"Capacitor" for regulating AC line voltage?
You can choose to use a separate breaker and power distribution cable, but if the ACU draws excessive surge starting current and your Voltage line drops more than 10% , all you can do is use regulated LED lighting to reduce the effects.

Capacitors perform the job of stabilizing voltage and providing the necessary jolt ( combined with higher current ) to start the motor in the first place. In an air conditioner, capacitors are connected to the  compressor motor for start and run operation.

Your residence wiring or ACU load  is sub-standard during startup and this may be outside your control.

ACU compressors often draw 300% to 500% of rated power during startup.  Check the start-cap for failure.  Ref



Essentially the Start Cap must be very big to act as a Power Factor (pf) Correction to the low inductance starter winding and thus reduce the reactive load current on the line causing voltage sag during startup. It must be rated for large ripple current and high voltage.  It reduces the line current loss thus raising the voltage to improve start times to normal and reduce light dimming effects.  In other words, the motor startup has higher reactive current which is partly supplied by the negative reactance of the caps. Ideally all of it, but this may be costly and very bulky.

I do not know the exact pf criteria they choose for residential start motor caps but the intent is to reduce the surge ratio above rated load current.


Anyone?


But I found this