Multistage stochastic optimization of a mono-site hydrogen infrastructure by decomposition techniques

The deployment of hydrogen infrastructures requires to reduce their costs. In this paper, we develop a multistage stochastic optimization model for the management, at least cost, of a hydrogen infrastructure which consists of an electrolyser, a compressor and a storage to serve a transportation demand. This infrastructure is powered by three different sources: on-site photovoltaic panels, renewable energy through a power purchase agreement and the power grid. We consider uncertainties affecting on-site photovoltaic production and hydrogen demand. Renewable energy sources are emphasized in the hydrogen production process to ensure eligibility for a subsidy, which is awarded if the proportion of nonrenewable electricity usage remains under a predetermined threshold. We formulate a multistage stochastic optimization problem, made of two coupled subproblems: an operational problem, management of the hydrogen equipment and the demand satisfaction; an electricity allocation problem, allocation of the electricity sources. Once decoupled with Lagrange duality, each subproblem is tackled by the dynamic programming algorithm, giving two sequences of Bellman functions, depending on a Lagrange multiplier which is updated. Finally, we obtain a state policy, based on a one-step minimization of an instantaneous cost plus a surrogate Bellman function, made of the sum of the operational and electricity allocation Bellman functions. The numerical results indicate that the algorithm provides relevant trajectories, and achieves a small duality gap, thus proving the effectiveness of this approach.