In addition to renewable energy sources, the transition of the German energy system will increasingly involve the use of decentralized combined heat and power plants (CHP). In order to use this promising technology cost-optimally, modeling approaches must be developed that enable optimization of the systems. Mixed integer linear programming (MILP) is a powerful tool for solving mathematical optimization problems. However, to reduce the computing time the model formulation requires compelling simplifications in relation to reality. The aim of this paper is to present a modeling approach for a combined heat and power plant that depicts dynamic power changes more accurately than existing approaches. Power gradients are mapped by differentiating between the control signal of the CHP unit and the actually generated power output for thermal and electrical power. Finally, the accuracy of the modeling approach is examined in a field test and evaluated according to the accuracy achieved.