Orateur
Description
The increasing penetration of renewable energy sources in power systems amplifies the need for storage to manage their inherent intermittency. In this context, evaluating the opportunity cost of stored energy—commonly referred to as usage values—becomes essential. These values can be computed by solving a multistage stochastic optimization problem, where uncertainty arises from net demand (the aggregation of consumption and non-dispatchable generation), the availability of dispatchable units, and inflows for hydroelectric storage.
We aim to compute these usage values for each country in the interconnected European electrical system in the context of the prospective studies currently carried out by RTE using their simulation tool, Antares. The energy system is mathematically modeled as an oriented graph, where nodes represent countries and arcs represent interconnection links. The combination of spatial complexity (50 nodes, one storage per node) and temporal complexity (a one-year horizon modeled at two timescales—weeks and hours) makes the application of classical stochastic dynamic programming techniques, such as SDDP, challenging.
To address this, we apply Dual Approximate Dynamic Programming (DADP), which decomposes the global multistage stochastic optimization problem into smaller independent nodal problems and a transport problem. This decomposition produces nodal usage values that depend only on the local state, independently of the states of other nodes.
To assess the accuracy of this approach, we present a case study involving three countries—France, Germany, and Switzerland—each modeled with a representative energy mix, a single storage unit, and a few dispatchable generators. Interconnections between countries are modeled as aggregated exchange links between countries. For this tractable model, we compute the exact usage values as functions of the three storages, and benchmark them against the approximations produced by decomposition methods under varying approximation levels.
Finally, we present numerical results illustrating the behavior of the DADP algorithm in this two-timescale setting, where usage values are computed at the weekly scale, while decomposition prices are computed at the hourly scale.
