Optimizing Power Generation in Uncertain Environments via Deterministic and Stochastic Approaches

The article discusses limitations in optimizing the French electricity grid’s operational window, which is critical for managing risk and uncertainty in the sector. The authors identify three main limitations:

Risk Aversion Limitation

The first limitation lies in the need to well-calibrate the risk aversion to the TSO (Transmission System Operator) risk policy. While other risk-averse strategies could be employed, such as chance-constraint approaches or considering Conditional Value-at-Risk instead of a risk-neutral approach, this limitation exists because the current model only considers a neutral approach.

Problem Formulation Limitation

The second limitation is the problem formulation itself, as the single-phase approach provides results but the problem is multi-stage by design due to technical constraints. To address this, two research directions are proposed: (1) using time reduction computation from previous extensions to test a two-stage stochastic MPC approach and compare it with the single-phase approach, and (2) better modeling uncertainty with a scenario tree and solving the multi-stage formulation with decomposition techniques such as SDDP (Sequential Deterministic Domination Points).

Computational Burden Limitation

The third limitation is related to computational burden. Three solutions are proposed:

1. Importance Sampling Techniques: Using advanced importance sampling techniques can help identify relevant scenarios for stochastic optimization, reducing the number of scenarios required to model uncertainty.
2. Advanced Decomposition Techniques: Utilizing accelerated Benders decomposition approaches [19] and [20] can speed up computation. These techniques can be combined with specific constraints-reformulation methods to address computational challenges.
3. Hybrid Machine Learning and Optimization Approach: Investigating a hybrid approach that combines machine learning and optimization can help compute quickly a feasible solution. This approach could leverage optimization proxies [21] and [22], which allow replacing time-consuming optimization models with machine-learning proxies that can be used in real-time and/or computationally demanding applications.
   In summary, the article highlights limitations in optimizing the French electricity grid’s operational window and proposes solutions to overcome these challenges. By using advanced importance sampling techniques, leveraging acceleration methods, or exploring hybrid machine learning and optimization approaches, the computational burden can be significantly reduced, enabling more efficient risk management in the sector.