DC Optimal Power Flow with Joint Chance Constraints

TL;DR

This paper introduces a scalable, sample-based algorithm for solving joint chance-constrained DC optimal power flow problems, effectively managing renewable energy uncertainty with less conservativeness and improved computational efficiency.

Contribution

It proposes a novel S$ ext{l}_1$QP-type trust-region algorithm that handles large-scale, uncertain power systems without strong distribution assumptions, reducing conservativeness.

Findings

Algorithm outperforms existing methods in computational speed.

Solutions are less conservative, satisfying constraints with desired probability.

Effective on IEEE test cases, demonstrating practical applicability.

Abstract

Managing uncertainty and variability in power injections has become a major concern for power system operators due to the increasing levels of fluctuating renewable energy connected to the grid. This work addresses this uncertainty via a joint chance-constrained formulation of the DC optimal power flow (OPF) problem, which satisfies \emph{all} the constraints \emph{jointly} with a pre-determined probability. The few existing approaches for solving joint chance-constrained OPF problems are typically either computationally intractable for large-scale problems or give overly conservative solutions that satisfy the constraints far more often than required, resulting in excessively costly operation. This paper proposes an algorithm for solving joint chance-constrained DC OPF problems by adopting an S$\ell_1$QP-type trust-region algorithm. This algorithm uses a sample-based approach that avoids making strong assumptions on the distribution of the uncertainties, scales favorably to large problems, and can be tuned to obtain less conservative results. We illustrate the performance of our method using several IEEE test cases. The results demonstrate the proposed algorithm's advantages in computational times and limited conservativeness of the solutions relative to other joint chance-constrained DC OPF algorithms.