(119a) Capturing Spatial, Temporal and Technological Detail in Hydrogen Supply Chains By a Bilevel Optimization Strategy

Hydrogen is one of the key enablers of the energy transition and the decarbonization of our societies as confirmed by the most recent energy roadmaps ¹ and national plans aiming for carbon neutrality by 2050. For hydrogen to play a significant role in the future demand mix, its costs should yet go down implying improved infrastructure design and operations. This paper presents a methodological framework for the optimal design of Hydrogen Supply Chains (HSC) to provide effective support for the study of deployment scenarios. According to the energy source used for its production, hydrogen can be labeled as: green, if produced through Power-to-Gas (PtG) systems, converting renewable electrical energy into green hydrogen and offering a more flexible power grid, better management of the intermittency of renewable energy sources, and a low-carbon fuel supply: as grey if obtained from fossil energy sources with Steam Methane Reforming (SMR) which is the most common process used today and finally as blue h if produced by the SMR process combined with carbon capture, utilization, and storage (CCUS).

Due to the characteristics of the HSC network, economic and environmental assessment is key to its optimal design and deployment that requires the consideration of the set of all possible raw materials, energy sources, technology maturity levels, potential sites for location, transportation and distribution options, storage, end uses, as well as the dynamic change of hydrogen demand over time.

Several works have been identified in the scientific literature to address this complex optimization problem ². Most studies involve mathematical models with mixed-integer linear programming (MILP) formulation, associated with an epsilon-constraint technique for tackling the multi-objective issue, mainly based on the total daily cost of hydrogen (TDC) and the Greenhouse Gas (GHG) emissions of the whole supply chain ^3,4. Yet for more than one objective, the construction of the Pareto front by mathematical programming techniques is usually a time-consuming task, since each Pareto solution requires at least one scalar optimization. An alternative to the solution of such problems is to use metaheuristics, and specifically, Multi-objective Evolutionary Algorithms (MOEAs). MOEAs are stochastic population-based nature-inspired algorithms, able of handling multiple objectives, continuous and discrete variables, nonlinear and multimodal functions. However, as these search algorithms are designed to work over unconstrained search spaces, they generally exhibit poor performance when solving highly constrained problems, even if sophisticated constraint-handling techniques have been developed. The scientific objective of this work is thus to propose a hybrid methodology to solve the HSC problem, which decomposes the global problem in such a way that some advantages can be taken of the strengths of every single approach, mitigating simultaneously their disadvantages.

Methods

The original HSC problem ⁴ is decomposed into two parts (see Figure 1): the (master) sub-problem and the continuous (slave) sub-problem. The master sub-problem is treated by the multi-objective evolutionary algorithm, in which the integer variables (number of production units) and their size (continuous variables) are encoded in every individual in the population. For each individual, a linear programming sub-problem is solved to determine the corresponding optimum production rates and transportation flows. This Linear Programming (LP) problem is constructed according to the values of the integer variables provided by the MOEA in such a way that it is almost a canonical transportation problem. The integer variables produced by the MOEA can be repaired to ensure that this problem is feasible. Subsequently, the MOEA recovers the continuous variables from the LP solver, to compute the TDC and GHG objectives. Once evaluated, each individual has its fitness function value assigned by the MOEA, which evolves the population for the next generation.

The proposed model takes the economy of scale for production and storage facilities into account with the “six-tenth-factor rule” ⁵. The technological maturity of the various units that is reflected in their installation cost, power efficiency, maximal production capacity and the cost evolution of the different energy feedstocks over time is considered. The resulting model can thus be formulated as a mixed-integer nonlinear programming problem (MINLP) with MATLAB environment. An MOA algorithm is a tailored made version used to solve the upper-level problem, whereas the solution of the lower-level problem is performed using CPLEX v12.8.0.

Computational experiments

The proposed model is applied to a case study, i.e., Midi-Pyrénées part of the Occitanie Region in France ⁶. The available resources are renewable energy sources (wind, solar and hydro) and natural gas, which must be exported. The set of options for hydrogen production accounts for green hydrogen (alkaline electrolysis cells (AEL) or polymer electrolyte membranes (PEM) with renewable energy sources), blue (SMR with CCUS), and grey (SMR without CCUS). Hydrogen demand is related to the transport sector for use in fuel cell electric vehicles (FCEV).

The region under study is divided into eight subregions (grids) and the time horizon (2020-2050) is divided into seven periods of five years each. Figure 2 presents the obtained Pareto front for this instance. It is composed of 1000 points yielded by MOEA. Each point represents a complete solution, that is, the result of strategic decisions, i.e., size, type, location of production and storage technologies, as well as logistics related to hydrogen transport between grids, for each period.

The Pareto front is divided into segments that are colored according to the shade of hydrogen mostly used to meet the hydrogen demand. Segment 1 comprises non-inferior solutions with Levelized Cost of Hydrogen (LCOH) from 1.64 - 1.90 USD/kgH₂ ; segment 2 from 1.90 - 1.95 USD/kgH₂ TDC; segment 3 from 1.95 - 2.13 USD/kgH₂ TDC; segment 4 from 2.13 - 2.49 USD/kgH₂ TDC; and segment 5 from 2.49 - 2.86 USD/kgH₂ TDC. In this way, the solutions in the left part of the front mainly involve the SMR technology, whereas the solutions at the right part of the front mainly use PEM electrolysis powered by renewable (wind) energy to meet the hydrogen demand.

For the sake of illustration, let us examine the composition of the segment that is mainly constituted of solutions using water electrolysis technology to satisfy the hydrogen demand. These solutions can be considered as the most expensive alternatives for deploying the HSC, but involve the best green options. Figure 3 shows a detailed solution from this segment. The squares indicate the number of production units, the arrows between grids indicate transport flows, and the pie charts indicate demand satisfaction by production type. It can be observed that the solution presents an LCOH of 2.62 USD/kgH₂, and GHG emissions of 1.86 kgCO₂-eq/kgH₂. Alkaline electrolysis (AEL) technology is employed using electricity from wind. In the first period, 33% and 67% of H₂ demand are fulfilled by AEL/wind and PEM/wind, respectively. Note that the AEL demand satisfaction drops from 33% to only 6%, from the first to the second period, due to the decrease in PEM technology cost compared to AEL. In periods 5 and 6, the network shows the installation of PEM electrolysis coupled with photovoltaic systems; nevertheless, most of the hydrogen is still produced by PEM/wind technology. In the last two periods, the contribution of demand satisfaction by technology remains the same, even if two new electrolysis PEM/wind plants are installed in the last period.

Conclusions

This work proposed a comprehensive methodological framework for the optimal design, deployment and management of Hydrogen Supply Chains HSC focusing on eco-mobility applications and their spatio-temporal integration considering the potential of Renewable Energy Sources. This framework can be viewed as a decision support system for scenario analysis. to achieve the desired step-up across the hydrogen value chain. An innovative point of the methodology is to explore the wide range of capacity sizes for a range of new technologies that may be involved gradually on the market.

The optimization strategy could now be extended to address other objective functions such as risk, the inclusion of dynamic aspects associated with the seasonal variability of energy sources, and the incorporation of other hydrogen demands and interactions with systems (ammonia and methanol production, buildings and industrial sector, etc.).

Reference

(1) IEA - International Energy Agency. The Future of Hydrogen; 2019.

(2) Li, L.; Manier, H.; Manier, M. A. Hydrogen Supply Chain Network Design: An Optimization-Oriented Review. Renew. Sustain. Energy Rev. 2019, 103 (January), 342–360. https://doi.org/10.1016/j.rser.2018.12.060.

(3) Almansoori, A.; Shah, N. Design and Operation of a Future Hydrogen Supply Chain: Multi-Period Model. Int. J. Hydrogen Energy 2009, 34 (19), 7883–7897. https://doi.org/10.1016/j.ijhydene.2009.07.109.

(4) De-León Almaraz, S.; Azzaro-Pantel, C.; Montastruc, L.; Boix, M. Deployment of a Hydrogen Supply Chain by Multi-Objective / Multi-Period Optimisation at Regional and National Scales. Chem. Eng. Res. Des. 2015, 104, 11–31. https://doi.org/10.1016/j.cherd.2015.07.005.

(5) Böhm, H.; Zauner, A.; Rosenfeld, D. C.; Tichler, R. Projecting Cost Development for Future Large-Scale Power-to-Gas Implementations by Scaling Effects. Appl. Energy 2020, 264 (December 2019), 114780. https://doi.org/10.1016/j.apenergy.2020.114780.

(6) Région Occitanie / Pyrénées-Méditerranée. Scénario Région à Énergie Positive de La Région Occitanie / Pyrénées-Méditerranée; 2017.