft starter TRIAC. and it is actually already grossly overrated for the 13 amp AC unit.

@KyleB Yes the compressor also has a big capacitor; most AC motors have them. My problem is that I don't know what is destroying the TRIAC; It doesn't matter that compressor is smaller, whatever that is destroying the TRIAC should still be present in the scope but perhaps in a smaller amplitude yet I cannot find anything.

Instead of an NTC, switch in/out a power resistor to soft start the circuit.

@ErikR The problem with that idea is that it requires a huge resistor. For example to get around %50 less amps by having 11 ohm resistor passing around 7 amps through it would be 539W of power loss for couple seconds!

@Oli, your code has a number of defects. You do not need to disable interrupts in an isr on an AVR as the already does this. Do not use |= on TIFR, just use = to clear a flag. It is much simpler to use a diac, resistor and capacitor for a triac soft start circuit. You may be exceeding the triac’s I2T rating, an inductor would help here. You probably need a snubber as well to clamp any high voltage spikes. The triac will also need to be heatsinked. A dual thyristor may be required at this current level rather than the triac. This should have a much better I2T rating.

@Kartman, Thanks for the recommendations on the code I wasn't sure if Arduino had changed anything or not and wanted to be sure. I did end up adding a crude snubber on to it with R = 100, C = 300 nf but I don't think that is the problem since I cannot see any voltage spikes on the scope with the air compressor also, I don't think I'm exceeding the TRIACs specs since I cannot see anything on the scope. I measured both the AC and air compressors resistances and they where both around 6.5 ohm. maybe there's something else that is happing with the AC and not with the air compressor but I doubt it.

Where is the Start Cap in your compressor? Does it correct the lower factor? Compare voltage and current phase for pf.

@TonyStewartEE75, The cap is in parallel with the air compressor motor, I think it should be the same with the AC unit because I think they are there to improve the PF of the motors. I will have a look at the voltage and current phase on the scope and update the post.