Voltage Drop On Transformer When A/C Turns On

Depending upon the age, type, and efficiency of your A/C, it draws 12 to 20 Amps while running, unfortunately it can draw up to 10 times that when it starts. It's a highly inductive load during this period and it is overloading your transformer such that the A/C only receives half the required voltage. The result is that the compressor trips on its internal thermal overload faster than the breaker can trip.

You might be able to get around this problem by getting a "low-voltage starting kit" from the manufacturer, otherwise you're going to need a bigger transformer, but that will then transfer the problem to the 30A circuit feeding it since 20 Amps on the 220V side requires 40 Amps on the 120 V side.

Sounds like your start/run capacitor has failed and unit is drawing LRA and going off on overload.....The A/C unit may have additional problems that have caused undue stress on the compressor, such as low freon, failing fan motor etc....How old is the A/C unit?

You need an ammeter to check the amp draw of the compressor....on start-up the compressor should momentarily spike to near FLA(full load amps) and settle near RLA(running load amps), on a 2 ton LRA should be around 80-90 amps and RLA should be around 10-12 amps...this should be marked on the compressor tag...On start-up if the compressor will not start, and the wiring is intact, it will draw FLA for 3-5 seconds before going off on overload, this is an internal protective device...If this is the case then you should check any capacitors with a capacitor tester....If the capacitor tests good, then the compressor is seized and must be replaced....Another possibility is that one of the wires has burnt off the start winding of the compressor, so you should pull the cover off the compressor terminal, with power off of course, and inspect the connections for any damage....

The S(start) R(run) C(common) positions will be marked possibly on the cover or at the terminals....

Does the voltage on the primary of the transformer change during attempted startup?

Change of conductor size downwards cannot take place without introducing a further protection device at the node where the change takes place, according to BS7671, so as to protect the downstream cable. Otherwise, as smaller cables have a larger resistance-per-unit-length, such features can constitute bottlenecks to power flow in inadequately-protected systems; they are things of great interest to fire insurance investigators and, particularly, to Loss Adjusters given an incidental loss involving a less-than-standard installation.

It sounds as though the whole installation requires re-assessment and re-design. As it cannot be seen from here, consulting a qualified local Electrician is the best way forwards. The act of making sure this individual's out-coming documentation is complete and correctly filed will ensure maintenance of popularity with the building's fire insurance company.

The first problem I see is you are trying to run a 24 KBTU 240 VAC powered A/C unit off of a stepped up 120 VAC power source so whatever the units running amp rating is needs to be multiplied by 2 plus the transformers losses added in as well which in my books would put its likely 120 volt input circuit current at 20+ amps with a likely 100+ on start up which would be way beyond the working capacity of your present 6 mm wire unless its a very short run for the main power source in your house.

If the unit came with 4 mm wire for its power cord that would imply it draws a pretty high startup current and likely has a fair running current as well.

The fact you have it on a 30 amp breaker and despite the apparent large voltage drop at the units input it doesn't trip in the first few seconds suggests you have a substantial amount of line resistance in play.

If it was me I would switch the 30 amp 120 volt line over to a double fed 20 amp 240 volt circuit at the main breaker panel and run the A/C unit with the proper supply power and eliminate the transformer all together being that's what the unit was designed to work with.