Combined heat and power (CHP) plants are widely used in industrial applications. In the aftermath of the recession, many of the associated production processes are under-utilized, which challenges the competitiveness of chemical companies. However, under-utilization can be a chance for tighter interaction with the power grid, which is in transition to the so-called smart grid, if the CHP plant can dynamically react to time-sensitive electricity prices. In this paper, we describe a generalized mode model on a component basis that addresses the operational optimization of industrial CHP plants. The mode formulation tracks the state of each plant component in a detailed manner and can account for different operating modes, e.g. fuel-switching for boilers and supplementary firing for gas turbines, and transitional behavior. Transitional behavior such as warm and cold start-ups, shutdowns and pre-computed start-up trajectories is modeled with modes as well. The feasible region of operation for each component is described based on input-output relationships that are thermodynamically sound, such as the Willans line for steam turbines. Furthermore, we emphasize the use of mathematically efficient logic constraints that allow solving the large-scale models fast. We provide an industrial case study and study the impact of different scenarios for under-utilization. (C) 2013 Elsevier Ltd. All rights reserved.