DC Link capacitor current rating for three phase inverter

For ac drives or three phase inverter, the DC link capacitor calculations can be done based on the ripple voltage for Dc link voltage say 3% or 5% from the energy calculation i.e. 0.5*C*V*V =E.
But how to find the rms current rating for my case 4kw around 9A load current.
I cant put 9 A ripple current or full load current required as capacitor ripple current.


Thanks,
Mukehs

with DC link caps, you usually rate the cap for the rms ripple current, and the ripple voltage you get from that usually always puts you within ripple spec.
But anyway, you need the actual waveform of the current being drawn by the three phase inverter. Then you assume that the entire AC content of that is being drawn from the dc link cap.
So you re-base that waveform so that it has zero DC.....and then you are looking at what is flowing in the dc link cap......so you then look at the amount of charge coming out Of the cap during a switching cycle and do dv = dQ/C......That gives the dv ripple based on the pure capacitance alone.....but then you have to do it again for the dv based on the ESR of the dc link cap........so thats just an I.R calculation...

then the overall voltage ripple that you get is

ripple voltage = sqrt(v1^2 + v2^2)

where v1 is from the first calc explain
v2 is from secong dv calc explained

Its kind of working backwards, but you do first need to have a cap that can withstand the rms ripple current.

Rather a lot depends on if we are talking single phase or three phase.

If either the input rectifier or load on the dc link capacitors is three phase, its a totally different situation to having a single phase rectifier link input, or single phase inverter load.

At your power level, a motor drive will almost certainly have a three phase power source, so ripple voltage and ripple current will be much less and at a higher frequency.

If the motor was not a nasty reactive load, you might even get away with having almost no dc link capacitance. The worst situation in a motor drive might be dynamic braking, where motor inertia tries to over speed the drive during slow down, and tries to drive up the link voltage.
So the link capacitors are there to stabilise the link voltage under transient motor conditions rather than filter out rectifier ripple current.

The situation is very complex and probably defies strict formal analysis.

Its probably (?) more a case of sizing capacitors from experience, and noting what other drive manufacturers have found to work reliably at similar power levels.

I have repaired a great many drives over the years, and am often surprised at how small the link capacitors are, considering the power levels involved.

I am glad this question came up, i have been wondering how the link capacitor was chosen myself. I suspected that because of it's cost, management had there fingers in there dictating price.

I need some good paper or derivations for ac ripple current rating required for DC link capacitor in terms of modulation index and power factor.Although i can get waveforms and decide based on matlab simulation.
As we know total Ilink^2 = Ilink_DC^2 + Ilink_AC^2.
Ilink_AC is the ripple current rating required for the DC link capacitor
In one paper i got the derivation as

Ilink_ac= √(∛3/π)*〖Il〗^2*Dp{1/2+1/3 cos⁡(2θ) }-9/4*〖Dp〗^2*〖Il〗^2*〖cos〗^2 (θ) (equation 2.18 in the attached paper)
Solving this equation for worst case analysis
Ilink_ac=0.5033Il (as equation 2.22 in the attached paper)
Here Il is my load current i.e inverter or motor current as i am calculating DC link sipple current rating for
Il is my load current i.e. inverter or motor current as I am calculating DC link ripple current rating for three phase induction motor drive.
Dp is the modulation index
So, based on this if for 5HP 400V three phase induction motor driven by three phase inverter my maximum rms current is 10A,so is that I can take approximately 5A or 6A as the ripple current rating of the capacitor at say 4kHz(my switching frequency).
Because in standard say ABB or siemens drives for 5HP/400V,three phase, I have seen capacitor ripple current rating as 3A or 2.5A, SO LOW,also they dont have DC link choke. I am wondering and get confused as how they are able to manage with such low rms ripple current for capacitor for such large current rating.

If someone can analyse this...

Thanks,
Mukesh