Integrating machine learning and mathematical programming for efficient optimization of operating conditions in organic Rankine cycle (ORC) based combined systems

Operations optimization in an organic Rankine cycle (ORC) based combined system is important while computationally difficult by using mechanistic models due to complex nonlinearities and constraints. In this study, a hybrid framework integrating machine learning and mathematical programming has been proposed to optimize the operations of the system for the best exergy performance. The combined system is first decomposed into two single ORCs for reducing computational complexity. Classification models and regression models based on artificial neural network (ANN) and linear regression are developed using simulation data, where classifications can be employed for high-throughput screening feasible inputs which meet the mechanistic constraints in ORC. The results demonstrate high performances of machine learning with at least 99% accuracies for classifications and with mean relative errors of less than 1% for regressions. These data-driven models and the relation of two ORCs were then embedded with mathematical programming for optimization and maximum net exergy of 28.66 MW is obtained. By linear expansion of ReLU operators in ANN, mixed-integer linear programming (MILP) based on machine learning models achieve high efficiency with ∼0.1 s required for optimization compared to mixed-integer nonlinear programming (MINLP) (>1000 s) and heuristic optimization based on mechanistic models (>10 h).