A linear optimization model for peer-to-peer energy exchange for residential homes is presented. The model takes into account heterogeneous consumption patterns, shared battery storage and supports intra-group trading among households within the same building, as well as inter-group trading between multiple buildings. Using energy usage data from Icelandic households and meteorological data for the same period, a scenario with two groups of users was simulated, and the effects of direct trading within and between the groups were studied. Results indicate that most of the cost savings arise from intra-group trading instead of inter-group and exchanges with the utility grid. Sensitivity analysis of battery maintenance costs shows that this parameter needs to be estimated carefully.