- We present an analytical dynamic mathematical model and a design optimization of a residential scale combined heat and power system. The mathematical model features a detailed description of the internal combustion engine based on a mean value approach, and simplified sub-models for the throttle valve, the intake and exhaust manifolds, and the external circuit. The validated zero-dimensional dynamic mathematical model of the system is implemented in gPROMS, and used for simulation and optimization studies. The objective of the design optimization is to estimate the optimum displacement volume of the internal combustion engine that minimizes the operational costs while satisfying the electrical and heating demand of a residential 10-house district. The simulation results show that the mathematical model can accurately predict the behavior of the actual system while the design optimization will later be the basis for advanced control studies. 2014 Springer-Verlag Berlin Heidelberg.