(116f) Multi-Period Dynamic Optimization of Multi-Scale Energy Systems

Many chemical engineering systems involve optimal decision making over multiple timescales, where decisions must be made over the course of daily operation, but also the span of months or years. One example of such a system is that of a reactor with catalyst deactivation (where the fast timescale comprises reaction kinetics and mass and energy balances, and the slow timescale consists of catalyst deactivation) [1]. Another example of a process with distinct timescales is that of a solid-oxide cell (SOC) under chemical degradation [2]. Here, degradation takes place over thousands of hours of operation but is a function of the fast dynamic operating conditions of the cell. The key feature of the problems under consideration is the large disparity in the timescale of the fast and slow phenomena.

One approach that is commonly used to handle multiple timescales is to discretize the system according to the dynamics of the fast timescale. However, this does not scale well for systems where the slow timescale phenomena are significantly slower than the fast timescale. In such cases, the time horizon necessary to observe an appreciable change in the slow timescale is very long, making the problem intractable. Furthermore, it is neither desirable nor necessary to couple the two timescales at every discretization point of the fast timescale. Another approach is to make simplifying steady-state assumptions for either the fast or slow timescale to reduce the problem size [2,3]. While such simplifications are easy to implement, they eliminate the multi-scale nature of the process. Consequently, during optimization, decisions can only be made with respect to the dynamic timescale. Furthermore, there can be multiple periods as the demands and supply of products change due to diurnal/seasonal variation. For some systems, the product being produced can also change within a given period.

In this work, we present an approach to the dynamic optimization of such multi-period multi-scale optimization problems. This allows for simultaneous optimization of decisions pertaining to both the fast and slow timescales. Unlike traditional multi-period optimization problems [4], the number of periods is not known a priori as this depends on the frequency of coupling between the two timescales. Trigger conditions for coupling events are developed such that coupling of the two timescales only takes place when necessary and is incorporated into the equation-oriented optimization algorithm. The optimization algorithm also considers when one or more critical equipment items may have a shorter lifetime than the plant lifetime, thus optimal replacement time and frequency of replacement are critical decision variables. We develop a decomposition approach that not only optimally decomposes the nonlinear programming problem to be solved in parallel but also optimizes the coupling decisions between slow and fast timescales while satisfying the state/parameter-based and event-based coupling constraints. The developed algorithm is applied to the multi-timescale optimization of an SOC system considering long-term chemical degradation and diurnal and seasonal variation in the demand of hydrogen and electric power. Decision variables include design decisions such number of cells in a stack and the stack replacement time, while period-specific decision variables include hourly operational considerations such as SOC inlet temperatures, voltage, and current densities.

Acknowledgments:

This work was conducted as part of the Institute for the Design of Advanced Energy Systems (IDAES) with support from the U.S. Department of Energy’s Office of Fossil Energy and Carbon Management (FECM) through the Simulation-Based Engineering Program.

Disclaimer:

This project was funded by the United States Department of Energy, National Energy Technology Laboratory an agency of the United States Government, through a support contract. Neither the United States Government nor any agency thereof, nor any of its employees, nor the support contractor, nor any of their employees, makes any warranty, expressor implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof, or any of their contractors.

References

[1] Froment, G. F. (2001). Modeling of catalyst deactivation. Applied Catalysis A: General, 212(1-2), 117-128.

[2] Giridhar et al. (2024) Optimal Operation of Solid-Oxide Electrolysis Cells Considering Long-Term Chemical Degradation [Manuscript in preparation].

[3] Lai, H., & Adams, T. A. (2024). Eco-Technoeconomic Analyses of Natural Gas-Powered SOFC/GT Hybrid Plants Accounting for Long-Term Degradation Effects Via Pseudo-Steady-State Model Simulations. Journal of Electrochemical Energy Conversion and Storage, 21(2).

[4] Yoshio, N., & Biegler, L. T. (2021). A Nested Schur decomposition approach for multiperiod optimization of chemical processes. Computers & Chemical Engineering, 155, 107509.