Deterministic global optimization of steam cycles using the IAPWS-IF97 model

Abstract

The IAPWS-IF97 (Wagner et al. (2000) J Eng Gas Turbines Power 122:150) is the state-of-the-art model for the thermodynamic properties of water and steam for industrial applications and is routinely used for simulations of steam power cycles and utility systems. Its use in optimization-based design, however, has been limited because of its complexity. In particular, deterministic global optimization of problems with the IAPWS-IF97 is challenging because general-purpose methods lead to rather weak convex and concave relaxations, thus resulting in slow convergence. Furthermore, the original domains of many functions from the IAPWS-IF97 are nonconvex, while common global solvers construct relaxations over rectangular domains. Outside the original domains, however, many of the functions take very large values that lead to even weaker relaxations. Therefore, we develop tighter relaxations of relevant functions from the IAPWS-IF97 on the basis of an analysis of their monotonicity and convexity properties. We modify the functions outside their original domains to enable tighter relaxations, while we keep them unchanged on their original domains where they have physical meaning. We discuss the benefit of the relaxations for three case studies on the design of bottoming cycles of combined cycle power plants using our open-source deterministic global solver MAiNGO. The derived relaxations result in drastic reductions in computational time compared with McCormick relaxations and can make design problems tractable for global optimization.