The main goal of this paper is to explore the performance of a residential grid-tied hybrid (GTH) system which relies on economic and environmental aspects. A photovoltaic- (PV-) wind turbine- (WT-) battery storage system with maximizing self-consumption and time-of-use (ToU) pricing is conducted to examine the system efficiency. In so doing, technical optimization criteria with taking into consideration renewable energy benefits including feed-in-tariff (FIT) and greenhouse gas emission (GHG) reduction are analyzed. As the battery has a substantial effect on the operational cost of the system, the energy management strategy (EMS) will incorporate the daily operating cost of the battery and the effect of the degradation. The model can give the opportunity to the network to sell or purchase energy from the system. The simulation results demonstrate the effectiveness of the proposed approach in which the new objective function achieves the maximum cost-saving (99.81%) and income (5.16 $/day) compared to other existing strategies as well as the lowest GHG emission. Furthermore, the battery enhances the best daily self-consumption and load cover ratio. Then, as the model is nonlinear, a comparison with other existing algorithms is performed to select the feasible, robust, and reliable model for the residential application. A hybrid algorithm (HGAFMINCON) is developed to demonstrate the superiority of the algorithm over FMINCON and GA shown in terms of cost savings and income.