When modeling low capacity energy systems, such as a small size (5–150 kW_el) organic Rankine cycle unit, the governing dynamics are mainly concentrated in the heat exchangers. As a consequence, the accuracy and simulation speed of the higher level system model mainly depend on the heat exchanger model formulation. In particular, the modeling of thermo-flow systems characterized by evaporation or condensation requires heat exchanger models capable of handling phase transitions. To this aim, the finite volume (FV) and the moving boundary (MB) approaches are the most widely used. The two models are developed and included in the open-source ThermoCycle Modelica library. In this contribution, a comparison between the two approaches is presented. An integrity and accuracy test is designed to evaluate the performance of the FV and MB models during transient conditions. In order to analyze how the two modeling approaches perform when integrated at a system level, two organic Rankine cycle (ORC) system models are built using the FV and the MB evaporator model, and their responses are compared against experimental data collected on an 11 kW_el ORC power unit. Additionally, the effect of the void fraction value in the MB evaporator model and of the number of control volumes (CVs) in the FV one is investigated. The results allow drawing general guidelines for the development of heat exchanger dynamic models involving two-phase flows.

In this paper, the optimal operation of a stationary sub-critical $11{\mathrm{kW}}_{\mathrm{el}}$ organic Rankine cycle (ORC) unit for waste heat recovery (WHR) applications is investigated, both in terms of energy production and safety conditions. Simulation results of a validated dynamic model of the ORC power unit are used to derive a correlation for the evaporating temperature, which maximizes the power generation for a range of operating conditions. This idea is further extended using a perturbation-based extremum seeking (ES) algorithm to identify online the optimal evaporating temperature. Regarding safety conditions, we propose the use of the extended prediction self-adaptive control (EPSAC) approach to constrained model predictive control (MPC). Since it uses input/output models for prediction, it avoids the need for state estimators, making it a suitable tool for industrial applications. The performance of the proposed control strategy is compared to PID-like schemes. Results show that EPSAC-MPC is a more effective control strategy, as it allows a safer and more efficient operation of the ORC unit, as it can handle constraints in a natural way, operating close to the boundary conditions where power generation is maximized.

This paper addresses the issues linked to simulation failures during integration in finite-volume flow models, especially those involving a two-phase state. This kind of model is particularly useful when modeling 1D heat exchangers or piping, e.g., in thermodynamic cycles involving a phase change. Issues, such as chattering or stiff systems, can lead to low simulation speed, instabilities and simulation failures. In the particular case of two-phase flow models, they are usually linked to a discontinuity in the density derivative between the liquid and two-phase zones. In this work, several methods to tackle numerical problems are developed, described, implemented and compared. In addition, methods available in the literature are also implemented and compared to the proposed approaches. Results suggest that the robustness of the models can be significantly increased with these different methods, at the price of a small increase of the error in the mass and energy balances.