As I understand, it is difficult to regulate voltage in your case. In power systems which is interconnected, the synchronous generators regulate the voltage by changing its field current. However, your system is a kind of off-grid and induction machine (IM) by nature cannot regulate the voltage.

So, I see two solutions:

1) Use PV inverter which can regulate the voltage at the point of common coupling (PCC). You can look in literature as "Grid-forming inverter"

2) Second is you should properly size the capacitor size for voltage regulation. As I said earlier, IM requires reactive power which is supplied by the capacitor in your case; But, as the input changes (water flow), the reactive power demand from IM will also change. So, it is crucial that you do a proper sizing of capacitor banks.

The capacitor bank should be such that it should be able to supply reactive power to IM from no-load to full load condition.

Please have a look at the link below. Similar problem is also seen in off-grid induction machine based pico-hydros.

https://www.bookdepository.com/Micro-hydro-Design-Manual-Adam-Harvey/9781853391033?redirected=true&utm_medium=Google&utm_campaign=Base12&utm_source=TH&utm_content=Micro-hydro-Design-Manual&selectCurrency=THB&w=AF5NAU963HDXMGA8VCHV&pdg=pla-293946777986:cmp-6921261838:adg-81438836562:crv-389852909219:pos-:dev-c&gclid=CjwKCAjwsan5BRAOEiwALzomX5p7iPFa3eNQcwnkOIYk3klgyb7BeGkYIXN_Lz_QUtqhiPXN_4VPFBoCfN8QAvD_BwE

To stabilize the DC voltage across the capacitor you need a voltage regulator. But more likely, you need a rechargeable battery instead of capacitor, depending on your energy storage needs. Most likely you will have a solar panel charging a battery via a charge controller; the battery output voltage is reasonably stable and it can drive an inverter, which in turn can power AC motor.

Yuli Starodubtsev thanks for your answer. The challenge is that I am modelling the system on Matlab, and I am regulating the voltage of the capacitor after inserting the power from the induction machine into the boost converter.

Do you have a block diagram? I am not sure I understand your system. A simple diagram that shows where the power comes from and where it goes to will help. For instance, from your first question I thought the "induction machine" is an AC motor that drives the water pump. Now, I am not that sure.

This is briefly my block diagram, as you said Yuli Starodubtsev the induction machine is an AC motor that drives the pump.

My challenge is that the power coming from the machine will act as the 'Load' resistance in the boost converter scheme. My goal is to stabilize the voltage across the boost converter to 220V in steady state.

Thanks for your help :D

I see. the power does not come from the machine, but comes to the machine. So yes, the machine looks like a resistor to the converter. If you know the power needed by the machine P[Watts], then R = V^2/P, where R is in Ohms, P in watts, and V - voltage in volts. and the voltage V is the nominal voltage of the machine.

Yes you are right, my concern is that in the equation of the boost converter, I have to integrate the derivative of the voltage, which is dU/dt, which comes to having an integration of a 0 in the denominator. So when integrating I have to put an initial value different from 0, which leads me to having a constantly increasing voltage in the boost converter. I can send you the equations by email if you want