Throughout the last years the use of on-site renewable energy sources (RES) in residential houses has continuously increased in many industrial countries and it is expected that many of the supply systems will be based solely on renewable sources in the medium term future. However, the explicitly higher installation costs compared to conventional systems and the variability of the energy sources require an optimized design of the overall system. To achieve this, a new approach is needed which accounts for the interdependencies between the different supply technologies as well as consumption profiles of residents and on-site energy resource availability. This paper aims at developing a model based on linear programming for the optimal sizing of 100% renewable supply systems in terms of the overall system costs. It has been successfully applied in a case study for a so called Net Zero Energy Building in Denmark with three technology options. It is shown that under the chosen conditions the optimal configuration is given by a PV model combined with a heat pump for heat supply. The model allows for a fast evaluation of different supply options and is intended to be extended in future to all kind of residential RES technologies. (C) 2012 Elsevier Ltd. All rights reserved.