(467e) Stochastic Optimization for Green Hydrogen Production Using Quantile Neural Networks

Electrolysis-based hydrogen processes will likely play a major role in the energy transition, enabling the production of so-called “green hydrogen” using renewable energy sources [1]. These plants can supply hydrogen directly to industrial processes or can be used to store excess energy, converting hydrogen back to electricity via fuel cells. Given the flexibility of these systems, it is essential to develop optimization tools that can effectively support decision-making at both the design and operational levels. However, uncertain electricity price forecasts can significantly affect the optimal configuration of the plant. In this context, two-stage stochastic programming [2] is a widely used approach to model uncertainty by distinguishing between first-stage tactical decisions (“here and now”) and the second-stage operational decisions (“wait and see”), including for numerous chemical engineering applications [3-4] This method enables adaptive recourse of second-stage variables once uncertainty is revealed. However, solving these problems with monolithic, scenario-based methods like Sample Average Approximation (SAA) can be challenging when the number of scenarios increase. To address this, surrogate-based modelling [5-6] has emerged as a promising alternative to approximate the second-stage decisions and value.

This study addresses the optimal design and operation of an electrolyser-based process [7] that supplies hydrogen to a direct iron reduction process and exchanges electricity directly with the grid under uncertain electricity prices. We formulate the model as a two-stage stochastic program, and we use Quantile Neural Networks [8] (QNNs) to approximate the second stage objective function. QNNs are multi-output neural networks, which allow them to treat the distributional aspect of the response variables. In the context of stochastic programming, the inputs of the QNN are represented by first-stage decisions, while the output layer retains multiple quantiles allowing for the reconstruction the conditional distribution of the second-stage objective value. The main advantage of this formulation compared to other approaches using neural networks [5-6] is its capability to model risk-averse formulations, thereby extending the surrogate approximation beyond the second-stage expected value. Additionally, the training phase only requires a single scenario for each sampled first-stage inputs. We show that the QNN-based stochastic program represents an effective approach to optimize the design and the operation of the hydrogen production plant, which includes an electrolyser, a storage, a heater, and a fuel cell. This approach also allows for the inclusion of risk measures, as illustrated using the Conditional Value at Risk (CVaR) in our case study.

[1] Oliveira, A. M., Beswick, R. R., & Yan, Y. (2021). A green hydrogen economy for a renewable energy society. Current Opinion in Chemical Engineering, 33, 100701.

[2] Birge, J. R., Louveaux, F. (2011). Introduction to stochastic programming. Springer Science & Business Media.

[3] Li, C., & Grossmann, I. E. (2021). A review of stochastic programming methods for optimization of process systems under uncertainty. Frontiers in Chemical Engineering, 2, 622241.

[4] Grossmann, I. E., Apap, R. M., Calfa, B. A., García-Herreros, P., & Zhang, Q. (2016). Recent advances in mathematical programming techniques for the optimization of process systems under uncertainty. Computers & Chemical Engineering, 91, 3-14.

[5] Patel, R. et al. (2022). Neur2sp: Neural twostage stochastic programming. Advances in Neural Information Processing Systems, 35, 23992–24005

[6] Kronqvist, J., Li, B., Rolfes, J., & Zhao, S. (2023). Alternating mixed-integer programming and neural network training for approximating stochastic two-stage problems. Machine Learning, Optimization, and Data Science. Lecture Notes in Computer Science, vol 14506. Springer.

[7] Tsay, C., Qvist, S. (2023). Integrating process and power grid models for optimal design and demand response operation of giga-scale green hydrogen. AIChE J. 69(12), e18268.

[8] Alcántara, A. et al. (2024). A Quantile Neural Network Framework for Two-stage Stochastic Optimization. arXiv preprint arXiv:2403.11707