Fault detection of photovoltaic array based on Grubbs criterion and local outlier factor

IET Renewable Power GenerationVolume 14, Issue 4 p. 551-559 Research ArticleFree Access Fault detection of photovoltaic array based on Grubbs criterion and local outlier factor Kun Ding, Corresponding Author Kun Ding dingk@hhu.edu.cn College of Mechanical & Electrical Engineering, Hohai University, No. 200 Jinling North Rd., Changzhou, People's Republic of ChinaSearch for more papers by this authorJingwei Zhang, Jingwei Zhang College of Mechanical & Electrical Engineering, Hohai University, No. 200 Jinling North Rd., Changzhou, People's Republic of ChinaSearch for more papers by this authorHanxiang Ding, Hanxiang Ding College of Mechanical & Electrical Engineering, Hohai University, No. 200 Jinling North Rd., Changzhou, People's Republic of ChinaSearch for more papers by this authorYongjie Liu, Yongjie Liu College of Mechanical & Electrical Engineering, Hohai University, No. 200 Jinling North Rd., Changzhou, People's Republic of ChinaSearch for more papers by this authorFudong Chen, Fudong Chen College of Mechanical & Electrical Engineering, Hohai University, No. 200 Jinling North Rd., Changzhou, People's Republic of ChinaSearch for more papers by this authorYuanliang Li, Yuanliang Li Changzhou Key Laboratory of Photovoltaic System Integration and Production Equipment Technology, No. 200 Jinling North Rd., Changzhou, People's Republic of ChinaSearch for more papers by this author Kun Ding, Corresponding Author Kun Ding dingk@hhu.edu.cn College of Mechanical & Electrical Engineering, Hohai University, No. 200 Jinling North Rd., Changzhou, People's Republic of ChinaSearch for more papers by this authorJingwei Zhang, Jingwei Zhang College of Mechanical & Electrical Engineering, Hohai University, No. 200 Jinling North Rd., Changzhou, People's Republic of ChinaSearch for more papers by this authorHanxiang Ding, Hanxiang Ding College of Mechanical & Electrical Engineering, Hohai University, No. 200 Jinling North Rd., Changzhou, People's Republic of ChinaSearch for more papers by this authorYongjie Liu, Yongjie Liu College of Mechanical & Electrical Engineering, Hohai University, No. 200 Jinling North Rd., Changzhou, People's Republic of ChinaSearch for more papers by this authorFudong Chen, Fudong Chen College of Mechanical & Electrical Engineering, Hohai University, No. 200 Jinling North Rd., Changzhou, People's Republic of ChinaSearch for more papers by this authorYuanliang Li, Yuanliang Li Changzhou Key Laboratory of Photovoltaic System Integration and Production Equipment Technology, No. 200 Jinling North Rd., Changzhou, People's Republic of ChinaSearch for more papers by this author First published: 11 February 2020 https://doi.org/10.1049/iet-rpg.2019.0957Citations: 11AboutSectionsPDF 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 Aiming at improving the effectiveness and real-time performance of the fault detection of the photovoltaic (PV) array under different outdoor conditions, a novel method based on Grubbs criterion and local outlier factor (G-LOF) method is proposed in this study. The simulation model of the PV array is built to obtain the reference current of each PV string. The local outlier factor (LOF) is a ratio of the average local reachability density of sample neighbourhoods relative to its local reachability density. In this study, the LOF is used to quantify the abnormality by comparing the measured current and the simulated reference current. To reduce the false alarm probability of LOF, the Grubbs criterion is utilised as the test criterion to detect the abnormality of PV strings and it is merged with the LOF to derivate the G-LOF. The experiments of partial shading, open-circuit fault and short-circuit fault of PV modules are implemented in sunny and cloudy days. Experimental results verify that the proposed G-LOF method can sensitively detect above abnormalities, especially can detect the slight performance reduction caused by the partial shading or faults. 1 Introduction In recent years, the photovoltaic (PV) market has increased by leaps and bounds, which motivates the emergence of the considerable grid-connected PV system and the increment of the total installed capacity of PV system all over the world. The International Energy Agency reported that in 2018 the total installed capacity of PV plants has crossed 500 GW and China is still the leader in terms of total installed capacity with more than 176 GW [1]. With a huge capacity of PV plants, the maintenance cost of PV array is increasing each year. The PV arrays are exposed to harsh outdoor environments and may suffer from various potential abnormality or faults caused by corrosion, rainfall, ultraviolet radiation, soiling, thermal cycling etc. The abnormal operation of PV array directly reduces the output power of the PV array, which inevitably decreases the system efficiency. In order to detect the occurred fault in real-time, the fast analysis of the sampled data measured from PV array and determine the fault degree of PV array is always the urgent demand for the maintenance of PV plants. The fault detection and diagnosis of PV array attract much attention. At present, many common faults or abnormality of PV arrays have been investigated, including the degradation of cell materials, solder corrosion, short-circuit failures, partial shading etc. [2-5]. These methods can mainly be divided into three categories. The first category is the diagnosis method based on the installed infrared camera or infrared instruments with unmanned aerial vehicles (UAVs) [5-9]. The advantages of methods in this category are that the obtained infrared images or videos contain much explicit information of PV array and the hot spots of PV modules can be identified. The features in infrared images can also be easily extracted via artificial intelligence methods, e.g. deep convolution neural networks, which are rapidly developed in the recent decade. The drawback of the above methods is also obvious. The infrared instruments and UAVs are much more expensive than other commonly used sensors, e.g. voltage or current sensors. Thus, currently, above methods are only applied for large-scale PV plants [6]. The second category is the diagnosis methods based on monitoring the current–voltage (I–V) curves of the PV array via the inverters or other DC–DC converters [10-18]. In [10], the kernel-based extreme learning machine is used to build the fault diagnosis model and to extract fault information from measured I–V curves. In [11], the ambient data and I–V curves of PV array are investigated using simulation and compared with the measurements. In [12], a multiclass adaptive neuro-fuzzy classifier is utilised for fault classification. In [13], the 1-D deep residual network is trained to extract fault features from measured I–V curves to obtain higher accuracy. In [14], the deep residual network using I–V curves and ambient conditions are studied. In [15], the trust-region-reflective deterministic algorithm is combined with the particle-swarm-optimisation is proposed and the characteristic parameters from I–V curves are extracted for fault diagnosis. In [16], the long short-term memory networks are applied to automatically extract features from simulated I–V curves. In [17], the features of I–V curves under different partial shadings are extracted and analysed by the principal component analysis for fault classification. In [18], the I–V curves of PV array are measured and the fault parameters are extracted by optimising the fault simulation model. The measured I–V curves contain more comprehensive information to indicate the operating status of the PV array and can be used to diagnose some common faults or abnormalities, e.g. line-line faults, abnormal degradation, partial shading etc. However, currently for most commercial inverters or DC–DC converters, the function of measuring the I–V curves is not widely equipped, and only the output voltage and current of the PV array can be measured. The third category is the diagnosis methods that only rely on the measured voltage and current of the PV array [19-30]. The method presented in this paper also belongs to this category. In this category, some methods directly use the sampled data to train the neural networks or other machine learning models for the classification of the detected faults [19-22]. However, these methods rely on sufficient fault data samples for training the neural networks or learning machine. These fault data samples can be collected from simulation models or fault experiments of the PV array. Once the investigated PV array is changed, these fault data should be replaced and the new fault data samples are required. Thus, some other methods that do not rely on neural networks are applied [23-30]. In [23], the improved k-nearest neighbours are trained and used to detect faults. In [24], the fault detection method using the measured array voltage and current by means of wavelet packets are presented. In [25], the superior fault detection efficiency is obtained by using the kernel generalised likelihood ratio test with less computational complexity. In [26], different fault indicators are designed to distinguish the healthy and faulty states of PV array. In [27], the fault diagnosis architecture without additional sensors is presented for the large-scale PV array. In [28], the sensorless line-line and line-ground fault detection techniques are proposed based on the maximum power point (MPP) tracking. In [29], the robust fault detection scheme is used to monitor the PV array and the measurement noises in the data are dealt with. In [30], the temporal-spatial distributions of the output of PV array under different fault conditions are investigated and the fuzzy rules are designed for fault diagnosis. Most of them need a reference model of PV array for comparing it with the actual measured voltage and current data of the PV array. Due to the fact that only the real-time voltage and current data of PV array are required and these sensors are already equipped by the inverter or DC–DC converter, the above methods can be directly used for most of the installed PV systems. This is also the aim of the proposed method in this paper, i.e. effectiveness and wide application. In recent decades, the outlier detection is a feasible method for data mining. It is adopted to detect outliers and identify rare phenomenon or behaviours. Thus, the outlier detection has been widely used in many fields, e.g. the weather forecasting, fault detection of chemical process and network intrusion [31]. As a method of outlier detection, the local outlier factor (LOF) can be used to detect the fault and reflect the degree of fault. However, the LOF is more suitable to detect abnormal data from large samples. In the previous study, the LOF is modified for the fault detection of the small scale PV systems with fewer samples [32]. Though the sensitivity of LOF is good enough, the real-time performance and the accuracy of the LOF should be further improved. In statistics, Grubbs criterion is usually used to detect the abnormal data and eliminate the coarse error. Some researchers pointed out that the Grubbs criterion can make less erroneous judgement [33]. However, this method cannot evaluate the fault degree. The main contribution of this work is the research and development of accurate real-time fault detection of the PV array for sensitively and quantitatively evaluating the fault degree of partial shadings and several common faults, i.e. large and small-scale shadow, open-circuit and short-circuit of PV modules. At first, the simulation model of the PV array is applied to obtain the reference current. Furthermore, in order to detect the fault and evaluate the fault degree, the outlier detection and the Grubbs criterion are utilised to form a novel Grubbs criterion and local outlier factor (G-LOF) method. Then, the proposed G-LOF method is applied to detect the outliers of the measured current. The deviation between the detected outliers and the reference current is evaluated. This paper is organised as follows: in Section 2, the model of an actual 10 kW grid-connected PV plant is presented; in Section 3, the theories of the LOF and Grubbs criterion are introduced, then the novel G-LOF method is proposed; in Section 4, the novel G-LOF method is verified by the experiments, and the results are analysed; in Section 5, the conclusions are summarised. 2 Model of PV array In this paper, the simulation model of the PV array is adopted to obtain the reference current. At present, the single diode model is widely used for modelling solar cells. However, the error of estimated maximum power for this model is significant. For reducing the estimation error of maximum power, some improved models have been proposed [34, 35]. The method in [34] is adopted in this paper. The output current and voltage of a solar cell can be written as follows: (1) where Irefis the output current under the standard test condition (STC); Isc is the short-circuit current; Isc,ref is the short-circuit current under STC; Vrefis the output voltage under STC; Vocis the open-circuit voltage; Voc,refis the open-circuit voltage under STC; Rsis the series resistance. Iref is expressed as follows: (2) where krefis the coefficient, and it can be calculated by the parameters at the MPP [34]: (3) where VMPP,refis the output voltage at the MPP under STC; IMPP,ref is the output current at MPP under STC. Isc under various ambient conditions is described as follows: (4) where α is the temperature coefficient of current, T is the temperature of the PV module; Tref is the reference temperature under STC. S is the tilted solar irradiance. Sref is the reference irradiance under STC. Besides, Voc can be calculated as (5) where β is the temperature coefficient of voltage. The output current and voltage of the PV module in various irradiances and temperatures can be calculated based on (1)–(5). In this paper, the parameters of the investigated PV module TSM-240 is shown in Table 1, which is provided by the manufacturers. Table 1. Characteristics of TSM-240 PV module Parameters Symbols Value maximum power PMPP,ref 240 W maximum power voltage VMPP,ref 29.7 V maximum power current IMPP,ref 8.1 A open circuit voltage Voc,ref 37.3 V short circuit current Isc,ref 8.62 A current-temperature coefficient α 0.047%/°C voltage-temperature coefficient β −0.32%/°C equivalent series resistance Rs 0.343 Ω Then, the I–V curve can be represented by (6) [34] (6) In this paper, 40 PV modules TSM-240 are used to form the 10 kWp PV plant, as shown in Fig. 1. Based on the above mathematical model of PV modules, the simulation model of the PV array is built in MATLAB/Simulink, as shown in Fig. 2a. The PV array comprises of 4 PV strings connected in parallel, and each PV string is composed of 10 PV modules, each PV module is 240 W. The real-time temperature and in-plane irradiance are applied as the input of the above simulation model. Correspondingly, the output of the simulation model under the measured irradiance and temperature includes the reference current and voltage of each PV string. To verify the accuracy and the feasibility for complex faults, the shade fault, i.e. a small-scale shadow, is tested. In the simulation, the equivalent irradiance of a PV module in the second string is set as 300 W/m2. The irradiances of all the other PV modules are set as 480 W/m2. In addition, the equivalent temperatures of all PV modules are set to 35°C. The simulation results are shown in Fig. 2b. The power–voltage curve of the PV array appears at two local peaks, which are caused by the non-uniform irradiance on the second PV string. Fig. 1Open in figure viewerPowerPoint 10 kWp PV plant, it contains 4 PV strings and each PV string contains 10 PV modules Fig. 2Open in figure viewerPowerPoint Simulation model of PV array and the result of simulation under 480 W/m2, 35 °C ambient condition (a) Simulation model of PV array based on MATLAB-Simulink in [34], (b) Simulated I–V curves of PV array, (c) Simulated P–V curve of PV array 3 Principle of LOF and Grubbs criterion 3.1 Local outlier factor The outlier detection is a feasible method for data mining. The outlier detection algorithm can be divided into five categories, i.e. the outlier detection based on distribution, based on depth, based on distance, based on clustering and based on density [36]. The LOF is a density-based method, which was first proposed by Breuning et al. [37] and Song et al. [38]. In [37], the observations deviated from the overall observations are considered as the outlier, and the LOF value is used to evaluate the degree of deviation. The definition of LOF value is the ratio of the average local reachability density of neighbourhoods relative to its local reachability density [32]. If the sample is normal, the average local reachable density of neighbourhoods would be similar to the corresponding local reachable density of the sample. As a result, the LOF value approaches to 1 for typical samples. On the contrary, if the sample is abnormal, the LOF value will be much greater than 1. A greater deviation of the abnormal sample leads to the greater value of LOF. Therefore, LOF value can effectively describe the degree of deviation of a sample relative to its neighbourhoods. However, the LOF is sensitive to abnormal data, and may lead to a false alarm. To identify the abnormality of the PV array accurately, the LOF should be combined with other algorithms to improve its performance. 3.2 Grubbs criterions for fault detection For all measurements, the observations that deviated from the overall observations are regarded as suspicious objects. To determine the outlier from the suspicious objects, the test criterion, e.g. Grubbs criterion, Dixon criterion, skewness-kurtosis criterion and Nair criterion, can be applied. However, in statistics, due to the fact that the loose decision criterion, insensitive experimental design and great differences in measurements, none of the above methods can avoid misjudgement or false alarm. Some researchers pointed out that the Grubbs criterion can achieve fewer misjudgements [33]. The reason is that Grubbs criterion is based on normal distribution theory and two important indicators of normal distribution theory, i.e. the standard deviation and the mean value. To detect the outliers in observations, the mean value , the standard deviation S and the Grubbs value Gi are used, which are described as follows: (7) (8) (9) Then, Gi is compared with the normal threshold of the Grubbs criterion Glim, which can be determined through the Grubbs test threshold table, as shown in Table 2 [39]. Table 2. Grubbs fiducial probability n Threshold n Threshold 3 1.135 12 2.285 4 1.463 13 2.331 5 1.672 14 2.371 6 1.822 15 2.409 7 1.938 16 2.443 8 2.032 17 2.475 9 2.110 18 2.504 10 2.176 19 2.532 11 2.234 20 2.557 It should be noted that the critical threshold of Grubbs criterion is related to the detection level p and the number of samples n. Generally, if the detection level is too high, the probability of false alarm will increase and vice versa. Therefore, an appropriate detection level should be determined. In general, the value of p has several choices, i.e. p = 90%, p = 95%, p = 97.5%, p = 99%, p = 99.5%. Considering the accuracy of sensors and complexity of calculation, the detection level is set to 95% for fault detection of PV array in this paper. Table 2 shows the thresholds for different number of samples under the 95% confidence probability of the Grubbs criterion [39]. 4 Proposed fault detection procedure and experimental validation 4.1 Procedure of fault detection For the built actual PV array, the output current of each string of the PV array is measured by the Hall-effect sensors. The in-plane irradiance and the module temperature are measured by the pyranometer and thermal sensors, respectively. The specifications of the sensors are shown in the Appendix. The measured in-plane irradiance and the module temperature are inputted to the simulation model. Then, the corresponding reference current can be obtained by the model. The monitoring and fault detection system of the PV array are shown in Fig. 3. Fig. 3Open in figure viewerPowerPoint Schematic diagram of monitoring and fault detection system Owing to the disadvantages of false alarm for LOF and Grubbs criterion, the method combining LOF method with Grubbs criterion, i.e. G-LOF is proposed to improve the accuracy of fault detection. Fig. 4 shows the detailed flowchart of G-LOF for monitoring and fault detection of the PV array. The detail steps are as follows: Step 1: Sampling the current of PV strings, the irradiance and temperature every 5 s; Step 2: Simulating the model of PV array by using the measured irradiance and temperature as the inputs to obtain the reference current of each PV string; Step 3: Subtracting the measured current to the reference current to obtain the residuals; Step 4: Applying Grubbs criterion to the residuals of current. If the fault is detected, set the fault signal to 1; otherwise, set the fault signal to 0; Step 5: Storing the residuals of current, if the number of residuals is 20, sort the current residuals by time, respectively; Step 6: Applying LOF to the residuals of current and calculating the corresponding LOF values, respectively; Step 7: Assigning the LOF value to each string, matching the LOF value with the fault signal obtained by the Grubbs criterion; Step 8: Combining the LOF value with the corresponding fault signal and determining the final G-LOF value according to the rule in Table 3. Fig. 4Open in figure viewerPowerPoint Flowchart of the fault detection system of G-LOF Table 3. Rules of determining final LOF value Signal-fault Condition Final LOF value 0 LOF value > a set the LOF value as a 0 LOF value ≤ a reserve LOF value 1 LOF value > a reserve LOF value 1 LOF value ≤ a reserve LOF value In Table 3, it should be noted that constant a is the sensitivity adjustment value and is also the upper limitation of the LOF value, which is determined by the accuracy of the sensors in the PV array. In theory, if all the PV modules work normally, a will be equal to 1. However, considering the measurement error of the sensors, commonly the LOF value is greater than 1. To avoid the false alarm of the monitor system, a should be limited in a reasonable range. According to the current sensors used in the PV array, the value of the threshold a is set to 5 in this paper. The Appendix shows the detail determination of a. 4.2 Slight partial shading experiments in sunny day To verify the effectiveness and sensitivity of the proposed method, a slight shadowing test was implemented on a sunny day. The data are collected from 7:30 to 18:00 on 11 September 2016. From 7:30 to 8:30, one PV module in the first PV string was covered by a plastic glass with the transmittance 0.7 to artificially imitate the partial shading. The shaded area covers 25% of the PV module. Obviously, for this PV string in the PV array, the influence is slight, and the current reduction is also slight as shown in Fig. 5a. Fig. 5Open in figure viewerPowerPoint Experiments with slight shadow under a sunny day (a) Measured current of 4 PV strings, (b) Value of Grubbs independently calculated by the Grubbs criterion, (c) LOF value independently calculated by the LOF method, (d) LOF value calculated by the proposed G-LOF method Figs. 5b and c show the results of fault detection independently detected by the LOF and Grubbs method, respectively. During the test from 12:00 to 15:00, the false alarm of the LOF occurred, as shown in Fig. 5c. The results of Grubbs values reveal that the Grubbs criterion can detect the fault accurately. However, it cannot evaluate the fault degree. The results of fault detection for minor shadows by the proposed G-LOF are shown in Fig. 5d. From 7:30 to 8:30, the LOF value of the measured current is greater than the threshold, which indicates that the fault occurs. After 8:30, the LOF value is in the range of 0–5, which indicates the PV array works in a normal state. Thus, the method of G-LOF can effectively detect the faults and evaluate the fault degree. Besides, the improved kernel nearest neighbour-based (kNN-based) monitoring schemes presented in [23] is applied for comparison with the proposed G-LOF method in this paper. Corresponding kNN-exponentially weighted moving average (kNN-EWMA) statistic are calculated and shown in Fig. 6. Obviously, due to the fact that the influence of the partial shading is too slight, the kNN-EWMA cannot sensitively detect the partial shading from 7:30 to 8:30. Fig. 6Open in figure viewerPowerPoint Calculated kNN-EWMA statistic with parametric threshold for the experiments with slight shadow under a sunny day 4.3 Typical fault experiments under cloudy day To verify the effectiveness and adaptability of the proposed G-LOF method, complex weather, e.g. cloudy day is selected. On 6 July 2017, four different time ranges are implemented for the fault of large-scale shadow, small-scale shadow, open-circuit and short-circuit as shown in Fig. 7. Fig. 8 shows the positions of faults in the PV array and the positions of current sensors. Corresponding time ranges for testing different abnormalities are shown in Table 4. For the large-scale shadow, two plastic glasses are used to cover two PV modules in the second PV string. For each shaded PV module, the shaded area is ∼50% of the surface area. Similarly, for the small-scale shadow, one plastic glass is used to cover one PV module in the second PV string with ∼25% area. For the open-circuit fault, one PV module in the second string is open-circuit, which may lead the disconnection of the second PV string. For the short-circuit fault, only one PV module in the second PV string is bypassed by a wire. Table 4. Time periods of different faults Time 9:12–9:38 9:38–10:05 10:59–11:39 15:29–16:18 fault large-scale shadow small-scale shadow open-circuit fault short-circuit fault Fig. 7Open in figure viewerPowerPoint Experiments process (a) Large-scale shadow fault from 9:12 to 9:38, (b) Small-scale shadow fault from 9:38 to 10:05, (c) Open-circuit fault from 10:59 to 11:39, (d) Short-circuit fault from 15:29 to 16:18 Fig. 8Open in figure viewerPowerPoint Diagram of the positions of faults in the PV array and current sensors Fig. 9 shows the results of fault detection using Grubbs criterion, LOF and the mixed G-LOF method, respectively. In Fig. 9c, the false alarm occurs from 14:05 to 14:20 for the LOF. However, compared to the Grubbs criterion, the LOF can quantitatively show the degree of partial shading or faults. In Fig. 9d, the different degrees of faults can be presented by the corresponding LOF values of the proposed G-LOF method. The more serious the fault is, the greater the LOF value is. Besides, the detected time periods of faults for Grubbs criterion are also accurate. Thus, the advantages of both methods are merged to form the G-LOF method. Obviously, the results of fault detection detected by the proposed G-LOF are better than that independently detected by the LOF or Grubbs criterion. Fig. 9Open in figure viewerPowerPoint Fault experiments under a cloudy day (a) Measured current of 4 PV strings, (b) Value of Grubbs independently calculated by the Grubbs method, (c) LOF value independently calculated by the LOF method, (d) LOF value calculated by the proposed G-LOF method To observe the details more clearly, Fig. 10 shows the partial enlargement of Figs. 9a and d at the vicinity of the time when the fault occurs. Corresponding measured current of each PV string and calculated LOF are shown in Table 5. At 9:11:20, the current of second PV string decreases and the abnormality occurs. In Fig. 9b, at 9:11:40, the LOF value is greater than the threshold. Three abnormalities can both be detected after 20 s, which verifies the G-LOF method has good real-time performance. In addition, the accuracy values are calculated as 97.3 and 94% under the sunny day and cloudy day, respectively. It should be noted that the LOF value can also indicate the fault degree. For the faults in the experiments, the LOF values are ∼30, 60 and 10 for the partial shading, open-circuit and short-circuit fault, respectively, as shown in Table 5. The open-circuit fault leads to a greater LOF value. The reason is that the open-circuit of the PV module causes the disconnection of the entire PV string, which directly makes the current of the second PV string reduce to zero. Table 5. Measured data and results of fault detection Fault Time I1, A I2, A I3, A I4, A LOF a State large-scale shading 9:11:00 3.79 3.82 3.84 3.78 0.82 5 no fault 9:11:20 3.92 3.96 3.97 3.93 0.97 5 9:11:40 3.88 1.21 3.93 3.88 30.01 5 fault occur 9:12:00 3.92 1.21 3.97 3.92 36.87 5 9:12:20 4.05 0.89 4.1 4.05 31.70 5 9:12:40 4.24 0.92 4.29 3.32 32.23 5 open-circuit 10:58:20 3.95 4.03 4 4.11 2.75 5 no fault 10:58:40 3.95 4.03 4 4.11 2.39 5 10:59:00 4.29 0 4.34 4.46 61.43 5 fault occur 10:5