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Transient overvoltage response performance of transformer windings with short‐circuit fault

2018; Institution of Engineering and Technology; Volume: 12; Issue: 10 Linguagem: Inglês

10.1049/iet-gtd.2017.0702

1751-8695

Qing Yang, Yong Chen, Rui Han, Peiyu Su,

Lightning and Electromagnetic Phenomena

IET Generation, Transmission & DistributionVolume 12, Issue 10 p. 2265-2272 Research ArticleFree Access Transient overvoltage response performance of transformer windings with short-circuit fault Qing Yang, Corresponding Author Qing Yang yangqing@cqu.edu.cn State Key Laboratory of Power Transmission Equipment & System Security and New Technology, Chongqing University, No. 174 ShaZheng Street, Chongqing, People's Republic of ChinaSearch for more papers by this authorYong Chen, Yong Chen State Key Laboratory of Power Transmission Equipment & System Security and New Technology, Chongqing University, No. 174 ShaZheng Street, Chongqing, People's Republic of ChinaSearch for more papers by this authorRui Han, Rui Han State Key Laboratory of Power Transmission Equipment & System Security and New Technology, Chongqing University, No. 174 ShaZheng Street, Chongqing, People's Republic of ChinaSearch for more papers by this authorPeiyu Su, Peiyu Su State Key Laboratory of Power Transmission Equipment & System Security and New Technology, Chongqing University, No. 174 ShaZheng Street, Chongqing, People's Republic of ChinaSearch for more papers by this author Qing Yang, Corresponding Author Qing Yang yangqing@cqu.edu.cn State Key Laboratory of Power Transmission Equipment & System Security and New Technology, Chongqing University, No. 174 ShaZheng Street, Chongqing, People's Republic of ChinaSearch for more papers by this authorYong Chen, Yong Chen State Key Laboratory of Power Transmission Equipment & System Security and New Technology, Chongqing University, No. 174 ShaZheng Street, Chongqing, People's Republic of ChinaSearch for more papers by this authorRui Han, Rui Han State Key Laboratory of Power Transmission Equipment & System Security and New Technology, Chongqing University, No. 174 ShaZheng Street, Chongqing, People's Republic of ChinaSearch for more papers by this authorPeiyu Su, Peiyu Su State Key Laboratory of Power Transmission Equipment & System Security and New Technology, Chongqing University, No. 174 ShaZheng Street, Chongqing, People's Republic of ChinaSearch for more papers by this author First published: 28 March 2018 https://doi.org/10.1049/iet-gtd.2017.0702Citations: 5AboutSectionsPDF 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 The fault diagnosis of transformer windings is a basis for condition maintenance. Conventional online or offline diagnosis methods require additional pulse or impulse signal. If the overvoltage signal can be regarded as the broadband excitation source for the fault diagnosis of transformer windings, the interference caused by signal injection is likely eliminated without additional pulse or impulse signals. In this study, the transient overvoltage response performance of transformer windings with short-circuit fault is presented, which could provide a new method for the diagnosis on transformer fault diagnosis. A 10 kVA, 2400 V/220 V, 50 Hz, 1-phase tapped transformer was designed, and a test platform for the fault diagnosis of transformer windings is established. The excitation signals for the fault diagnosis of the transformer windings included different lightning waves and damped oscillation waves, as indicated by the differences among actual overvoltage waveforms. The voltage and current of windings under normal and fault conditions are determined, and the frequency responses of admittance and voltage transfer function are calculated. The criterion for the fault diagnosis of transformer windings is obtained by comparing and analysing statistical indicators that reflected the differences in the frequency response of transfer function under normal and fault. 1 Introduction Power transformers are the core component in power systems, and the safe and stable operation of these transformers affect the reliability of power supply and the economy. Transformer faults [1–3], such as winding grounding and interlayer short-circuit faults, can be caused by transient overvoltage, overcurrent, or insulation aging. Therefore, transformer faults, as well as early warning and timely maintenance, should be diagnosed in real time. The operation of the two float switches of the Buchholz relay immersed in transformer oil and the no-load power loss of a transformer provide indications of winding faults. However, the Buchholz relay cannot detect an incipient winding interturn fault very fast. According to the IEEE Standard C37.91–2000 in power transformers, for incipient faults, or when the number of shorted turns is <10% of total winding turns, there is no significant change in the terminal current to provide protection. Therefore, the detection and diagnosis of a few winding turn-to-turn faults is a difficult task. These faults can lead to a catastrophic failure and, hence, cause outages if they are not detected in early stages [4]. Fault diagnosis methods for transformer windings mainly depend on simulations and experiments. Most simulations via a finite-element method focus on the electromagnetic field distribution of transformer cores and windings to determine the state of windings [5–7]. To a certain extent, winding faults can be identified through these simulations. In traditional tests for winding fault diagnosis, offline diagnosis is employed. Several common methods include low-voltage impulse test [8], short-circuit impedance measurement [9, 10], and frequency response analysis (FRA) [11, 12]. Among these methods, FRA is the most widely used. FRA can be divided into two main types, namely sweep frequency response analysis (SFRA) and impulse frequency response analysis (IFRA). A lot of experimental researches have been done about online diagnosis transformer based on FRA since the very first papers of Malewski [13, 14]. Also, the trends and new developments of such well-known and popular methods in fault diagnosis in power transformers are presented by Leibfried [15–17]. The exciting signal of SFRA is a sine sweep signal with different frequencies with a voltage amplitude of several volts [18]. However, the exciting signal of IFRA is an aperiodic impulse with multi-frequency components with a voltage amplitude of several hundred volts. Both of them are offline test methods. FRA can determine winding fault by comparing the differences in the frequency response of transfer function under normal and fault conditions [19]. Statistical indicators can indicate whether a fault occurred and specify the type of fault. Online fault diagnosis for transformer windings based on FRA is also presented [20–22]. However, these methods require extra pulse or impulse signals and may weaken the insulation of transformer bushing by changing its structure. Lightning and operating or other overvoltages widely exist in an actual power grid. Overvoltage signals are characterised by broad spectrum and high amplitude. From our observation based on overvoltage monitoring system [23, 24], it can be found that the front time of the lightning overvoltage surges can reach the level of microsecond. So the equivalent frequency of the lightning surges can reach the level of MHz. The equivalent frequency of switching overvoltage could also reach to 30–100 kHz. Moreover, the front time of the very fast transient overvoltage in GIS system can reach to the level of nanosecond. Therefore, the overvoltage signals could meet the requirements of being as the exciting signal for the transformer winding fault diagnosis. Therefore, if an overvoltage signal can be monitored by overvoltage monitoring systems, overvoltage signals can be used as excitation sources, and the frequency response of transfer function can be calculated by monitoring the corresponding overvoltage and overcurrent signal of windings. Thus, transformer faults can be identified by comparing the differences in the frequency response of transfer function under normal and fault. In this method, additional pulse or impulse generators are unnecessary and transformer outage overhaul is avoided. In [25], an on-line transformer FRA method based on a three-phase, 2000 MVA, 500/230 kV auto-transformer is presented, which is an initial research on the winding fault diagnosis based on transient overvoltage measurement. Thus, a detailed analysis on whether the method could find all kinds of faults or to distinguish the different faults could be an important supplement to this method. Therefore, different winding faults should be designed in the transformer model. The measurement of transfer function in the different types of lightning and oscillation voltage can be applied to evaluate whether this method can be applied to the power system. Recent studies on transformer winding fault diagnosis based on small transformer could be found in some transaction and JEET papers [26, 27]. Moreover, such reduced-scale model could also be found in other studies on transformers [28, 29]. Reduced-scale transformer presented in this paper can simulate all kinds of winding short-circuit fault by reasonable design of the transformer winding tap. Due to the reduced-scale transformer is made of according to the shrinkage ratio criterion, it can reflect the winding transfer function. Thus winding short-circuit fault diagnosis can be realised in the experiments. Therefore, in this paper, in order to determine whether the transient overvoltage response performance of the transformer can be applied to the winding fault diagnosis. Overvoltage and overcurrent monitoring in substations have been proceeded for 10 years in Chongqing University. The contact capacitive divider sensor in series to the transformer bushing, and the non-contact sensor, of lightning and switching transient overvoltage based on capacitive coupling and Pockels effects are widely adopted to measure the overvoltage in many substations [24, 30]. The current can also be obtained by Rogowski coil with wide band frequency. In this paper, the transient overvoltage response performance of transformer windings with short-circuit fault is presented on the basis of long-term studies on overvoltage monitoring. A 10 kVA 220 V/120 × 20 V tapped transformer model has been designed, and the test platform of winding fault diagnosis for the use of lightning impulse voltage and damping oscillation voltage as an excitation signal has been established. The voltage and current of windings under normal and fault are measured. The frequency responses of admittance and voltage transfer function are calculated. The criterion for the fault diagnosis of transformer windings is obtained by analysing the statistical indicators that reflect the differences in frequency response of the transfer function under normal and fault conditions. 2 Transfer functions of winding short-circuit fault under transient overvoltage Transformer windings can be regarded as a passive linear two-port network [31]. The frequency response of network transfer function H (jω) can reflect the transfer characteristics of the network and is closely related to the distributed parameters of transformer windings. The equivalent parameters of resistors, inductors, and capacitors will be changed, that is the frequency response of network transfer function will be changed when a short-circuit fault or mechanical failure occurs. The state of windings can be determined by measuring the frequency response of transfer function. Frequently used transfer functions are voltage transfer function TFA and admittance transfer function TFB, and the definitions are as follows: (1) (2) where UL, UH, and IH are the voltages in low-voltage (LV) winding, the voltage in high-voltage (HV) winding, and the current in HV winding, respectively. Overvoltage and overcurrent would be transferred to the transformer windings when substations suffer from lightning and operating overvoltage with broadband equivalent frequency. Voltage transfer function TFA and admittance transfer function TFB can be calculated by overvoltage and overcurrent measured by monitoring system. The fault diagnosis of windings can be achieved by quantitative analysis of the differences in transfer function under normal and fault conditions described by statistical indicators, such as a correlation coefficient ρ (X, Y), a spectrum deviation σ (X, Y), and an absolute sum of logarithmic error (ASLE) [32]. These quantities are defined as follows: (3) (4) (5) where vectors X = (x1, x2, …, xn) and Y = (y1, y2, …, yn) denote data vectors of two frequency responses and n is the number of frequency points. The correlation coefficient can reflect whether the two different curves is similar, which could transfer the graph deviation of the curves to the numerical value. Thus it will be helpful to find out in what degree of the deviation. The correlation coefficient ρ (X, Y) approaches 1 when the shapes of X and Y are similar to each other. In this paper, the fault diagnosis of transformer windings can be realised by analysing the differences of different curves of the transfer function frequency response under normal and fault conditions. The vertical axis of transfer function is using logarithmic coordinate system, so the ASLE is extremely useful for the comparison of the differences of transfer functions between normal and fault. With the overvoltage in HV side as excitation signal, the overvoltage in LV side is measured, and fault diagnosis of transformer windings can be realised by the calculation of the voltage transfer function as in (1); the overcurrent in LV side is measured, and fault diagnosis of transformer windings can be realised by calculating the admittance transfer function as in (2). The overvoltage and overcurrent passing to the transformer can be collected by using overvoltage online monitoring in HV windings in combination with current monitoring. Thus, the transformer winding faults can be determined through quantitative analysis, as in (3)–(5). 3 Experimental setup for winding short-circuit fault under transient overvoltage To find the transient overvoltage response performance of transformer windings with short-circuit fault and provide the foundation of a new transformer windings faults diagnosis method, a 10 kVA 220 V/120 × 20 V tapped transformer for the experiment based on an actual transformer is designed. A unique tap structure design is adopted to simulate different winding grounding and interlayer short-circuit faults. The impulse voltage and oscillation voltage are applied to the transformer to verify the proposed method. As experimental tests are proceeded in laboratory, the transformer is tested offline. 3.1 Structure of transformer The design of transformer mainly includes the design of the transformer core, windings, and taps. The rectangle-shaped iron core is fabricated from silicon steel sheet. The cross-section of iron core is shown in Fig. 1a. Fig. 1Open in figure viewerPowerPoint Schematics of transformer core and tapper winding (a) Cross-section of transformer iron core, (b) Tap schematic of transformer winding The number of HV winding turns is 960. HV winding is divided into two parts evenly. Forty-eight turns are considered as one layer and a total of 20 layers are enwound continuously around the outside of the core. Each layer leads to a tap, and there are 20 taps at the HV. The LV winding is also a layer winding. The schematic of taps in HV winding is shown in Fig. 1b. The design of HV winding taps is convenient for simulating short-circuit fault in windings. Short-circuit connections between taps and ground wire and among taps are used to simulate the winding grounding and interlayer short-circuit fault, respectively. 3.2 Test circuit During the tests, lightning voltage is applied to the transformer model. Moreover, when lightning and operating overvoltage intrude into the transformer, the actual lightning invasion wave in transformer windings may not be the standard lightning waveform but a damped oscillation wave [23]. Therefore to simulate a real wave invasion situation, the damped oscillation voltage is also applied to the transformer model as the excitation signal. The platforms for lightning voltage and oscillation voltage tests are shown in Fig. 2a. Fig. 2Open in figure viewerPowerPoint Test platform for winding short circuit (a) Test platform for measuring the transfer function under lightning voltage and damped oscillation wave, (b) Schematic diagram measuring the transfer function In Fig. 2a, the lightning impulse voltage with a front time of 1–5 μs, and the voltage magnitude of 0.5–5 kV can be generated. A standard resistance box can provide 5, 10, and 15 kΩ standard resistances. A Tokogawa DL850E six-channel wave recorder with a maximum sample frequency of 100 MHz is adopted for measuring voltage. The damped oscillation wave tests used a damped oscillation wave of 2 kV amplitude, with the equivalent frequency of 20 kHz. Two groups of tests are conducted. In one test, the voltage can be measured in LV side and HV winding taps when the voltage is applied to the LV winding, and the voltage transfer function can be calculated. In the other test, the current at the end of HV winding can be measured when the voltage is applied to HV winding, and the admittance transfer function can be calculated as shown in Fig. 2b. In Fig. 2b, the winding tap grounding short-circuit fault is simulated by the metal connection of different taps and the ground. In addition, the winding interlayer short-circuits is simulated by the metal connection of different winding taps. The voltage transfer function TFA (dB), in the form of gain, can be calculated by fast Fourier transform (FFT) of the input voltage Uin on the LV side and the output voltage Uout on the HV side as (6) Also, the admittance transfer function TFB (dB) in the form of gain can be calculated by FFT of the LV side Uin and the output current Iout on the HV side on the HV side as (7) After the voltage and current under different short-circuit faults are being measured, the statistical indicators can be calculated. 4 Test results 4.1 Winding grounding short-circuit fault under lightning impulse voltage The voltages in HV and LV winding are measured when the lightning impulse voltage of 170 V amplitude is applied to the LV side. According to formula (6), the applied voltage can be represented by Uin, and the voltage response at LV side can be represented by Uout, the voltage transfer functions can be calculated by applying FFT. The voltage transfer functions of normal and different tap grounding short-circuits are shown in Fig. 3. In the following figures and tables, the 'norm' symbol means the voltage is obtained when transformer is normally functioning, 0 stands for the end of HV winding grounding, the numbers 1–20 stand for the respective taps, 0–1 stands for tap 1 grounding short-circuit, and 1–2 stands for interlayer short-circuit between tap 1 and tap 2. Fig. 3Open in figure viewerPowerPoint Voltage transfer function under different tap grounding short circuits As can be found in Fig. 3, the differences between normal and grounding short-circuit fault voltage transfer functions in frequency response are clearly large, and the differences in different grounding short-circuits are relatively small. The statistical indicators of the voltage transfer function of grounding short-circuit fault can be calculated by taking the voltage transfer function under normal condition as X and the voltage transfer functions under winding grounding short-circuit fault condition as Y into formula (3)–(5). The statistical indicators of different tap grounding short-circuits are calculated as shown in Table 1. Table 1. Statistical indicators of the voltage transfer function of grounding short-circuit fault Fault f, MHz ρ (X, Y) σ (X, Y) ASLE 0–1 0.02–0.5 0.9988 0.0275 0.5576 0.5–1 0.9445 0.1414 3.3084 0.02–2 0.9746 0.0996 2.2260 0–3 0.02–0.5 0.9996 0.0168 0.3357 0.5–1 0.9681 0.1095 2.6830 0.02–2 0.9889 0.0578 1.3359 0–5 0.02–0.5 0.9993 0.0204 0.4051 0.5–1 0.9811 0.0774 1.9421 0.02–2 0.9934 0.0360 0.8290 0–8 0.02–0.5 0.9993 0.0217 0.4380 0.5–1 0.9806 0.0922 2.1404 0.02–2 0.9927 0.0489 1.0933 0–10 0.02–0.5 0.9995 0.0160 0.3156 0.5–1 0.9817 0.0766 1.6811 0.02–2 0.9869 0.0686 1.5080 0–14 0.02–0.5 0.9527 0.1649 3.3314 0.5–1 0.7674 0.3584 8.2199 0.02–2 0.9191 0.1779 3.9168 Table 1 shows that the statistical indicators of voltage transfer function in 0.5–1 MHz changes more markedly compared with those in the 0.02 to 0.5 MHz range and the 0.02–2 MHz range. In order to compare the transient overvoltage response performance to the SFRA test results, the voltage transfer functions under different tap grounding short circuits are obtained by SFRA, which the sweep frequency voltage signal is applied to the HV side, as shown in Fig. 4. Fig. 4Open in figure viewerPowerPoint Voltage transfer function under different tap grounding short circuits by SFRA As can be found in Fig. 4, the differences between normal and grounding short-circuit fault voltage transfer functions in frequency response obtained by SFRA method are relatively large. Also, the statistical indicators are calculated as shown in Table 2. Table 2. Statistical indicators of the voltage transfer function of grounding short-circuit fault by SFRA Fault f, MHz ρ (X, Y) σ (X, Y) ASLE 0–1 0.02–0.5 0.9723 1.1183 1.5162 0.5–1 0.9845 0.0578 2.0767 0.02–2 0.9947 0.2944 1.2304 0–3 0.02–0.5 0.9617 1.4881 1.8480 0.5–1 0.9914 0.0527 1.8630 0.02–2 0.9933 0.3917 1.6715 0–5 0.02–0.5 0.9500 0.4392 2.1970 0.5–1 0.9981 0.0238 0.8020 0.02–2 0.9852 0.1538 2.4910 0–7 0.02–0.5 0.9448 0.3446 2.5419 0.5–1 0.9747 0.1032 3.1639 0.02–2 0.9836 0.1543 3.1972 0–8 0.02–0.5 0.9465 0.3083 2.9325 0.5–1 0.9611 0.1404 4.0715 0.02–2 0.9724 0.1604 3.8155 0–10 0.02–0.5 0.9284 0.4330 6.8080 0.5–1 0.9470 0.1944 5.3498 0.02–2 0.9315 0.2593 7.1345 As shown in Tables 1 and 2, the value of statistical indicators is different. However, it can be found that the statistical indicators represent the same level at magnitude for both tables. Therefore, the transient overvoltage response performance has the similar sensitivity with the SFRA method to find out the winding fault. The voltages and currents in HV winding are measured when the lightning impulse voltage of 270 V amplitude with the front time of 4.2 is applied to the HV side. After the voltages and currents are measured, the applied voltage can be represented by Uin, and the current response at HV side can be represented by Iout. According to formula (7), the admittance transfer functions could be calculated. The calculated admittance transfer functions of normal and different tap grounding short-circuits conditions are shown in Fig. 5. Fig. 5Open in figure viewerPowerPoint Comparison of admittance transfer function when lighting impulse voltage is applied to HV side Fig. 5 shows that there are marked differences between normal and grounding short-circuit fault admittance transfer function in frequency response. The differences of frequency response between taps 1, 3, and 5 grounding short-circuit fault are small, but those in 13–17 grounding short-circuit fault are large. The statistical indicators of the admittance transfer function of grounding short-circuit fault can be calculated by taking the admittance transfer function under normal condition as X and the admittance transfer functions under winding grounding short-circuit fault condition as Y into formula (3)–(5). The calculated statistical indicators are shown in Table 3. Table 3. Statistical indicators of the admittance transfer function of grounding short-circuit fault Fault f, MHz ρ (X, Y) σ (X, Y) ASLE 0–1 0.02–0.5 0.9699 0.1403 4.3397 0.5–1 0.9541 0.1889 3.6250 0.02–2 0.9747 0.1442 4.4900 0–3 0.02–0.5 0.9661 0.1480 4.5974 0.5–1 0.9525 0.1849 3.5884 0.02–2 0.9698 0.1571 4.9760 0–5 0.02–0.5 0.9657 0.1487 4.6405 0.5–1 0.9560 0.1887 3.6936 0.02–2 0.9651 0.1569 5.1002 0–14 0.02–0.5 0.8861 0.3337 11.2011 0.5–1 0.9631 0.1715 3.2449 0.02–2 0.9485 0.1947 6.5087 0–16 0.02–0.5 0.8486 0.3704 10.6808 0.5–1 0.9689 0.1553 2.8932 0.02–2 0.9487 0.2008 6.2918 0–17 0.02–0.5 0.8380 0.4146 10.2041 0.5–1 0.9608 0.1859 3.5196 0.02–2 0.9354 0.2284 6.8045 In Table 3, the correlation coefficients of admittance transfer function in different frequency bands are <0.97. Compared to voltage transfer function, the correlation coefficients of admittance transfer function are smaller. In the frequency range of 0.02–0.5 MHz, the correlation coefficients decrease with the increase in number of winding taps. From Figs. 3 and 5, the curves of admittance transfer function start shifting upper left in the range of 0–0.5 MHz with the increment in tap numbers in Fig. 5. However, the curves of voltage transfer functions in 0–0.5 MHz change slightly with the increment in tap numbers. Therefore, the admittance transfer function is able to recognise winding grounding short-circuit fault better than voltage transfer function. Since the admittance transfer function can reflect the transfer characteristics within HV winding by measuring the voltage and current in HV winding. However, the voltage transfer function reflects the transfer characteristics between the HV and LV winding by measuring voltage and HV winding is in contact with LV winding by the core coupling without directly electrical connection. Thus, method using admittance transfer function has a better sensitivity than that using voltage transfer function. So only the admittance transfer function is further studied in the rest tests of this paper. 4.2 Winding grounding short-circuit fault under damped oscillation wave To simulate the invasion of voltage waveform in real transformer windings as really as possible, the damped oscillation voltage is applied as excitation signal. A damped oscillation wave of 2 kV amplitude, with the equivalent frequency of 20 kHz is applied to HV winding. After the voltages and currents are measured, the applied voltage can be represented by Uin, and the current response at HV side can be represented by Iout. According to formula (7), the admittance transfer functions could be calculated. The calculated admittance transfer functions under damped oscillation wave are shown in Fig. 6. Fig. 6Open in figure viewerPowerPoint Comparison of admittance transfer functions under grounding fault and under damped oscillation wave The statistical indicators of the admittance transfer function of grounding short-circuit fault under damped oscillation wave can be calculated by taking the admittance transfer function under normal condition as X and the admittance transfer functions under winding grounding short-circuit fault condition as Y into formula (3)–(5). The calculated statistical indicators in different frequency range are shown in Table 4. Table 4. Statistical indicators of the admittance transfer function of grounding short-circuit fault Fault f, MHz ρ (X, Y) σ (X, Y) ASLE 0–1 0.02–0.5 0.9807 0.1499 2.7522 0.5–1 0.8548 0.4065 6.8585 0.02–2 0.8958 0.3308 7.0191 0–3 0.02–0.5 0.9865 0.1700 2.1629 0.5–1 0.8961 0.3567 5.6777 0.02–2 0.9215 0.2757 6.1219 0–5 0.02–0.5 0.9845 0.1186 2.4755 0.5–1 0.8725 0.3252 6.6966 0.02–2 0.9080 0.2687 6.4632 0–8 0.02–0.5 0.9860 0.1176 2.2259 0.5–1 0.7431 0.6372 9.1498 0.02–2 0.8494 0.4742 9.0932 0–11 0.02–0.5 0.9871 0.1134 2.3338 0.5–1 0.8763 0.3665 6.3333 0.02–2 0.8513 0.64308 8.1922 0–12 0.02–0.5 0.9709 0.1858 3.1421 0.5–1 0.8228 0.3939 7.2218 0.02–2 0.9102 0.2799 6.4835 Table 4 shows that the correlation coefficients of admittance transfer functions in 0.5–1 MHz of different grounding short-circuit under damped oscillation wave are <0.985. The difference in admittance transfer function between normal and grounding short-circuit fault can be reflected by the statistical indicators in 0.5–1 MHz better than those in other range of frequency. Also whether grounding short-circuit occurs can be easily determined. 4.3 Winding interlayer short-circuit fault under lightning impulse voltage The voltages and currents in HV winding are measured when the lightning impulse voltage of 170 V amplitude is applied to the LV side. Taking the applied voltage as Uin, and the current response at HV side as Iout into formula (7), the admittance transfer functions can be calculated. The admittance transfer functions of interlayer short-circuit fault under lightning impulse voltage are shown in Fig. 7. Fig. 7Open in figure viewerPowerPoint Comparison of the admittance transfer function with different layer winding short-circuit faults Fig. 7 shows that the overall trend of frequency response characteristics of admittance transfer function does not markedly change. In the frequency range of 0–0.5 MHz, the curves shift up with the increment in tap numbers. The statistical indicators of the admittance transfer function of layer winding short-circuit fault can be calculated by taking the admittance transfer function under normal condition as X and the admittance transfer functions under winding grounding short-circuit fault condition as Y into formula (3)–(5). The calculated statistical indicators are shown in Table 5. Table 5. Statistical indica