Power Grid Topology Classification Based on Time Domain Analysis Jia He, Maggie X. Cheng and Mariesa L. Crow, Fellow, IEEE Abstract—Power system monitoring is significantly im- all depend on the correct network topology information. proved with the use of Phasor Measurement Units (PMUs). Topology change, no matter what caused it, must be The availability of PMU data and recent advances in ma- immediately updated. An unattended topology error may chine learning together enable advanced data analysis that lead to cascading power outages and cause large scale is critical for real-time fault detection and diagnosis. This blackout ( [2], [3]). In this paper, we demonstrate that paper focuses on the problem of power line outage. We use a machine learning framework and consider the problem using a machine learning approach and real-time mea- of line outage identification as a classification problem in surement data we can timely and accurately identify the machine learning. The method is data-driven and does outage location. We leverage PMU data and consider not rely on the results of other analysis such as power the task of identifying the location of line outage as flow analysis and solving power system equations. Since it a classification problem. The methods can be applied does not involve using power system parameters to solve in real-time. Although training a classifier can be time- equations, it is applicable even when such parameters are consuming, the prediction of power line status can be unavailable. The proposed method uses only voltage phasor done in real-time. angles obtained from PMUs. It first extracts frequency Compared to previous works on line outage detec- domain features from the PMU data streams, and then trains a classifier to learn the network topology based on tion and identification, this work does not rely on the the frequency domain features. The proposed method is results of other critical tasks such as state estimation tested by using simulated data from PSAT. It is shown ( [4]) or load-flow analysis ( [5]). These tasks require that the frequency domain features are robust against not only network connectivity information but also line dynamic load changes and noise in data. The prediction parameters and power injections. In this paper, we use performance is comparable to previous works that require measurement data only to determine the status of power detailed system information such as line parameters. lines, thus there is no interlocking with other tasks Index Terms—Line Outage, Machine Learning, Classi- such as state estimation. It is paramount that the line fication, Network Topology outage identification can be performed independently and prior to the tasks that rely on network topology I. INTRODUCTION information to work. The data-driven approach compared to the previous works that involve solving accurate state In recent years topics on anomaly detection in power equations is a fundamental breakthrough. systems and subsequent fault localization are heavily Compared to earlier works that use machine learning investigated. They received much attention due to the approaches, the proposed work distinguishes itself in importance of the topics and the challenges to address several ways: 1) It is not based on a particular flow them. We focus on one type of anomaly in this paper: model (DC or AC). The input to the classifiers is derived power line outage. information from PMU measurements, and the classifiers Power line outages caused by overgrown trees, wild do not use model-specific information; 2) We do not use animals, and inclement weather conditions account for voltage magnitudes and power injections. We only use most power disruptions ( [1]). It is critical to develop phasor angles. Instead of using phasor angles directly, real-time procedures that can quickly detect and identify we use the difference between the phasor angles from the outage location since other important tasks such as two adjacent buses to build time series. We then use the flow analysis, state estimation, and contingency analysis spectrum features extracted from the time series as input This work was supported in part by the National Science Founda- for the classifiers. These features more accurately capture tion of USA under grants 1854077 and 1854078. the correlation with the network topology than those used J. He and M. Cheng are with Illinois Institute of Technology, in previous work; 3) The performance of the classifiers Chicago, IL 60616 USA (e-mail: [email protected]). M. Crow is with Missouri University of Science and Technology, are reported by using precision and recall as metrics, Rolla, MO 65401 USA (e-mail: [email protected]). instead of an overall accuracy or error rate as in the past 2 work. The overall accuracy is high mainly because the method is developed to solve the line outage identifi- classifiers perform well for the non-case, i.e., it predicts cation problem by using the DC model. An important the network has no outage when there is no outage. For assumption is that line outage is sparse in the power grid. rare event detection, the non-case is the majority case The proposed method also achieves low-complexity, but in the dataset. Even though a classifier performs poorly different from [5], the proposed method is completely for the ”yes” case, the overall accuracy is still high. data-driven, and does not need the line parameters (e.g., However, we think it is a reasonable argument that to reactance). detect the ”yes” case accurately is more important. We [9] solved outage detection and state estimation as therefore emphasize how to improve the detection rate coupled problems. It is also not rare to address line (recall) in this paper; 4) Our work does not depend on the outage detection and identification as one coupled prob- sparsity assumption as in [5]. Since each line is predicted lem (see [10], [11]). Both [10] and [11] use incremental separately, the number of line outages that it can predict changes from measurements between two time instances is unlimited; 5) Using our feature extraction method, as random variables to build time series. [10] uses the classifiers do not require PMU data from all buses. phasor angles and [11] uses voltage magnitudes. In [10] Experiment results show that it requires only a subset change point detection is performed based on the time of PMU data. We further show which PMU location series directly, and line outage is detected from the is dispensable and which is not, and the conclusion first series that reported the change. In [11] detection is specific to the line we try to predict. This implies and identification are based on changes on conditional that accurate topology information of the network is not correlation. There are also several works using message essential to the machine learning algorithms. However, passing algorithms for network topology inference, e.g., knowing which pair of buses is connected by a line [12], [13]. can reduce the feature space. The knowledge of the full In recent years, there are a handful of works using topology is a plus, without which the algorithms still machine learning approaches for power line outage de- work although with longer training time; 6) Finally, to tection. To name a few, in [14], a classical support vector our knowledge, this is the first work to predict power machine (SVM) approach is developed for single line line outage in a very large system (1354-bus with 1991 outage detection. In [15] and [16] neural networks are lines) at high detection rates. developed to predict single and double line outages, and The rest of the paper is organized as follows: in both use only a single hidden layer. In [15], the input Section II, we review some related work on the topics of to the neural network includes phasor angles and power power line outage in modern power systems; in Section injections; in [16] the input is voltage magnitudes and III, we provide an overview of the methodology, the phasor angles. [16] addressed partial data inference and analysis behind the proposed method, and then detailed [17] discussed optimal locations for PMUs. It was solved description of the feature extraction method and descrip- as an optimization problem to maximize the system’s tion of the classifiers; Section IV provides extensive ability to detect single-line outages. simulation results on line outage identification; Section V concludes the paper with a plan for future work. III. PROPOSED METHODS II. RELATED WORK A. Overview We briefly review some representative works on power This paper focuses on the identification of power line line outage detection and identification. In [6], a proce- outage, i.e., to locate which lines are out. We use the dure is developed to detect a single line outage based measurement data from buses for this task. Throughout on line connectivity information and PMU data. Line the implementation of the method, we assume no prior outage is identified based on pre-outage flow analysis. knowledge about the admittance matrix or state equa- To perform flow analysis, the system admittance matrix tions of the system. is needed. In [7], the method is extended to address First, we need to identify the measurement that shows double line outages. It is pointed out in [7] that missing high correlation with power line topology. PMU data may lead to indistinguishable outages. This Recall that the active power transfer is a function of conclusion is consistent with our findings in this paper. phasor angles. Let θi be the phasor angle at bus i, and Multiple line outage detection and identification using Pij be the active power transfer from bus i to bus j. We PMU data are addressed in recent works.