A general mixed-integer programming framework for efficient modeling, integration and optimization of thermodynamic cycle-based energy systems

Abstract

Thermodynamic cycles are imperative systems for energy conversion, and optimization has been an important tool to improve their thermo-economic benefits. However, off-the-shelf software is often limited by long computational time, inflexibility for modeling and numerical difficulties. Here, we present an equation-based optimization framework featuring: (1) an inclusive modeling structure applicable to various thermodynamic cycles design problems; (2) versatile thermodynamic properties estimation for different working fluids; (3) capability of working fluids optimization with complex composition; (4) an efficient formulation method to model potential phase change of streams in simple/complicated heat exchangers; (5) a systematic optimization strategy to improve solution efficiency. The framework is formulated as mixed-integer nonlinear programming models, and its performance is demonstrated by two thermodynamic cycle optimization problems and one system design problem, including a supercritical CO2 Brayton cycle, cryogenic cycle (PRICO), and concentrated solar power (CSP) system. The Brayton cycle case serves as an illustrative example to show thermodynamic cycle design combining the consideration of stream properties calculation, unit operations, and flowsheet optimization. The PRICO example shows the efficacy of the proposed framework in simultaneously optimizing flowsheet and working fluids composition with complex heat exchangers and stream phase unknown a priori. The CSP case demonstrates that the framework can be extended to system optimization problems with high accuracy multi-parameter equation of state. Results prove that the framework is efficient and effective in solving thermodynamic cycle and related energy systems optimization problems.