**1. Introduction**

With the increasing demand on the power energy in the modern industry, power transmission systems are becoming more and more large-scale and complicated [1,2]. Due to the system complexity, anomalies and disturbances are often unavoidable in real power systems. If these unexpected events are not handled timely, they may cause huge accident risks and even the widespread power outages, which are companied by the huge economic loss and severe life inconvenience. Therefore, it is of grea<sup>t</sup> value to detect the abnormal events quickly and maintain the safe running of power systems [3]. In recent years, the wide area measurement system (WAMS) based on synchronous phaser technology has been successfully applied in the power industry. The phasor measurement units in WAMS provide the basic data support for the real-time dynamic monitoring of the power system [4]. Accordingly, safety monitoring and disturbance detection of power systems based on the measurement data analysis has been a hot topic in academic and engineering fields [5–7].

Aiming at the power system disturbance detection task, researchers have conducted a lot of studies, which can be roughly divided into two categories: time/frequency domain analysis and multivariate statistical analysis. The time/frequency domain analysis investigates the power system changes from the perspective of the signal processing, which involves the time domain, frequency domain, or time-frequency domain. In consideration of the good time-frequency localization property, Huang et al. [8] discussed the application of the Morelet wavelets method in power system disturbance detection. The Hilbert Huang

**Citation:** Wang, S.; Tian, Y.; Deng, X.; Cao, Q.; Wang, L.; Sun, P. Disturbance Detection of a Power Transmission System Based on the Enhanced Canonical Variate Analysis Method. *Machines* **2021**, *9*, 272. https:// doi.org/10.3390/machines9110272

Academic Editors: Hongtian Chen, Kai Zhong, Guangtao Ran and Chao Cheng

Received: 11 October 2021 Accepted: 4 November 2021 Published: 6 November 2021

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Transform is another time-frequency signal analysis tool. Manglik et al. [9] applied it to the disturbance detection for the electric power system. Ghaderi et al. [10] proposed the time-frequency analysis method assisted by current waveform energy and normalized joint time-frequency moment and demonstrated its performance in the high-impedance ground fault detection. Salehi et al. [11] designed a morphological edge detection filter to obtain the transient features of fault signals. Liu et al. [12] used the wavelet packet Tsallis singularity entropy algorithm for disturbance detection. In general, the time/frequency domain analysis methods mainly analyze the single signal and fail to fully consider the correlation between different parameters. In response to this shortcoming, some scholars started their work by applying multivariate statistical analysis. Multivariate statistical analysis (MSA) methods can realize the simultaneous detection of multiple parameter changes and have outstanding advantages in the complex industrial systems. However, most of the present MSA studies focus on the system modeling and disturbance detection in the chemical process, steel industry, and high-train system [13–17], but MSA's application to power system monitoring is very rare. Barocio et al. [18] first introduced the principal component analysis (PCA) method into the field of power system monitoring and discussed the detection and visualization of power system disturbances based on PCA. Guo et al. [19] built a transmission line fault detection method by combining PCA and support vector machine. Considering the masking influence caused by the oscillation trend and strong noise of power system data, Cai et al. [20] further proposed a PCA*k*NN method, which is superior to the basic PCA method in the numerical model testing and New England power system model data. These research articles point out that the multivariate statistical analysis has grea<sup>t</sup> application potential in the field of power system monitoring.

Although PCA and PCA*k*NN methods have achieved significant success in the power system monitoring field, they have some shortcomings deserving further studies. On the one hand, these methods do not take into account the dynamic characteristics of power system data, which easily leads to a high missing detection rate. Different from the other industrial process data with the steady operation mode, the power system data, such as the voltage and current, are with obvious dynamic trends. On the other hand, the present methods do not consider how to enhance the detection of weak disturbances. In real applications, some disturbances may be with small amplitudes, slow changes, unclear disturbance characteristics, and are easy to be covered by noises [21,22]. How to enhance the detection capability on these weak disturbances is one challenging task.

Aiming at the aforementioned problems, this paper proposes a SLCVA*k*NN-based disturbance detection method for power transmission system monitoring by combining canonical variate analysis (CVA), *k*NN, and statistical local analysis (SLA). Compared with the traditional PCA-based power system monitoring methods, CVA has a stronger dynamic feature extraction ability [23–25], which provides a new and powerful tool for power system data analysis. Referring to the present PCA*k*NN method, the CVA*k*NN statistical model is developed to deal with the dynamic periodic oscillation signals. Furthermore, in order to enhance the detection of weak faults, SLA is integrated for SLCVA*k*NN modeling, which mines the local statistical information for better weak disturbance monitoring.

The rest of the paper's content is arranged as follows. The principle of the proposed SLCVA*k*NN methodology is given in the Section 2, while the corresponding disturbance detection procedure is detailed in Section 3. One case study on the actual industrial data is used to verify the effectiveness of the proposed method.
