A novel virtual instrument for power quality surveillance based in higher-order statistics and case-based reasoning

Measurement 45 (2012) 1824–1835

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A novel virtual instrument for power quality surveillance based in higher-order statistics and case-based reasoning Juan José González de la Rosa a,b,⇑,1, Agustín Agüera-Pérez a, José Carlos Palomares-Salas a, José María Sierra-Fernández a, Antonio Moreno-Muñoz a,c a

Research Group PAIDI-TIC-168, Computational Instrumentation and Industrial Electronics (ICEI), Spain University of Cádiz, Area of Electronics, EPSA, Av. Ramón Puyol S/N, E-11202 Algeciras, Cádiz, Spain c University of Córdoba, Area of Electronics, Campus de Rabanales, Leonardo da Vinci building, E-14071 Córdoba, Spain b

a r t i c l e

i n f o

Article history: Received 1 November 2011 Received in revised form 21 March 2012 Accepted 28 March 2012 Available online 7 April 2012 Keywords: Case-Based Reasoning (CBR) Higher-Order Statistics (HOSs) Power Quality (PQ) Surveillance Virtual Instrument (VI)

a b s t r a c t This paper presents the performance results of a Virtual Instrument (VI) based in Case-Based Reasoning (CBR), conceived to online monitor the power-quality. The PC-based instrument receives data through a DAQ board and a differential probe, while maintaining economy by eliminating the extra network construction and hardware. Being flexible, presents an userfriendly interface and a large data storage capacity, since it uses the hard disk. The computational guts of the instrument are based in third and fourth-order statistics (along with the variance), which enhance detection capability and reject noise influence. A time-domain sliding window sweeps the register under test and offers a time-variation pattern which reflects the deviation of the statistical estimator with respect to the steady state. This three-valued time-series comprises variance, skewness and kurtosis evolution, and constitutes a triple input to the innovative CBR module, which in turn is capable of distinguishing electrical anomalies among five categories (the sixth is reserved to the healthy signal): non50 Hz, 50-Hz-asymmetrical, 50-symmetrical non-sinusoidal, swell and sag. Online surveillance tests developed over the local electrical network show acceptable accuracy (96%). Ó 2012 Elsevier Ltd. All rights reserved.

1. Introduction With the introduction of new signal processing techniques, Power Quality (PQ) anomalies’ targeting has been notably enhanced during the last decade [1]. These efforts have been focused in the analysis, characterization, classification and data compression, with the subjacent goal of designing a distributed automatic-smart electronic instrument for PQ on-site monitoring.

⇑ Corresponding author at: University of Cádiz, Area of Electronics, EPSA, Av. Ramón Puyol S/N, E-11202 Algeciras, Cádiz, Spain. Tel.: +34 956028020; fax: +34 956028001. E-mail address: [email protected] (J.J.G. de la Rosa). URL: http://www.uca.es/grupos-inv/TIC168/ (J.J.G. de la Rosa). 1 Main Researcher of the Research Unit PAIDI-TIC-168. 0263-2241/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.measurement.2012.03.036

The worldwide interest in PQ is sustained in the basis that more sensible systems are constantly exposed to voltage disturbances, which are in turn caused by industrial equipment they are connected to. There is also the need for standardization and performance criteria for consumers and utilities, in order to develop measurement systems accessible to an average citizen. Nevertheless, in searching for the solution to a PQ problem, serious handicaps have to be considered; associated to the acquisition and monitoring of ‘heavy’ data records from the system under test, along with an automated detection and classification strategy, which allows the unambiguous identification of the cause of these voltage anomalies. What is more, these transitory perturbations are intrinsically non-stationary; moreover noise processes are commonly present in the acquired registers. So it is necessary an ensemble of observations (sample

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registers) to be confident with the results of the measurement process. Motivated by this issue, the transversal axis of this work consist of the improved (easy-to-compute) use of HigherOrder Statistics (HOSs) to extract statistical features, which have being successfully used (as features extractors) in former works involving PQ analysis [2–4]; these features are in turn processed by a smart modulus within a Virtual Instrument (VI). This work follows this line, introducing the CBR paradigm as the novel element in this conducting wire, which constitutes the intelligent block of the VI. The present work aims to detect the waveform anomaly looking primarily to the power-line frequency (50-Hz in the present case), so that making a previous discrimination. Secondly, the smart measurement nucleus centers on the PQ events which preserve the power-line frequency in order to target the type of anomaly. Consequently, the VI concentrates on the identification of the anomalies that primarily affect the customer, whose simplest forms are sags and swells. During a sag, the voltage is not zero but is significantly lower than in steady-state operation. The extreme situation is described by an interruption, in which the voltage falls to zero, which is the worst quality of supply. Swells are momentary over-voltages in the power-line sine wave. The procedure of analysis is based in the use of a timedomain sliding window through which the statistical estimator is computed. If the PQ events preserve the frequency (like sags and swells) of the ‘healthy’ signal (ideal steadystate power-line sine wave), they can be characterized by constant statistical parameters. This maximum HOS computational performance is reached by conveniently adjusting the window’s width, as described in [2]. Thus, signal processing techniques benefit from this fact by measuring-detecting changes in the stable statistical values, meanwhile the target signal is tested-swept. During the sweep of the signal under test, when this moving window bumps into the perturbed zone, a change in the estimator is observed, like a real-time step, and thereby the anomaly is automatically targeted, i.e., a constant value zone which characterizes the steady-state evolves to another constant value, this time associated to the fault. Then, when the fault ceases, the steady state constant value comes back. The computational ‘guts’ of the VI implement second, third and fourth order time-domain estimators. As summarized in the next section, the implemented PQ measurement algorithms in hand-held and PC-based measurement systems for this purpose are being traditionally based in threshold functions and spectral analysis. Wavelet analysis has been applied in labs, and not definitively extended among on-site network analyzers. Other computing tools are linear classifiers and neural networks. In the last 5 or 6 years, some works have introduced a strategy founded HOS, dealing with PQ analysis [2–5], chronologically, and other fields of Science and Technology, to cite [6–8]. Whereas the second-order classical characterization (2nd-order moments, cumulants and power spectrum) of the PQ events only provides information related to the changes in the instant power, 3rd and 4th-order statistical estimators give a more complete characterization of these

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non-Gaussian attributes, related to the symmetry and shape of the waveform, respectively [3]. The potential of the HOS tools also resides in the capability of rejecting symmetrical noise processes, e.g., the symmetrically distributed noise (uniform and Gaussian) is usually coupled to measurement system’s inputs, affecting the short-time stability of the magnitude under test. Thus, HOS pre-processing enhances measurement accuracy and repeatability of the electronic instruments. The paper is organized in the following way: The next Section 2 includes a review on PQ disturbances. Section 3 explains the fundamentals and the importance regarding PQ monitoring, focussing in the evolution of systems’ development. HOS are outlined then in Section 4, where the proposed VI is described in detail. Lastly, results are drawn in Section 5 and conclusions are discussed in Section 6. 2. PQ disturbances: a focussed review Whereas more electronic equipments enter the residential areas and businesses, the issues related to PQ and its relationship to vulnerability of installations are not known as desirable, thus becoming a pressing concern. Particularly has arisen the need to protect susceptible electronic equipment from damaging voltage anomalies. Lightning, large switching loads, non-linear stresses, inadequate wiring and grounding or accidents involving electric lines, create problems to equipment which is designed to operate within a narrow voltage interval, or if it does not incorporate the capability of filtering fluctuations in the electrical supply [9,10]. A consistent set of definitions in PQ surveillance was coined and can be found in [11,12]. Regulation in Europe proposes to use the standard EN-50160 to define the voltage quality ranges, which actually describes the electricity through the technical product characteristics that it has to comply. But there are a lot of undefined aspects, e.g., the only voltage quality aspect that is enforced is the maximum level variation settled to ±7% (which is actually different to the ±10% fixed on the EN-50160). IEEE 1159-2009 classify the disturbances into seven categories: transients, short duration variations, longduration variations, unbalanced voltages, waveform distortions, voltage fluctuations and power frequency variations. In each category, the disturbances are categorized as a function of their magnitude, duration and spectral content [11,12]. The category short-duration variations includes both short interruptions and IEC voltage dips (voltage sags in IEEE 1159-2009); moreover, this category also covers voltage swells (the inverse phenomena to voltage dips). The category long-duration variations is added to deal with ANSI C84.11989 limits [13] and includes long interruptions, under-voltages and over-voltages. The category waveform distortions is used as a grab-bag category for the IEC harmonics, inter-harmonics and DC in AC networks phenomena, as well as for an additional perturbation called notching. In the last category the phenomenon noise is also introduced to deal with broadband phenomena. Another useful classification of PQ disturbances divides the disturbances into ‘events’ and ‘variations’ [14]. Events

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are occasional but significant deviations of voltage or current from their nominal waveforms. Variations are small deviations of the voltage or current from their nominal or ideal waveforms. In addition, variations are practically characterized by a value at any moment in time (or over a sufficiently long time interval) and they have to be monitored continuously. This classification is similar to separate the disturbances into ‘discrete’ and ‘continuous’. Events include the following PQ disturbances: interruptions, voltage dips (sags), voltage swells, transient over-voltages and phase-angle jumps. Within the category of variations fall the following PQ disturbances: waveform distortions (including both harmonics and inter-harmonics), slow voltage variations, un-balances, voltage fluctuations, mains signalling voltages, power frequency variations, voltage notches and noise. The voltage sag (dip) and momentary interruption are the nemeses of the automated industrial processes. Voltage sag is commonly defined as any low voltage event between 10% and 90% of the nominal RMS voltage lasting between 0.5 and 60 cycles. Momentary voltage interruption is any low-voltage event of less than 10% of the nominal RMS voltage lasting between 0.5 cycles and 3 s. In medium voltage distribution networks, voltage sags are mainly caused by power system faults. Fault occurrences elsewhere can generate voltage sags affecting consumers differently according to their location in the electrical network. Even though the load current is small compared to the fault current, the changes in load current during and after the fault strongly influence the voltage at the equipment terminals. It has been discovered that the 85% of power supply malfunctions attributed to poor PQ are caused by voltage sag or interruptions of fewer than one second duration. Starting large motors can also generate voltage sags, although usually not so severe. In comparison with interruptions, voltage sags affect a larger number of customers and may cause extremely serious problems, specially to sensitive equipment which operates within narrow limits, or it does not have adequate ride-through capabilities to filter out fluctuations in the electrical supply. Over-voltage or surge is an RMS increase in the AC voltage, at the power frequency, for durations greater than a few seconds, and may result of a programmed utility operation, or the effect of an external eventuality [15]. Under normal operation, the steady-state voltage is regulated by the utility within a limits band accepted by the EN50160. Deviations from these limits are rare, and the utility can actuate readily to correct them, if known their occurrence, by acting on conventional distribution technologies, such as tap-changing transformers [16]. However, under the typical operating conditions of a power system there is risk of damaging due to a momentary excess of voltage. Although by themselves they would be described as ‘abnormal’, it is possible to distinguish between surges and swells. A surge is an over-voltage that can reach thousands of volts, lasting less than one cycle of the power frequency, that is, less than 16 ms. A swell is longer, up to a few seconds, but does not exceed about twice the normal line voltage. Surges based on waveform shapes, can be classified into ‘oscillatory transients’ and ‘impulsive transients’ [11].

Oscillatory transient surges show a damped oscillation with a frequency range from 400 Hz to 5 kHz or more. Impulsive transient surges present a fast rise time in the order of 1 ns to 10 ls over the steady state condition of voltage, current or both, that is unidirectional in polarity (primarily either positive or negative), reaching hardly twice the peak amplitude of the signal. They are damped quickly, presenting a frequency range from 4 kHz to 5 MHz, occasionally reaching 30 MHz. They have been extensively studied in [3]. 3. PQ monitoring systems The goal of developing VI monitoring systems has been treated during the last twenty years in the issues of designing architectures and related features. The problem of analyzing data from PQ measurement equipment was discussed in [17]: capturing trends, architectures and installation issues of the monitoring systems were discussed. Wagner et al. [18] developed an experiment aimed at identifying disturbances causing problems in production environments. Guidelines for implementing a power quality monitoring system were presented in [19] by Rauch et al., and in [20] by Liu. The general evolution and trends according to architecture, installation, and software facilities was discussed in by Sawyer [21]. Looking at concrete aspects, the advantages of introducing the object-oriented paradigm were remarked in [22]. With respect to web-based systems, Leou et al. [23] presented a system for monitoring steady-state disturbances. To cite among other works, the paper focused on the web technologies and their advantages by De la Rosa et al. [24], discussed the requisites for the design of a web-based measurement instrument for PQ assessment, based on a micro-controller. Lastly, an Internet-based system for detecting and measuring steady-state disturbances was reported by Waclawiak et al. [25]. Numerous algorithms and methods for disturbance detection and analysis, have been proposed in research articles during the last two decades. The first one to cite consist of a circuit for transient detection, proposed by Shakarijan et al. [26]. A common principle but improved version (architecture, communication and triggering) was adopted by Daponte et al. implementing TransientMeter, a monitoring system for the detection, classification, and measurement of transient disturbances on electrical power systems based on the wavelet transform [27]. Wavelets became a powerful tool, so myriads of applications arose. A virtual digital wavelet-based instrument capable of automatically extracting and measuring disturbances superimposed on power line voltages in electrical power systems was presented in [28] and improved in [29]. The application of wavelet transform, in order to decompose the power signal and to extract the disturbance from the fundamental, has been studied in various works. To cite, [30] by Gaouda et al., and [31], integrated wavelets transforms in VIs for PQ monitoring. More precisely, the application of wavelets in the measurement of disturbances in a noisy environment was discussed in [32].

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With respect to DSP-based systems, a system to analyze steady-state power disturbances was proposed by Lakshmikanth and Morcos [33]. Bucci et al. [34] proposed a distributed VI, implemented in LabVIEWTM, aimed to measure steady-state disturbances (sags, swells, flickering), and also perform some time-domain analysis on transients (rise and fall time, amplitude, duration). It is also remarkable the work by Chung-Ping et al. described in [35], where a real-time system controller for multiple power sources was developed. Finally, it is worth mention the work conducted by Makinen et al. [36], which summarized the history of PQ monitoring systems in Finland. In this scenario, the contribution of our work is twofold. By one side, HOS is implemented as the signal processing engine, in order to add 3rd and 4th-order features to PQ events’ features and to reject noise influence. Secondly, the CBR paradigm is added as a novelty in the intelligent modulus, which now produces an output (a decision on wether a perturbation is present and which type of perturbation) from the three-valued inputs associated to the statistical estimators. Once the foundations of PQ measurement instruments have been summarized, in the following section we synthesize time-domain HOS estimators of the VI. 4. Measurement algorithms and software structure 4.1. Higher-order statistics: description and interpretation Higher-order cumulants are being used extensively to deduce newly statistical features from the data of nonGaussian measurement time-series [37–41]. To reach a compact expression, nomenclature is first introduced. Let us consider {x(t)} be an rth-order stationary realvalued random process; the rth-order cumulant is defined as the joint rth-order cumulant of the random variables x(t), x(t + s1), . . . , x(t + sr1). This compacted notation is expressed via Eq. (1):

C r;x ðs1 ; s2 ; . . . ; sr1 Þ ¼ Cum½xðtÞ; xðt þ s1 Þ; . . . ; xðt þ sr1 Þ;ð1Þ where s1, s2, . . . , sr1 are time-shifts, and the nth-shifting is a multiple of the data acquisition sampling period, Ts, and is usually expressed as sn = n  Ts. Cumulants, defined in the Eq. (1) are estimated by using the Leonov–Shiryaev formula, which expresses the compact relationship among the cumulants of stochastic signals and their moments [2]. The particular cases for the 2nd-, 3rdand 4th-order cumulants for a zero-mean time-series (central cumulants) x(t) can be estimated via [2]:

C 2;x ðsÞ ¼ EfxðtÞ  xðt þ sÞg

ð2aÞ

C 3;x ðs1 ; s2 Þ ¼ EfxðtÞ  xðt þ s1 Þ  xðt þ s2 Þg

ð2bÞ

C 4;x ðs1 ; s2 ; s3 Þ ¼ EfxðtÞ  xðt þ s1 Þ  xðt þ s2 Þ  xðt þ s3 Þg  C 2;x ðs1 ÞC 2;x ðs2  s3 Þ  C 2;x ðs2 ÞC 2;x ðs3  s1 Þ  C 2;x ðs3 ÞC 2;x ðs1  s2 Þ;

ð2cÞ

where E{⁄} is the expected value operator. Then, looking at Eq. (2), each cumulant is easily interpreted as a correlation

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among the original time-series and its associated timeshifted versions. Therefore, the computational result of an rth-order cumulant is the rth degree of similarity among the aforementioned time-series. Avoided time shifting, s1 = s2 = s3 = 0 in Eq. (2), leads to the simplest computational expressions for cumulants, in Eq. (3):

c2;x ¼ Efx2 ðtÞg ¼ C 2;x ð0Þ c3;x ¼ Efx3 ðtÞg ¼ C 3;x ð0; 0Þ c4;x ¼ Efx4 ðtÞg  3ðc2;x Þ2 ¼ C 4;x ð0; 0; 0Þ

ð3aÞ ð3bÞ ð3cÞ

The ensemble of Eq. (3) constitutes indirect measurements of the variance, skewness and kurtosis; the most known statistics for a continuous random variable, which are the basis of the VI processing modulus. If x(t) is symmetrically distributed, its skewness is zero (but not vice versa, improbable situations); if x(t) is Gaussian distributed, its kurtosis is necessarily zero (but not vice versa). Standardization (statistical normalization) makes estimators shift and scale invariant. Standardized quantities are defined as c4,x/(c2,x)2 and c3,x/(c2,x)3/2, for kurtosis and skewness, respectively. As a final remark related to the nature of the statistics, in this paper, unbiased estimators are used, in order to avoid post-computing biasing corrections. Regarding the use of the estimators over the signals under test, the results are obtained by using sliding cumulants, i.d. a moving window in the time domain over which to compute each cumulant (3rd and 4th-order cumulants for zero time-lag). The hypothesis of robustness (repeatability) for the HOS estimators is satisfied all over the measurement process. This means that the same type of electrical anomaly is always characterized by the same ensemble statistics’ values, quantified in the triplet vector: variance–skewness–kurtosis. For this purpose, a prenormalization of signals is compulsory in order to establish a common starting point for different RMS healthy signals. This stage is considered as an in situ calibration and allows the adaptation of the instrument to different powergeneration systems. Thus, normalized values (for healthy a signal) correspond to unit amplitude and variance of 0.5. Based in the former premise, the proposed detection strategy is described hereinafter. The expected 50-Hz voltage waveform exhibits a particular constant statistical behavior (stationarity), i.e. with concrete stable statistical parameters as the sliding windows checks it. Then, any disturbance that alters these nominal values keeping its frequency (50 Hz), would exhibit another stable statistical state, being characterized this time by a new set of statistical parameters, different from the ones regarding the undistorted steady-state. On the other hand, perturbations which does not preserve the frequency, will be targeted but will not exhibit constant statistical parameters. They will be targeted but not labeled. The logical reasoning process, shown in Fig. 1, represents all the possible cases resulting from the calculation of the estimators (for each position of the sliding window) and the interpretation that the CBR modulus performs on the triplet vector. On this basis, in the case of a 50-Hz sine, variance (second-order statistic) is an indicator of the amplitude

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or power excess. Skewness (third-order statistic) is zero-valued for symmetrical signals (like sinusoids), and different values give a measure of the asymmetry. For a symmetrical signal, kurtosis (fourth-order statistic) is an indicator of the signal shape: valued 1.5 for sine waves and other but constant values for non-sinusoidal signals. Considering skewness zero and kurtosis 1.5, i.e. a symmetrical 50-Hz sinusoid, values of the variance higher than 0.5 correspond to swells. Similarly, a reduction in the variance indicates the presence of a sag (voltage reduction). These defects (sags and swells) are completely characterized by the above reasoning. The complete reasoning process is depicted in Fig. 1. Intriguingly, the procedure outputs important information related to other types of electrical anomalies. For example if a signal is non-symmetrical its skewness is non-zero. If the skewness is zero but the kurtosis is different from 1.5, the signal is symmetrical but not sinusoidal. In this sense, Fig. 2 is thought to show the five possible defects which can be detected by the CBR modulus in the VI: sag, swell, 50-Hz symmetrical non-sinusoidal, 50-Hz asymmetrical and non- 50-Hz. This cases are associated to the CBR’s logical outputs depicted in Table 1. In this frame, the stability of the estimators is a key point in computing.

4.2. Estimators’ stability assessment The instrument is mainly conceived to process electrical perturbations which maintain the frequency of the powerline. This idea is closely related to the concept of stability of the HOS estimators. In fact, stability is crucial in order to test immunity to the error sources associated to noise processes, and it implies frequency stability (50-Hz constant value) in the sense that a frequency deviation produces statistical values shifts, i.e., that the computation (along the sliding window) outputs constant statistical values for the analysis of the 50-Hz corrupted and noncorrupted signals. In practice, stability is achieved by ’tuning’ the window length, i.e., a sliding HOS-computation window covers a positive integer number of power-line periods (in the present work, one cycle-length is selected, 20 ms). A threshold-based criterion has been chosen and implemented in the VI to test stability. This threshold is considered as a confidence interval within which the measurement of the statistic is considered stable. Hence, little variations in the frequency and amplitude of the power-line waveform will not be considered a remarkable event. This is the reason why an external frequency calibration is not needed. A frequency (and amplitude) fluctuation which provokes deviations of

Fig. 1. Measurement algorithm: CBR flowchart of PQ perturbation classification.

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Healthy Signal

Sag

Swell

1

1

1

0.5

0.5

0.5

0

0

0

−0.5

−0.5

−0.5

−1

−1 0

0.02

0.04

0.06s

−1 0

50Hz−Symmetrical

0.02

0.04

0.06s

0

50Hz−Asymmetrical 1

1

0.5

0.5

0.5

0

0

0

−0.5

−0.5

−0.5

−1

−1

−1

0.02

0.04

0.06s

0

0.02

0.04

0.04

0.06s

Non−50Hz event

1

0

0.02

0.06s

0

0.02

0.04

0.06s

Fig. 2. Five types of defects that can be detected by the instrument. From top to bottom (left to right): sag, swell, 50-Hz symmetrical non-sinusoidal, 50-Hz asymmetrical and non- 50-Hz.

Table 1 Logical responses from the CBR unit in the VI, depending on the anomaly type. Case (type of anomaly)

Value (CBR output)

Healthy signal Sag Swell 50-Hz symmetrical non-sinusoidal 50-Hz asymmetrical non-sinusoidal Non-50-Hz event

0 1 0.5 0.3 0.6 1

window’s width is set to 100, and in Fig. 4, this width is set to 10. This variability in the stability window and in the thresholds allow the user to set a more rigid detection criterion. In the present research, threshold has been fixed to 0.05 to overcome the standard EN-50160 (Voltage Characteristics in Public Distribution Systems). On this basis, we pass to describe the design of the VI following both the flow chart of Fig. 1 and the front panel. 4.3. Software: the VI

the statistics inside the limits of the confidence interval does not affect the identification results of the CBR, i.e. the stable statistical value remains constant if frequency’s changes induce fluctuation of the statistics inside the threshold limits. The value of the threshold can be adjusted by the user via the main panel of the VI. For the three estimators, in the present paper, the selected stability biased thresholds are set to 0.05 (absolute value), for the variance, the skewness and the kurtosis. Fig. 3 shows an example of how stability is assessed over a portion of the kurtosis’ estimator. Four possible positions of the sliding window (segments) have been selected to illustrate how the stability test works. Segments labeled ‘A’ and ‘C’ are considered as stable situations, while ‘B’ and ‘D’ are labeled as unstable, and indicate a significant change in the kurtosis’s value. The stability test is performed over a window (the stability window) which is not the same as the fixed one used for calculation purposes (calculation window). The stability window does not slide on the signal, but on the estimators and can be variable. The objective is: given a signal’s segment, check if threshold is overcome. In Fig. 3, this stability

The cascade decision diagram of Fig. 1 shows the sequence of the complete measurement process, which is implemented in the VI. The first stage consists of the implementation of the estimators’ stability testing. Each graph of the resulting estimators’ values of the statistic is swept by a sliding window in order to test stability. For each computation in a window, if the difference between the maximum and the minimum falls inside a confidence interval, then the stability is achieved. Thus, if the stability is satisfied, this means that a 50-Hz signal is targeted, and the instrument pass to calculate the mean value over the considered sliding window. This averaged value constitutes the input to the decision engine in the CBR modulus. In practice, there are three inputs to the CBR modulus: variance, skewness and kurtosis constitute the triplet input vector. Fig. 4 shows the front panel of the VI. Lets describe it through the explanations of the controls. The calculation window’s width is constant and covers one cycle of the power-line; then the tests have been performed over a 20 ms-width sliding calculation window, which sweeps

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A

A

B

B

C D

C

D

Fig. 3. An example on how to determine the stability of an estimator’s calculation (the kurtosis) for 100-point stability window’s. The four segments (A–D), or sliding windows situations, have been extracted from the upper graph and referred to zero (plus 1.5 in this case), which in turn corresponds to a variance time-series. It can be seen that each segment has a 100 point-width, but the VI offers the possibility of changing.

the time domain power-line signals. We recall that this fixed window is different from the one used to perform the stability test (called stability window), that can be adjusted by the user in this front panel. The upper zone in Fig. 4 includes the configuration elements for the stability window’s settings and the HOS confidence intervals (from left to right). The user adjusts the Stability window’s width and the Stability window’s advance controls. In this situation, the stability window is set to 10 points and the window’s advance, or the displacement ratio (the number of points that this second window shifts to the following computation segment), is one point, i.e, 90% of overlapping between two consecutive segments. The button System’s limits variation restore stability default values, which are set to the maximum allowed variability considered for the signal under test to be healthy. It is also possible to load the results from the last analysis (Analyze actual), or all cumulative analysis vectors for previous analysis. The instrument is capable of storing a 500-s results’ history for the signal under test.

Graphs in the left side of Fig. 4 are instant HOS features resulting from the sliding window computation. Central graphs show the results of the stability analysis for the skewness, kurtosis and variance, along with the mean value corresponding to each realization. The squared bivalued signals in the central graphs are indicative of the stability evolution. They take a zero logical value for the stable situation, and a logical one if the stability is not accomplished, e.g, looking at the central variance graph, each time the instant variance initiates a change, the associated logical signal also changes. If value is ‘0’, then stability is satisfied and it comes to sense to asses the state of the signal, from the statistics values. By the contrary, in the zones where the logical signal is ‘1’, the stability is not achieved, and the estimators’ values associated to this intervals do not pass to the CBR module. This means that a non-50-Hz periodical event is present, and frequency stability and/or amplitude stability is not achieved. On the other hand, these graphs in the central-column are simultaneously re-scaled by making a zoom in the

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Fig. 4. Front panel of the VI. The three sub-graphs on the left show the computation results of the sliding cumulants over the main window, which takes one cycle of the signal. The three central graphs show the averaged cumulants. The square signals are the plane-zone (stable) indicators. Finally, the upper-right graph outputs the CBR modulus results along with the analyzed signal.

variance graph (clicking). A change in the horizontal range in the variance central graph re-scales the skewness and the kurtosis graphs. Furthermore, the sliding element under the stability variance graph controls the positions of the cursors at the same time. In each central graph there are two cursors (corresponding to the curves in each graph). They provide the user with the value of a concrete point of the analysis. The CBR modulus returns the signal analysis in the Result string indicator, next to variance graph (e.g., 50-Hz Asymmetrical in Fig. 4), and shows the values of the cursors inside the element Point values. This indicator shows the results from the HOS stability test and the averaged values of the HOS features: skewness, kurtosis and variance, respectively. The indicator Normal Operation Limits contains the ensemble the ranges which are also considered by the CBR modulus in order to take a decision. These limits can be imported from the HOS module or can be manually introduced. The last graph, at the top right zone of the panel, shows the output of the CBR module, along with the signal under test (last measurement time-series). To get this, the user must press the button Analyze actual. The squared graph representation takes a different value associated to each case or measurement situation. Table 1 shows the collection of possible results from the CBR module, each one is associated to a diagnosed situation. Thus, the CBR module works like a multilevel logic decision system. Alternatively, the option Analyze accumulate leads to a graph which only shows the last acquired signal, because signal associated of all accumulate data are not available to merge with casebased reasoning result.

Once the mathematical foundations and the VI software description have been established, we expose the experimental results. 5. Experimental results A previous test with synthetic signals (computerdesigned) has been designed. This stage is conceived to adjust VI’s blocks and other software components, and in order to illustrate the VI’s ideal behavior. Synthetics have coupled random white noise of 1% of the signal’s amplitude. This noise is rejected by HOS estimators. Fig. 5 shows an example with the first synthetic, which comprises eight different signals (labeled ‘A’–‘H’). Signal ‘A’ is healthy, and the CBR returns zero as logical output. Signals ‘B’–‘D’ are sinusoids whose frequencies are differ from 50 Hz, so HOS estimators do not stabilize and that’s exactly the VI response; the corresponding output in Table 1 is ‘1’ (non-50-Hz event). The following signal (‘E’) in Fig. 5, has a very low frequency with a coupled transient, neither periodical. Consequently, the response is the same than in the former situation (logical output equal to ‘1’). The case ‘F’ presents a signal predominately positive, and the response (logical output in Table 1) corresponds to ‘0.6’, according to a 50-Hz asymmetrical signal. The next signal, ‘G’, is symmetrical, but is not a sinusoid. This deformation has been detected and the CBR returns ‘0.3’, according to a 50-Hz symmetrical non-sinusoidal signal. The last one, labeled ‘H’, is a uniform white noise. Its HOS features are stationary during the time, so the system catalogues it like a 50-Hz event, producing a stable output due to the stationarity of statistics. Changing the limits of the maxima

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Fig. 5. CBR’s logical output over the first set of synthetics.

Fig. 6. CBR’s logical output over the second set of synthetics.

variation to others more permissive leads to a different statistical values; this noise process is then catalogued like 50-Hz symmetrical non-sinusoidal. This fact can be explained because a random noise has time-invariant properties, so it could be considered a quasi-periodical signal; and it is statistically symmetric because roughly it has the same number of points over and under zero.

The second synthetic is shown in Fig. 6. Signals marked with an ‘H’ are healthy 50-Hz sinusoids, and the logical output of the CBR unit is zero. Sag and swell cases are also recognized correctly, with a result of a logical ‘1’ for sag and a logical ‘0.5’ for a swell. Asymmetrical cases, indicated by an ‘A’, no matter of the asymmetry type, are recognized and marked with a ‘0.6’ logical response. Symmetrical

Fig. 7. Front panel processing results for a 60% sag.

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0.4 0.3

Normalized amplitude

0.2 0.1 0 −0.1 −0.2 −0.3 −0.4

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Time,sec.

5 −5

x 10

Fig. 8. Electrical anomaly which consists of an asymmetric reduction.

Fig. 9. Front panel processing results for the asymmetric reduction of Fig. 8. This signal belongs to the set of the 4% misclassified.

signals, ‘S’-labeled segments, are unambiguously detected, returning a ‘0.3’ value. Despite the fact that all the segments in this second synthetic are 50-Hz signals, the instrument finds zones of non-50-Hz (‘1’ logical response). This is because in one cycle the signal has a group of properties, and in the next cycle the properties change (i.e., amplitude). A 50-Hz event not only means a signal of 50-Hz, but it keeps its features along the time.

In the second stage, the instrument dealt with real signals. Power network waveforms (real-life signals) come from the Agilent 6811B AC source/analyzer, which outputs the same anomalous power-line signals as occur spontaneously in the industrial and power systems under test. A differential probe and a DAQ board digitize the registers with a sampling frequency of 10,000 Hz, and 16 bits of resolution. This means that cumulants have been computed over

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a 200 points-width sliding window (20 ms), which swept the time domain power-signals. Time shifting of 1 point is chosen. A number of 133 real-life recordings have been used to test the VI: nine sags with different amplitudes, eight with different starting points, 28 sags with different slopes, eight swells with different amplitudes, eight swells with different starting instants, 32 swells with varying slopes, 10 oscillatory transients with different damping factors at 2,500 Hz, 10 oscillatory transients with different phase shifts, 10 oscillatory transients with different frequencies, and finally 10 healthy signals. The percentage of misclassifications is equal to 4% and is associated to oscillatory. The reason is that these oscillatory transients are identified by the CBR as a mixed non-50-Hz event and asymmetrical signal. We have selected two examples among the graphical results, consisting of a 60% sag and an asymmetric amplitude reduction. The first one is depicted in Fig. 7, and the processing result allows an undoubted identification. The asymmetric amplitude reduction is shown in Fig. 8 for a better visualization. In Fig. 9, processing results can be read in the VI’s panel; this PQ event cannot be identified by the CBR, and constitutes an example of misclassification (inside the group of 4%). This event is not included in the CBR data base, thus the system outputs an erroneous classification in this case. As said above, the absolute stability margin has been fixed in 0.05 for the three estimators (variance, skewness and kurtosis). It is observed that, if this margin is broaden the error tax increases. 6. Conclusions Our work indicates that a HOS-based VI that uses the CBR paradigm, is capable of distinguishing among five types of electrical anomalies attending to the 2nd, 3rd and 4th statistical orders. The system outputs an ensemble of values depending on the electrical anomaly and classified in Table 1. Our work also raises that the measurement system rejects noise inherently, by means of HOS estimators’ conception. This VI uses pre-defined limits to evaluate the stability of HOS features. When stability is confirmed, the CBR modulus uses other pre-defined values to decide the current case: healthy signal, sag, swell, symmetrical non-sinusoidal or asymmetrical defects. The percentage of misclassifications increases with the estimators’ stability threshold. The error tax is relatively small, 4% for a threshold of 0.05. If the threshold is very small, the VI does not work properly as it is impossible to stabilize the value of the estimators. A future improvement is oriented to achieve dynamic threshold control. The software (in LabVIEW™) is easy to maintain and extensible because of the simple algorithms and it can be used in conjunction to mid price differential probes and DAQs. In this sense, future versions would include an improved intelligent engine, capable of detecting more electrical anomalies like types of oscillatory transients and flickering. Lastly, the future version would communicate with DSP, in order to develop real-time signal processing.

Acknowledgements The authors would like to thank the Spanish Ministry of Science and Innovation for funding the research projects TEC2009-08988 and TEC2010-19242-C03-03 (SIDER-HOSAPQ). Our unforgettable thanks to the trust we have from the Andalusian Government for funding the Research Group PAIDI-TIC-168 in Computational Instrumentation and Industrial Electronics-ICEI.

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