This paper presents the results of a case study to investigate different alternatives for the energy supply to a municipality on the western coast of Norway. The following alternatives for energy supply are modelled and analysed: i) a district heating system with three different heat centrals, ii) a natural gas distribution system and iii) a low temperature distribution system. The case study is performed with the optimization model eTransport developed for the planning of local energy systems where several alternative energy carriers and technologies are considered simultaneously. The model minimizes the total energy system cost of meeting the demands of electricity, heating, cooling and gas within a geographical area over a given planning horizon. The model uses a detailed network representation of infrastructures to consider investments in distributed central stations, components, cables and pipelines. The object function includes investments, operating and environmental costs.