How to make a power divider control for battery supercapacitor work on the HESS PLTS Stand alone system?

I made a battery supercapacitor HESS on a Stand Alone Solar Power Plant, and to divide the work of the supercapacitor and battery I used a First-Order Filter with a Low Pass Filter type, the parameters needed are Time Constant (s) and Sample Time, but I was confused when determining these parameters to work properly. what I know is that the greater the Time Constant (s), the smaller the frequency that is passed. and when I use 0. 005 s, a large frequency will be sent to the battery and a small frequency will be sent to the supercapacitor, and instead of that the battery current when there is no change in either the source or the load, the battery current will be constant which indicates a constant battery while the supercapacitor current continues to go up and down or charging discharging when the radiation or load does not change at all. is there a solution to my problem? please help. (I use Matlab 2018b-2023b)

Answer 1

[Sabin]

In a battery-supercapacitor HESS, the time constant of the low-pass filter determines the frequency split between the battery and supercapacitor. If the time constant is too small (e.g., 0.005 s), high-frequency components (rapid power changes) are routed to the battery, which is undesirable since batteries are better suited for low-frequency, steady-state energy supply, while supercapacitors handle fast transients. To solve the problem, increase the time constant to a value that allows only slow, low-frequency changes to pass to the battery, while the supercapacitor handles rapid fluctuations. Start by analyzing your load and source profile to estimate the typical transient and steady-state periods, and set the time constant accordingly. Values in the range of 0.1-1 second should work better for solar HESS applications.