Dynamic Optimization of Proton Exchange Membrane Water Electrolyzers Considering Usage-Based Degradation

TL;DR

The paper develops a dynamic, degradation-aware techno-economic optimization for grid-connected PEM electrolyzers that co-designs stack size, storage, and operating schedules. It uses a 0-D stack model with mass/energy balances plus a usage-based degradation correlation, solved via nested outer/inner optimization and a 7-representative-day approximation to capture variable electricity prices. Key findings show that including degradation raises $LCOH$ significantly in 2022 scenarios and shortens stack life, while 2030 projections with lower CAPEX and larger stacks substantially reduce $LCOH$ and storage needs. The framework highlights the importance of degradation in shaping optimal operation, heat management, and safety considerations, and it can be adapted to other electrochemical decarbonization systems. This approach provides a concrete, computationally tractable method to assess design and operation under uncertainty in electricity prices and technology costs.

Abstract

We present a techno-economic optimization model for evaluating the design and operation of proton exchange membrane (PEM) electrolyzers, crucial for hydrogen production powered by variable renewable electricity. This model integrates a 0-D physics representation of the electrolyzer stack, complete mass and energy balances, operational constraints, and empirical data on use-dependent degradation. Utilizing a decomposition approach, the model predicts optimal electrolyzer size, operation, and necessary hydrogen storage to satisfy baseload demands across various technology and electricity price scenarios. Analysis for 2022 shows that including degradation effects raises the levelized cost of hydrogen from \$4.56/kg to \$6.60/kg and decreases stack life to two years. However, projections for 2030 anticipate a significant reduction in costs to approximately \$2.50/kg due to lower capital expenses, leading to larger stacks, extended lifetimes, and less hydrogen storage. This approach is adaptable to other electrochemical systems relevant for decarbonization.

Figures (19)

• Figure 1: Flowsheet for the current work. Cell level details with flows across the membrane are shown in the cutout. Downstream treatment of the anode gas stream is not considered. The H2 stream is dried and can either be compressed and stored to satisfy demand at a later time, or directly used to satisfy demand. Stream 11 is a nitrogen purge stream available for the model to use at a cost as a fail-safe should the concentration of H2 in O2 reach the 2% safety limit.
• Figure 2: Summary of the bilevel optimization. The outer problem iterates over number of cells and H2 storage capacity. The inner problem solves the cost optimal variable operation problem given a fixed number of cells and storage from the outer problem.
• Figure 3: Left Figure: Current voltage relationship at 1 bar and 76$^{\circ}$C. Data from Lee2020-db. Fitted parameters $\alpha_{an} = 0.58$, $\alpha_{cat} = 1.28$. Right Figure: Current voltage relationship at high pressure. Data from Marangio2011-jc. Fitted parameters at 40$^\circ$C: $\alpha_{an} = 1.9$, $\alpha_{cat} = 0.1$, fitted parameters at 55$^\circ$C: $\alpha_{an} = 1.38$, $\alpha_{cat} = 0.11$
• Figure 4: Degradation rate as a function of the square of the current density plotted on a log-log axis. Data taken from Suermann2019-kzRakousky2017-tePapakonstantinou2020-hjAlia2019-lwLi2021-njFrensch2019-ff. Current density and degradation are time averaged over the operation lifetime. Points shown in the graph here are for square and hold wave patterns. Some cells showed negative degradation rates likely due to membrane thinning; these negative degradation rates were not considered for this study.
• Figure 5: Left Figure: Duration curves for 2022 and 2030 prices used in this study. The south load zone (avg. price: $62.55) and west load zone (avg. price: $63.83) prices are for 2022. The 2030 case is the mid-case for NREL's Cambium model for 2030 Texas (avg. price: $21.43). Right Figure: Duration curves for 2030 prices used in this study. The low decarbonization scenario projects 95% decarbonization of the grid by 2050 (avg. price: $21.97). The high decarbonization scenario projects 100% decarbonization of the grid by 2030 (avg. price: $22.67).