PowerModelsRestoration.jl: An open-source framework for exploring power network restoration algorithms

Highlights

• Algorithms for optimal ordering of repairs in power system restoration.

• Exploration of accuracy and computational burden of different power flow formulations.

• Open-source software implementation as the Julia package PowerModelsRestoration.

Abstract

With the escalating frequency of extreme grid disturbances, such as natural disasters, comes an increasing need for efficient recovery plans. Algorithms for optimal power restoration play an important role in developing such plans, but also give rise to challenging mixed-integer nonlinear optimization problems, where tractable solution methods are not yet available. To assist in research on such solution methods, this work proposes PowerModelsRestoration, a flexible, open-source software framework for rapidly designing and testing power restoration algorithms. PowerModelsRestoration constructs a mathematical modeling layer for formalizing core restoration tasks that can be combined to develop complex workflows and high performance heuristics. The efficacy of the proposed framework is demonstrated by proof-of-concept studies on three established cases from the literature, focusing on single-phase positive sequence network models. The results demonstrate that PowerModelsRestoration reproduces the established literature, and for the first time provide an analysis of restoration with nonlinear power flow models, which have not been previously considered.

Introduction

As the threat of exogenous grid disturbances, e.g., natural disasters or sophisticated targeted attacks, continues to intensify, so does the importance of expedient power network restoration. There is thus an increasing need for decision support tools that can assist network operators in identifying optimal restoration plans, and ultimately provide autonomous self-healing capabilities to the grid. Unfortunately, high-fidelity modeling of power system restoration has proven notoriously difficult due to the challenge of finding an AC-feasible operating point in networks where hundreds to thousands of components have been damaged [1], [2]. However, recent advances in convex relaxations of the AC power flow equations have shown promise for single-time-point N-k analysis [3].

While traditional work on power system restoration has focused on system reenergization following a blackout where the vast majority of components are undamaged [4], [5], [6], the work in this paper considers the longer-term problem of restoring power supply following extreme physical impacts, such as hurricanes or earth quakes, where a large number of components must be repaired before they can be re-energized. Specifically, it focuses on component restoration ordering, i.e., selecting the sequence in which components should be prioritized for restoration, in order to minimize energy not served over time. This prioritization task results in a sequential network design problem, which, in practice, can be remarkably challenging to solve [7], due in part to the combination of discrete and continuous optimization variables as well as nonlinear, non-convex constraints. Consequently, significant network approximations and/or heuristic methods are often required to make the problem tractable. Optimizing the restoration order can provide a significant reduction in energy not served relative to what is achieved through applying simple rules or heuristics [8]. However, previous work [2], [9] have demonstrated that popular approximations, e.g., DC power flow, fail to capture important aspects of the problem, leading to suboptimal restoration ordering, infeasible intermediate solutions, and higher-than-necessary energy not served.

Designing and validating the effectiveness of different approaches to this problem requires significant research, and is an essential step towards the aspiration of a resilient, self-healing grid. To support this design challenge, the core contribution of this work is a novel software framework, PowerModelsRestoration, which enables rapid exploration of power network restoration algorithms. By building on the PowerModels framework [10], PowerModelsRestoration is able to consider a broad range of power flow formulations, spanning the full AC equations [11], convex relaxations [12], [13], and active-power-only approximations [14]. This restoration framework includes exact restoration algorithms, modeled as mixed-integer nonlinear programs (MINLPs), and in the future will contain heuristic restoration algorithms, such as largest capability first. Some of the notable features of PowerModelsRestoration include: (1) support for AC-based restoration, (2) restoration plan quality guarantees provided by convex relaxations, (3) incorporation of storage devices in power system restoration, and (4) tools for simulating restoration plans with the AC power flow equations. With these features, PowerModelsRestoration aspires to be a valuable tool for rapidly exploring the wide variety of possible restoration algorithms, and providing a baseline implementation of established restoration algorithms for resilience analysis.

Utilizing the proposed software framework, this work develops case studies that highlight the benefits and drawbacks of established power flow formulations. On the one hand, the results demonstrate the flexibility and value of the software framework, while on the other hand provide new insights into restoration nonlinear formulations, not previously considered to our knowledge. An unexpected contribution of the paper is the insight that convex relaxations of the power flow equations may provide a valuable tool for balancing accuracy and performance when developing power restoration plans.

This work begins with a brief overview of the power system restoration context that motivates this work in Section 2, followed by a review of mathematical programming and the PowerModels framework in Section 3. The mathematical modeling layer of PowerModelsRestoration is presented in Section 3.3. Section 4 illustrates how the modeling layer can be combined into more complex analysis workflows. Section 5 develops restoration studies to validate the framework and Section 6 concludes the paper.