Chance-Constrained DC Optimal Power Flow Using Constraint-Informed Statistical Estimation

Abstract

Chance-constrained optimization has emerged as a promising framework for managing uncertainties in power systems. This work advances its application to the DC Optimal Power Flow (DC-OPF) model, developing a novel approach to uncertainty modeling and estimation. Current methods typically tackle these problems by first modeling random nodal injections using high-dimensional statistical distributions that scale with the number of buses, followed by deriving deterministic reformulations of the probabilistic constraints. We propose an alternative methodology that exploits the constraint structure to inform the uncertainties to be estimated, enabling significant dimensionality reduction. Rather than learning joint distributions of net-load forecast errors across units, we instead directly model the one-dimensional aggregate system forecast error and two-dimensional line errors weighted by power transfer distribution factors. We evaluate our approach under both Gaussian and non-Gaussian distributions on synthetic and real-world datasets, demonstrating significant improvements in statistical accuracy and optimization performance compared to existing methods.

Figures (5)

• Figure 1: Comparison of the classical (fit and then transform) and constraint-informed (transform and then fit) approaches for reformulating chance constraints. The matrix $\bm{A}$ denotes the low-dimensional linear projection identified from the constraint structure.Comparison of Classical and Constraint-Informed Approaches for Reformulating Chance Constraints
• Figure 2: Aggregate forecast errors of five wind units using parameters in hodge2011wind
• Figure 3: Aggregate errors and best-fit probability density curves estimated using the classical and constraint-informed approaches.
• Figure 4: Out-of-sample worst-case constraint violations across ten runs. The right panel corresponds to the test system discussed in Section \ref{['sec:scalability']}, where the classical approach produced infeasible optimization models in all runs.
• Figure 5: Best BIC score versus $K$ for the aggregate forecast error $\Omega$ at different uncertainty dimensions on the Polish 2746-bus system.