Wind and solar energy have become very popular options for energy conversion over the past years. This is particularly true for wind energy which is experiencing significant growth year-on-year. A significant part of this growth is at large-scale commercial power systems. However, there is a growing interest in small-scale renewable energy technologies to capture this intermittent but plentiful resource. A combined wind and solar energy hybrid system utilises two renewable energy resources, in doing so diversifies supply and as a result will make the system power output more stable and continuous. In this paper the details of the hybrid system model, using Matlab Simulink, are given. The model developed, is discussed giving key details on the characteristics of each part of the wind and solar energy hybrid system. The hybrid system model developed includes four subsystems: the solar energy subsystem, the wind energy subsystem, the inverter subsystem, the battery storage subsystem. The renewable energy resource is converted, using the wind turbine and photovoltaic panels to AC, via an inverter, which supplies the load. Any surplus energy is stored in the battery. It was found, from the simulation that the maximum power can be obtained under different circumstances using the developed maximum power point tracking algorithm.