Nowadays, power quality issues are becoming a significant research topic because of the increasing inclusion of very sensitive devices and considerable renewable energy sources. In general, most of the previous power quality classification techniques focused on single power quality events and did not include an optimal feature selection process. This paper presents a classification system that employs Wavelet Transform and the RMS profile to extract the main features of the measured waveforms containing either single or complex disturbances. A data mining process is designed to select the optimal set of features that better describes each disturbance present in the waveform. Support Vector Machine binary classifiers organized in a “One Vs Rest” architecture are individually optimized to classify single and complex disturbances. The parameters that rule the performance of each binary classifier are also individually adjusted using a grid search algorithm that helps them achieve optimal performance. This specialized process significantly improves the total classification accuracy. Several single and complex disturbances were simulated in order to train and test the algorithm. The results show that the classifier is capable of identifying >99% of single disturbances and >97% of complex disturbances.
The significant increase in the inclusion of devices sensitive to current and voltage fluctuations causes a growing interest in the study of power quality (PQ). A PQ event can be defined as a variation in the regular voltage or current waveform. Some of them can be classified as sags, swells, harmonics, fluctuations, interruptions, and over voltages. IEEE-1159 [
The sources of disturbances are very broad, and cause economic losses as well as equipment degradation, for both consumers as well as utilities [
In the online version of the tool once a PQ event is detected, a set of features are extracted from that waveform in order to reduce the size of the data. This is followed by a classification step in which the classification algorithm links a set of features with appropriate labels that represent the type of disturbance.
Learning techniques based on artificial intelligent (AI) methods are ideal for this kind of task due to their pattern recognition strength. Several classification algorithms that are appropriate for this are Artificial Neural Networks (ANN) [
Due to the varying causes of power disturbances, it is not uncommon to have the two or more types of disturbances within a measured signal window. A disturbance that consists of a combination of two or more individual disturbances is usually called a complex power quality disturbance. Historically these complex disturbances have not been adequately addressed in previous research. Most of the previous work addressed the problem as an addition to single disturbances analysis but not as a particular problem [
For instance, the proposed approach is a multiclass SVM classifier arranged to operate in a One vs Rest architecture, designed to process information in parallel where each classifier defines one class. The main advantages of the proposed methods are: 1) Optimal feature selection, 2) independent parameter configuration for each stage and each class present in the training set vector, 3) parallel data processing, 4) due the binary classifiers work independently of each other, there is no need to incorporate additional stages to classify complex power quality events.
This paper is organized as follows: Section 2 explains the concept of complex power quality disturbances and presents some previous works that focused on them. In the third Section, a general methodology to design, train and test an SVM classifier is presented. Section 4 explains the experimental test and their results. Finally, Section 5 presents the most important conclusions from the research.
A complex power quality event is a particular disturbance that comprises of a combination of two or more single disturbances. The most common complex disturbance is a combination of stationary disturbances such as harmonics or fluctuations with a short duration disturbance such as transient surges or sags.
In addition, it is also possible to find a combination of short-duration disturbances, for example, transient surges combined with oscillating voltage dips.
It is also possible to find complex power quality disturbances as a combination of three or even more single disturbances.
Complex disturbances increase the difficulty during the identification stage due to the co-existences and overlapping of different disturbance characteristics. This complication may result in an incorrect characteristic determination.
Some authors addressed these topics by mean different algorithms. For example, authors in [
Another alternative method is presented in [
Biswal, & Dash, [
Reference [
Contemporary research is increasingly using classifiers based on SVM due to their simplicity. L. Gang, & L. Fanguang present a method [
Sovan Dalai [
Reference [
A strategy that is quite common, but not always the most appropriate when designing the classification stage, is to treat a complex power quality disturbances as a new type of event, assigning in consequence a new class to each type of complex disturbance [
In addition, most of the previous proposals, the multiclass classifiers are implemented in a one-process unit. This architecture does not allow optimizing the feature extraction based on a particular class. Therefore, they need to use all features to describe all the classes. Furthermore, when it is necessary to add a new class for each additional complex event that wants to be identified, if the classifier is implemented in a one-process unit, the optimization problem could become even more complex.
Based on the current needs and an evaluation of the different methodologies previously presented it can be inferred that development of new algorithms that can handle both single and complex events, easy to implement as well as train, that allow a class-based optimization, and requires low computation cost is needed [
The proposed method can be explained in two separate stages:
・ The design and training algorithm.
・ The classification algorithm.
The summary of the different steps is presented in
The design and training algorithm’s main objective is to find the configuration that maximizes the classification's accuracy by optimizing the parameters that rule the behaviour of a classifier based on SVM algorithms. The algorithm's input corresponds to a training arrange that consists of the entire set of N disturbance classes that needs to be classified, for example swell, harmonics, sag, etc. The training set is represented by an [m,s] matrix where m is the number of waveforms and s the amount of samples that represent each waveform, parameter that depends on the selected sample rate and the configured length of the analysis windows.
The algorithm performs a series of calculations in order to extract the optimum set of features that better describes each class of disturbances and to obtain the best configuration of the parameters that govern the accuracy of the learning algorithm.
For more detail,
These calculations are explained next:
The objective of this process is to transform the training set waveform vector into equivalent representations in order to simplify the process of detecting the presence of a disturbance. Since the proposed method is focused on real, noisy signals, it is necessary to apply a de-noising technique to mitigate the effect of the noise in the sampled waveforms. Ref [
scheme improves the classifier ability. This method also narrows the signal dura- tion to a fixed numbers of fundamental cycles and additionally establishes the best sample rate.
The information obtained from the sampling process of a representative waveform contains a high percentage of redundant, noisy, and inconsistent information. In order to reduce the data and yet maintain most of the information present in the waveform, feature extraction is typically performed on all the waveforms. A feature is a numeric value obtained from a transformation performed on either the waveform samples or the coefficients obtained from the selected signal processing technique. All the parameters are obtained with the objective of representing some particular characteristic of the original waveform [
The first stage’s objective is to obtain the minimum set of features that characterizes each particular disturbance. It is important to remark that, at this phase of the algorithm, no information about a given class is used to calculate the features. They are selected to represent all classes present in the training set. The original training set, which dimension is [m, s], is reduced to an [m, n] arrangement, called the feature matrix, where s >> n. Since the features are obtained from diverse types of calculations, their dynamic ranges of the finalized parameters are very large. For this reason, the values of every column of the feature matrix are normalized to the region [−1; 1].
The feature extraction reduction procedure, presented in Section 3.1.2, is a process that generates an [m, n] matrix obtained from a set of signal waveforms, where n represents every extracted feature from each one of the m waveforms and is not dependent on or attuned to any particular class of disturbances.
The data mining process is the second stage used to reduce to the dimension of the training set [
Two different techniques are sequentially applied to the training set in order to select an optimal feature subset: The heuristic filtering and the exhaustive search algorithm.
The exhaustive search algorithm involves the training of the classifier employing different feature set combination. The exhaustive search computational cost increases as the amount of features to be processed grows. To reduce the processing load of the exhaustive search algorithm a heuristic filtering stage is previously applied with the objective to separate the most relevant feature set from the original training set. The results of the filtering process serve as input to the exhaustive search algorithm. Next, both stages are briefly explained:
・ Heuristic Filtering: The proposed filtering stage uses a label vector that maps each class to each row of the original feature matrix in order to calculate a feature ranking for each type of disturbance. The implemented methodology is based on Chi-square attributes feature selection [
・ These three heuristic techniques build a sorted list that ranks (from the highest to the lowest) which parameter describes a particular class the best. The algorithm combines the results and generates a unique ranking. Then, according to the user criteria, the j most relevant features are selected for each class. Because of this process, N different feature matrices (whose dimensions are [m, j] are generated from the [m, n] original feature matrix.
・ Exhaustive Search Algorithm: In order to find the optimal combination of the features, an exhaustive search strategy is implemented. It consists of testing the performance of the classifier for all 2j possible feature combinations. The j features explored by the algorithm are the ones generated at the heuristic filtering stage. This method is known as a wrapper algorithm [
A grid search algorithm [
Finally, the classifier is configured with the results of the grid search algorithm and trained using the features selected by the data mining process.
A trained and optimized classifier model is the outcome of the of the design and training algorithm.
In the next section of this paper, we explain how the classification algorithm to identify a disturbance in a measured waveform will use this conceptual model.
The objective of the classification algorithm is to process a waveform, detect the presence of a disturbance, indicate when the disturbance starts (only for short time disturbances) and classify them into a predefined group.
The signal processing techniques applied to train the classifier must be the same as that implemented in the Design and training algorithm (Section 3.1.1).
The purpose of this module is to detect the presence of an abnormality in the sampled signal and identify the instant when the power quality disturbance event begins or ends. If no disturbances are detected the classification algorithm discards all samples obtained from the measured waveforms.
Several methods have been developed to detect a disturbance in a waveform. Methods in reference [
The objective of this step is similar to the method presented in Section 3.1.2. However, this process only extracts the optimum feature set according to the Data Mining process results calculated in the Design and training stage. This reduced subset of features allows faster computation and thus ideal for real-time implementation.
This process uses the trained classifier model obtained from the design and training algorithm, to categorize the set of features extracted in the previous classification algorithm’s stages. This results in a label that indicates which class the measured disturbed waveform belongs to.
To test the proposed algorithm with Complex Power Quality disturbances a One vs. Rest of five binary SVM classifiers is developed. This section is organized in the following way: The first subsection presents the classifier architecture. Then, a description of the training set used to train and test the classifier is provided. The third subsection presents the techniques employed in the Design and Training algorithm and the respectively obtained results. Finally, the fourth subsection presents the classification results.
A kernel-based methodology called Support Vector Machine (SVM) is selected to build the classifier. Support Vector Machine mathematical theory can be found in [
Different machine learning methods were considered for classification stage: Support Vector Machine (SVM), Probabilistic Neural Network (PNN) and Extreme Learning Machine (ELM).
SVM method is selected mainly because: It has a strong founding theory; In general, the optimization problem involved in the training reaches the global optimum due to convex quadratic programming; It has no issue for choosing a proper number of parameters; It is less prone to over fitting; Yields more clear results and a geometrical interpretation; Since SVM is trained using dual representations and sparse arrays it is very efficient.
According to [
In [
Another comparative study concludes that ELM and SVM have similar accuracy performance for the most classification problems [
In [
To test the proposed method, five binary Support Vector Machine classifiers configured in a One vs. Rest architecture is set up as shown in
Due to their unique architecture, the classifier can classify single as well as complex disturbances without the need of adding new binary classifiers.
The selected kernel function for each of the five SVM binary classifiers is the Radial Basis Function (RFB) because it proves to be the most appropriate function for pattern recognition [
To train the classifier, 2600 disturbances were generated using a MATLAB tool developed by the authors [
| Single Quality Event | Total | Class | Sag | Swell | Harmonics | Interruption | Fluctuations |
|---|---|---|---|---|---|---|---|
| Sag | 400 | 1 | 1 | −1 | −1 | −1 | −1 |
| Swell | 400 | 2 | −1 | 1 | −1 | −1 | −1 |
| Harmonics | 400 | 3 | −1 | −1 | 1 | −1 | −1 |
| Interruption | 400 | 4 | −1 | −1 | −1 | −1 | −1 |
| Fluctuations | 400 | 5 | −1 | −1 | −1 | 1 | 1 |
| Complex Power Quality Event | Total | Class | Sag | Swell | Harmonics | Interruption | Fluctuations |
|---|---|---|---|---|---|---|---|
| Harmonics and Sag | 100 | 3 + 1 | 1 | −1 | 1 | −1 | −1 |
| Harmonics and Swell | 100 | 3 + 2 | −1 | 1 | 1 | −1 | −1 |
| Harmonics and Interruption | 100 | 3 + 4 | −1 | −1 | 1 | 1 | −1 |
| Fluctuations and Sag | 100 | 5 + 1 | 1 | −1 | −1 | −1 | 1 |
| Fluctuations and Swell | 100 | 5 + 2 | −1 | 1 | −1 | −1 | 1 |
| Fluctuations and Interruption | 100 | 5 + 4 | −1 | −1 | 1 | −1 | 1 |
While there is a wide range of disturbances, to simplify the analysis, only a subset that contains the most common types of disturbances is considered in this paper.
The following subsections explain the details of the techniques used and the associated results for each process of the stages shown in
To process the simulated or measured waveforms, the sample rate is configured to 10 [Kilo sample/sec]. Snapshots of 400 ms are used to for each waveform’s length, which is equivalent to 20 cycles of an undisturbed signal (assuming a fundamental frequency of 50 Hz).
Before the selection of Wavelet Transform (WT) as the signal processing methodology, other alternatives were studied. For example Stockwell Transform (ST) and Gabor Transform (GT). Previous work determined that these two signal processing methods perform very well with signals, which include noise. However, WT is better in term of simplicity and computational cost, therefore WT was selected for the signal processing stage [
A nine-level Discrete Wavelet Transform (DWT) using Daubechies number four wavelet mother was selected [
To complete the set of relevant features, the root mean square profile calculation is also proposed.
The feature extraction algorithm calculates the signals rms. profile as well as the nine DWT coefficients of the 2600 waveform of the training set to obtain the parameters presented in
| Signal Processing Technique | Extracted Feature | Nomenclature |
|---|---|---|
| RMS Profile | Minimum RMS Profile | Min RMS |
| Maximum RMS Profile | Max RMS | |
| Wavelet Transform | Maximum di module coefficient | Max abs di |
| Standard Deviation di coefficient | Std di | |
| Normalized Energy di coefficient | di Energy | |
| Maximum a9 module coefficient | Max abs a9 | |
| Standard Deviation a9 coefficient | Std a9 | |
| Normalized Energy a9 coefficient | a9 Energy |
Where i represents the ith calculated wavelet level.
As an output of this process, a [2600, 32] matrix is obtained. This matrix contains all features that characterize each type of disturbance.
This section presents the reduced selected features using the techniques elaborated in Section 3.1.3.
From the original [2600, 32] feature matrix, five matrixes were obtained, one for each class of disturbances, whose dimension are equal or less than [2600, 7].
After the number of features is significantly reduced by the filtering stage, it is important to find which combination of them produces the most accurate percentage in the training and validation stage.
To train and test the algorithm performance, 60% of the 2600 disturbances are used for the supervised training of the classifier, while the remaining 40% are employed for the validation process.
The results of the grid search algorithm are presented in
Once the best set of features that represent each disturbance and the optimum parameters C and Sigma that govern each binary SVM classifier is found, the design stage is concluded. Then, each binary classifier is trained using the LibSVM library [
| PQ Event | Selected Feature | Dimension |
|---|---|---|
| Sag | Min RMS, Max RMS, Max abs a9, d7 Energy, Max abs d5, Std d4. | 2600 × 6 |
| Swell | Min RMS, Max RMS, Std d9, d7 Energy, Max abs d4, Max abs d3, Max abs d2. | 2600 × 7 |
| Harmonics | Min RMS, Max RMS, Std d9, Max abs d9, Std d8, Max abs d5. | 2600 × 6 |
| Interruption | Min RMS, Max RMS, Max abs a9, Std d9, Max Abs d4. | 2600 × 5 |
| Fluctuations | Min RMS, Max RMS, Max Abs a9, Std d9, Max abs d9, Std d8, Max abs d8. | 2600 × 7 |
| PQ Event | Selected Feature | Validation Accuracy | Dimension |
|---|---|---|---|
| Sag | Min RMS, Max RMS, Max abs a9, Std d4. | 98.8% | 2600 × 4 |
| Swell | Min RMS, Max RMS, Std d9, Max abs d2. | 99.6% | 2600 × 4 |
| Harmonics | Std d8, Max abs d5. | 100% | 2600 × 2 |
| Interruption | Min RMS. | 100% | 2600 × 1 |
| Fluctuations | Min RMS, Max RMS, Max Abs a9, Std D8. | 99.7% | 2600 × 4 |
| SVM Classifier | Sigma | C | Validation Accuracy |
|---|---|---|---|
| 1. Sag | 2 | 4000 | 98.8% |
| 2. Swell | 2 | 1000 | 99.6% |
| 3. Harmonics | 3.5 | 3000 | 100% |
| 4. Interruption | 1e−5 | 50 | 100% |
| 5. Fluctuations | 4 | 500 | 99.7% |
To test the classifier architecture designed and optimized by the process presented in Section 4.3, two scenarios are used. In the first scenario, the classifier is tested using a set of single disturbances. On the other hand, the second scenario tests the classifier with a set of complex power quality disturbances.
Although this paper focuses on complex disturbances analysis, first at all, it is necessary testing the algorithm performance with simple disturbances.
To test the algorithm, 1000 waveforms are generated, 200 for each type of PQ events. All parameters that govern the disturbances, like magnitude, inception angle, duration, among others, are randomly generated considering the ranges established in [
The confusion matrix represented in
Analyzing
One dataset from the harmonics and interruption set are partially classified as a complex disturbance containing the respective single disturbance. This may be inferred as a partially correct classification.
To test the algorithm for a complex power quality scenario, a set 1200 waveforms are generated with a combination of simulated waveforms with real waveforms measured in an oil factory [
The results are summarized in the matrix presented in
The values displayed with parenthesis () refer to the event index described in
Considering a total of 1200 complex power quality events used to test the algorithm, only 33 were misclassified giving a success rate of 97.25%.
Analyzing the erroneous classification data set, the classifier was capable of identifying one of the two disturbances that was present in the complex event and thus was partially classified. In other words, 2334 disturbances, from 2400, were correctly classified. Under this consideration the complex power quality accuracy rate reach the 98.583%.
| Sag | Swell | Harmonics | Interruption | Fluctuations | Misclassified | Double | |
|---|---|---|---|---|---|---|---|
| 1. Sag | 200 | 0 | 0 | 0 | 0 | 0 | 0 |
| 2. Swell | 0 | 200 | 0 | 0 | 0 | 0 | 0 |
| 3. Harmonics | 0 | 0 | 198 | 0 | 0 | 1 | 1 (2 + 3) |
| 4. Interruption | 0 | 0 | 0 | 199 | 0 | 0 | 1 (4 + 3) |
| 5. Fluctuations | 0 | 0 | 0 | 0 | 200 | 0 | 0 |
| Harm. and Sag | Harm. and Swell | Harm. and Int. | Fluct. and Sag | Fluct. and Swell | Fluct. and Int. | Single | Triple | |
|---|---|---|---|---|---|---|---|---|
| Harmonics and Sag | 197 | 0 | 0 | 1 | 0 | 0 | 1 (3) | 1 (1 + 3 + 5) |
| Harmonics and Swell | 0 | 198 | 0 | 0 | 0 | 0 | 1 (3) | 0 |
| Harmonics and Interruptions | 0 | 0 | 194 | 0 | 0 | 1 | 4 (3) | 1 (3 + 4 + 5) |
| Fluctuation and Sag | 0 | 0 | 0 | 190 | 0 | 0 | 10 (5) | 0 |
| Fluctuations and Swell | 0 | 0 | 0 | 0 | 189 | 0 | 11 (5) | 0 |
| Fluctuations and Interruptions | 0 | 0 | 0 | 0 | 0 | 199 | 1 (5) | 0 |
The accuracy to identify complex power quality disturbances of different methodologies is compared in
This paper proposes a simple, efficient, fast and easily trainable method to classify single and complex power quality disturbances. The methodology is based on a combination of the Discrete Wavelet Transform (DWT) and the rms profile of each of the measured disturbances for feature extraction: a two-stage method to select the optimum set of representative features that reduce the feature set considerably maximizing the accuracy of the classification. A One vs. Rest multiclass SVM classifier was developed as a binary node array, and it was used to classify the extracted features.
The proposed methodology does remarkably well in classifying all single disturbances and outperforms most of the contemporary methodologies. The accuracy achieved exceeds those presented in [
| Liu Z. [ | EEMD | Rank-SVM | - | 95.36 |
|---|---|---|---|---|
| Biswall [ | FDST | DT | - | 98.19 |
| Cheng Long Chuang [ | WT | DS-ANN | ES | 98.4875 |
| Soval Dalai [ | CHT | ESVM-PCA | - | 97.6 |
| Proposed Method | WT | OvR SVM | ES | 98.588 |
EEMD = Ensemble Empirical Mode Decomposition; FDST = Fast Discrete Stockwell Transform; WT = Wavelet Transform; CHT = Cross Hilbert Transform; DT = Decision Tree; DS ANN = Dynamic Structural Neural Network; ICA = Independent Component Analysis; PCA = Principal Component Analysis; OvR SVM = One versus Rest Support Vector Machine; ES = Exhaustive Search.
This paper also demonstrates that excellent results can be achieved using a small set of features that are appropriately selected. The whole process can be parallelized because each node can be processed independently leading to faster computation times and thus ideal for online real-time implementation.
When a new complex power quality event needs to be included, the method has to be completely retrained to allow each classifier to consider the new event. This fact represents a weakness of the proposed method, which is shared with most of the algorithms based on linear learning. However, the classification remains robust even with increasing complexity of disturbances present in the signal compared to the ones presented in previous works [
Future work will focus on finding an optimum training set size that can be present and still provide acceptable results as well as overcoming the need for a full retraining in cases of newer exotic disturbances.
According to [
The authors wish to thank to Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET) and Universidad Nacional de Río Cuarto (UNRC) for their invaluable support.
De Yong, D., Bhowmik, S. and Magnago, F. (2017) Optimized Complex Power Quality Classifier Using One vs. Rest Support Vector Machines. Energy and Power Engineering, 9, 568-587. https://doi.org/10.4236/epe.2017.910040