Abstract Combined heat and power (CHP) systems due to their high efficiency compared to the conventional power generation systems have received considerable attention as they have less harmful impact on the environment. Recently, the serious concern with reducing the greenhouse gas emissions has focussed the attention on the possibility of a carbon tax in some countries. Here, we address the impact of such tax on the sizing and economics of a CHP system. Optimum sizing of CHP systems is of great importance to maximize the benefits of these systems. To select the optimum prime mover of a CHP system, performance characteristics of engine as well as economic parameters should be taken into consideration. A general thermo-economic approach to optimum sizing of internal combustion engines as the prime movers (any type and size) of a medium scale CHP system (500–5000 kW) and planning their operational strategy is developed. Net Annual Cost (NAC) as the criterion for making decision is introduced and appropriate equations for estimating thermodynamic and economic parameters as well as greenhouse gas emissions are presented. We consider three modes of operation: one-way connection (OWC) mode, two-way connection (TWC) mode, and heat demand following (HDF) mode. The proposed method has been used for a case study where data is available in the literature and the optimum nominal powers using gas engines are 3.3 MW, 3.2 MW, and 1.2 MW and in the case of using diesel engines are 3.4 MW, 3.4 MW, and 1.4 MW for TWC, OWC, and HDF modes, respectively. To determine the sensitivity of results to input parameters (e.g. electricity price) a comprehensive parametric study was conducted.