Optimization of the Design and Partial-Load Operation of Power Plants Using Mixed-Integer Nonlinear Programming

Abstract

Summary. This paper focuses on the optimization of the design and operation of combined heat and power plants (cogeneration plants). Due to the complexity of such an optimization task, conventional optimization methods consider only one operation point that is usually the full-load case. However, the frequent changes in demand lead to operation in several partial-load conditions. To guarantee a technically feasible and economically sound operation, we present a mathematical programming formulation of a model that considers the partial-load operation already in the design phase of the plant. This leads to a nonconvex mixed-integer nonlinear program (MINLP) due to discrete decisions in the design phase and discrete variables and nonlinear equations describing the thermodynamic status and behavior of the plant. The model is solved using an extended Branch and Cut algorithm that is implemented in the solver LaGO. We describe conventional optimization approaches and show that without consideration of different operation points, a flexible operation of the plant may be impossible. Further, we address the problem associated with the uncertain cost functions for plant components.Keywords. cogeneration plant, partial load performance, design optimization, cost minimization, nonconvex mixed-integer nonlinear programming, branch and cut IntroductionIn deregulated energy markets the optimization of the design and operation of energy conversion plants becomes increasingly important. To reduce the product cost during the entire operation time of a plant, both selection of an optimal plant structure and selection of optimal operating parameters in different load situations are necessary. Several design optimization methods were developed and applied to energy conversion systems in the past, e.g.,

Purpose in Thermodynamics

“…For an existing system, the contribution of investment cost is not considered in the cost minimization because it represents a sunk cost. In the mathematical cost minimization [66][67][68][69][70] of the design of a non-existing energy system, decisions need to be made about the thermodynamic variables. Therefore, we need to know the investment costs of components as functions of thermodynamic variables: such information is not readily available.…”

A column generation algorithm for solving energy system planning problems

“…Alternatively, the models can be more comparable to rigorous models with reduced complexity to enable deterministic solving methods to handle them. Model simplification can be achieved by considering only a few characteristic load points to limit the number of variables, and introduce model equations with lower mathematical complexity, e.g., to describe the thermodynamic properties (Ahadi-Oskui et al 2010;Jüdes et al 2009). In both cases, the results are commonly nonlinear mathematical models (NLP).…”

Optimization of the design, operating conditions, and coupling configuration of combined cycle power plants and CO2 capture processes by minimizing the mitigation cost

“…The gas and liquid enthalpies are calculated by Eqs. (42) and (43), respectively, which are taken from Greer [125]:…”