Among household electricity end users, there is growing interest in local renewable electricity generation and energy independence. Community-based and neighborhood energy projects, where consumers and prosumers of electricity trade their energy locally in a peer-to-peer system, have started to emerge in different parts of the world. This study investigates and compares the costs incurred by individual households and households organized in electricity trading communities in seeking to attain greater independence from the centralized electricity system. This independence is investigated with respect to: (i) the potential to reduce the electricity transfer capacity to and from the centralized system and (ii) the potential to increase self-sufficiency. An optimization model is designed to analyze the investment and operation of residential photovoltaic battery systems. The model is then applied to different cases in a region of southern Sweden for year 2030. Utilizing measured electricity demand data for Swedish households, we show that with a reduced electricity transfer capacity to the centralized system, already a community of five residential prosumers can supply the household demand at lower cost than can prosumers acting individually. Grouping of residential prosumers in an electricity trading community confers greater benefits under conditions with a reduced electricity transfer capacity than when the goal is to become electricity self-sufficient. It is important to consider the local utilization of photovoltaic-generated electricity and its effect on the net trading pattern (to and from the centralized system) when discussing the impact on the electricity system of a high percentage of prosumers.