This paper presents a numerical model to analyse the thermal and fluid dynamic behaviour of a mechanical vapour compression MVC desalination system, which uses renewable energy to supply the electricity required by the whole system. The reason to use renewable energy is that the MVC desalination system has been though to work in remote places, where an electric grid is not available. The transient and steady-state of the desalination system are evaluated taking into account the variability of the renewable energy sources (solar energy). A scalability study has been carried out to find the relation between the variability of the renewable energy sources and the capacity of the desalination system (distilled water production). Different components which making up the desalination system are considered in the numerical simulation, all of them are solved in a coupled way by mean of an object-oriented tool called NEST. The influence of the feed seawater conditions is also analysed on the system performance.