The investigation of the designed hybrid energy system is based on the mathematical analysis, simulation and optimization of a model, which consists of a transportation system (e.g. in this case, a car), vertical axis wind turbine, fuel cell and storage system. In order to optimize the performance of the hybrid system, the objective functions of the system have been considered to be design coefficients including wind turbine energy production, hydrogen production, voltage and current.
2.1. Wind Energy Production
The power harnessed by wind turbines fall under a mechanical energy category, which relies on the turbine’s power coefficient, 
and wind speed. It can therefore be expressed by the following equation:
(1) where P is the power output,
is the air density,
is radius of turbine propeller, and
is the average wind speed. The coefficient of power (
) can be described as part of the mechanical power extracted from the overall wind energy and it is an especial characteristic for each turbine.
In addition, apart from the power output, the average wind speed can be estimated according to Equation (2):
(2) where
is the number of wind turbines and n is the number for wind speed datasets (Yin et al., 2017).