This paper presents a model-based predictive control approach for operation of sustainable buildings with on-site photovoltaic and battery systems. A battery life span is highly dependent on the operation strategy. To capture the battery capacity loss during operation, a simplified battery cost formulation, derived from a physically-based battery degradation model, is implemented in the control optimization. A model predictive control problem is formulated to find the balance between the building utility cost and the battery life cycle cost. To reduce computational complexities, a set of piece-wise linear fits are used to approximate the battery capacity degradation and a convex formulation is derived for the control problem. Simulation test results have shown that the proposed strategy could reduce the battery degradation rate by 40 % and the total operation cost by 9% to 16% under time-of-use electricity tariffs.