Research on the fitting method to describe the mathematical expression of VFTO in GIS

The Journal of EngineeringVolume 2019, Issue 16 p. 2053-2057 Session – Report Session AOpen Access Research on the fitting method to describe the mathematical expression of VFTO in GIS Reem A. Almenweer, Reem A. Almenweer School of Automation, Wuhan University of Technology, Wuhan, Hubei, People's Republic of ChinaSearch for more papers by this authorSu Yixin, Su Yixin School of Automation, Wuhan University of Technology, Wuhan, Hubei, People's Republic of ChinaSearch for more papers by this authorWu Xixiu, Corresponding Author Wu Xixiu wuxixiu@163.com School of Automation, Wuhan University of Technology, Wuhan, Hubei, People's Republic of ChinaSearch for more papers by this author Reem A. Almenweer, Reem A. Almenweer School of Automation, Wuhan University of Technology, Wuhan, Hubei, People's Republic of ChinaSearch for more papers by this authorSu Yixin, Su Yixin School of Automation, Wuhan University of Technology, Wuhan, Hubei, People's Republic of ChinaSearch for more papers by this authorWu Xixiu, Corresponding Author Wu Xixiu wuxixiu@163.com School of Automation, Wuhan University of Technology, Wuhan, Hubei, People's Republic of ChinaSearch for more papers by this author First published: 04 January 2019 https://doi.org/10.1049/joe.2018.8753Citations: 4AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract Very fast transient over voltage (VFTO) is a unique electromagnetic transient phenomenon occurring in Gas Insulated Substation (GIS), which determines the insulation level of the GIS (above 330 kV). Unfortunately, up to the present, there is no standard VFTO waveform to test the high voltage equipment to ensure the safety of power grid. For this reason, this paper focuses on obtaining the standard VFTO waveform through finding a method to fit the curve of VFTO. Hence, a UHV disconnector operation experiment of GIS was carried out on the UHV GIS test platform. The representative waveform of VFTO generated by a single SF6 gas discharge was extracted from the measured data. Furthermore, The Fast Fourier Transformer is applied to analyze the frequency features of VFTO. As one of the switchgear operation voltage, VFTO can be concluded to be a superposition of the power-frequency waveform with the non-periodic impulse waveform. Thus, it is found that The Squares Method is convenient for fitting the expression of VFTO according to its transient characteristics. Then the standard VFTO waveform can be obtained from the fitting expression, which coincides well with the measured waveform. The simulation results using ATP-EMTP software are compared with the calculation results and the measured results. 1 Introduction Very fast transient over voltage (VFTO), which is generated by SF6 gas discharge in the disconnector gap in gas insulated substation (GIS) system, could bring damage to power devices, especially to power transformers. It exists as a superposition of a large number of different multiple reflected EM waves with complex non-harmonic time dependence and cover a wide frequency range from 100 kHz to 100 MHz [1, 2]. Two types of VFTO appeared as internal and external overvoltages. The stress on the internal insulation of the GIS could be caused by the overvoltage created by internal transient between conductor and enclosure, while external VFTs are travelling waves which propagate outside GIS [3]. The peak magnitude and high-frequency oscillations of VFTO cause reduction in dielectric of gas insulation [4, 5]. High inter-turn voltages and internal resonance in the transformer windings are caused because of VFTO, so many manufacturers of the high-voltage electrical equipment, especially power transformer, are working to provide insulation analysis results under VFTO condition. Owing to all of these disadvantages related to VFTO, VFTO becomes as a criterion to determine the insulation level of the GIS. However, the waveform of VFTO has not been standardised till now. Thus, finding a method to fit the curve of VFTO is an important issue to be discussed, which is the purpose of this paper. There are few steps to obtain the proposed VFTO equation which describes the curve fitting waveform: at first, VFTO waveform at load side under opening operation is obtained by ATP-EMTP. Then, the curve fitting method is applied to find out the data fitting waveform of VFTO by Matlab, which will be explained deeply later. Finally, the measured, simulated, and data fitting results are compared to confirm the validity of this method. 2 Analysis of transient characteristics of VFTO waveform VFTO wave has the characteristics of short rise time and high amplitude. The transient parameters of VFTO can deeply and clearly describe VFTO waveform. However, system parameters determine the rise time of VFTO wave, and the oscillation frequency depends on the arrangement of GIS. A complete analysis about the transient characteristics of 1100 kV VFTO waveform is conducted based on the experimental test. Typical transient parameters, which describe the transient characteristic of VFTO, are defined to understand the transient characteristics clearly. Statistic characteristics of rise time t r, breakdown steepness k, voltage overshoot coefficient H, and decay time t d are discussed in details [6]. The UHV GIS disconnector operation experiment base the IEC6227-102:2001 standard is implemented at the State Grid UHV base. Figs. 1 and 2 show the picture of the 1100 kV GIS test platform and the corresponding equivalent circuit, respectively. The circuit simulation has been performed by using the ATP-EMTP to obtain the VFTO waveforms. Fig. 1Open in figure viewerPowerPoint UHV GIS test platform Fig. 2Open in figure viewerPowerPoint Equivalent circuit of UHV GIS test platform Figs. 3 and 4 show the VFTO full waveform measured in the experiment under the opening and closing operation, respectively. Fig. 3Open in figure viewerPowerPoint Full waveform of VFTO under opening the disconnector Fig. 4Open in figure viewerPowerPoint Full waveform of VFTO under closing the disconnector 2.1 Fast Fourier transform analysis of VFTO waveform under opening operation at load side (point 1) The fast Fourier transform (FFT) technique is used to obtain the frequency spectra from the time-domain current waveforms by Matlab (see Fig. 2). As noted in Fig. 5, the dominant frequency components at load side under opening operation are up to 1.5 MHz. The main frequency with high amplitude is in the range of 1.466–1.468 MHz. The frequency amplitude of 1.468 MHz has the maximum magnitude. However, there are high-frequency components with lower amplitudes in the range <0.15 MHz. Fig. 5Open in figure viewerPowerPoint FFT analysis for VFTO waveform at load side 3 Curve fitting method The aim is to derive a mathematical equation which describes the VFTO for a single SF6 gas discharge with high amplitude as shown in Fig. 6 b. Fig. 6 a shows the VFTO waveform at load side (point 1) under opening operation. Four SF6 gas discharge moments were chosen for observing the changes to each wave. Through the comparison of a lot of single discharge VFTO waveforms at different moments as shown in Fig. 7, the same trend is noticed for the changes in VFTO waveforms at initial time. According to the changes of VFTO waveforms, we divided each waveform into three sections. The waveform of VFTO of the 0–1 segment is almost the same at each moment, so the curve fitting of this segment was carried out. For more accurate results, the highest amplitude moment was chosen at 0.0195 s, as shown in Fig. 6 b. Fig. 6Open in figure viewerPowerPoint VFTO waveform at load side (a) VFTO waveform when opening the disconnector DS1 at load side, (b) VFTO for a single SF6 gas discharge at 0.0195 s. with high amplitude Fig. 7Open in figure viewerPowerPoint Amplifier VFTO waveform at load side under opening operation for different breakdown processes (a) At 0.0195 s, (b) At 0.0139 s, (c) At 0.0115 s, (d) At 0.0090015 s As shown in Fig. 6, four different breakdown processes were presented at 0.0195, 0.0139, 0.0115, and 0.0090015 s. There are two different changes of the waveform for each moment: the first part '0–1' and the second part '1–2'. The waveform of the first part is almost the same. We have chosen 0.0195 s to calculate the equation at part '0–1' due to its high amplitude. 3.1 Mathematical equation Finding out the exact waveform of VFTO is so difficult due to the short rise time and wide frequency range of VFTO. The authors in [7, 8] presented VFTO substitution waveform and the influence factors of VFTO waveform, but their method is not so suitable in precision and expansibility. In this paper, the least-squares method was adopted to obtain the VFTO waveform, and by this method, we are not searching for finding the substitution waveform, but we are working on data fitting to find out the equation which describes VFTO by its fitting curve. Non-linear curve fitting (data fitting) problems are solved by the least-squares method by MATLAB software. 'The Least squares' method means that the overall solution minimises the sum of the squares of the residuals made in the results of every single equation. Thus, we minimise the sum of the square of the distances between the approximation and the data. 3.1.1 Solving the least-squares problem The purpose of this method is to modify the values of a model function to achieve a best fit of a data set. A simple data set consists of n points (data pairs) , where is an independent variable and a dependent variable whose value is found by observation. The model function has the form , where m adjustable parameters are held in the vector , since the function model contains m parameters. By measuring the difference between the actual value of the dependent variable and the value predicted by the model, the fit of a model to a data point is determined by its residual where is the sum of squared residuals To minimise the sum of squares, we set the gradient to zero, which means . Since the model contains m parameters, there are m gradient equations and since , the gradient equations become We can apply the gradient equations to all least-squares problems, but each particular problem requires particular expressions for the model and its partial derivatives [9]. The mathematical function of VFTO waveform is selected by using Fourier function as a model function, because the VFTO waveform displays irregular fluctuations. The discrete data extracted from the Fourier function is used to form the fitting wave as shown in Fig. 8 b. By using MATLAB software and applying the least-squares method with Fourier 7, the general model of the equation is where f (x) represents the voltage amplitude of VFTO in kV and x the time in seconds. Fig. 8Open in figure viewerPowerPoint VFTO waveform at 0.0195 s (a) VFTO wave obtained by ATP-EMTP, (b) Curve fitting of VFTO waveform by MATLAB Coefficients (with 95% confidence bounds) are shown in Table 1. Table 1. Coefficients of VFTO equation = −1.388×105 = 1.343×104 = 1.182×105 = −3.157×104 = −1.175×105 = −1.955×104 = 5.995×104 = −2948 = −2355 = −3.695×104 = 1.603×104 = 1.184×105 = 1.891×105 = 2.347×104 = −4.028×104 w = 1.223×107 The most important factor which illustrates the goodness of fit is R 2. This value measures what proportion of the variation in the outcome f (x) can be explained by the predictors. If R 2 is close to 1, it means that the covariates can jointly explain the variation in the outcome f (x). In our simulation, the R 2 is 98%, which shows that the good matching between the obtained equation of the fitting curve and the obtained waveform is achieved. It is clear that the goodness of this choice is appropriate, especially on the extreme surrounding 3.2 Verification through the comparison between curve fitting waveform and simulation waveform It has been mentioned that ATP-EMTP is one of the most commonly used software to calculate VFTO in GIS. In this paper, the simulation results using ATP-EMTP are compared with the curve fitting method results and the measured result. Fig. 9 shows the same trend for the changes in VFTO waveforms under opening operation for one single SF6 discharge at discharge time for the two curves of VFTO; one of them is simulated by ATP and another one is a curve fitting waveform of VFTO. Fig. 9Open in figure viewerPowerPoint Comparison between the curve fitting method (red colour) and the ATP simulation (blue colour) at load side under opening operation Table 2 illustrates the transient characteristics of VFTO waveform under opening operation at point 1 (see Fig. 2) for experimental results as mentioned in [6], the curve fitting method results, and the ATP-EMTP simulation results. Table 2. Transient characteristics of VFTO waveform under opening operation at point 1 VFTO characteristics parameters Experimental results Simulation results Curve fitting method results rise time, ns 10 35 20 average breakdown steepness, kV/ns 50.754 96.92 51.465 maximum amplitude of VFTO, p.u. 1.580 1.82 1.6327 average voltage overshoot coefficient 0.4026 0.289 0.5099 delay time, µs 31.277 32 32 It is clear from Table 2 that the measured results are well consistent with the curve fitting method results under the same conditions. 4 Conclusion This paper described the VFTO with the steep font, high amplitude, and high frequency generated during the opening operation of disconnector switch in 1100 kV GIS. When the rated voltage increases, the ratio of the lightning impulse withstand voltage to the system voltage decreases, which means that VFTO in GIS has become a serious problem at the highest rated voltages. However, VFTO can become the limiting dielectric stress which defines the dimensions of both the switchgear equipment and the connected equipment in certain UHV cases. For this reason, this study was conducted on fitting method to calculate the mathematical equation of a single SF6 discharge VFTO waveform to be an important basis to check the electrical equipment. Finally, the measured, simulated, and curve fitting results are examined to confirm the validity of this method. 5 Acknowledgments The author would like to acknowledge her gratitude to The National Natural Science Foundation of China (51107093), State Key Laboratory of Advanced Electromagnetic Engineering and Technology (Huazhong University of Science and Technology), Prof. Su Yixin, and associated Prof. Wu Xixiu for interesting discussions and valuable suggestions during the simulation work presented in this paper. 6 References 1Li Y., Shang Y., Zhang L. et al.: 'Analysis of very fast transient overvoltages (VFTO) from onsite measurements on 800 kV GIS analysis of very fast transient overvoltages (VFTO) from onsite measurements on 800 kV GIS', IEEE Trans. Dielectr. Electr. Insul., 2012, 19, (6), pp. 2102 – 2110 2Kuczek T., Florkowski M.: 'Analysis of transient overvoltages in high voltage gas insulated substations', Zesz. Nauk. Wydz. 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