This paper brings together the benefits of hydrogen and battery storage devices in the electrical network integrated with solar energy. The introduced hybrid storage system is utilized to achieve two purposes including uncertainty leveling and energy arbitrage. The volatility of solar energy and electrical-thermal loads is developed by Normal distribution. The hydrogen storage system is designed to smooth such uncertainty and storing the electrical energy in hydrogen form. Therefore, the hydrogen storage levels the uncertainties associated with solar power and loads. The battery is utilized to shift energy from pricey hours to the inexpensive time intervals and minimizing energy cost in network. The optimization programming finds optimal setting and charging-discharging pattern for both storage technologies. The seasonal profile is considered for electrical-thermal loads and solar energy. It is verified that the given hybrid storage scheme saves the cost by 117000 $/year and the solar system decreases the cost by 28%.