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APPLICATION OF ABRUPT CHANGE DETECTION-BASED SIGNAL SEGMENTATION IN POWER SYSTEM OSCILLATION ANALYSIS A Ukil*, R Živanović* *Tshwane University of Technology, Private Bag X680, Pretoria, 0001, South Africa. Abstract. Abrupt change detection-based signal segmentation has significant role to play in automatic segmentation of signal. The segmented signal can be used for automated analysis and effective further processing. Abrupt change detection-based automatic signal segmentation has been effectively utilized for automatic disturbance recognition in South Africa. In this paper, we describe the application of the abrupt change detectionbased automatic signal segmentation for the analysis of the inter-area power oscillation signals obtained from the Mexican Interconnected System (MZD-DGD). We have utilized the wavelet transform-based method and the adjusted Haar wavelet method for performing the segmentation. Effective comparison of our segmentation application results to the original segmentation by the Mexican research team is presented in this paper Key Words. Abrupt change detection; Signal segmentation; Inter-area oscillation analysis.
1.
INTRODUCTION
Detection of abrupt changes in the signal characteristics has significant role to play in automatic segmentation of signal. The segmented signal can be used for automated analysis and effective further processing. Abrupt change detection-based automatic signal segmentation has been effectively utilized, as in [1], for the purpose of automatic disturbance recognition using the disturbance signals recorded in the ESKOM power network in South Africa. In the direction towards a recognition-oriented task, we first applied the abrupt change detection algorithms to segment the fault recordings into different segments. This was followed by appropriate feature vector construction and pattern-matching algorithm to accomplish the fault recognition and associated tasks. In the scope of this paper, we describe the application of the abrupt change detection-based automatic signal segmentation for the analysis of the power oscillation signals obtained from the Mexican interconnected system (MZD-DGD) [2]. We present the applications results by applying our segmentation algorithms to the test signals for the inter-area oscillation in the MZD-DGD, acquired in collaboration with the Mexican team. 2.
ABRUPT CHANGE DETECTION
Detection of abrupt changes in signal characteristics is a much studied subject with many different approaches. A possible approach to recognitionoriented signal processing consists of using an automatic segmentation of the signal based on abrupt changes detection as the first processing step. Many of these signals are quasi-stationary, that is, the signals are composed of segments of stationary behavior with abrupt changes in their characteristics in the transitions between different segments. It is imperative to find the time-instants in which the changes occur and to develop models for the different segments during which the system does not change. A segmentation algorithm splits the signal into homogeneous segments, the lengths of which are
adapted to the local characteristics of the analyzed signal. This can be achieved either on-line or off-line [3]. Assuming a parametric system model, we consider a quasi-stationary sequence of k independent observations x , with a d-dimensional parameter vector θ which describes the properties of the observations. Before the unknown change time t 0 , the parameter θ is equal to θ 0 , while after the change, it is equal to θ 1 ≠ θ 0 . At this stage, two tasks are necessary: to detect the change time-instant t 0 and to estimate the corresponding parameter vectors θ 0 and θ 1 . With the primary focus on detecting the change time-instant t 0 , it is useful to consider t 0 a random unknown variable with unknown distribution [3]. 3.
DIFFERENT ALGORITHMS
To accomplish the abrupt change detection, hence segmentation of the power system disturbance signals, the following algorithms are considered. •
Recursive Identification Method [4]
•
Wavelet Transform Method [5]
•
Adaptive Whitening Filter and Wavelet Method [6]
•
Adjusted Haar Wavelet Method [7]
•
Complete Algorithm [1].
In Fig 1, we show an application result for the segmentation of a fault signal obtained from the ESKOM digital fault recorders (DFRs) implemented using MATLAB, based on the wavelet transform method [5].
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Fig 2: Active Power Flow Oscillations in the Mexican Interconnected System (MZD-DGD).
Fig 1: RED Phase Current Signal Segmentation.
In Fig 1, the original DFR recording for current during the fault in the RED-Phase is shown in the top section, wavelet coefficients for this fault signal (in blue) and the universal threshold (in black, dashed) are shown in the middle section and the change timeinstants computed using the threshold checking (middle section) followed by smoothing filtering [5] is shown in the bottom section. The time-instants of the changes in signal characteristics in the lower plot in Fig 1, indicate the different signal segments owing to different events during the fault, e.g., segment A indicates pre-fault section and fault inception, segment B the fault, segment C the opening of circuit-breaker, segment D the auto-reclosing of circuit-breaker and system restore. 4.
INTER-AREA OSCILLATIONS
Ruiz-Vega, Messina and Enriquez-Harper [2] discussed the use of nonlinear, nonstationary analysis techniques to characterize the forced inter-area oscillations problem in the power systems, recorded in the Mexican interconnected system. In order to analyze the active power flow oscillations, they used nonlinear spectral representation of the data in the form of the wavelet transform and the Hilbert-Huang transform [2]. They also compared the results with the linear spectral representation of the data in form of Fourier spectral analysis and Prony analysis [2]. Fig 2 shows the active power flow oscillations recorded in the Mexican interconnected system (MZD-DGD) [2]. Based on their analysis, the recorded signal was divided into four main observation (time) windows. Each time window was then segmented into subintervals to investigate specific characteristics of interests as shown in Fig 3.
Fig 3: Selected Time Windows for the Linear Spectral Analysis.
5.
SIGNAL SEGMENTATION
In collaboration with the Mexican team, we also tested our segmentation algorithms on the power oscillation signals obtained from the Mexican interconnected system (MZD-DGD). We tested our algorithms on the same signal shown in Fig 2. We tested the adjusted Haar wavelet algorithm [7] and the wavelet algorithm [5] (with the db4 and the db1 mother wavelet). We describe them below. 6.
WAVELET TRANSFORM METHOD
Wavelet analysis is the breaking up of a signal into shifted and scaled versions of the original (mother) wavelet which is an oscillatory waveform of effectively limited duration that has an average value of zero [5]. Wavelet transform is particularly suitable for the power system disturbance and fault signals which may not be periodic and may contain both sinusoidal and impulse components [5]. Based he continuous wavelet transform (CWT) is defined as the sum over all time of the signal multiplied by scaled, shifted versions of the wavelet function ψ . The CWT of a signal x(t ) is defined as
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∞
CWT (a, b) =
∫ x(t )ψ
* a ,b
(t )dt ,
(1)
where ψ a ,b (t ) =| a | −1 / 2 ψ ((t − b) / a) .
(2)
−∞
ψ (t ) is the mother wavelet, the asterisk in (1) denotes a complex conjugate, and a, b ∈ R, a ≠ 0, ( R is a real continuous number system) are the scaling and shifting parameters respectively. By choosing a = a 0m , b = na 0m b0 , t = kT in (2), where T = 1.0 and k , m, n ∈ Z , and Z is the set of positive integers, we get the discrete wavelet transform (DWT), DWT (m, n) = a 0− m / 2
(∑ x[k ]ψ
*
)
Fig 5: Segmentation of the Power Oscillation Signal using the db1 Mother Wavelet.
[(k − na 0m b0 ) / a 0m ] .
(3) In this application, wavelet transform is used to transform the original fault signal into finer wavelet scales, followed by a progressive search for the largest wavelet coefficients on that scale [5]. Large wavelet coefficients that are co-located in time across different scales provide estimates of the changes in the signal parameter. The change time-instants can be estimated by the time-instants when the wavelet coefficients exceed a given threshold (which is equal to the ‘universal threshold’ of Donoho and Johnstone [8] to a first order of approximation). For our application, Daubechies 1 and 4 [9] mother wavelets are used. Using these mother wavelets and multiresolution signal decomposition technique [5], the original signal is transformed into the smoothed and detailed versions. We use the detailed version for threshold checking to estimate the change timeinstants. Fig 4 and 5 show the results of the segmentation using the wavelet method based on the Daubechies 4 (‘db4’) [9] and Daubechies 1 (‘db1’) [9] mother wavelets respectively.
Fig 4: Segmentation of the Power Oscillation Signal using the db4 Mother Wavelet.
7.
ADJUSTED HAAR WAVELET METHOD
In general, the FIR scaling filter for the Haar wavelet looks like h = 0.5 [1 1] , where 0.5 is the normalization factor. As adjustment and hence improvement of the characteristics of the Haar wavelet, we propose to introduce 2n zeroes (n is a positive integer) in the Haar wavelet scaling filter, keeping the first and last coefficients 1 (n is the set of positive integers). Following the orthogonality property for the scaling filter, the filter length has to be even [7]. So, we have to introduce 2n adjusting zeroes, n being the adjustment parameter. The Haar wavelet corresponds to n = 0 . The introduced additional zeroes in the filter kernel have zero coefficients. The authors have shown mathematically in [7], that the introduction of the adjusting zeroes do not violate the key wavelet properties like compact support, orthogonality and perfect reconstruction. It has also been proven mathematically that the introduction of the 2n adjusting zeroes to the Haar wavelet scaling filter improves the frequency characteristics of the adjusted wavelet function by an order of 2n+1, by decreasing the strong ripples [7].
Fig 6: Segmentation of the Power Oscillation Signal using the Adjusted Haar Wavelet.
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Adjusted Haar Wavelet technique has been successfully applied for segmenting the power oscillation signal as shown in Fig 6. 8.
CONCLUSION
In this paper, we have discussed the abrupt change detection-based automatic signal segmentation for the analysis of the power oscillation signals obtained from the Mexican interconnected system [2]. We have utilized the wavelet transform-based method [5] and the adjusted Haar wavelet method [7] for performing the segmentation. Comparisons of the original time-window selection (see Fig 3) and our signal segmentations (see Fig 4 to 6), reveal that the Adjusted Haar Wavelet-based [7] approach (see Fig 6) is reasonably accurate in proper signal segmentation for analyzing the active power flow oscillations. ACKNOWLEDGEMENTS The authors would like to acknowledge the financial support by the National Research Foundation (NRF), South Africa.
[2] D.R. Vega, A.R. Messina, and G.E. Harper, “Analysis of Inter-area Oscillations via Non-linear Time Series Analysis Techniques,” in Power Systems Computation Conf., Liege, Belgium, Aug 2005. [3] M. Basseville and I.V. Nikoforov, Detection of Abrupt Changes – Theory and Applications, Prentice-Hall, Englewood Cliffs, NJ, 1993. [4] A. Ukil and R. Živanović, “The Detection of Abrupt Changes using Recursive Identification for Power System Fault Analysis,” Electric Power Systems Research, Elsevier, (Under review). [5] A. Ukil and R. Živanović, “Abrupt Change Detection in Power System Fault Analysis using Wavelet Transform,” in Int. Power Systems Transient Conf., Montréal, Canada, Jun 2005. [6] A. Ukil and R. Živanović, “Abrupt Change Detection in Power System Fault Analysis using Adaptive Whitening Filter and Wavelet Transform,” Electric Power Systems Research, Elsevier, (To be published).
Technical collaboration by D.R. Vega, A.R. Messina and G.E. Harper from Mexico is hereby greatly acknowledged.
[7] A. Ukil and R. Živanović, “Adjusted Haar Wavelet for application in the Power Systems Disturbance Analysis.,” EURASIP Journal of Applied Signal Processing, (Under review).
REFERENCES
[8] D.L. Donoho and I.M. Johnstone, “Ideal Spatial Adaptation by Wavelet Shrinkage,” Biometrika, vol. 81, no. 3, pp. 425-455, 1994.
[1] A. Ukil, “Abrupt Change Detection in Automatic Disturbance Recognition in Electrical Power Systems,” Ph.D. dissertation, Dept. Mathematical Technology, Tshwane University of Technology, Pretoria, South Africa, 2005.
[9] I. Daubechies, Ten Lectures on Wavelets, Society for Industrial and Applied Mathematics, Philadelphia, 1992.
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