Rule-based classification of power quality disturbances using S-transform

Electric Power Systems Research 86 (2012) 113–121

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Rule-based classification of power quality disturbances using S-transform ˜ A. Rodríguez ∗ , J.A. Aguado, F. Martín, J.J. López, F. Munoz, J.E. Ruiz Department of Electrical Engineering, University of Málaga, Spain

a r t i c l e

i n f o

Article history: Received 3 March 2011 Received in revised form 16 September 2011 Accepted 16 December 2011 Available online 5 January 2012 Keywords: Power quality disturbances Classification Rule-based Neural networks

a b s t r a c t This paper presents a rule-based approach for the classification of power quality disturbances. The disturbed signal is first characterized using the multi-resolution S-transform, which acts as a feature extraction tool. Then, a simple but robust rule-based classification algorithm is used to identify disturbances. This algorithm uses linear and parabolic rules as pattern classifiers where decision boundaries are established by a heuristic search. The classification algorithm has a modular structure where each module works separately to detect specific disturbances. The most common types of disturbances, including sags, interruptions, swells, harmonics and oscillatory transients, were analyzed. Moreover, complex disturbances consisting of combinations of two simple events (simultaneous or consecutive in the same interval) were also analyzed. In both cases, noise, ranging from 40 to 20 dB, was also considered. The tested data set contains power quality signals obtained using mathematical models, power quality events obtained from power network’s simulations using PSCAD/EMTDC and measured signals at electrical installations. Finally, evaluation results verifying the accuracy of the proposed method are presented and compared to those obtained from a classification system based on an artificial neural network. © 2011 Elsevier B.V. All rights reserved.

1. Introduction Regular operations in the distribution network, such as switching loads and capacitors, fault clearing and lightning, along with the proliferation of power electronic equipment and non-linear loads in industrial, commercial and domestic applications, have led to increased amounts of polluted power systems in terms of distorted voltage and current signals. These distortions can lead to failures or malfunctions of the many sensitive loads connected to the power system, thus incurring a high cost for end users. Several studies quantify these costs in modern power systems [1,2]. Improvement of power quality (PQ) standards has a positive impact not only on the distribution utility but also on PQ-sensitive energy customer satisfaction. PQ is becoming increasingly important and is widely recognized as one of the major issues to be addressed in modern power systems [2]. One major requirement to ensure power quality in distribution systems is the monitoring of power system performance. PQ monitoring is not an easy task, and it typically involves sophisticated hardware instrumentation and software packages. A key point in this task is the analysis of large amounts of monitored data with minimum intervention from PQ experts [3]. Therefore, it is desirable to develop expert-based tools for automatic analysis and classification of PQ events.

∗ Corresponding author. Tel.: +34 951952335; fax: +34 951952512. E-mail address: [email protected] (A. Rodríguez). 0378-7796/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.epsr.2011.12.009

A number of techniques have been proposed for automated classification of different types of PQ events [4–21]. These approaches share a common working scheme, which is depicted in Fig. 1. Monitored signals are first filtered using some type of signal processing tool for feature extraction. Then, distinctive features are fed into a previously trained classifier module for identification and classification. In this work, the general scheme proposed in Fig. 1 has been followed. For the distorted signals, several sources have been considered: (i) synthetic signals obtained from parametric equations, (ii) signals generated by network simulation using PSCAD/EMTDC [22], and (iii) measured signals at electrical installations. These groups of signals contain most typical simple disturbances, including sags, interruptions, swells, harmonics and oscillatory transients, as well as complex disturbances consisting of combinations of two simple simultaneous or consecutive events in the same interval. The pattern extraction phase consists of the identification of characteristics that facilitate joint distinctive patterns belonging to each perturbation group that are immune to noise and easy to obtain and interpret. There exists no general approach for feature selection; this strongly depends on expertise knowledge [23]. In PQ analysis, many approaches make use of signal processing tools to extract distinctive features. Among existing signal processing tools, the Fourier transform (FT) is inadequate for analysis of non-stationary events, and the short-time Fourier transform (STFT), although to a lesser extent, also fails to achieve good resolution in both time and frequency. On the other hand, time-frequency transforms such as the wavelet transform (WT) have also been used in

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Fig. 1. Automated classification scheme.

The ST can be derived from the WT by modifying the phase of the window function or mother wavelet. Given a time-dependent signal, x(t), the ST can be derived [24] as the product of the signal and a phase correction function e(−j2␲f) . The S-transform of x(t) is defined as:



∞

S(, f ) = PQ studies [4–12]. The WT extracts information from the signal in the time and frequency domains simultaneously. However, it also exhibits some disadvantages, such as sensitivity to noise level and dependency of its accuracy on the selected basis wavelet. More recently, the S-transform (ST) has been proposed in PQ analysis to overcome the drawbacks of the WT [13–21]. The ST can conceptually be interpreted as a hybrid of the STFT and the WT. It uses variable window length and, through use of the FT kernel, can preserve phase information during decomposition [24]. In this work, extracted features from distorted signals are obtained using the ST. It is shown that even in the presence of complex disturbances with different levels of noise this tool successfully characterizes the signals. Finally, a classifier must be designed. Most of the artificial intelligence techniques have been used as classifiers in PQ analysis. They have been combined with the WT or ST, such as in artificial neural networks (ANNs) [5–7,14–16], fuzzy logic [8,17], decision trees [9,18], hidden Markov models [12], support vector machines [10,19], and expert system [12,20,21]. The main highlights at every single stage represented in Fig. 1 are the following: • As an extension to previous works [9,10,13–21] where it is only analyzed complex disturbances consisting of combinations of sag and harmonics and swell and harmonics, we have also analyzed some other plausible complex perturbations such as sag and transient oscillation, swell and transient oscillation, and, finally, transient oscillation and harmonics. This new perturbations clearly introduce higher complexity in the data set. Noise ranging from 40 to 20 dB has also been considered. • A reduced and simple set of features extracted from the Stransform are associated to each distorted signal class enabling the classifying stage. This allows advancing in accuracy, simplicity and reliability. • The development of a rule-based classifier consisting of several units, each of which is specialized for one type of disturbance and only makes use of the proposed features that are necessary for its function. These units work separately such that the whole system can easily detect complex disturbances. This paper is organized as follows. In Section 2, the development of the basic theory of multi-resolution ST is briefly described and is used to obtain distinctive features for classification. The rule-based classifier design is described in Section 3. Classification results using synthetic, simulated and measurement signals are presented in Section 4. These results are compared with those obtained from a system based on a feedforward backpropagation ANN. Finally, conclusions are presented in Section 5.

x(t)gf ( − t)e−j2ft dt

(1)

−∞

where gf () is the Gaussian modulation function, defined as: |f | 2 2 gf () = √ e−( /2 ) 2

(2)

and =

1 |f |

(3)

The expression becomes:



∞

2 2 |f | x(t) √ e−((−t) f /2) e−i2ft dt 2 −∞

S(, f ) =

(4)

The discrete version of (4) is calculated, taking advantage of the efficiency of the fast Fourier transform. The discrete Fourier transform of the time series x(t) is obtained as: H

 n  NT

=

N−1 

x(kT )e−(2i/N)nK

(5)

k=0

The discrete S-transform is obtained by allowing f → n/NT and  → jT:

 S jT,

n NT



=

N−1    m+n

H

NT

G(m, n)ei2mj/N

(6)

m=0

where G(m, n) = e−2

2 m2 /n2

(7)

and j, m, n = 0, 1, . . ., N − 1. The discrete inverse of the S-transform can be obtained as:

⎡ ⎤ N−1  N−1    ⎣ S jT, n ⎦ ei2nk x(kT ) = NT

n=0

(8)

j=0

The output from ST analysis is a complex matrix whose rows and columns represent frequency and time, respectively. Each column represents the local spectrum in time. Frequency–time contours with the same amplitude spectrum are also obtained. This information is used to detect and characterize power disturbance events. An example of a multi-resolution ST analysis for a complex signal containing an oscillatory transient and a 7th harmonic is presented in Fig. 2. The perturbed signal is plotted in the time domain in Fig. 2(a). In Fig. 2(b), the manner in which these two disturbances are located in a time–frequency domain can also be observed. Finally, in Fig. 2(c), a 3-D mesh showing amplitude, frequency and time plots where, for the sake of clarity, the values associated with the fundamental frequency have been omitted is depicted.

2. Pattern design using the S-transform 2.2. Distinctive features 2.1. Mathematical formulation The ST [24] was introduced as an alternative to the STFT for localization of time–frequency spectra. The ST gives time and frequency information, as does the STFT, but it uses a variable window length that provides information at different resolutions, such as in the case of the WT [24].

The accuracy of the classification depends not only on the number of distinctive features but also on the characteristics of these features that make them unique and salient. An efficient pattern can be defined from the observation of ST contours. Below, some examples of signals with various disturbances are analyzed in order to illustrate the pattern proposed in this approach.

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Fig. 2. Signal with an oscillatory transient and a 7th harmonic (a). ST analysis contours (b) and 3-D mesh giving amplitude, frequency and time (c).

A voltage sag to 50% that begins at 31 ms with a duration of 47 ms is depicted in Fig. 3(a). In Fig. 3(b), the 50 Hz contour can be seen to decrease in value during the disturbance. The frequency contours corresponding to 350 Hz and 700 Hz in Fig. 3(c) and (d), respectively, present a low energy value at the beginning and at the end of the sag. These contours are distinctive of the disturbance and can be translated for automatic recognition of the disturbed signal. Fig. 4(a) depicts a signal with an oscillatory transient and seventh harmonic content, with 0.4 and 0.25 p.u. magnitudes, respectively. The oscillatory transient starts at 25 ms and has a duration of 6 ms, whereas the harmonic starts at 60 ms and has a length of 30 ms. In Fig. 4(b), the 50 Hz contour is a horizontal line that demonstrates no change in magnitude at the fundamental frequency. A large amount of energy can be identified in the contours of 350 Hz and 700 Hz in Fig. 4(c) and (d), respectively. The results shown above have been taken into account in the selection of the characteristic features and during the development of the classification strategy. The fundamental frequency contour has proven to contain valuable information regarding sags, swells and interruptions. Hence, the mean value of the 50 Hz contour has been taken as a distinctive feature. However, this value does not clearly discriminate between sags and interruptions, and therefore,

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Fig. 4. Oscillatory transient signal (a), 50 Hz contour (b), 350 Hz contour (c) and 700 Hz contour (d).

the minimum value of the 50 Hz contour, which is indicative of the severity of the disturbance, has been taken as the second feature. In order to discriminate disturbances in the presence of harmonics, the energy of the third, fifth and seventh harmonic (150 Hz, 250 Hz and 350 Hz, respectively) contours is used as distinctive features. This approach has been restricted to these frequencies, although it could be extended to other harmonics within the Nyquist condition [7]. The sum of the energies from 600 Hz to 1600 Hz (the Nyquist frequency) has also been taken as another characteristic feature. This feature yields information related to oscillatory transient events. A summary of the distinctive features used in the rule-based classification scheme is given in Table 1. 3. Rule-based classifier design Similar to the pattern design phase, there exists no general approach as to the manner in which the rules should be defined; rather, this depends strongly on expert knowledge. In this section, a simple, robust rule-based algorithm is proposed. The definition of the algorithm follows the procedure shown in Fig. 5. It is further explained in the subsequent sections. 3.1. Rule definition A set of distorted signals, the training set, is selected to define simple rules that are able to discriminate the disturbances. In this stage, the expert knowledge is used to define the rule by disaggregating the disturbances [23,25,26] into three large groups: magnitude disturbances, transients and waveform distortion (Fig. 6). The first level is defined using the patterns distinctive features. For instance, a swell is an elevation of the fundamental frequency contour, and thus, the F1 feature should be higher for this Table 1 Features description.

Fig. 3. Voltage sag (a), 50 Hz contour (b), 350 Hz contour (c), and 700 Hz contour (d).

Feature

Description

F1 F2 F3 F4 F5 F6

Mean of the fundamental frequency contour (50 Hz) Minimum of the fundamental frequency contour Energy of the 3rd harmonic contour (150 Hz) Energy of the 5th harmonic contour (250 Hz) Energy of the 7th harmonic contour (350 Hz) Sum of energy from 600 to 1600 Hz contours

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Fig. 7. Graphical representation of inconsistency and uncovered errors in classification.

Fig. 5. Block diagram for rule definition.

Fig. 6. A structure inference process for classifying PQ disturbances. Fig. 8. Heuristic metric for determination of the best boundary value.

disturbance than in other classes. For this case, a linear boundary can be defined to separate different disturbances in classes.

of 1.0104, the maximum M (M = 0.99889, p = 2697, n = 0, P = 2700) is obtained.

3.2. Heuristic search A rule to separate a single class from the remainder requires a decision limit based on a specific feature. A linear boundary may yield inconsistency and uncovered errors [27]. As depicted in Fig. 7, using decision boundary 1 to separate examples from class A produces inconsistency errors, as it captures negative examples (from other classes) covered by the rule. As a solution, the limit is moved to a higher value, decision boundary 2. This shift of level produces a decision line that leaves some correct examples (class A) uncovered. A quantitative assessment based on the number of classification errors produced by each decision level can be made. Thus, a heuristic measure, M, can be defined, and a search for the value of the decision limit that yields the maximum M is performed such that: M=

p−n P

(9)

Here, p is the number of positive examples from a specific class covered by the rule, n is the number of negative examples from other class covered (inconsistency) and P is the total number of positive examples in the dataset. In Fig. 8, M, p and n values for different decision levels are shown. It should be noted that n has been changed into (P − n)/P for a better graphical representation. It can be observed that for a decision level

3.3. Separate uncovered signals Next, all positive examples that are covered by the defined rule are separated from the training set, and an additional (secondary) sentence to the rule is defined to cover the remaining positive examples. These two steps can be iterated until, if possible, all positive examples are covered and all negative examples are uncovered; a simple rule that presents some errors is better than a rule with many sentences and no errors to avoid the risks associated with a loss of selectivity [28]. The rules obtained by this procedure are presented in Eqs. (10)–(13) and the relative decision values are shown in Table 2. The reference value has been established on the basis of expert knowledge and analysis of maximum and minimum values of each class, in addition to p, n, P and M values. if F1 > 1.0104 · (F1min ∈ SWELL) then UP

(10)

if F1 < (F1min ∈ NORMAL) then DOWN

(11)

if (F3 > F3max ∈ INT) or (F4 > 1.4(F4max ∈ INT)) or (F5 > F5max ∈ INT) then HARM

(12)

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Table 2 Optimal boundary decision value obtained for heuristic search. Rule

Reference value

Heuristic search

p

UP DOWN

F1min ∈ SWELL F1min ∈ NORMAL

1.0104 1

2697 900

HARM

F3max ∈ INT F4max ∈ INT F5max ∈ INT

1 1.4 1

OT

F3max ∈ INT F6max ∈ SWELL

SAG/INT

0.047

n

P

M

0 0

2700 900

0.9989 1

3600

0

3600

1

1.05 1.976

3600

0

3600

1

0.060

1781

29

1800

0.9789

Fig. 10. Rule-based classifier scheme.

if (F6 > 1.05 · (F3max ∈ INT)) or (F6 > 1.976 · F6max ∈ SWELL and F1 > F1min ∈ NORMAL) then OT

(13)

These decision rules classify the disturbances in the first level as indicated in Fig. 7, with regard to DOWN (magnitude), UP (magnitude), TRANSIENT and harmonic DISTORTION. The DOWN class is used to distinguish between sags and interruptions. In Fig. 9, two sets of these events are plotted in the plane F1–F2. A linear rule that splits the two sets is not possible. Because the set of sags has a quadratic profile, a parabolic rule can be established for splitting both sets. In order to discriminate these two signals, a quadratic function that discriminates sags and interruptions has been used. The method used to obtain the parabolic rule (14) is simple; the quadratic equation is fitted to the plot of the set of interruptions in the F1–F2 plane. The constant term was evaluated in the same manner as the linear boundaries for the rest of the rules, and a maximum value for M of 0.9789 (p = 1781, n = 19 and P = 1800) was found. F2 − 0.97(F1)2 > 0.060

(14)

This rule consists of relational values between two features and therefore the relationship is maintained when various levels of signal noise are added, yielding good results. The scheme of the resulting classifier algorithm is presented in Fig. 10, where each module generates a logic value 1 if the signal satisfies the respective rule. When the DOWN module is fulfilled,

indicating that the signal has a diminution of the magnitude, the SAG/INT module operates. Next, the results module acts as a digital-to-analog converter, receiving from each module a 1 or 0, indicating whether the disturbance is present or not, respectively. As the modules (rules) operate separately, several modules can detect the corresponding events within a complex disturbance.The module HARM ORDER facilitates the evaluation of the 3rd, 5th and/or 7th harmonics when the HARM module detects the presence of a harmonic using the rules of the HARM module but evaluating each rule separately. Finally, normal signals are classified by elimination, i.e., the absence of any disturbance. It is often noted that negative aspects of expert systems are their limited capacity for portability and the confinement of their validity to a very specific space of signals and systems that can be analyzed [28,29]. These disadvantages are overcome by two actions. On one hand, the voltage of the analyzed signals must be normalized to 1 in such a way that the system is portable to any environment regardless of the voltage to be evaluated. On the other hand, feature values for each signal are normalized with respect to that obtained from a perfect sinusoidal signal. Thus, the established decision levels are valid for any signal regardless of the system and its voltage level. In any case, it is necessary to verify that the resulting system improves upon these weaknesses. This check is performed using simulated signals obtained from a simulation environment and real signals obtained from measurement by a data acquisition system, and the system is compared with one based on neural networks. 3.4. Details of implementation aspects The computational effort is determined by the ST and is proportional to N(N + log N). Fig. 11 shows the data size and the elapsed CPU time obtained with a Pentium(R) Dual-Core 2.50 GHz. The results reveal the ability of the algorithm for working in real time since it spends 71 ms in analyzing five cycles of signal (100 ms). 4. Classification results

Fig. 9. S-transform features plot F1–F2 for several voltage sags and interruptions.

A comparison of results with those from a classifier based on an ANN is presented. An ANN is discussed as an example of a robust classification algorithm [5–7,14–16] and is used for comparison. An ANN can be trained to perform a particular function by adjusting the values of the connections between elements organized in multilayer networks. In this paper, a feedforward backpropagation (BP) ANN has been used. Once the network weights and biases have been initialized, the network is ready for training. The training process requires a set of

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4.1. Synthetic data To design a rule-based algorithm, it is necessary to use a broad and generalized signal set to obtain sufficient statistical coverage of the most possible situations. Synthetic signals generated by mathematical models are easier to obtain and, therefore, of higher quantity; in addition, they can be generated closer to the limits of each class where errors may occur from incorrect classification. These synthetic signals have been used in the pattern design to extract information regarding each disturbance class and to define distinctive features. They are also used later in the classifier design to define the rules and the optimal boundaries to classify each class properly. In this work, some differences have been incorporated to the mathematical models presented by several authors [10,11,20,25] to obtain synthetic signals. These authors define the normal class as a pure sinusoidal signal. On the contrary, principal standards [32,33] establish that a signal within a 10% variation of the ideal magnitude can be regarded as normal; hence, there is a large difference between these two approaches. In this work, normal signals have been generated according to the following model: Fig. 11. Data size and elapsed CPU time.

examples of proper network behavior, network inputs and target outputs. During training, the weights and biases of the network are iteratively adjusted to minimize the network performance function. The default performance function for feedforward networks is mean square error (i.e., the average squared error between the network outputs and the target outputs). The BP has been set with only two layers: hidden and output. A network with one hidden layer can calculate a uniform approach to a training set represented by a set of inputs and corresponding desired outputs [30]. The number of nodes in the hidden layer has been chosen as a function of number of inputs (i.e., the number of pattern features) according to the expression (2n + 1) [31], where n is the number of inputs. Therefore, for the pattern with six features that is used, the hidden layer has 13 nodes, and the output layer has one node. The transfer functions for the hidden and output layers are tansigmoidal and lineal, respectively. The learning ratio is set to 0.1, and the epoch is set to 3500. The Levenberg–Marquadt training algorithm was used.

(t) = {1 ± ˛ · [u(t2 ) − u(t1 )]} · sin(ωt)

(15)

where ˛ < 0.1. Moreover, the most typical simple disturbances have been considered, including those resulting from sags, interruptions, swells, oscillatory transients and harmonics in addition to all plausible complex combinations of these simple events. Finally, the times that define the start and length of each event within a complex signal are independent of each other. In this way, the two events within the same signal may be coincidental in time, in whole, in part, or not at all. As an example, a signal with a voltage sag and 3rd harmonic is depicted in Fig. 12. In Fig. 12(a), the disturbances are present but are not simultaneous, while in Fig. 12(b) both disturbances occur simultaneously during a certain time interval. All synthetic signals have been generated using Matlab [34] code and are mixed with random white noise of zero mean having a signal to noise ratio (SNR) varying from 40 to 20 dB. The sampling frequency is 3.2 kHz and the signal length is 100 ms. Data obtained by mathematical models, consisting of 11,000 signals, are split into two subsets; one is used for training (9900), and the other is used for testing (1100), with 900 and 100 signals for each class, respectively. The training stage in the case of the rulebased algorithm has been used to establish the rules and boundaries

Fig. 12. A complex disturbance formed by two simple events, consecutively (a) and, in part, simultaneously (b).

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Table 3 Comparison of classification results in test stage using BP-ANN and rule-based systems. No noise

40 dB

30 dB

20 dB

WTBP

STBP

STRB

WTBP

STBP

STRB

WTBP

STBP

STRB

WTBP

STBP

STRB

Normal Sag Int Swell OT Harm Sag + Harm Swell + Harm Sag + OT Swell + OT Harm + OT

0.92 0.88 0.74 0.85 0.91 0.95 1 1 0.98 1 0.92

0.93 0.93 1 1 1 0.99 0.98 1 1 1 1

0.96 0.99 1 1 1 1 1 1 1 1 1

0.98 0.94 0.6 0.76 0.99 0.95 1 1 1 1 1

0.98 0.96 0.91 0.98 1 1 0.98 1 1 1 0.79

0.96 0.99 1 1 1 1 1 1 1 1 1

0.91 0.71 0.72 0.85 0.9 0.99 0.99 1 1 0.97 1

0.97 0.78 0.73 0.98 1 1 1 1 1 0.99 1

0.96 0.99 0.98 1 1 1 1 1 1 1 1

0.47 0.43 0.64 0.39 0.73 0.49 0.56 0.85 0.62 0.54 0.57

0.91 0.67 0.74 0.64 0.99 0.93 0.99 1 0.95 0.99 0.98

0.7 0.47 0.33 0.64 1 0.65 0.64 0.57 1 1 1

Total

0.923

0.984

0.995

0.929

0.964

0.995

0.913

0.950

0.993

0.572

0.890

0.727

WT, wavelet transform; ST, S-transform; BP, backpropagation; RB, rule based.

decision values. A comparison of classification results using the ANN and rule-based algorithms for different noise levels is presented in Table 3. As can be observed from this table, and in terms of rate of success the approaches based on the S-transform outperform those based on Wavelet transform. For instance, for noise-free signals a 92% success rate is achieved within the wavelet transform where a 98% success rate is obtained for the S-transform using the same ANN-based classifier. This advantage is maintained almost constantly even with acceptable noise levels. As a conclusion, the proposed structure outperforms classical ANN-based approaches which heavily relay on the training stage. It can be observed that the rule-based classification system obtains better results than does that based on the ANN, and this advantage is maintained almost constantly even with acceptable noise levels. This success declines steeply with very significant levels of noise (20 dB). 4.2. Simulation data Although the use of synthetic signals has important advantages, use of real signals is essential to verify the applicability of the implemented system. In order to validate the resulting rule-based classification system, simulated signals have been generated using the power network simulation environment PSCAD/EMTDC [22]. This application is an industry standard simulation tool for the study of transient behavior of electrical networks [35]. Several electric power systems with different events have been simulated to obtain a completely diverse set of disturbance signals to validate the resulting classification system. The classification

results for these PQ disturbances obtained from power network simulations, both simple and complex, are shown in Table 4.

4.3. Real data Finally, the resulting classification system has also been further validated using real signals obtained from measurement in different networks by a data acquisition system. The frequency of the networks is 50 Hz and the sampling frequency is 12.8 kHz. These acquired signals have been downsampled to obtain the sampling frequency defined in this work, 3.2 kHz. The signals obtained are of different lengths and have been divided into windows of 100 ms to be analyzed by the implemented system. Table 4 describes the behavior of the classifiers against these signals. The results obtained by the rule-based system for the acquired signals are considerably better than those obtained by the ANNbased system. This is in part because of its modular structure wherein each module is specialized for a particular type of disturbance and therefore can respond with a greater guarantee of success in the classification of complex disturbances. In Fig. 13, the signals obtained from simulations and those that were acquired have been plotted in a coordinated F1–F6 space. The decision boundaries that facilitate the classification of disturbances according to these features (sag, interruption, swell and oscillatory transient) have also been plotted. It can be seen that even signals are perfectly classified because they are within the limits established for each type of disturbance. In this coordinate system, it is not possible to represent the limits of decision to classify the harmonics because they depend on the F3, F4 and F5 features.

Table 4 Classification results using BP-ANN and rule-based systems for simulated and acquired signals. Simulation signals Number Normal Sag Int Swell OT Harm Harm + Sag Harm + Swell OT + Sag OT + Swell Harm + OT Total

10 45 10 16 30 0 20 30 34 15 0 210

Acquired signals WTBP

STBP

STRB

Number

WTBP

STBP

STRB

0.70 0.93 0.50 0.88 0.87 – 1.00 0.97 1.00 1.00 –

0.70 0.93 0.90 0.87 0.90 – 1.00 0.97 1.00 1.00 –

1.00 0.95 1.00 1.00 1.00 – 1.00 0.97 1.00 1.00 –

22 41 10 0 5 2 4 0 10 0 2

0.59 0.73 0.40 – 1.00 1.00 0.50 – 0.60 – 0.00

0.73 0.83 0.60 – 1.00 1.00 0.50 – 0.90 – 0.50

1 0.85 1 – 1 1 1 – 1 – 1

0.828

0.938

0.985

96

0.645

0.781

0.938

WT, wavelet transform; ST, S-transform; BP, backpropagation; RB, rule based.

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Fig. 13. Signals obtained from simulations and acquisitions plotted in a coordinated F1–F6 space.

Fig. 14. Electrical system scheme in PSCAD.

Fig. 15. Signal generated from power network simulation (a) and comparison with ST contours of signals within the limits of decision, 50 Hz ST contours (b), 150 Hz ST contours (c) and 700 Hz St contours (d).

A. Rodríguez et al. / Electric Power Systems Research 86 (2012) 113–121

One example is shown and described here with the purpose of illustrating the reliability of the rule-based method of classification. This case consists of a low voltage load fed by two parallel lines through a power transformer, as shown in Fig. 14. A three-phase fault occurs in the middle of one of the two parallel transmission lines at time to . Approximately two cycles later (t = 0.045 s), the fault is cleared. In Fig. 15(a) one of the generated signals can be seen, in which an oscillatory transient produced by the fault, a voltage sag during two cycles, and another oscillatory transient when the fault is cleared can be observed. Moreover, a third harmonic, generated by a non-linear load, presents during the entire signal. Therefore, this signal is a combination of three simple disturbances: oscillatory transients, a voltage sag and a third harmonic component. The ST contours of this signal are compared with those used as references for the definition of the classification rules. It can be observed that the simulation signal contours advise the presence of voltage sag, and the 50 Hz ST contour is below normal voltage level at 0.9, as shown in Fig. 15(b). A third harmonic component, the energy in 150 Hz ST contour, is higher than signal used as reference, as shown in Fig. 15(c). Moreover, an oscillatory transient, the energy in the 700 Hz ST contour, is higher than the oscillatory transient used as reference, as shown in Fig. 15(d). For a better representation, these contours have been normalized with respect to the contours obtained for a pure sinusoidal signal. It is noteworthy that although this combination of three perturbations in one signal has not been previously considered, the modular structure of the classifier allows for the detection of each disturbance separately and the signal can be correctly classified. 5. Conclusions A rule-based approach for classifying PQ events has been presented. It is based on a reduced and simple set of features extracted from the ST in order to advance accuracy, simplicity and reliability. Even in the presence of complex disturbances with different levels of noise, these features characterize the signals successfully, enabling the use of simple linear and parabolic rules as pattern classifiers. The boundary decision values for these rules have been determined using a heuristic search. The resulting rule-based algorithm consists of several units, each of which is specialized for one type of disturbance and only makes use of the features that are necessary for its function. These units work separately such that the whole system can easily detect complex disturbances. Due to the simplicity and efficiency of these rules, the approach works properly when classifying normal signals, sags, interruptions, swells, harmonics and oscillatory transients, as well as any plausible combination of these. Moreover, the proposed approach has low sensitivity under considerable levels of noise. References [1] M. McGranaghan, B. Roettger, Economic evaluation of power quality, IEEE Power Engineering 2 (2002) 8–12. [2] M. Bollen, Understanding Power Quality Problems, first ed., Wiley-Interscience, New York, 2000. [3] R.S. Dugan, M.F. McGranaghan, S. Santoso, H.W. Beaty, Electrical Power Systems Quality, second ed., McGraw Hill, New York, 2002. [4] S. Santoso, E.J. Powers, W.M. Grady, Electric power quality disturbance detection using wavelet transform analysis, in: Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis, 1994, pp. 166–169. [5] A.M. Gaouda, M.M. Salama, M.R. Sultan, A.Y. Chikhani, Power quality detection and classification using wavelet-multiresolution signal decomposition, IEEE Transactions on Power Delivery 14 (1999) 1469–1476.

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