Chance-Constrained AC Optimal Power Flow: Reformulations and Efficient Algorithms

TL;DR

This paper introduces a new chance-constrained AC optimal power flow formulation that guarantees system security under uncertainty, along with efficient algorithms and reformulations that improve scalability and accuracy in handling renewable energy variability.

Contribution

It presents an accurate, tractable reformulation of chance constraints for AC power flow and develops scalable algorithms, including an iterative method, for solving the problem efficiently.

Findings

The analytical reformulation accurately enforces chance constraints.

The iterative algorithm demonstrates scalability for large systems.

The proposed approach outperforms sample-based reformulations in tests.

Abstract

Higher levels of renewable electricity generation increase uncertainty in power system operation. To ensure secure system operation, new tools that account for this uncertainty are required. In this paper, we formulate a chance-constrained AC optimal power flow problem, which guarantees that generation, power flows and voltages remain within their bounds with a pre-defined probability. We then propose an accurate, yet tractable analytical reformulation of the chance constraints. The reformulation maintains the full, non-linear AC power flow equations for the forecasted operating point, and models the impact of uncertainty through a linearization around this point. We discuss different solution algorithms, including one-shot optimization with and without recourse, and an iterative algorithm which enables scalable implementations. We further discuss how more general chance constraint reformulations can be incorporated within the iterative solution algorithm. In a case study based on four different IEEE systems, we compare the performance of the solution algorithms, and demonstrate scalability of the iterative scheme. We further show that the analytical reformulation accurately and efficiently enforces chance constraints in both in- and out-of-sample tests, and that the analytical approach outperforms two alternative, sample based chance constraint reformulations.