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.
Highlights
Water is one of the most important substances in energy conversion systems
The results demonstrate that deterministic global optimization of problems with the IAPWS-IF97 can get intractable for larger problems when using McCormick relaxations as a general purpose technique, whereas larger problems can be solved with the proposed tailored relaxations
For Case Study 1, at the solution for maximum power output the cycle pressure pS2 is at its upper bound (note that the bound pS2 ≤ 10 MPa was chosen for consistency with the original problem of Bongartz and Mitsos (2017); therein, it was chosen because of the simplistic model that was expected to perform best at moderate pressures) when using the IAPWS-IF97 model, whereas with the simple model, it is approximately 50% lower
Summary
Water is one of the most important substances in energy conversion systems. Today, around three quarters of the global power generation relies on steam power cycles (IEA 2019), either in pure steam power plants or as part of combined-cycle plants. Many existing optimization studies on steam power cycle or utility system design have either directly opted for a simpler model (Bruno et al 1998; Bongartz and Mitsos 2017) or replaced the IAPWS-IF97 with a simplified surrogate model, typically polynomials of lower degree (Ahadi-Oskui et al 2010). The latter approaches have sometimes been combined with smoothing techniques to remedy the nondifferentiabilities that occur at phase boundaries (Tică et al 2012; Åberg et al 2017). The proposed relaxations are implemented in the MC++ library (Chachuat et al 2015) used by our open-source global optimizer MAiNGO (Bongartz et al 2018).
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
