In recent years, grid-connected residential PV generation systems have been greatly encouraged in China. In a residential power system containing PV, three types of power sources, namely, PV generation, battery storage and the utility grid, need to be properly scheduled. The time-of-use tariff and step tariff have been widely accepted in China. Correspondingly, this paper proposes two optimal energy management strategies for residential power systems to adapt to the two tariffs towards largest benefits. The strategies are formulated as optimization problems, where minimizing the household energy cost is taken as the objective and the dispatching ratio of electricity sold to the grid and used locally is treated as the optimization variable. A genetic algorithm (GA) is then employed to solve the formulated nonlinear optimization problems. A typical residential power system, containing grid-connected PV panels and a battery storage system, is used for verification study. The results show that the proposed energy management strategies, along with a GA based solving method, are effective in scheduling the operation status of the three power sources optimally to achieve maximum economic benefits under the time-of-use tariff and step tariff, respectively.