1. Introduction
In recent years, with the expansion in the scale and capacity of power systems, many electronic devices in electrical equipment have been widely used. Inevitably, they introduce power quality (PQ) disturbances to the power supply grid, such as harmonics, high-frequency instantaneous variations [1]. At the same time, large numbers of renewable energy sources have been accessing the power grid [2, 3]. In addition, many strong impulse and fluctuating loads are applied widely, such as electrified railways and electric arc furnaces [4, 5]. These PQ disturbance sources have directly or indirectly affected the safe and reliable operating conditions of the power supply system. Conversely, with the development of high-tech industries and the improvement in automation technology applied to equipment, power users are demanding greater PQ. It is therefore necessary to monitor and analyze large volumes of PQ data to identify, in a timely manner, potential hidden PQ problems, and inform both the power suppliers and users to take corresponding counter measures to improve the PQ.
At present, the research on PQ early warning systems is still minimal and mainly concentrates on analyzing the PQ characteristics of different disturbance sources and the detection and identification of disturbance signals [6-9]. Conversely, the research on PQ evaluation is relatively mature [10-12]. A new fuzzy-wavelet packet transformbased power quality assessment approach for evaluating PQ in three-phase systems has been proposed in [10]. Many advantages such as simplicity, flexibility, ability to handle uncertainties and imprecision can be achieved when using this approach. An intelligent method based on artificial neural networks and fuzzy logic has been proposed in [11]. Using this method, a unified PQ index can be obtained and real measured PQ data evaluated accurately. Some simple algorithms for fast measurement were presented in [12], which enabled the estimation of the unknown changing frequency, amplitude, phase, and other parameters in evaluating PQ disturbances.
The main purpose of previous studies on PQ evaluation has been to make comprehensive judgments on the status of PQ over a previous period. However, the combined demands of the approach to power marketing and users requiring improved PQ have revealed that the existing evaluation methods have been unable to meet some advanced application requirements such as online real-time abnormal data mining. To remedy these defects, an early warning approach is proposed in this study. In comparing the evaluation methods, an early warning approach requires the following improvements: 1) Expand the applications of the information: PQ evaluation generally reflects the status of the previous period, whereas the requirements for early warning can be applied to provide reference information on the future power quality status for both the power suppliers and users; 2) Further data mining: evaluation is focused on quantifying indices for the data, and rarely performs abnormal data detection and analysis. Whereas early warning can use anomaly detection when mining limitexceeding and abnormal data, for identifying potential hidden power quality problems and providing warning prompts; 3) The content of early warning is more abundant than its evaluation: for normal PQ problems that exist in the operation of a power supply system, the evaluation results are poor, and warning prompts are not given. This is because early warning concentrates on occasional problems, which deserve more immediate attention and improvement. Early warning can better meet the wide range of experience and needs of power users. Thus, it is necessary and meaningful to carry out research on PQ early warning.
This paper is organized as follows. The steady-state PQ early warning index system is established in Section 2. Anomaly detection algorithms and early warning flow are presented in Sections 3 and 4 respectively. Cases are discussed in Section 5. In Section 6, conclusions are drawn.
2. Establishing a Steady-state PQ Early Warning Index System
Before analyzing early warning requirements, a PQ index system needs to be established. It is the object and basis of the research. Therefore, it is essential to present a series of PQ indices that can reflect the nature of PQ problems.
2.1 The PQ characteristics of different disturbance sources
At present, there are many PQ disturbance sources existing in the power grid, and their PQ characteristics are different and relatively complex. Therefore, existing traditional PQ indices cannot fully reflect PQ problems caused by these different PQ disturbance sources. It is necessary to fully analyze their PQ characteristics to extract more meaningful indices and establish a PQ early warning index system.
On the basis of different PQ characteristics, this study divides disturbance sources into five types; strong disturbance source, strong harmonic source, strong impulse load, strong fluctuating load and others respectively. This study then takes specific typical disturbance sources as samples to analyze the different power quality characteristics of the five types. The analysis results are shown as Table 1.
Table 1.The PQ characteristics of different disturbance sources
From the above analysis, we know that these disturbance sources have a major impact on PQ at the point of common coupling (PCC). Therefore, establishing a complete PQ early warning index system for them is necessary. It should effectively reflect changes in operating conditions for different disturbance sources and the PQ at the PCC.
2.2 Establishing an early warning index system
The above established key indices are all steady-state PQ indices. Based on these, a steady-state PQ early warning index system can be established. Referring to the Chinese PQ national standards, these PQ indices can be classified. The results are shown in Table 2.
Table 2.The steady-state PQ early warning index system
3. Anomaly detection algorithms
Anomaly detection algorithms for steady-state indices mainly use a data mining method based on time sequences. Anomaly detection algorithms based on the pattern representation of a time series, or pattern density of a time series, all focus on the Gaussian signals of the second order statistics [13-15]. For non-Gaussian signals, the second order statistics are just one part of the information. They do not contain phase information. Therefore, second order statistics become powerless for identifying non-minimum phase systems. An anomaly detection algorithm based on higher order statistics of the time series can solve this problem effectively [16-20].
Skewness and kurtosis of the higher order statistics are often used to detect a status change in the stochastic process. It has been used in biological signals containing noise to separate them from the noise, and is also widely applied in the field of earthquake prediction.
Skewness is a statistic that can describe the distribution symmetry of variate values. If the value of skewness is negative, it indicates the sample slants to the left; if the value of skewness is 0, it indicates the sample has a symmetric distribution; if the value of skewness is positive, it indicates the sample slants to the right. It shows that the greater the absolute value, the more serious the degree of deviation. There are many definitions of skewness. The skewness of a normal distribution and all symmetrical distributions is 0, and its widely used computation formula is:
where, μ is the average of the variable X, μi is the i-th order central moment and E() is the mathematical expectation.
Kurtosis is a statistic describing the degree of steepness of all variate distribution values. The peak value of the normal distribution is 3, if one particular distribution is steeper than a normal distribution, its peak value will be greater than 3. The computation formula for kurtosis is:
The kurtosis of a normal distribution is often normalized to 0, this is the so-called “kurtosis beyond”. If kurtosis becomes greater than 0, the distribution contains a spike and the data is likely to exist as an exception.
In practical applications, the above two statistics can be obtained by computing respectively their unbiased estimates: g1 and g2. For example, a sample whose length is N: x={x(n): n=1,2, ···, N}. The computation formulas for g1 and g2 are:
where, is the average of x(n) and is the standard deviation of x(n).
The mathematical expectation of g1 and g2 is 0 and -6/(N-1) respectively. When the variable obeys a normal distribution, the variances of g1 and g2 are:
In this study, we assume that the existing PQ indices are normally distributed. Therefore, the above formulas can be directly used to compute skewness and kurtosis.
The specific steps of the algorithm based on the skewness and kurtosis are as follows:
1) Determine the length of the sliding window;2) Slide the window from the first data of the day. When the window experiences each slide, it will move back to the next value. For example, the j-th window is: wj = {x(k) : k = j, j +1,..., j+W-1} . The algorithm needs to compute the statistics (g1,j and g2,j), average(u) and standard deviation (σ) for every window;3) The algorithm uses interval estimation of the normal distribution: . When the random variable X meets the above distribution, two intervals can be deduced: and Where a=1-q (q generally takes the value 0.95).If g1 and g2 are within the two intervals respectively, skewness and kurtosis should be equal to the mathematical expectation of g1 and g2; if not, skewness and kurtosis should be equal to g1 and g2 respectively;4) Repeat step 2: sliding to the next window and calculating the corresponding values. The statistics needed for all windows will then be obtained;5) Update the maximum of the product: after the above steps, the product of skewness and kurtosis for each window can be calculated. When skewness and kurtosis all exceed the thresholds, the necessity of updating the maximum of the product will be considered. Besides, in this step, it is also worth noting that only when any one of the average and 95% probability values of the selected window exceeds the threshold, the progress of updating the maximum will be completed really;6) According to the maximum of product computed in the fifth step, the early warning grade can then be determined. If the maximum falls below the threshold of Grade 2 or Grade 1, the index should be judged as being normal.A detailed flowchart of the above steps is shown in Fig. 1.
Fig. 1.Detailed flowchart of the anomaly detection algorithms
4. Hierarchical PQ Early Warning Flow
In this study, the steady-state PQ indices are used to establish the early warning index system. One direct method to judge the good or bad of the steady-state indices is to compare them with the corresponding national standard limits. If the data of one index at a certain monitoring point seriously exceed the national standard limits, it should provide an early warning and an alert to find the reason for the warning and take measures to improve the PQ. However, in most cases, most steadystate PQ indices are relatively good, and their values are lower than the national standard limits. If the 95% probability value of monitored data at a certain monitoring point is relatively large, it should also be taken seriously. Moreover, if the 95% probability value is relatively small, it should perform data mining to test whether the monitored data is abnormal. Because some indices, such as active/reactive power fluctuations, have no national standard, they cannot be determined at the first two levels of early warning detection. They can only detect anomalies.
The premise for determining an early warning is that the monitoring points are able to provide enough data. If the data are not complete, early warning detection cannot be effective. In most cases, when monitoring equipment works normally, the monitored data can be uploaded every 1 to 3 minutes. In particular, the presence of short flicker creates data every 10 minutes. Under normal circumstances, 50% of the monitored data can be used to serve as a data integrity limit. For example, current harmonics produce data every 3 minutes, so there should be 480 sets of data in a day. If the quantity of data falls below a threshold, the voltage deviation data for the day are invalid as a PQ early warning.
4.1 PQ Early warning flow of indices that have national standard limits
For PQ indices that have Chinese PQ national standards, the PQ early warning flow at three levels and four grades can be adopted. After judging the integrity of the monitored data, PQ early warning can be carried out. The flowchart of PQ early warning is shown in Fig. 2.
Fig. 2.Flowchart of PQ early warning
The first level is limit-exceeding detection. Comparing the index data of the day with the national standard limits of the corresponding voltage grade, the number of data that exceed the national standard limits can be computed. The number can then be used to compare with the thresholds for Grade 4 or 3. If the number exceeds the threshold for Grade 4, the early warning for Grade 4 should be given. If the number falls below the threshold for Grade 4, but exceeds the threshold for Grade 3, the early warning of Grade 3 should be given.
Otherwise, the second level 95% probability value detection should be implemented. The 95% probability value for the index can be read directly from the database. Comparing the 95% probability value with the threshold can determine the grade of early warning. When the 95% probability value falls below the threshold for Grade 2, third level anomaly detection should be implemented.
In Fig. 2, Step 5: early warning detection is the core of PQ early warning. The specific method and steps for detecting anomalies have been analyzed in detail in Section 3. The specific flowcharts for detecting the limit-exceeding detection and 95% probability value detection are shown in the dotted boxes of Fig. 3 respectively.
Fig. 3.Flowchart of the first two levels
Obviously, in the PQ early warning flow, the definition of thresholds plays an important role in the early warning results. However, defining some general or fixed values for these thresholds seems not to be appropriate. This is because different disturbance sources have their unique PQ characteristics. General or fixed values cannot reflect the characteristics of changes in the index data caused by these unique PQ characteristics, so we define different thresholds for different PQ disturbance sources. The specific definition method is as follows:
1) According to historical PQ monitored data, we can analyze the distribution characteristics of the index data during the normal operation of PQ disturbance sources, such as the number of limit-exceeding, 95% probability value, skewness and kurtosis for different sliding windows and so on;2) Based on performance characteristics of PQ disturbance sources, and distribution characteristics of the index data analyzed in 1), we can define thresholds for different early warning grades by appropriately increasing, retaining or decreasing normal values;3) The thresholds computed in 2) mainly reflect the characteristics of changes in historical index data, and they can be defined as subjective thresholds w1. In practical application, it is necessary to compute the thresholds that reflect the characteristics of changes in present monitored index data, and they can be defined as objective thresholds w2. Subjective thresholds w1 and objective thresholds w2 reflect different requirements for index data in different time scales.
Based on the method that was present in [21], objective thresholds w2 can be obtained by computing the critical points that can separate normal data from abnormal data. The final thresholds w0 can be obtained by combinatorial weighting method as follows:
where, w1 are the subjective thresholds; w2 are the objective thresholds; a and b are the proportionality coefficients of w1 and w2 respectively.
Refer to the calculation method of weight coefficients in PQ evaluation, the following formulas are used to compute them:
where, L and pi are the number of categories and the probability value of different categories that are sorted in ascending order respectively when carrying out clustering analysis.
The greater the value of i, the more likely pi is abnormal categories. Therefore, the formula can reflect the principle: abnormal data play a more important role than normal data in computing the final thresholds. If the number of abnormal data becomes more, the proportionality coefficient of objective threshold should be greater.
4.2 PQ Early warning flow of indices that have no national standard limits
Some indices such as active or reactive power fluctuations are not traditional PQ indices, but, to some extent, they can reflect PQ problems. It is necessary to carry out PQ early warning for them. Because these indices have no national standards, limit-exceeding detection or 95% probability value detection cannot be used. In this paper, we only use anomaly detection for them.
For indices that have no national standard limits in PQ early warning index system, using directly indices values to compare with given thresholds is not appropriate. Take negative/zero sequence current for example. Because the rated short-circuit capacity and maximum current for each power line are not the same, the severity of the problem reflected by the same amount of values is also different. Refer to the definition of three-phase voltage unbalance [22], if we choose the ratio of negative/zero sequence current and positive current as the research objective, it will be better at reflecting the severity of PQ problem. If the status change of a ratio achieves a certain level, it should be given early warning prompts; if not, it should be judged as being normal.
Other indices have the similar characteristics, and they all need some simple transformation before performing PQ early warnings. Based on this consideration, looking for new research objects to replace those indices has become necessary. In this paper, we mainly choose different kinds of ratios as new research objects to transform indices that have no national standard limits. The specific transformation formulas are:
where, d is the new replaced index; SN is the rated shortcircuit capacity of PCC; Pmax and Pmin are the maximum and minimum of active power over three minutes; ΔPl and ΔQl are the variation values of active power and reactive power; RL and XL are the resistance and reactance of the power grid; UN is the rated voltage of PCC; Qmin is the minimum of the reactive power over three minutes; Imax is the maximum of the RMS current over three minutes; Isc is the short current of the power line; Ipseq is the positive current; and I is the negative/zero sequence current.
When performing a PQ early warning for these indices that have no national standard limits, new replaced indices that can reflect the real seriousness of the problem need to be computed firstly as research objectives. Using these new replaced indices, the detection of anomalies as shown in Fig. 1 can then be carried out to perform a PQ early warning.
4.3 The flow of writing to PQ early warning databases
The PQ early warning results can be written to three different databases. They are the “limit-exceeding”, “early warning” and “normal” databases. By combining the history of early warning results from buses and lines, it is possible to write any early warning results of a specific day to the corresponding databases, and display them in the platform. When and only when early warning results exceed national standard limits on two consecutive days and above, the results will be written to a limit-exceeding database. Once early warning results exceed the national standard limits or become abnormal, the results will be written to the early warning database. The normal database contains some normal indices that show an improved power quality state compared with the historical monitored data. The specific steps for writing to the databases are as follows:
1) Compute the early warning results for one PQ index from one power line for a specific day and then judge whether the index exceeds the national standard limits. If so, proceed to Step 2. If not, proceed to Step 5;2) Write the early warning results for the specific day to the early warning database, delete the index from the normal database and carry out the following judgment process: query the limit-exceeding database and judge whether the index for the power line exists in the limitexceeding database. If so, proceed to Step 3. If not, proceed to Step 4;3) Write the early warning results of the specific day to the limit-exceeding database. Because the results have been written to the early warning database and deleted from the normal database, there is no necessity to judge how the index should have been disposed of in these two databases;4) Query the early warning grade of the index for yesterday from the early warning database. If the index for yesterday exceeds the national standard limits, write the early warning results of the specific day to the limitexceeding database. If not, nothing should been done to the limits-exceeding database. When the above are completed, proceed to Step 7;5) Judge whether the data are abnormal. If so, write the early warning results of the specific day to the early warning database and delete the index from the limitexceeding and normal databases. Then proceed to Step 7. If not, proceed to Step 6;6) Compared with historical data, the state of the PQ index can be judged as to whether it has improved. If so, write the early warning results of the specific day to the normal database and delete the index from the limitexceeding database. If not, nothing further needs to be done;7) End PQ early warning for the specific day.
5. Case Studies
5.1 Platform displaying the early warning results
With the development of modern network technology (including LANs and WANs), optical fiber communication technology and standardized protocols can provide the basic conditions for data collection, remote transmission, analysis and sharing. Thus, the PQ monitoring system has become a standardized net-based system. In China, some provinces are starting to construct PQ monitoring systems. Taking the Jiangsu province as an example, after years of construction, Jiangsu has established a large-scale provincial PQ monitoring network. At present, it has installed 1032 monitoring points and is able to monitor the PQ of large impact loads, new energy sources and key substations. A unified monitoring platform system has basically been completed.
To supplement and perfect a PQ monitoring system, the steady-state PQ early warning platform based on the above algorithm model to detect anomalies and early warning flow can be designed as a separate part and embedded in the monitoring system. The early warning platform can serve as a high-level application module of the monitoring system. Its design objective is to mine the PQ limitexceeding and abnormal data and give corresponding alerts. The main function modules of the platform are introduced as follows:
5.1.1 Display the ratio of the early warning results
To acquire a full understanding of the status of the PQ in a power grid and find potential hidden PQ problems, the early warning results for all buses and power lines and the ratio of “limit-exceeding”, “early warning”, and “normal” need to be computed and summarized. In a real application, these early warning results will come from different databases.
5.1.2 Abnormal state proportional graph
In the operation of the power grid, the changes in the abnormal state of the PQ early warning indices during different monitored days are not the same. Therefore, it is necessary to establish abnormal state proportional graphs of all the monitored days to make the changes in different abnormal indices more specific and visual.
5.1.3 The early warning detailed information
The platform can not only display the above information, but can conduct early warning and provide warning alerts for abnormal data from specific PQ disturbance sources. When the early warning platform operates normally, the warning alerts and the corresponding early warning detailed information can be obtained through simple operations.
Above all, according to the information provided by this platform, both the power suppliers and users can know the status of PQ and possible problems in a timely and accurate manner, to take effective counter measures to minimize any losses. In the following section, a common PQ disturbance is introduced, and is emphasized by the application of the early warning platform.
5.2 PQ early warning for non-linear loads access points
To illustrate the application of the PQ early warning platform, this study takes PQ early warning results from the 35 kV I-bus bar at the Baodong substation of the Taizhou Power Supply Company from May 5th to 7th, 2013, as an example. Through the corresponding calculations, the PQ early warning detailed information can be obtained. The results are shown in Table 3.
Table 3.PQ early warning detailed information
Table 3 prompted PQ early warning grades and categories of different steady-state indices, and gave the corresponding early warning detailed description information, where the limit-exceeded thresholds for Grade 4 and Grade 3 were 24 and 12 respectively. The 95% probability value thresholds of Grade 3 and Grade 2 were 0.9 and 0.7 times the national standard limits respectively. The length of the sliding window was set at 50. The maximum product thresholds for Grade 2 and Grade 1 were 2000 and 100 respectively.
From this table, both the power suppliers and users can in a timely and accurate manner know the status and early warning detailed information of different PQ indices in one power line on a specific day.
Table 3 gave some relatively fragmented and specific early warning information about different PQ indices, but how the whole PQ status of one power line changed over a period of time may not be apparent to power suppliers and users. To make their PQ variation trend more visual, the early warning results from Table 3 can be used to compare with historical data.
To achieve this goal, the flow of writing to different databases that has been analyzed in detail in Part 3 of Section 4 needs to be carried out. From Table 3, we can find that short flicker always exceeded limits in three days, so it should be written to the limit-exceeding database. Some indices such as THD of voltage exceeded limits or became abnormal on one day, so they should be written to the early warning database. Other indices such as 7th harmonic current became normal on the third day, so they should be written to the normal database.
Then changes in ratios of the analysis results in different databases on different monitored days can be computed to reflect the PQ variation trend. They are shown in Fig. 4.
Fig. 4.The ratios for the early warning results on different monitored days
From the Fig. 4, we can find that PQ on the first day was the worst, for it had no indices that became better when compared with the front day, and the number of the early warnings was the most in three days. According to changes in ratios on the second and third day, we can basically see that the whole variation trend of PQ in this area was to some extent improved during the period. This is because the number of the early warnings decreased and the number of indices in the normal database increased when compared with the front day.
To put forward the treatment measures, the changes in abnormal state of the PQ early warning indices during different monitored days need to be obtained. After statistical analysis on early warning results shown in Table 3, abnormal state proportional graphs for different indices on different monitored days can be drawn. The graphs are shown in Fig. 5.
Fig. 5.Abnormal state proportional graph on different monitored days
In general, based on the above different kinds of information, both the power suppliers and users can then be provided with knowledge of potential hidden PQ problems from typical power quality disturbance sources and important buses or lines, and enable important power customers to understand, in a timely manner, the changing process of their own PQ and adjust their loads or operation modes to avoid unnecessary economic loss.
5.3 Platform displaying the original data
If necessary, the original data can be queried and displayed on this platform. Fig. 6 shows the original data waveforms of short flicker and total harmonic distortion of voltage. These two indices are typical examples of all limit-exceeding indices. Among them, short flicker has been given a limit-exceeding warning of Grade 4 for three days, and THD of voltage has been given a limit-exceeding warning of Grade 3 for the previous two days. The following waveforms obviously reflect these changes.
Fig. 6.The original data waveforms for short flicker and THD of voltage
Fig. 7 shows the original data waveforms for voltage deviation and the 5th harmonic current. These two indices are typical examples of all abnormal indices. Among them, voltage deviation gave an abnormal warning of Grade 2 on the second day, and the 5th harmonic current gave an abnormal warning of Grade 1 on the third day. The following waveforms obviously reflect these changes.
Fig. 7.The original data waveforms for voltage deviation and the 5th harmonic current
Fig. 8 shows the original data waveforms for the 11th harmonic voltage and 7th harmonic current. These two indices are typical examples that become normal. The following waves reflect these changes.
Fig. 8.The original data waveforms for the 11th harmonic voltage and 7th harmonic current
From this figure, the two indices obviously improved, and these situations also verify the early warning results of Table 3.
Through the above analysis, we ascertain that the main PQ problems for the bus bar are short flicker and harmonics. By querying the PQ disturbances for the bus bar, we find that there was a large-scale foundry that powered many electric arc furnaces. Therefore, the above early warning results are entirely consistent with the PQ characteristics of electric arc furnaces. This shows that the proposed approach is effective and feasible.
5.4 Looking for the root causes of the early warnings and improving the PQ
Based on the above early warning results, Taizhou Power Supply Company timely communicated with the power user. They ascertained that the power user was testing new electric arc furnaces on those days, compensation devices for short flicker did not work and filter devices worked off and on for those days. The information can explain the root causes of some early warnings very well.
After that, to improve the PQ and the security of this power system, Power Supply Company asked the power user to put relevant compensation devices into the power grid again. Taking short flicker and THD of voltage as examples, their original data waveforms in the next three days are shown as Fig. 9. From the figure, we can basically see that flicker and harmonic events were compensated. Other indices have similar changes. At the same time, the system also judged the relevant indices were normal and no early warnings were given. All of these show that the PQ of this area was improved.
Fig. 9.The original data waveforms for short flicker and THD of voltage in the next three days
6. Conclusions
Based on the PQ characteristics analysis for typical disturbance sources, the steady-state PQ early warning index system is proposed in this study. An anomaly detection algorithm based on the higher order statistics of the time series and the hierarchical PQ early warning flow are applied to mining limit-exceeding and abnormal problems of PQ monitored data. Taking the PQ early warning for one 35 kV I-bus bar access point as an example, the accuracy and effectiveness of the proposed algorithm and flow process has been verified.
The approach proposed in this study and the analysis results can be used to carry out steady-state PQ early warning and serve as a monitoring platform to display related information about PQ limit-exceeding and abnormal problems to both power suppliers and users. In this way, all types of abnormal changes in PQ can be identified and warnings issued in a timely manner. Therefore, through taking necessary counter measures, the power grid can avoid the evolution of an accident and effectively improve its reliability and economy.
References
- A. McEachern, "Designing electronic devices to survive power-quality events," IEEE Industry Applications Magazine, vol. 6, no. 6, pp. 66-69, Nov-Dec.2000. https://doi.org/10.1109/2943.877842
- Z. Chen, E. Spooner, "Grid power quality with variable speed wind turbines," IEEE Transactions on Energy Conversion, vol. 16, no. 2, pp. 148-154, Jun. 2001. https://doi.org/10.1109/60.921466
- M. Castilla, J. Miret, J. L. Sosa, et al, "Grid-fault control scheme for three-phase photovoltaic inverters with adjustable power quality characteristics," IEEE Transactions on Power Electronics, vol.25, no.12, pp. 2930-2940, Dec. 2012.
- H. Lee, H. Lee, C. Lee, et al, "Energy storage application strategy on DC electric railroad system using a novel railroad analysis algorithm," Journal of Electrical Engineering & Technology, vol.5, no.2, pp. 228-238, Jun. 2010. https://doi.org/10.5370/JEET.2010.5.2.228
- A. Kiyoumarsi, M. Ataei, R. Hooshmand, et al, "Electric arc furnace voltage flicker mitigation by applying a predictive method with closed loop control of the TCR/FC Compensator," Journal of Electrical Engineering & Technology, vol. 5, no. 1, pp. 116-128, May. 2010. https://doi.org/10.5370/JEET.2010.5.1.116
- S. Mishra, C. N. Bhende, B. K. Panigrahi, "Detection and Classification of Power Quality Disturbances Using S-Transform and Probabilistic Neural Network," IEEE Transactions on Power Delivery, vol. 23, no. 1, pp. 280-287, Jan. 2008. https://doi.org/10.1109/TPWRD.2007.911125
- Y. Liao, J. B. Lee, "A fuzzy-expert system for classifying power quality disturbances," Electrical Power and Energy Systems, vol.26, pp.199-205, May. 2004. https://doi.org/10.1016/j.ijepes.2003.10.012
- C. H. Huang, C. H. Lin, C. L. Kuo, "Chaos Synchronization-Based Detector for Power-Quality Disturbances Classification in a Power System," IEEE Transactions on Power Delivery, vol. 26, no. 2, pp. 944-953, April. 2011. https://doi.org/10.1109/TPWRD.2010.2090176
- C. H. Lin and C. H. Wang, "Adaptive wavelet networks for power quality detection and discrimination in a power system," IEEE Trans-actions on Power Delivery, vol. 21, no. 3, pp. 1106-1113, Jul. 2006. https://doi.org/10.1109/TPWRD.2006.874105
- W. G. Morsi, M. E. El-Hawary, "Power quality evaluation in smart grids considering modern distortion in electric power systems," Electric Power Systems Research, vol. 81, no. 5, pp. 1117-1123, May. 2011. https://doi.org/10.1016/j.epsr.2010.12.013
- A. Salarvand, B. Mirzaeian, M. Moallem, "Obtaining a quantitative index for power quality evaluation in competitive electricity market," IET generation, transmission & distribution, vol. 4, no. 7, pp. 810-823, Jan. 2010. https://doi.org/10.1049/iet-gtd.2009.0479
- D. Agrez, "Estimation of the Component Parameters for the Evaluation of the Power Quality Disturbances in the Frequency Domain," IEEE Instrumentation and Measurement Technology Conference, pp.1548-1553, May. 2008.
- J. Lin, Y. Li, "Finding structural similarity in time series data using bag-of-patterns representation," Scientific and Statistical Database Management, vol. 5566, pp. 461-477, Jun. 2009. https://doi.org/10.1007/978-3-642-02279-1_33
- B. W. Brook, C. J. A. Bradshaw, "Strength of evidence for density dependence in abundance time series of 1198 species," Ecology, vol. 87, no. 6, pp. 1445-1451, Jun. 2006. https://doi.org/10.1890/0012-9658(2006)87[1445:SOEFDD]2.0.CO;2
- M. Stellmes, A. Roder, T. Udelhoven, et al, "Mapping syndromes of land change in Spain with remote sensing time series, demographic and climatic data," Land Use Policy, vol. 30, no. 1, pp. 685-702, Jan. 2013 https://doi.org/10.1016/j.landusepol.2012.05.007
- J. B. McDonald, J. Sorensen, P. A. Turley, "Skewness and kurtosis properties of income distribution models," Review of Income and Wealth, vol. 59, no. 2, pp.360-374, Jun. 2013. https://doi.org/10.1111/j.1475-4991.2011.00478.x
- D. N. Joanes, C. A. Gill, "Comparing measures of sample skewness and kurtosis," Journal of the Royal Statistical Society: Series D (The Statistician), vol. 47, no. 1, pp. 183-189, April. 1998. https://doi.org/10.1111/1467-9884.00122
- J. S. Bai, S. Ng, "Tests for skewness, kurtosis, and normality for time series data," Journal of Business & Economic Statistics, vol. 23, no. 1, pp. 49-60, Jan. 2005. https://doi.org/10.1198/073500104000000271
- D. P. Bernardon, M. Sperandio, V. J. Garcia, et al, "AHP decision-making algorithm to allocate remotely controlled switches in distribution networks," IEEE Transactions on Power Delivery, vol. 26, no. 3, pp. 1884-1892, Jul. 2011. https://doi.org/10.1109/TPWRD.2011.2119498
- Y. Huang, S. Wang, "Multilevel thresholding methods for image segmentation with otsu based on QPSO," In Proc. CISP, 2008, pp. 701-705.
- X. Yuan, J. Bai, W. Gu, et al, "One definition method for abnormal thresholds in steady-state power quality early warning," C.N. Patent, 201310656915.3, Dec. 9, 2013.
- A. J. Von, B. Banerjee, "Assessment of voltage unbalance," IEEE Transactions on Power Delivery, vol. 16, no. 4, pp. 782-790, Oct. 2001.
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