Energy supply systems are usually considered as individual sub-systems with separate energy vectors. However, the use of Combined Heat and Power (CHP) units, heat pumps and electric boilers creates linkages between electricity and heat networks. Two combined analysis methods were developed to investigate the performance of electricity and heat networks as an integrated whole. These two methods were the decomposed and integrated electrical-hydraulic-thermal calculation techniques in the forms of power flow and simple optimal dispatch. Both methods were based on models of the electrical network, hydraulic and thermal circuits, and the coupling components, focusing on CHP units and circulation pumps. A case study of Barry Island electricity and district heating networks was conducted, showing how both electrical and heat demand in a self-sufficient system (no interconnection with external systems) were met using CHP units. The comparison showed that the integrated method requires less iteration than the decomposed method. (C) 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).