1 Modeling and Control of Co-generation Power Plants: A Hybrid System Approach Giancarlo Ferrari-Trecate, Member, IEEE, Eduardo Gallestey, Member, IEEE, Paolo Letizia, Matteo Spedicato, Manfred Morari, Member, IEEE,, and Marc Antoine Abstract— In this paper the short term scheduling optimization of a combined cycle power plant is accomplished by exploiting hybrid systems, i.e. systems evolving according to continuous dynamics, discrete dynamics, and logic rules. Discrete features of a power plant are, for instance, the possibility of turning on/off the turbines, operating constraints like minimum up and down times and the different types of start up of the turbines. On the other hand, features with continuous dynamics are power and steam output, the corresponding fuel consumption, etc. The union of these properties characterize the hybrid behavior of a combined cycle power plant. In order to model both the continuous/discrete dynamics and the switching between different operating conditions we use the framework of Mixed Logic Dynamical systems. Then, we recast the economic optimization problem as a Model Predictive Control (MPC) problem, that allows us to optimize the plant operations by taking into account the time variability of both prices and electricity/steam demands. Because of the presence of integer variables, the MPC scheme is formulated as a mixed integer linear program that can be solved in an efficient way via dedicated software. Index Terms— Hybrid systems; model predictive control; com- bined cycle power plant; mixed integer linear programming I. I NTRODUCTION In the last decade, the electric power industry has been subject to deep changes in structure and organization. On the one hand, market liberalization and its associated fierce competition has led to a strong focus on cost reduction and optimal operation strategies. On the other hand, more strict environmental legislation makes operational constraints tighter. In this context, the use of combined cycle power plants (CCPP) has become more and more popular: they are more efficient and flexible than conventional configurations based on boilers and steam turbines, not to speak about nuclear power plants. A typical CCPP is composed of a gas cycle and a steam cycle. The gas cycle is driven by some fossil fuel (usually natural gas) and produces electric power via expansion of hot gasses in a (gas) turbine. The steam cycle is supplied with the still hot exhaust gases of the gas turbine and generates both electricity and steam for the industrial processes. Clearly, the liberalization of the energy market has promoted the need of operating CCPPs in the most efficient way, that is by maximizing the profits due to the sales of steam and electricity and by minimizing the operating costs. In this paper we consider the problem of optimizing the short-term operation of a CCPP, i.e. to optimize the plant on an hourly basis over a time horizon that may vary from few Manuscript received December 1, 2001; revised December 20, 2003. hours to one day [31]. A large stream of research in the power systems area focused on this problem. The usual paradigm (also used in this paper) is to recast the economic optimization into the minimization of a cost minus revenues functional and to account for the physical model of the plant through suitably defined constraints. The results available in the literature differ both in the features of the CCPP modeled and in the scope of optimization. In [31], [8], [17], [32] the CCPP is assumed in a standard operating condition and optimal scheduling of the resources is performed via non linear programming techniques. The main limitation is that the possibility of turning on/off the turbines is not considered and therefore it is not possible to determine the optimal switching strategy. The discrete features of a CCPP (i.e. the fact that turbines can be turned on/off, the start up dynamics, the minimum up and down time constraints and the priority constraints in start up sequences) can be captured by using binary decision variables along with continuous-valued variables describing physical quantities (e.g. mass, energy and flow rates). In [27] binary variables are introduced to model the on/off status of the devices and the corresponding optimization problem is solved through the use of genetic algorithms. The same modelling feature is considered in [21] where the automatic computation of the optimal on/off input commands (fulfilling also operational priority constraints) is accomplished through Mixed Integer Linear Programming (MILP). However in both papers, the modelling of the CCPP is done in an ad- hoc fashion and the generalization to plants with different topologies and/or specifications seems difficult. Moreover, other important features such as minimum up and down times or the behavior during start up are neglected. A fairly complete model of a thermal unit, using integer variables for describing minimum up/down time constraints, ramp constraints and different startup procedures, is given in [2]. The behavior of the unit is then optimized by solving MILP problems. Even if this approach could be adapted for modelling a single turbine of a CCPP, no methodological way for describing the coordination between different turbines is provided. The aim of this paper is to show how both the tasks of modeling and optimization of CCPPs can be efficiently solved by resorting to hybrid system methodologies. Hybrid sys- tems recently have attracted the interest of many researchers, because they can capture in a single model the interaction between continuous and discrete-valued dynamics. Various models for hybrid system have been proposed [24], [26], [10] and the research focused on the investigation of basic