Optimal trajectory-guided stochastic co-optimization for e-fuel system design and real-time operation

TL;DR

MasCOR, a machine-learning-assisted co-optimization framework that learns from global operational trajectories, shows that most locations benefit from reducing system load below 50 MW to achieve carbon-neutral methanol production, with production costs of 1.2 USD per kg.

Abstract

E-fuels are promising long-term energy carriers supporting the net-zero transition. However, the large combinatorial design-operation spaces under renewable uncertainty make the use of mathematical programming impractical for co-optimizing e-fuel production systems. Here, we present MasCOR, a machine-learning-assisted co-optimization framework that learns from global operational trajectories. By encoding system design and renewable trends, a single MasCOR agent generalizes dynamic operation across diverse configurations and scenarios, substantially simplifying design-operation co-optimization under uncertainty. Benchmark comparisons against state-of-the-art reinforcement learning baselines demonstrate near-optimal performance, while computational costs are substantially lower than those of mathematical programming, enabling rapid parallel evaluation of designs within the co-optimization loop. This framework enables rapid screening of feasible design spaces together with corresponding operational policies. When applied to four potential European sites targeting e-methanol production, MasCOR shows that most locations benefit from reducing system load below 50 MW to achieve carbon-neutral methanol production, with production costs of 1.0-1.2 USD per kg. In contrast, Dunkirk (France), with limited renewable availability and high grid prices, favors system loads above 200 MW and expanded storage to exploit dynamic grid exchange and hydrogen sales to the market. These results underscore the value of the MasCOR framework for site-specific guidance from system design to real-time operation.

Figures (19)

• Figure 1: MasCOR: ML-assisted stochastic co-optimization framework for renewable power management systems. a, Generation of an oracle dataset by combining a renewable scenario generative model with LP-based operational optimization across sampled designs. b, Training of transformer-based actor–critic agents to learn optimal operational policies and two future performance metrics, cumulative profit (return-to-go, $RTG_t$) and net carbon emissions (carbon-to-go, $CTG_t$), conditioned on renewable trends $E$ and system design $D$. c, MasCOR infers distributions of profit and net carbon emissions ($CTG_0$) for each design using the generative model and trained agent, selecting the design–policy pair that minimizes production cost and net carbon emissions while satisfying a chance constraint on positive carbon emissions ($CTG_0>0$). d, MasCOR generates future renewable trend sets $E$ and performs online operation conditioned on these trends and the optimal design $D^*$, ensuring robust performance under uncertainty. Details of the architecture, algorithms, and benchmark comparisons of the two ML models are provided in Supplementary Notes 2, 3.
• Figure 2: Performance evaluation of the MasCOR framework for renewable data generation and dynamic operational problem solving. a, T-SNE embedding of synthetic renewable profiles generated by the generative model, compared with training and validation wind datasets, along with distributions of key operational features. b, Computational efficiency of the proposed MasCOR agent compared with the benchmark LP solver (Gurobi) for parallel LP problem solving. c, Dynamic operational performance comparison of benchmark data–driven models and the proposed MasCOR agent across different design categories. Details of computational efficiency and benchmark comparison experiments are provided in (Supplementary Notes 3.4)
• Figure 3: Regional design strategies and performance trade-offs in co-optimized power-to-methanol systems. a, Differences in the average renewable power availability and grid electricity prices across Dunkirk, Skive, Fredericia, and Weener (distributional details provided in Supplementary Figs. S12). b, Capacity shares of methanol (MeOH) production, PEMEC units, and BESS and CHT installations in representative Pareto-optimal designs, together with overall system size. c, Pareto-optimal capacity progression of PEMEC units, storage units (BESS and CHT), and MeOH production. d, Pareto frontiers of co-optimization results showing the trade-offs between the expected LCOM and net carbon emissions. MasCOR identifies two distinct design strategies for reducing carbon emission among the Pareto-optimal solutions: (i) an SE regime, characterized by increasing storage capacity, and (ii) a PR regime, characterized by decreasing MeOH production capacity under minimum PEMEC and storage capacity conditions (below 10 MW). In most regions, Pareto-optimal points shift from SE to PR as the expected net carbon emissions decrease below –50 ton/month. UQ results and full design specifications of Pareto points are provided in Supplementary Fig. S13.
• Figure 4: Regional operating strategies under different optimal design regimes. a, Capacity shares (%) of MeOH synthesis and PEMEC, BESS, and CHT units for the four representative Pareto-optimal designs illustrated in \ref{['fig2:co-op-result']}. The dotted line indicates system scale. b, Hourly operating strategies for optimal designs across regions. Distributions are obtained by averaging monthly operation profiles across 1,000 renewable scenarios using the MasCOR framework. The top panel illustrates how excess renewable power is used for either grid export or hydrogen export to the market. The bottom panel shows grid import, along with power charged to or discharged from the BESS and CHT units across the four locations.
• Figure 5: Validation of Pareto-optimal designs under dynamic operation. a, Comparison of the MasCOR-inferred Pareto front (nonbold points) with validation results (bold points) obtained from 1,000 monthly renewable generation datasets (2023–2024). b, Performance distributions at the two Pareto front endpoints: dotted areas indicate 85% confidence regions of MasCOR-inferred distributions; scatter points show validation results under varying monthly renewable power availability. Grid prices were held constant using historical data (2015–2022) to isolate renewable power uncertainty. c, Heat maps showing correlations between hourly renewable and grid variables and operational decisions for the two endpoint Pareto-optimal designs in each region.