# Representation of Photovoltaic cell and BESS in Microgrid by first order transfer function

I am working in the are of frequency control of Microgrid and have come across many publications (For example: https://www.sciencedirect.com/science/article/abs/pii/S0142061515005220 (Pg 3,5)), wherein the transfer function that relates power output and the solar insolation in a photovoltaic (PV) cell is represented as a first order lag transfer function. Also, the transfer function that relates the deviations in power output of the battery energy storage system (BESS) and the deviations in frequency by the first order transfer function with lag. Like: $$G_{bess} = \frac{\Delta P_{bess}}{\Delta f} =\frac{K_{bess}}{1 + sT_{bess}}$$

My question is: How to mathematically prove starting from the physical equations that such relations can be represented by a first order transfer function? Is there a mathematical proof or mathematical justification using which we can obtain these transfer functions?