Hydrogen storages systems rely primarily on immense pressures to increase energy density. However, a high storage pressure comes at the cost of energy-intensive compression. While polymer electrolyte membrane (PEM) electrolyzer shows, in theory, increased efficiency at low pressures [1, 2], the energy consumed by the compressor at low pressures is increased drastically. Therefore, a buffer storage system can be utilized to benefit from increased stack efficiencies at low operating pressures while maintaining low compression ratios. However, the best timing for loading and unloading the buffer storage depends on external factors like the availability of cheap renewable energy resources and a varying grid price. Determining the optimal operating strategy at any point in time regarding external factors can be done with mathematical optimization and model predictive control.

Therefore, we derive component models suitable for mathematical optimization from literature. We derive piecewise linear models (pwlm) of the theoretical operational behavior of the electrolyzer [2] and a compressor system [1] using hinging hyperplanes [3]. The pwlm are then transformed into Mixed-Integer Linear Programming (MILP) formulations suitable for optimization. Using the component models, we are able to transform the scheduling problem mentioned above into a MILP problem suitable for optimization. Figures (a) and (b) show a visualization of the piecewise linear models.

We solve the optimization problem using the state-of-the-art MILP solver Gurobi [4] to evaluate the economic potential of a buffer storage system in combination with a pressure variable operation of the electrolyzer. We compare the results of the pressure optimization with a system with an electrolyzer that operates at constant pressure with no buffer storage. We chose a pressure of 30 bars as a constant operating point since most electrolyzers since the nominal pressure of most industrial electrolyzers are around 30 bars [5, 6]. To evaluate the economic benefit, we consider the electricity price of the German energy market for the year 2020 and excess energy from a PV-Park.

We show that we can meet a hydrogen production target of 20 MWh per day at a pipeline pressure of 200 bar around 3% cheaper throughout the whole year by utilizing a 10 MWh buffer storage in comparison to direct compression of the hydrogen. Figure (c) visualizes the buffer storage pressure, and figure (d) compares the operational points of the electrolyzer systems with and without a buffer storage system for an exemplary time horizon. The results show that an operation at low pressures is theoretically beneficial for hydrogen production. However, the real-world applicability remains to be proven under real-world operational conditions.

[1] Tjarks. G. (2017). PEM-Elektrolyse-Systeme zur Anwendung in Power-to-Gas Anlagen [dissertation] Rheinisch-Westf¨alische Technische Hochschule Aachen. Aachen

[2] Scheepers, F., Stähler, M., Stähler, A., Rauls, E., Müller, M., Carmo, M., & Lehnert, W. (2020). Improving the efficiency of PEM electrolyzers through membrane-specific pressure optimization. Energies, 13(3), 612.

[3] Kämper, A., Holtwerth, A., Leenders, L., & Bardow, A. (2021). AutoMoG 3D: Automated Data-Driven Model Generation of Multi-Energy Systems Using Hinging Hyperplanes. Frontiers in Energy Research, 430.

[4] Gurobi Optimization LLC, (2021). “Gurobi Optimizer Reference Manual,” Available from: http://www.gurobi.com

[5] Buttler, A., & Spliethoff, H. (2018). Current status of water electrolysis for energy storage, grid balancing and sector coupling via power-to-gas and power-to-liquids: A review. Renewable and Sustainable Energy Reviews, 82, 2440-2454.

[6] Kopp, M. (2018). Strommarktseitige Optimierung des Betriebs einer PEM-Elektrolyseanlage. [dissertation] Kassel University Press GmbH.