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1 Classification of Pollution Severity on Insulator Model using Recurrence Quantification Analysis K.A. Chaou, A. Mekhaldi and M. Teguar Laboratoire de Recherche en Electrotechnique Ecole Nationale Polytechnique of Algiers, Algeria Avenue Hassen Badi, B.P 82, El-Harrach, 62 Algiers, Algeria. and Abstract In this work, a novel approach is established in order to investigate and monitor the performance of high voltage insulators. Since leakage current (LC) waveforms are intimately linked to pollution severity, it is primordial to study and investigate leakage current characteristics during the entire contamination process. In this paper, performance of a plane model insulator is studied through a number of laboratory tests under various levels of pollution contamination. LC waveforms are investigated through a nonlinear method called Recurrence Quantification Analysis (RQA). This method revealed successfully the non-linear characteristics of LC for identifying the dynamic behaviors on the insulator surface. Moreover, RQA indicators are found to be directly linked to the contamination severity. Thus, mean values of these indicators are computed and used as an input to three different classification algorithms (knearest neighbors, Naïve Bayes, Support Vector Machines) in order to classify contamination severity. Index Terms-- Insulator model, leakage current, Recurrence Quantification Analysis, feature extraction, classification algorithms. I. INTRODUCTION In order to improve power grids reliability, many researches are focused on high voltage insulators. This key element of the electrical transmission and distribution system remains, yet, vulnerable to various environmental conditions. Indeed, high voltage insulators are suffering from natural and industrial pollution with serious consequences of with serious consequences of electrical flashover occurrence. To avoid this phenomenon, many authors studied the effect of pollution accumulation on the insulator surface and found out that the leakage current (LC) is closely related to the contamination level [-2]. To predict and monitor level contamination on high voltage insulators, several methods, or techniques, known as feature extraction techniques, have been applied to study the characteristics of LC. Ramirez-Vazquez and Fierro-Chavez [] specified measurements as the pulse number, peak value and cumulative charge value of LC to assess pollution severity. Similarly, Li et al. [4] pointed out the mean value, maximum value and standard deviation of the LC as suitable feature extraction. Moreover, Jiang et al. [5] proposed to examine the phase angle between LC and applied voltage, the maximum pulse amplitude of LC and the total harmonic distortion as characteristic parameters to assess condition of polluted insulators. However, FFT analysis, power spectrum analysis and wavelet analysis are also frequently used. Principally, magnitudes of rd, 5th and 7th (corresponding to 5 Hz, 5 Hz and 25 Hz respectively) harmonics increase within the flashover process [6]. Wavelets are useful for decomposing LC into low frequency, medium frequency and high frequency components. According to Song et al. [7], these high frequency components remain useful to monitor the contamination process. Recently, Pylarinos et al. [8] presented 2 features from time and frequency domains, and compared classification performance of LC waveforms using three classification algorithms (Knn, Naïve Bayes, Support Vector Machines). Results from the frequency domain provide better results compared to those obtained from the time domain and also to a set containing both frequency and time features. Besides, Artificial Neural Network is widely used to monitor pollution severity [9], to predict LC and flashover voltage of insulators []. Nonetheless, fuzzy logic method is also used to estimate pollution severity []. Quantities expressing pollution severity are: the equivalent salt deposit density (ESDD), the surface pollution conductivity, the leakage current, the air pollution measurements, the non-soluble deposit density (NSSD) and the pollution flashover voltage gradient [2]. However, due to the lack of appropriate diagnostic methods able to monitor and evaluate rapidly an insulator condition, the Recurrent Plot (RP) was recently introduced in this area. Initially, this technique was conceived to detect nonlinearities and eventually chaotic dynamics in experimental signals in physics [], in financial data time series [4] and ecosystem time series [5]. Recently, it has been successfully applied to study LC and monitor the flashover process [6-7]. Nonetheless, the Recurrence quantification analysis (RQA), which based on RP to calculate indicators and provide useful informations even for the short and non-stationary data, was applied to classify healthy pattern from pathological ones in many medical domains. Thus, this paper uses RQA as a tool to classify pollution severity on high voltage insulators /4/$. 24 IEEE

2 II. METHODS A. Recurrent plot Recurrence plots are graphical tools which visualize the recurrence behavior of the phase space trajectory of dynamical systems. They were first proposed in 98 by Maizel and Lenk [8] as a method of visualizing patterns in sequences of genetic nucleotides. They have since been introduced into the study of dynamical systems. Recurrence plots are briefly defined in (). () where is the norm (in this research, Euclidian norm is adopted), ( ) is the Heaviside function and is the studied time series. This means if the distance between and is less than, then = and a dot is placed at in the RP. B. Recurrence Quantification Analysis The RQA is a method of nonlinear data analysis for the investigation of dynamical systems. This method, developed by Webber and Zbilut [2], aims to quantify differently appearing structures in recurrence plots. This paper focuses on five fundamental measures:. Recurrence Rate (), which is the density of recurrence points in a RP. corresponds to the probability that a specific state will recurrence. RR is calculated by (2). (2) 2. Determinism ( ), which is the ratio of recurrence points on the diagonal structures to all recurrence points. Diagonal lines represent epochs with similar time evolution of states. is related with the determinism of the system and is calculated as in (). () where is the frequency distribution of the lengths of the diagonal structures in the RP. is the threshold, which excludes the diagonal lines formed by the tangential motion of a phase space trajectory.. Average diagonal line length ( ). It represents the average time that two segments of the trajectory are close to each other, and can be interpreted as the mean prediction time. (4) where is the total number of diagonal lines. 4. Laminarity ( ), is analogous to determinism except that it is the ratio of recurrence points forming vertical structures. (5) where is the distribution of the lengths of the vertical structures. 5. Entropy (), refers to the Shannon entropy of the probability to find a diagonal line of exactly length l in the RP. reflects the complexity of the RP in respect of the diagonal lines. (6) C. Classification algorithms Three of the most commonly used classification techniques are employed in this paper: the k-nearest neighbors classifier (Knn), the Naïve Bayesian classifier and Support Vector Machines (SVM). These three algorithms have already been used in many domains [2]. The k-nearest neighbors (Knn) classifier [22] is a simple, easy to implement classifier, which requires no training and that assigns an object to a class based on the classes of its k- nearest neighbors. Several distances can be used to determine the nearest neighbors. Knn is suitable for little data set and can achieve better performance. The Naïve Bayes classifier [2] is a simple probabilistic classifier based on Bayes theory. It implies the assumption that the independent variables are statistically independent, it is known to be rather effective. Support Vector Machines (SVM) [24] is considered as one of the most accurate machine learning classifiers because of its ability to solve problems of linear and non-linear classification by finding the maximum margin hyper plane that separates the classes. Several kernel functions can be used, including linear, polynomial, RBF and sigmoid. However, SVM suffers from multi-class categorization problem. Its algorithm has to be adapted in the case of multi-class recognition problem. III. RESULTS AND DISCUSSION A. LC acquisition Experiments were carried out using a high voltage test transformer ( kv/5 kva, 5 Hz). The laboratory model was constituted by a glass plate (5 mm x 5 mm x 5 mm). Made up of aluminum paper, two electrodes (5 cm x mm x. mm) have been used on both HV and ground sides. The distance between the two electrodes represents the leakage path of the 52 L cap and pin insulator (292 mm). The artificial pollution is composed of distilled water and NaCl and is uniformly and continuously sprayed all over the model surface. Tests are conducted under an applied voltage varying from kv rms to 5 kv rms. In this voltage range, no partial arcs have been observed. The chosen conductivity values are:.,.9,.7,.2 and. ms/cm. The overall flowchart of the proposed method and following numerical processing is depicted in Fig.. Knn Start LC acquisition Phase space reconstruction RQA computation L Naïve Bayes Pollution classification SVM End Fig.. Flowchart of the proposed method for pollution classification based on RQA.

3 B. Recurrent plot Based on LC waveforms presented in Fig.a, RP is computed. Fig 2.b. shows RP of LC 25-5 khz frequency components under a fixed applied voltage. In case of. ms/cm conductivity value, few points compose the RP indicating weak discharge activity on the insulator surface. For.2 ms/cm, formation of white bands is noticed. This indicates the appearing of local arcing discharges on insulator model. Finally, for. ms/cm, RP contains very dense points and larger white bands. The white segments indicate the intermission of intensive discharges and the dense points indicate the intensive arcing discharges. C. Phase space reconstruction Before applying RQA on LC waveforms, a phase space reconstruction has to be performed. This is a primordial processing step, because it converts the LC signal into a recurrence plot in order to extract their features using recurrence quantification analysis. Therefore, by applying the Takens embedding theorem [25], LC time series is transformed into phase space trajectories as described in (7). LC (ma). ms/cm (7) where, is the length of the time series, represents the embedding dimension, represents the delay between samples and is phase space trajectory describing the dynamical behavior of LC. That is to say, by transforming the LC from a high dimensional space to an -dimensional sub-space, RPs and RQA can be established to investigate more efficiently LC properties. From [6] and according to the C-C method, and should be chosen equal to 5 and 2 respectively. D. RQA measures Since RP can describe time series visually but not quantitatively, the RQA quantities a time series through the measurements based on the RP. RQA indicators are computed as shown in Fig.2.c. When the conductivity increases, the LC waveforms amplitudes increase. We notice the presence of pulses around the maxima. All measurements, show larger variation when conductivity increases., which quantifies recurrent points, varies from to.45 for a conductivity of. ms/cm, decreases until.8 for.2 ms/cm and reaches (a) 6,2 ms/cm 2, ms/cm (b) RR DET L LAM ENTR (c) Fig. 2. LC waveforms for different conductivities in (a) with their corresponding RP in (b) and RQA indicators in (c) for 6kV rms

4 for. ms/cm. shows also tight peaks for small pollution conductivities (less than.2 ms/cm), and larger ones with the increasing of contamination. Physically, small values of indicates few recurrent points. This is explained by a changing of LC waveform from a quasi-sinusoidal signal, to a more chaotic or non-stationary one. In other way, by increasing the conductivity, discharges keep appearing on the insulator surface. These discharges bring deformations on the LC waveforms, which loses its sinusoidal and predictable pattern. Similarly, values decreases with the increasing of pollution severity. Since points out the dynamic of a system, it is high when pollution is limited which indicates that LC signal is periodic. However, at sever contamination case, values gets higher. This proofs a change in LC waveforms behavior, moving to a stochastically and nonperiodical dynamic, and shows low values when LC waveforms get distorted from its sinusoidal shape. Concerning the, which represents the average time that two segments of the trajectory on the RP are close to each other, and can be interpreted as the mean prediction time. It shows larger variations with the increasing of pollution. It diminishing indicates that LC is becoming less predictable. is an important indicator. Although being analogous to, it brings a considerable investigation. Indeed, shows lower values when pollution is intensified (. ms/cm) informing about the fewer occurrence of laminar states in the LC. Thus, there are more single recurrent points to describe the RP of LC. Such isolated recurrent points predict more random behavior of LC. Concerning, entropy is used for measuring the complexity of the system whose the signals are represented. For a low pollution severity (less than.2 ms/cm), is practically constant and equal to, but shows peaks due to LC deformations. Meanwhile, when pollution is intensifying (. ms/cm), presents lower values and looks like a sinusoidal signal. Such signal indicates the changing complexity of the LC waveform. Therefore, LC behavior is becoming non-periodical. Mainly, when pollution is intensified on the insulator surface, RQA values approach, suggesting a non-periodical LC signal. Also, contamination inducts distortions and pulses of the LC waveforms, especially on peaks regions. Therefore, RQA values are composed of many but small magnitudes and tight pulses for a low level of pollution (less than.2 ms/cm). However, when contamination is severe, RQA values contain few but long magnitude peaks and large pulses. Such variation quantifies and describes LC non-periodical behavior under pollution. E. Feature extraction To extract a feature vector from RQA measures, we opt for computing their mean values. This choice is explained and put forward by Fig.. It can be seen from it that all mean values of the five indicators decrease with the increasing of pollution conductivity. Thus, RQA mean values are directly linked to pollution level. However, it is important to note that RQA values are dependent of the applied voltage value. Indeed, for every applied voltage value, RQA measurements are unique. Note that, the feature vector, which will serve as an input for classification algorithms, is composed of the five RQA mean values, plus the applied voltage value. RQA mean values,96,92,88,84,8 RR DET LAM F. Classification results In order to estimate pollution severity through LC classification, 5 classes are assigned to test conductivities, from the least to the most severe, as described in table. Database is composed of LC waveforms. 9% of this database is used as the training set and % as the test set. Since the problem consists of multi-class recognition, the strategy one vs. all was used in the SVM algorithm, as well as the linear kernel. Concerning the Knn algorithm, the Euclidian distance was chosen, with a k value equal to. As table shows, classification results are successful for the samples in the case of SVM and Knn algorithms. However, naïve Bayes classifier offers very bad results with 7 misclassifications out of. These results were somehow predictable. SVM is known to be a high performance classifier. This is due to its ability to deal with linear and non-linear pattern recognition problems. Knn seems also to be a very good choice in this work. However, Naïve Bayes classifier, although being simple and fast, demonstrates low performance. This might be caused by its independent feature assumption. Further experimentations have to be done to differentiate SVM and Knn like using a larger training and test datasets, or setting a different feature extraction strategy. IV. CONCLUSION To diagnostic pollution severity on a plane model insulator, an examination of LC signals though RQA was established. Therefore, a brief RP representation of LC is given. Then, five RQA indicators are computed and examined for different level of pollutions. These measurements characterized very well LC signal behavior. Further, mean values of the five RQA indications are found to diminish when pollution is increasing under a fixed test applied voltage. Thus, these five features plus the applied voltage are chosen as input to three classification algorithms. Results of classification announce SVM and Knn as suitable algorithms to choose instead of the Naïve Bayes classifier. The work described in this paper presents an alternative technique to monitor and study LC signal under contamination process. 2,75 2,5 2,25 2,75,5 ENTR Fig.. RQA indicators mean values under different pollution levels L

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