Utilities have introduced demand charges to encourage customers to reduce their demand peaks, since a high peak may cause very high costs for both the utility and the consumer. We herein study the bill minimization problem for customers equipped with an energy storage device and a self-owned renewable energy production. A model-free reinforcement learning algorithm is carefully designed to reduce both the energy charge and the demand charge of the consumer. The proposed algorithm does not need forecasting models for the energy demand and the renewable energy production. The resulting controller can be used online, and progressively improved with newly gathered data. The algorithm is validated on real data from an office building of IFPEN Solaize site. Numerical results show that our algorithm can reduce electricity bills with both daily and monthly demand charges.