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.
Abstract. In this paper the 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. The possibility of turning on/off the gas and steam turbine, the operating constraints (minimum up and down times) and the different types of start up of the turbines 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. Next, 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 by using commercial solvers.
We study how the spectrum of a closed linear operator on a complex Banach space changes under a¯ne perturbations of the form A A ¢ = A + D¢E. Here A, D and E are given linear operators, whereas ¢ is an unknown bounded linear operator that parametrizes the possibly unbounded perturbation D¢E. The union of the spectra of the perturbed operators A ¢ , with the norm of ¢ smaller than a given¯> 0, is called the spectral value set of A at level¯. In this paper we extend a known characterization of these sets for the matrix case to in nite dimensions, and in so doing present a framework that allows for unbounded perturbations of closed linear operators on Banach spaces. The results will be illustrated by applying them to a delay system with uncertain parameters and to a partial di¬erential equation with a perturbed boundary condition.
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