Capacitor Bank-Can I install one on the 220v side?

I'm sure you are aware that the 220v side of the inverter is AC, and that capacitors cannot store AC power.  AC-rated capacitors are simply non-polarized caps that are designed to handle a constant high level of ripple current (due to the AC use).  Inverters use relatively small capacitors on the AC output of the inverter for the purpose of filtering out any SPWM hash/noise.

Adding more AC caps to the output side of the inverter will increase your no-load current due to the additional power required to charge up the caps every half wave (they get discharged back into the transformer on the falling edge of each wave).

Will it help?  I don't know.

Probably the much bigger problem is your inverter, which I am assuming from the forum topic, is a U-Power "15kw" inverter.  Let me explain:

Power Jack inverters are labeled at anywhere from 2-3x their actual capability.  An 8kw inverter probably will overheat at 2kw.  9kw inverter will overheat around 3kw.

U-Power takes an EXACT IDENTICAL PJ inverter, and doubles the PJ rating on top of that.  So a "15kw U-Power" is an "8kw PJ" with a fancy label...and the PJ is really a 2kw inverter when you get all the way down to real numbers.  In short: the labels, specifications and all the rest of that fun stuff--is purely and simply made-up nonsense that has absolutely no possibility of being actually met by what's inside the box.

With that in mind, that the inverter is able to run your motor some of the time is quite an accomplishment.  Unless my guesses are all incorrect, and you have something other than a U-Power inverter?

Thanks Sid for your reply and yes it is a U-Power inverter. I have just put a load test on it for 60 seconds of  6,344 watts. I put  1 -7 1/4" circular Skilsaw, 1- 6" bench grinder,2-1500w electric heaters,1-1200w heat gun,1-1500w hair dryer. That is about 53 Amps. I started to smell a hot inverter so I stopped the test. Inverter is still working OK and running. The fan did not stay ON very long after I removed the load,maybe 2 minutes.
What do you suggest I  should do to run an large 220v AC and start and run a 15 A air compressor? I believe it will run one at a time with no problems but not both at once.   Thanks again Sid for you input and suggestions.

Being a "15kw U-Power" (which I had one here on my bench once...gotta love that ~12AWG internal AC output wire), consider yourself fortunate to be able to run any large load.  The inverters simply aren't designed for the power amount emblazoned on the label.  Even if the FETs can handle a portion of that power, the transformer itself simply isn't wound for it--due to voltage drop losses, it may be impossible to get 15kw through the transformer alone.  With 12AWG output wires.  There are only (2) 6AWG wires going from the positive battery binding post to the FETs...and (4) 8AWG wires going from the negative battery binding post to the FETs.  You might have pairs of 4/0 wire going to the posts, but it doesn't mean a hill of beans to the internals.

If you're running 24v, that only makes the losses even worse. 

With their logic, I could make a 136,500W inverter simply by printing a label and plastering it on a device...and make up a completely fake spec sheet to go with it as well.  You're probably aware of the "9,900mAH Li-Ion 18650 cells" on eBay...which will do 900mAh if you're lucky. 

What can you do to improve this inverter?  Pretty much nothing.

In other words buy a different inverter, have you got any suggestion or a different 24 volt inverter that you sell?

I mean, as long as you stay away from the "bargain basement Chinese" names, you'll probably get pretty close to what is advertised.  We at Genetry Solar have a 6kw inverter...which mind you has a considerably bigger transformer than this U-Power "15kw" inverter.  It will run 6kw out all day long, with an estimated (but not tested) 200% surge capability.  Can start pretty much any load we've thrown at it...such as starting a 12,000btu air conditioner when already running near the full rated load.

TBH we haven't run heavy load testing at 24v though (lack of high amperage 24v power!)...but the transformer resistance is considerably lower, so it should do alright.

How much $ for your 6kw inverter?  Do you have a 10K or larger that is the same quality that will run at a consistent 8kw all day with no problems?  As you know I have 52-6 volt batteries that gives me 2,600AH's.  I am willing to switch over to 48 volt inverter if that will make it easier. Again thanks Sid for all your help.

Right at $1k for the 6kw inverter, which will run 6kw continuous all day (at ambient temps below 100F).  Of course, higher battery voltage will make it easier (reduced amperage and much more voltage for regulation headroom).  At the time of this post, we have some in stock: https://www.genetrysolar.com/gs-inverters/genetry-solar-3000-watt-inverter-b4w3h (EDIT: I know the link says 3000-watt, but it goes to the 6kw page...gotta love SquareSpace.  Actually don't have any 3kw inverters in stock right now anyhow.) 

We have a 12kw inverter planned, but that is awaiting a complete redesign of the PJ-designed mainboard...after we get all the kinks worked out of the design, we will order and get those ready for sale as well.  Currently no ETA unfortunately.

The price is OK, no problem there but I need more kw so I can run a large AC 24/7 this summer, a 220v water pump when pressure drops,TV,desk top PC with monitor and speaker 2 freezers,1 refrigerator,  a 220v  2hp air compressor in my auto repair shop plus other small items like bench grinder,electric sander,lights etc. I have the AH needed at 24 volt and solar panels to keep them charged. I also have 2 large 24 volt forklift battery charger that put out 150+ amps each and 2 backup diesel generators.  All I need is a large kw inverter, I think I will wait for your 12kw if nothing else comes along. So in the mean time I will have to run a limited amount of items at a time to make sure I am not overloading the inverter.  Thanks again for your help Sid I now know where I am and what is needed to get the job done. 

If you're subscribed to the YT Genetry Solar channel, you should see updates on the 12kw project there.  I need to get a couple pressing things taken care of first, then I'll be ordering test prototype boards for the 12kw to see if we can squash the FET drive issues on that project.  Once that's done, it'll be time to order a production run of 12kw inverters and be off to the races.

24v is the lowest current we will consider supporting for the 12kw...that's approximately 600A with an overly cautious efficiency estimate.  May or may not be possible...but 36v (400A), 48v (300A) and 60v (240A) should be quite doable.

You can try what is called a "hard start kit" on most capacitor-start motors. It is just a bigger start capacitor. 

Hi, InPhase, I have a 1  1/2HP 220V motor on an air compressor that is having a hard time starting some times even with 0 PSI in tank. It starts with no problems with ON grid power supply so the motor is good and runs perfect then.  It has a 125V   710-845 MFD start cap.  What size do you suggest I try and I am not worried about damaging the motor, I have others I can put on?   Thanks for anyone's feed back.

I have found some hard start kits and will probably purchase one and install it on the compressor.  Thanks for your suggestion.