This paper presents a battery-aware stochastic control framework for residential energy management systems (EMS) equipped with energy harvesting, that is, photovoltaic panels, and storage capabilities. The model and control rationale takes into account the dynamics of load, the weather, the weather forecast, the utility, and consumer preferences into a unified Markov decision process. The embedded optimization problem is formulated to determine the proportion of energy drawn from the battery and the grid to minimize a cost function capturing a user-defined tradeoff between battery degradation and financial expense by user preferences. Numerical results are based on real-world weather data for Golden, Colorado, and load traces. The results illustrate the ability of the system to limit battery degradation assessed using the Rain flow counting method for lithium ion batteries.