(587a) Nonlinear Model Predictive Control for Solid Oxide Electrolysis Cells

Integrated energy systems (IES) are a class of technologies that use thermal energy, normally wasted during electricity production, to provide heating, cooling, humidity control, energy storage and other process functions. IES based on solid oxide fuel cells (SOFCs) and solid oxide electrolysis cells (SOECs) have the potential to produce electricity and thermal energy and convert fuel into usable energy with high efficiencies. Moreover, due to their ability to alternate between power and hydrogen production, they represent a significant improvement over current combustion-based power generation technologies. SOFCs have developed to a mature technology and are able to achieve electrical efficiencies of more than 60% (up to 85% with co-generation.) They operate at a very high temperature (up to 1000⁰C.) They are sulfur and carbon monoxide resistant, which allows them to handle natural gas, biogas as well as gases made from coal. Thus, as intermittent renewable energy increasingly displaces more reliable fossil-based power generation, SOFC-based IES have the potential to improve efficiency and reliability of energy production and storage.

An SOFC consists of two porous electrodes, and the electrolyte is a solid, ceramic material. If a fuel such as natural gas is used, the high temperature allows the endothermic reforming reaction to take place in the cell itself. There are two possible configurations: planar and tubular. In the planar design, the components are assembled in flat stacks, with air and fuel flowing through channels in the electrodes. In the tubular design, components are assembled in the form of a hollow tube, with the cell constructed in layers around a tubular cathode, and air flows through the inside of the tube and fuel flows around the exterior. Planar SOFCs adapt faster to new operating conditions, which plays an important role in the case of dynamic load changes.

A primary objective of a controller for SOFC/SOEC is to meet the desired power output while operating at a high efficiency. At the same time, optimal operation must ensure reliability and long-term operability by avoiding degradation in the form of cracking and delamination. Several studies have been conducted on the effect of thermal cycling, temperature gradients and other factors on the physical and chemical degradation of the cell, especially during load-following operation. The key operational parameters typically involve minimum cell temperature, maximum temperature gradient, cell voltage, steam to carbon ratio, and fuel utilization.

In this work, we present a rigorous optimization model for a non-isothermal planar SOEC flowsheet. This first-principles dynamic model takes into account the electrochemistry and the material and energy balances in the electrode channels, electrodes, electrolyte and the electrode-electrolyte interfaces. Dynamic simulations reveal existence of very fast dynamics across the height of the cell, and reasonably fast dynamics across its width. We isolate the fast dynamics and reformulate the model using a quasi-steady state assumption in which the faster dynamics along the height of the cell are replaced with algebraic equations, while holdups along only the width are considered. For dynamic optimization, we develop a nonlinear model predictive control (NMPC) framework to demonstrate the optimal set-point transition between feed flowrates. Moreover, we demonstrate optimal control of the system to maximize hydrogen production while constraining the temperature gradients to ensure reliable and safe operation.

The dynamic SOEC flowsheet model is part of the unit model library in the IDAES Process Systems Engineering framework, an open-source platform that modularizes unit operations and flowsheet construction, and is based on Pyomo, an open-source framework for modeling and optimization. Using the NMPC framework, we demonstrate dynamic optimization of the system during set point transition of feed flowrates. Using fuel and air flowrates as decision variables, we also demonstrate the optimization of hydrogen production while maintaining temperature gradients within safety limits to ensure reliability and long-term operability of the system.