Stochastic optimization for unit commitment applied to the security of supply: extended version

TL;DR

The paper develops a probabilistic unit commitment framework to secure electricity supply under uncertainty, replacing the traditional one percent criterion with a risk-neutral, scenario-based optimization. It introduces a tractable two-stage stochastic MPC that approximates a multi-stage UC by solving a sequence of two-stage problems, and implements a single two-stage variant for practical use. The approach is evaluated on a real French case with nuclear, coal, CCGT, and OCGT units alongside PV and wind, showing improvements in lost load, lost production, and dispatch costs relative to deterministic planning, with scenario selection further enhancing performance and convergence. The work lays a foundation for real-time margin management under uncertainty, while identifying scalability, risk-aversion calibration, and more realistic unit-hydraulic modeling as avenues for future research.

Abstract

Transmission system operators employ reserves to deal with unexpected variations of demand and generation to guarantee the security of supply. The French transmission system operator RTE dynamically sizes the required margins using a probabilistic approach relying on continuous forecasts of the main drivers of the uncertainties of the system imbalance and a 1 % risk threshold. However, this criterion does not specify which means to activate upward/downward and when to face a deficit of available margins versus the required margins. Thus, this work presents a strategy using a probabilistic unit commitment with a stochastic optimization-based approach, including the fixed and variable costs of units and the costs of lost load and production. The abstract problem is formulated with a multi-stage stochastic program and approximated with a heuristic called two-stage stochastic model predictive control. It solves a sequence of two-stage stochastic programs to conduct the central dispatch. An implementation is conducted by solving an approximated version with a single two-stage stochastic program. This method is tested on a real case study comprising nuclear and fossil-based units with French electrical consumption and renewable production.

Figures (26)

• Figure 1: Probabilistic unit commitment approach. This UC tool has two main purposes: i) decide which units activate to make upward/downward variations to restore available margins if needed in the case of deficit margins; ii) provide a techno-economical approach to investigate the value of the short-term criterion by comparing the available upward/downward margins derived from the production plan of the stochastic optimizer to the required margins computed with the one % criterion. This study uses this UC tool for the first application.
• Figure 2: An overview of formulations for power system optimization under uncertainty. This Figure is presented in ROALD2023108725.
• Figure 3: Illustration of the problem timeline with $M$ LTTDs for a dispatch over $[T_1, T_2]$. For instance, the first LTTD at step 1 corresponds to the decision to start or not nuclear power plants based on the uncertainty available at this stage.
• Figure 4: Illustration of the sequence of multi-stage problems on a simplified example. In this example, we consider only three types of units: nuclear, coal, and CCGT (combined cycle gas turbine) power plants. $D^\text{ON}$ is the minimal duration to start a power plant. Notice that the values provided are examples that are not necessarily realistic. In the first multi-stage problem, the first-stage variables are nuclear units' ON/OFF status. In the second multi-stage problem, the first-stage variables are coal power plants' ON/OFF status. Then, in a third problem, it would be the ON/OFF of the CCGT power plants. This Figure is adapted from lucille2023.
• Figure 5: Scenario tree structure for multi-step algorithms Stochastic Nested Decomposition (SND) sddip and Stochastic Dual Dynamic Programming pereira1991multi, which exploits the Markovian assumption. This Figure is adapted from lucille2023.