Anomaly Detection And Localization In Power Grids Based On Random Matrix Theory And Deep Learning

With the development of Smart Grid,an increasing number of monitoring devices have been deployed in power grids and a large amount of measurement data have been collected in a timely manner.The spatio-temporal data contains rich information on the operating conditions of the grids.In order to make better use of the measurement data for realizing the vulnerability analysis and enhancing the situational assessment in power grids,based on random matrix theory and deep learning,the data is analyzed from two aspects in this dissertation:correlation analysis and sample feature analysis,with an application of anomaly detection and localization in power grids proposed.The first part of this dissertation(Chapter 3～6)studies the measurement data from the perspective of data correlation.The main research work is summarized as follows:1)With the arise of big power data,especially the increase in data dimensionality,a high-dimensional random matrix theory based anomaly analysis approach is proposed.It realizes early anomaly detection by tracking the variations of data correlations through the moving window method,which makes it sensitive to the abnormal grid behavior and robust against random fluctuations and measurement errors.The Marchenko-Pastur law and Ring law in the random matrix theory theoretically justify the feasibility of the proposed approach.The approach combines anomaly detection with localization functionalities by analyzing the eigenvectors corresponding to the outliers in the empirical spectrum.By analyzing the outlier behavior from multiplicative data windows,it demonstrates the product of multiple data windows can reinforce anomaly signals in abnormal grid operating conditions,which makes it easier for anomaly detection.Case studies on both the synthetic data from IEEE 33-bus,57-bus,118-bus systems and the real-world measurement data from a distribution grid demonstate the proposed approach is capable of detecting and localizing general power grid anomalies earlier than that would be possible by the raw data.2)In view that the spectrum from the real-world measurement data is often complex and it can’t be trivially dissected by using the Marchenko-Pastur law in the random matrix theory,the high-dimensional factor model is introduced for modeling the measurement data,with a spatio-temporal correlation analysis approach proposed for early anomaly detetion and localization.In the proposed approach,the analytical tools in the random matrix theory are used for high-dimensional factor estimation,which greatly reduces the calculating burdens and ensures the approach efficiency.The spatio-temporal estimators are proved to be effective in indicating the variations of spatial and temporal correlations of the data.Case studies on both the synthetic data from IEEE 33-bus,57-bus,118-bus systems and the real-world measurement data from a distribution grid verify the effectiveness of the proposed approach.Case study on comparison with some other existing detection techniques(such as support vector machine,auto-encoder,long short term memory network,etc)demonstrates the proposed approach is able to detect general power grid anomalies much earlier.3)Considering the low dimensional measurement data in low observability power grids can’t be accurately analyzed by the asymptotic theorems in the random matrix theory,based on the tensor version asymptotic theorems(also called random tensor theory),an increasing data dimensionality for anomaly detection and localization approach is proposed.The tensor version Marchenko-Pastur law and Ring law theoretically justify the effectiveness of the proposed approach,and the tensor version linear eigenvalue statistics gives insight into the data behavior from a high-dimensional perspective.The proposed approach solves the problem that low dimensional measurement data can’t be accurately analyzed by the random matrix theory.Case studies on both the synthetic data from IEEE 33-bus,low observability 118-bus systems and the real-world measurement data from a distribution grid verify the effectiveness of the proposed approach.Also,case study on the low observability IEEE 118-bus system demonstrates the proposed approach is able to detect anomalies earlier than the fundamental random matrix theory analysis approach.4)Considering some anomalies(such as osillations)in power grids are complex with random magnitudes and the features of them often can’t be generated well or even invisible,the nonliear random matrix theory is introduced for the measurement data analysis,with an application of anomaly detection proposed.Compared with the random matrix theory,the nonlinear random matrix theory combines the advantages of nonlinearity and correlation analysis approaches and demonstrates more powerful abilities,which makes it possible for identifying the invisible anomalies at an earlier stage.By combining random neural networks with tunable parameters(i.e.,the depth,width and activation function of the network),the proposed approach is more flexible for realizing anomaly detection in power grids.Considering it is impossible to install a μPMU at every bus of the IEEE 141-bus distribution system,an optimal μPMU placement algorithm based on improved weighted least square is designed.Case study on the IEEE 141-bus system demonstrates that:(1)54 μPMU should be installed for the system to be fully observable;(2)the proposed approach is able to detect anomalies earlier than the fundamental random matrix theory analysis approach.The second part of this dissertation(Chapter 7)analyzes the measurement data from the sample feature perspective.With the complicated operating conditions,the features of some anomalies are complex and can’t be accurately calculated.Based on bidirectional generative adversarial networks,an adversarial feature learning approach for anomaly detection in power grids is proposed.It is able to automatically learn the most representative features from the measurement data in an adversarial way.The adversarial learning process ensures the powerful ability of the approach in extracting arbitrarily complex features rather than the most simple features from the data.Based on the learned features,an anomaly detection index is designed to indicate the data behavior.Case studies on the IEEE 118-bus test system offer guidelines for the parameter selections of the proposed approach,including simple z-sampling distribution,moderate model depth and feature size.Case studies on the real-world measurement data from a distribution grid demonstate that the proposed approach is effective in reducing false alarms in anomaly detection compared with some other existing techniques(such as the threshold analysis,principal component analysis,deep auto-encoders,etc).