Dear Abdullahi Inusa,

The best software would be Matlab, Few examples are also available on Mathworks in the similar topic. 

For analyzing only energy potentials and other economic stuff HOMER software is excellent. But when it comes to controlling technologies MATLAB/PLECS softwares would be better. Other option would be building a real time system and using the Control drives for understanding its behavior.

Hope this would help you...!!

I highly recommend HOMER software for this purpose. You can download a copy of this software from Carnegie Mellon University at no cost. Here is the URL:

https://www.ece.cmu.edu/

Professor Yehia Khalil, Yale University, USA

Fellow of the University of Oxford, UK

Matlab/Simulink would be a good option if you would like to build a physical model. 

I recommend Matlab/Simulink.

Sir @Yehia F. Khalil, I visited the link but was unable to find the HOMER software, can u please help me in this issue. Thanking in anticipation.

Ok. Thanks used Matlab simulink state flow for the modeling and simulation. It worked out

2. How do I form the mathematical model of the four input and one output hybrid power system ? Help with the mathmatical model please

First or second order linear differential equation. 2. Get the controller transfer function

The posted items can help you to have a better understanding of modelling, sizing and energy management of a hybrid energy system:

Article Multi-objective Optimal Sizing and Energy Management of Hybr...

Article Real time energy management strategy for a fast charging ele...

Use Matlab Sims cape power system technology for hybrid renewable energy resource, off-grid design, modeling and simulation of available locality data (i.e. solar irradiance, ambient temperature, micro hydro flow rate, height, etc)

I suggest the TRNSYS software. TRNSYS (pronounced 'tran-sis') is an extremely flexible graphically based software environment used to simulate the behavior of transient systems. While the vast majority of simulations are focused on assessing the performance of thermal and electrical energy systems, TRNSYS can equally well be used to model other dynamic systems such as traffic flow, or biological processes.

TRNSYS is made up of two parts. The first is an engine (called the kernel) that reads and processes the input file, iteratively solves the system, determines convergence, and plots system variables. The kernel also provides utilities that (among other things) determine thermophysical properties, invert matrices, perform linear regressions, and interpolate external data files. The second part of TRNSYS is an extensive library of components, each of which models the performance of one part of the system. The standard library includes approximately 150 models ranging from pumps to multizone buildings, wind turbines to electrolyzers, weather data processors to economics routines, and basic HVAC equipment to cutting edge emerging technologies. Models are constructed in such a way that users can modify existing components or write their own, extending the capabilities of the environment.

After 35 years of commercial availability, TRNSYS continues to be a flexible, component-based software package that accommodates the ever-changing needs of both researchers and practitioners in the energy simulation community.