Hi,
an inverter is usually controlled with a PWM. This PWM is defined by frequency and duty cycle range.
None of them we do know. This makes it impossible to give detailed informations.
And a sine inverter usually involves an inductance at the output. Combined with the DC bus voltage ... this inductance determines the rise rate of the current I.
Again: missing inductance value makes it impossible to give detailed help.
Now YOU have inductance, dc bus voltage and frequency and duty cycle you can calculate the ripple current.
The ripple current of the capacitor you ask for.
Usually the frequency is too high for the battery to give useful capacitance to support the ripple current, thus all the ripple current is considered to be fed by the DC bus capacitor.
Now with the values of DC bus voltage, ripple frequency, ripple current ... you may dicede which ripple voltage you allow. And with all these informations you use the capacitor selection guide to find a suitable one. Often you may use several equally sized capacitors in parallel. Additionally - due to the lack of high frequency response of the electrolytics capacitors - you may add ceramics or floil capacitors to get rid of high frequency transients (EMI).
Btw: all the given informations you will find in almost every good SMPS / inverter application note.
Klaus