Microgrid power systems have been possible solution to supply electricity to rural communities living far in areas where grid extension is difficult. In this paper, the designing, modeling process and control operation of microgrid power system is studied. It is built based on a case study of electrification of a remote village of 450 house hold in kirakir village in Amahra region, Ethiopia. The power demand is estimated and the costs of equipment components are specified, microgrid design and modeling has been carried out using Hybrid Optimization Model for Electric Renewable (HOMER) software. The microgrid consists of photovoltaic, wind turbine, batteries, basic loads like lighting, water pumping, school and health clinic equipment loads, television, radio and flour milling machines. The study site has been identified with the following load data by specifying typical daily load profile: Primary energy demand of 349kWh/day, Primary peak load of 105kW, deferrable energy is about 22kWh/day, and deferrable peak load of 3.6kW was carried with total peak load of 108.6kW. In this thesis design, models and control for the microgrid power system components, winds, PV, DC/DC converter, VSI (Voltage source inverter), battery storage and control strategy of converter controller unit are developed. DC/DC boost converter duty cycle is controlled using P and O MPPT (maximum power point tracking) algorithm and VSI (Voltage source inverter) controlled to maintain stable voltage and frequency using PLL (phase lock loop) and voltage regulator. In order to control the charge and discharge state of the battery a PI controller is used. Then, a simulation model for the proposed microgrid power system has been developed using MATLAB/Simulink environment. From HOMER simulation result the cost of energy is $0.294/kWh and total net present cost is $508,775. The PV cost is $200,000, wind turbine cost is $56,000, and battery cost is $140,000. About 84% of the electricity is produced from PV array and 16% of the electricity production is produced from wind. The MATLAB/Simulink simulation result indicates that the overall system is efficient and coordination controls of the converters are effective, the modeled PV array and wind turbine meets the specifications provided by the manufacturer. Therefore, the overall system is efficient and cost effective.