Dynamic Optimization of Proton Exchange Membrane Water Electrolyzers Considering Usage-Based Degradation (2405.06766v1)

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.

• The paper introduces a dynamic optimization model that integrates usage-based degradation to accurately predict and minimize the levelized cost of hydrogen.
• It employs a bi-level optimization strategy with k-means clustering for representative day selection to manage 15-minute interval operations over an entire year.
• Key findings reveal that accounting for degradation mandates larger stack sizes and adjusted storage capacities, significantly impacting operational efficiency and cost.

The paper "Dynamic Optimization of Proton Exchange Membrane Water Electrolyzers Considering Usage-Based Degradation" (2405.06766) presents a detailed techno-economic optimization model for designing and operating Proton Exchange Membrane (PEM) electrolyzers used for hydrogen production, particularly when powered by variable renewable energy sources or connected to dynamic electricity markets. The core contribution is integrating a usage-based degradation model into a dynamic optimization framework that simultaneously determines the optimal electrolyzer stack size, hydrogen storage capacity, and hourly operational schedule over a year.

The model addresses key practical challenges in operating PEM electrolyzers dynamically, including:

1. Heat Management: Modeled via an energy balance accounting for heat generation due to overpotentials and removal via feed water.
2. Gas Crossover and Safety: Includes a model for hydrogen crossover from the cathode to the anode, particularly critical at low current densities under differential pressure, and incorporates a safety constraint limiting hydrogen concentration in the anode gas below the lower flammability limit.
3. Usage-Based Degradation: Incorporates an empirical correlation linking the rate of voltage degradation to the operating current density, based on experimental literature data. This allows the model to determine the optimal stack replacement frequency based on operational stress.

The optimization framework minimizes the levelized cost of hydrogen (LCOH) over a 40-year plant life. The total cost includes capital costs (stack, balance of plant, storage) and operating costs (electricity, water, nitrogen purge, planned/unplanned replacements).

Modeling Approach and Implementation:

The model utilizes a 0-D physics representation of the electrolyzer cell, incorporating:

• Electrochemical relations (Nernst potential, activation, and ohmic overpotentials).
• Detailed mass balances for water, hydrogen, and oxygen at the anode and cathode, including electro-osmotic drag, water vaporization, and hydrogen crossover with an assumed recombination catalyst efficiency.
• An energy balance to track cell temperature dynamics.

The optimization problem is formulated as a large-scale, non-linear, non-convex problem. To handle computational complexity, especially the dynamic operation over a full year (at 15-minute intervals), the authors employ several techniques:

1. Decomposition Approach: A bi-level optimization strategy separates the problem into an outer problem (sizing the electrolyzer stack area and hydrogen storage capacity) and an inner problem (optimizing the dynamic operation for a fixed size). A Golden Section Search (GSS) algorithm is used to iterate between the outer and inner problems until convergence.
2. Time Domain Reduction: Instead of modeling all 365 days of the year at high resolution, K-means clustering is applied to the hourly electricity price data to select a smaller number (7 in the base case) of "representative days." The operational optimization is performed over these representative days, with results weighted to approximate annual costs and production. Special constraints are included to link storage state-of-charge dynamics across the representative days and approximate year-long storage behavior.
3. NLP Solver: The inner operational optimization problem, formulated as a Non-Linear Program (NLP), is solved using Pyomo and the IPOPT solver.

The empirical degradation correlation is modeled as a piecewise function: a constant rate below 1 A/cm² and a rate proportional to the square of the current density above 1 A/cm². This is integrated into the operational model, allowing for cumulative degradation over time, which directly affects cell voltage, power consumption, and ultimately, the required stack replacement rate.

Practical Applications and Findings:

The model is applied to case studies based on electricity price data for Corpus Christi, Texas (ERCOT South Load Zone) in 2022 and projected prices for 2030, along with corresponding capital cost assumptions.

Key findings with practical implications include:

• Impact of Degradation: Accounting for usage-based degradation significantly increases the calculated LCOH compared to models ignoring it. For the 2022 scenario, LCOH increased from \$4.56/kg to \$6.60/kg. This is primarily due to increased planned replacement costs caused by a drastically reduced stack lifetime (from an assumed 7 years to about 2.2 years in the 2022 degradation case).
• Effect on Design and Operation: Degradation penalizes operation at high current densities. The optimal strategy with degradation involves sizing a larger stack area (116.2k cells vs. 50.1k cells in the 2022 cases) to meet demand with lower average current densities (25.8% utilization vs. 70.1%). This also reduces the need for hydrogen storage (0.51 days vs. 1.39 days), as the operating profile is less "bang-bang."
• Value of Integrated Design and Scheduling: Optimizing the operational schedule after fixing the design to the parameters found without considering degradation results in an even higher LCOH (\$6.92/kg) and much more frequent replacements (yearly), highlighting the importance of co-optimizing design and operation.</li> <li><strong>Constraint Importance:</strong> The temperature constraint (\$80^\circ$C upper bound in the base case) and the safety constraint (2% H₂ in O₂ limit) are often binding during optimal dynamic operation, particularly with degradation. Relaxing the temperature limit allows slightly higher current densities and slightly lower LCOH. Relaxing the safety constraint can lead to operating in the flammable region despite the presence of a recombination catalyst, emphasizing the need for continuous monitoring and control (e.g., N₂ purging).</li> <li><strong>Future Scenarios (2030):</strong> Projections for 2030 with lower capital costs and potentially more volatile electricity prices lead to significantly lower LCOH (around \$2.50/kg). The optimal design shifts towards larger stacks (156.8k+ cells) and less storage (around 0.1-0.2 days). Lower CAPEX further incentivizes larger stacks and lower current densities, resulting in longer stack lifetimes (3-5 years) compared to the 2022 degradation case, even with increased price volatility.

Implementation Considerations and Limitations:

• The use of a local solver means the identified solution is not guaranteed to be the global optimum.
• The empirical degradation correlation is based on limited experimental data from the literature. Standardized accelerated degradation testing procedures are needed to gather more reliable and comprehensive data covering various operating conditions (temperature, pressure, catalyst loading).
• The model assumes the electrolyzer is a price-taker and does not account for the potential impact of large-scale operation on local electricity prices.
• Implementing the dynamic operation profile in practice requires sophisticated process control systems capable of rapid adjustments to current density, water flow rate, and potentially nitrogen purging based on real-time conditions (electricity price, demand, cell temperature, anode gas composition, and potentially, estimated degradation).
• The increased stack replacement frequency predicted by the degradation model highlights potential strain on critical mineral supply chains (like iridium for anode catalysts) unless significant advancements in catalyst efficiency, loading reduction, or recycling are made.

Overall, the paper provides a valuable framework and quantitative insights into the complex trade-offs involved in dynamically operating PEM electrolyzers. It underscores that ignoring usage-based degradation can lead to significant underestimation of costs and misinformed design choices, particularly favoring smaller stacks and more storage than is techno-economically optimal when degradation is considered. The methodology, combining physics-based modeling, empirical data integration, dynamic optimization, and approximation techniques, is applicable to other electricity-intensive electrochemical processes facing similar challenges with variable power sources.