1. Introduction
Overhead transmission line icing refers to the phenomenon of freezing rain, rime, wet snow, and mixed icing on overhead transmission lines (National Meteorological Bureau of China 1979). Ice accumulation on transmission lines is one of the most serious threats to power grid safety (Kiessling et al. 2003; Pytlak et al. 2010). Extremely heavy ice loads and transmission line galloping (high-amplitude, low-frequency resonant oscillations of transmission lines, induced by the coupling effect of ice and wind) can be particularly expensive, resulting in repair costs of many millions of dollars and huge power losses due to large-scale blackouts (Sullivan et al. 2003; Call 2009). Damage from freezing rain causes an average annual property-related loss of $313 billion in the United States alone (Changnon and Creech 2003). The 1998 extreme freezing rain event in North America left 5.2 million people without power (Lecomte et al. 1998; Pytlak et al. 2010). The 2008 prolonged freezing-rain event in China had a major impact on the power grid system, with the icing storm causing the collapse of 691 000 base towers, the blackout of 153 000 high-voltage transmission lines, the failure of 884 substations, and power outages for more than 100 million people, leading to direct economic losses of more than ¥151.6 billion for electric companies (Zhao et al. 2008).
There have been many electric supply and meteorological studies that have focused on transmission line icing in recent years. Studies of the electric supply system have highlighted icing models and emergency disposal systems. These studies have considered the conditions and types of transmission lines in use and have analyzed the icing mechanisms and ice melting measures through a theoretical analysis (Yuan et al. 2004; Liu and Liu 2011), simulation tests (Jiang et al. 2010; Fan et al. 2011), artificial climate room simulations (Jiang and Shen 2010; Zhang et al. 2010), and natural test-site observations (Zhang et al. 2011; Lu et al. 2014; Niu et al. 2011; Zhou et al. 2012), and determined the relationship between transmission line icing and environmental temperature, humidity, wind speed, raindrops, and other factors (Yang et al. 2010; Huang et al. 2011). Meteorological studies have focused on the precipitation type and meteorological conditions during icing events. Due to the difficulty in the direct measurement of precipitation type, several precipitation-type determination methods have been proposed (Mullens and Mcpherson 2017), such as the Ramer algorithm (Ramer 1993), the Baldwin and Contorno algorithm (Baldwin and Contorno 1993), the Bourgouin algorithm (Bourgouin 2000), and the Schuur classification algorithm (Schuur et al. 2012). The meteorological conditions and specific parameters (such as precipitation amount, precipitation type, maximum temperature, minimum temperature, relative humidity, and wind speed; Tao et al. 2012; Gu et al. 2012; Wang et al. 2017) and circulation factors (such as a blocking high, the northwest Pacific subtropical high, India–Burma/Myanmar trough, and upper-level jet stream) are mainly obtained using statistical methods (Wang et al. 2008; Yang et al. 2008; Zhao et al. 2008; Li and Gu 2010; Liao and Zhang 2013).
The shortage of transmission line icing historical data has restricted the advancement of research in this field. Unlike many meteorological parameters, icing measurements are not routinely made at meteorological observation stations, and there is still no reliable icing sensor than can work effectively under all expected climatic conditions (Fikke 2009; Hosek et al. 2011). A complete, precise, and credible historical dataset is urgently needed for the study of icing events and icing climate research. The State Grid Corporation of China (SGCC; see Table 1 for expansions of key acronyms used in this paper) is responsible for the operation and maintenance of 26 provincial regional power grids in China (covering 88% of China’s land area and over 1.1 billion people), and has been seriously affected by icing disasters. After the catastrophic icing disaster in southern China in 2008, to improve the ability of dealing with icing events and reduce the losses associated with such disasters, the SGCC developed a numerical forecast system of transmission line icing (NFSTLI) for businesses that predict transmission line icing thickness during winter, and the prediction capability of NFSTLI verified by daily actual transmission line icing observations. According to the company's confidentiality regulations, NFSTLI was not disclosed to the public previously; however, NFSTLI is one of the core technologies in the “Key Technologies and Equipment for Large-scale Frozen Disaster Prevention and Control in Power Grid” project, which won first prize in China’s National Scientific and Technological Awards in 2013. In previous studies, there have been only a few systems proposed that could provide automated forecasts of ice accretion for electric power utilities (Musilek et al. 2009; Pytlak et al. 2010; Hosek et al. 2011). Compared with other systems, NFSTLI has the obvious advantage of being used for daily business operations rather than only in experiments. Based on gauge observations, transmission line icing observational data, ERA-Interim data, and the hindcasted predictors used by the NFSTLI, a new dataset of transmission line icing thickness (TLIT) data was constructed. The reliability of this new dataset is analyzed in this study.
Definitions of key acronyms used in this work.
The paper is organized as follows. Section 2 provides a brief introduction of the data and analysis methods used in the study. Section 3 describes three icing events used in case studies to provide a reliability analysis. A reliability analysis from the perspective of climate is provided in section 4. The conclusions are presented in the final section.
2. Data and analysis methods description
a. Data and statistical methods
The datasets used in this study include the following products:
The daily temperature, relative humidity, geopotential height, zonal (U) and meridional (V) winds at each pressure level, and sea level pressure are extracted from ERA-Interim data for the time period of 1987–2018.
The daily surface temperature, precipitation amount, wind speed, wind direction, relative humidity, and pressure observations at 738 stations over the same period are provided by the China Meteorological Administration. Datasets 1 and 2 are used in NFSTLI to reconstruct the TLIT dataset.
The meteorological observation station icing data (OIT) are taken for the time period of 1987–2018, including daily and hourly observational data of glaze/rime weather phenomena, precipitation amount data of glaze/rime phases, ice thickness, and ice-weight data on electric wire at the meteorological stations. According to the state standard of the People’s Republic of China [Specifications for surface meteorological observation: Wire icing (GB/T 35235-2017)], there are two brackets for electric wire icing observation shelfing used in meteorological stations: one is placed in the north–south direction and the other in the east–west direction. The thickness of the icing is measured with outside calipers, the weight of the icing is measured with a platform scale and a metric ruler, and the measurements are made manually. As not all of the meteorological stations have electric wire icing observations, there are only 46 meteorological stations that record freezing rain/rime/electric wire icing observations in southern China. The locations and elevations of 46 stations are presented in Fig. 1. The western part of southern China features plateau and mountainous terrain, the southern part of southern China is mountainous area, and the other areas of southern China are dominated by plains and hills. There are 46 stations spread across the plains, hills, and mountains. The elevations of the 46 stations range from 11 to 1840 m. Most of the 46 stations have freezing rain/rime/electric wire icing observation records for 50–120 days during 1987–2018, the minimum number of freezing rain/rime days is 28 days and the maximum number is 894 days (Huangshan station, a high-mountain station with an elevation of 1840 m). Overall, trends show the higher the station elevation, the larger of the number of days with freezing rain/rime/electric wire icing observations.
The TLIT data cover the time period of 2008–18, including the transmission line icing thickness data observed by surveyors and monitoring instruments. Surveyor observations and monitoring instrument data were the two main types of transmission line icing observations in the SGCC. During the winter icing period, surveyors collect daily icing thickness observations on every high-voltage line. Ice monitoring devices are installed on the line, with the icing thickness measured by image acquisition and line stress variation (Zhang 2008). The observations of transmission line icing thickness data comply with power industry standards of the People’s Republic of China [Technical regulations for overhead transmission line icing observation (DL/T 5462–2012)].
The locations (blue dots) and elevations (numbers under the dots; m) of 46 meteorological stations that record freezing rain/rime/electric wire icing observations, and the average elevation of each 0.125° × 0.125° region in southern China (shaded; m).
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0172.1
There are many types of ice that can form on transmission lines in the natural environment, including glaze, rime, and mixed icing, and the ice densities and shapes vary greatly between the different ice types (Fig. 2). According to the statistical analysis of transmission line icing data, the density of glaze icing is 0.55–0.8 g cm−3, the density of rime icing is 0.15–0.3 g cm−3, and the density of mixed icing is 0.3–0.5 g cm−3. The increase in mechanical load caused by icing weight is one of the main reasons for faults in transmission lines. Since the densities of different icing types vary greatly, the effects of icing on the transmission line vary with ice density (with the same unconverted ice thickness). Therefore, to analyze icing thickness data on the same standard, all the icing data used in this study had an equivalent uniform thickness in terms of ice radius. The conversion coefficient varies with ice type and region: 0.6–0.9 for glaze icing, 0.15–0.3 for rime icing, and 0.35–0.45 for mixed icing (Xie 1998).
Different types of transmission line ice in the natural environment.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0172.1
A correlation analysis, normalized root-mean-square error (NRMSE) analysis, and a rotated empirical orthogonal function (REOF) decomposition were used in this study. A t test was applied for significance testing.
In the correlation and NRMSE analyses, meteorological station ice thickness data were obtained by observation (OIT), and the transmission line icing thickness based on the position of the meteorological observation station was the average thickness at four 0.5° × 0.5° grid points around the station (TLIT).
Southern China, as referred to in this study, is the region spanning 24.5°–34°N, 108°–122°E.
b. Definition of a transmission line icing event
In this study, a transmission line icing event was identified as follows (Wang 2014):
If the transmission line icing thickness was larger than 0.2 mm across a grid, it was defined as an icing grid. If there were more than 40 icing grids in southern China on one day, the day was defined as an icing day.
A transmission line icing event occurred when two consecutive days were icing days, and the number of individual icing grids affected on both days was larger than 15.
If the interval between two events was ≤2 days, the two events were merged into one event.
According to the definitions, there were 67 transmission line icing events during 1987–2017.
3. Reliability analysis based on case studies
The prediction capability and reliability of the NFSTLI were analyzed using the TLIT data constructed by NFSTLI and actual transmission line icing observations during three icing events across southern China: January 2018, January 2016, and February 2014. There are three reasons for choosing these icing events. First, these icing events occurred in the high-frequency ice disaster area, and the representativeness of them is strong. Second, the three icing events are the most serious transmission line icing disasters since 2008, and the significance of studying them is high. Last, the actual transmission line icing observational data are complete and detailed during the three icing events, and the complete and detailed data provide the basis for research on NFSTLI’s predictive capabilities. As Hunan Province is the area most adversely affected by icing events in southern China, we described the three icing events in detail over this region.
a. Icing storms in January 2018
In January 2018, two ice storms brought prolonged freezing-rain events to many parts of southern China. The two ice storms were described by the TLIT data and the actual transmission line icing thickness observational data from SGCC.
From the average daily precipitation and minimum temperature curves, it was apparent that there were two freezing-precipitation episodes in Hunan Province in January 2018 (Fig. 3b). According to statistics provided by the Hunan Electric Power Company, the first storm took place from 4 to 9 January, with the maximum number of transmission lines covered by ice reaching 180 on 6 January. The second storm took place from 24 January to 1 February, with the maximum number of transmission lines covered by ice reaching 516 on 28 January (Fig. 3a).
(a) Number of transmission lines covered by ice and (b) daily precipitation (solid line; mm) and minimum temperature (dotted line; °C) in Hunan Province during January 2018.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0172.1
The area of occurrence, duration, and thickness of transmission line icing were the main indicators used to measure the accuracy of the descriptions of ice storms based on the TLIT data. The transmission line icing thickness and the icing thickness difference between the TLIT and the actual observations (TLIT minus observations) during the two storms in January 2018 are given in Figs. 4 and 5.
Spatial distributions of transmission line icing thickness constructed by the NFSTLI (contours; mm) and the icing thickness differences between the TLIT and actual observation (shaded; mm) in Hunan Province during 4–9 Jan 2018.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0172.1
As Fig. 4, but for 24 Jan–1 Feb 2018.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0172.1
Figure 4 shows that the ice-covered areas were mainly concentrated in the western parts of Hunan Province during 4–9 January. On 4 January, transmission line icing occurred in the northwest portion of Hunan Province, with a thickness of 1–2 mm. On 5 January, the icing thickness in the northwest region increased to 8–10 mm, and the icing area began to expand. During 6–7 January, the icing reached its most intense, with ice covering the entire western region of Hunan Province, and the maximum transmission line icing thickness reached 14 mm. On 8 January, the icing thickness increased in the southwestern part of Hunan Province, while the ice in the northwestern part of Hunan Province melted rapidly. On 9 January, the ice on all transmission lines melted.
Figure 5 shows that transmission line icing occurred in most regions of Hunan Province from 24 January to 1 February. On 24 January, 1–2 mm of ice occurred in the northwest of Hunan Province. On 25 January, the icing area expanded rapidly and the icing thickness in the western region increased to 6–8 mm. During 26–27 January, except for the southern area, ice covered all of Hunan Province, and the maximum transmission line icing thickness reached 12 mm. During 28–29 January, the ice belt moved southward and transmission line icing began to melt in the northern region, while it continued to increase in the southern region. The maximum transmission line icing thickness increased to 14–15 mm. During 30–31 January, the transmission line icing melted in most parts of Hunan Province, except across the southern areas. On 1 February, all of the ice on transmission lines melted.
b. Icing storm in January 2016
A severe cold wave affected most parts of China and a transmission line icing event occurred in southern China during this cold wave process in January 2016. The event was described by the TLIT data and the actual transmission line icing thickness observational data from SGCC in Fig. 6. On 20 January, slight icing occurred in the mountainous area of northwestern Hunan Province. On 21 January, the icing thickness in the northwest region increased to 2–4 mm. During 22–23 January, the icing was its most intense, and the maximum transmission line icing thickness reached 8–10 mm. On 24–25 January, the ice on all transmission lines melted quickly.
As Fig. 4, but for 20–25 Jan 2016.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0172.1
c. Icing storm in February 2014
A serious icing event occurred in the western part of southern China during February 2014, causing damage to electric power supply systems, transportation systems, and so on. The event was described by the TLIT data and the actual transmission line icing thickness observational data from SGCC, too. Figure 7 shows that the ice-covered areas were mainly concentrated in the western parts of Hunan Province during 7–12 February. On 7 February, 1 mm of ice occurred in the northwest part of Hunan Province. On 8 February, the icing thickness in the northwest region increased to 4–8 mm. On 9 February, the icing thickness in western Hunan Province increased to 8–10 mm. During 10–11 February, the ice belt moved southward and transmission line icing began to melt in the northern region. On 12 February, the ice on all transmission lines melted.
As Fig. 4, but for 7–12 Feb 2014.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0172.1
As shown in Figs. 4–7, the occurrence, development, and ablation stages of transmission line icing events described by the TLIT data constructed by NFSTLI were consistent with the actual observations. The icing thickness differences between the observational data and TLIT data calculated by the NFSTLI were less than 2 mm. Therefore, it was considered feasible to construct a dataset of transmission line icing historical data based on the NFSTLI.
4. Reliability analysis based on climate data
The reliability of the TLIT data was also analyzed using meteorological observations.
a. Analysis of the average values
The annual icing days and icing thickness from the OIT and TLIT data are presented in Fig. 8. The spatial distribution of the annual icing days calculated by the TLIT was consistent with the observed data. Most of the annual icing days occurred in the western part of southern China, with the maximum number exceeding 5 days, and the icing days in the eastern part of southern China being less than 2 days. The spatial distribution of annual icing thickness in the TLIT was also consistent with the observed data. The largest icing thickness occurred in the western part of southern China, and the annual icing thickness exceeded 10 mm. There were two areas with a larger icing thickness in the southern and northern parts of southern China, where the annual icing thickness exceeded 5 mm. The annual icing thickness in most of the eastern part of southern China was below 3 mm.
(a),(b) Frequency of annual icing (days) and (c),(d) icing thickness (mm) calculated by the (a),(c) OIT and (b),(d) TLIT data during 1987–2018. The dots in (a) and (c) indicate the locations of meteorological stations.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0172.1
The correlation between the TLIT and OIT data was analyzed using data from 46 meteorological stations. Due to the length of the time series, the correlations were lower in the western and southern parts of southern China and higher in the northern and eastern parts of southern China. The correlation coefficients in 46 meteorological stations were greater than 0.3 and were significant at the 5% confidence level (Fig. 9a).
(a) Correlation coefficients and (b) NRMSE of the TLIT and OIT data during 1987–2018. The dots indicate the locations of meteorological stations.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0172.1
The spatial distribution of the NRMSE of the TLIT and OIT data is presented in Fig. 9b. If the value of the NRMSE was greater (less) than 1, the root-mean-square error of the TLIT data and the OIT data was greater (less) than the standard deviation of the OIT data; that is, the difference between the value of TLIT data and the OIT data was large (small). The maximum value of the NRMSE was smaller than 1.5 across the 46 meteorological stations. Therefore, the NRMSE analysis revealed that there was little difference in the numerical values between the TLIT and OIT data.
Further analysis revealed that there was an inverse relationship between the results of the correlation and NRMSE analyses. The NRMSE between the TLIT data and the OIT data was small, while the correlation coefficient between the TLIT data and the OIT data was large, and vice versa. This indicates that there were both connections and differences between the correlation and NRMSE analyses. The results of the correlation analyses indicated that the trends were similar, while the results of the NRMSE analyses indicated the differences in the numerical values in the TLIT and OIT data were small.
b. Spatiotemporal distribution analysis
Since the spatial distribution structure determined by the REOF decomposition can clearly represent the characteristics of different geographical regions, the REOF method was used to analyze the dominant icing pattern in southern China. The REOF decomposition was conducted for TLIT and OIT data from 67 transmission line icing events in southern China. The spatial distribution of the first three characteristic vectors and their corresponding time coefficients are presented in Figs. 10 and 11. Although there were some differences in the numerical values between the first three characteristic vectors of the TLIT and OIT data, the spatial distributions were similar (Fig. 10). The spatial pattern of the first REOF mode was referred to as the southern type, with ice occurring in the southern part of southern China; the spatial pattern of the second REOF mode was referred to as the northern type, with ice occurring in the northern part of southern China; and the spatial pattern of the third REOF mode was referred to as the western type, with ice occurring in the western part of southern China. The proportional contributions of the first three characteristic vectors of the TLIT data were 26.2%, 19.8%, and 18.6%, respectively, with the cumulative contribution being 64.6%. The proportional contributions of the first three characteristic vectors of the OIT data were 34.3%, 18.2%, and 13.7%, respectively, with the cumulative contribution being 66.2%. The time coefficients of the first three characteristic vectors of the TLIT and OIT data were analyzed. The correlation coefficients for the time coefficients of the first three characteristic vectors were 0.801, −0.443, and 0.576, respectively, all of which were significant at the 5% confidence level.
Spatial patterns of the (a),(d) first, (b),(e) second, and (c),(f) third REOF modes of the (a)–(c) OIT and (d)–(f) TLIT data during 67 transmission line icing events.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0172.1
Time coefficient series for the (a) first, (b) second, and (c) third REOF modes of the OIT (line) and TLIT (bars) data during 67 transmission line icing events.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0172.1
The results indicated that the TLIT data can reflect the temporal and spatial variations of ice thickness in southern China following a climate analysis.
Based on the spatial distribution of the first three characteristic vectors for the OIT and TLIT data, the three regions at 25.5°–26.5°N, 111°–115.5°E; 30.5°–32°N, 111.5°–116.5°E; and 26.5°–29.5°N, 109°–112°E (as shown in Fig. 10) were identified as the southern key area, northern key area, and western key area, respectively, for transmission line icing events. The icing thickness for the 67 transmission line icing events in southern China and the three key areas were calculated using TLIT and OIT data (Fig. 12).
The average icing thickness of 67 transmission line icing events over (a) southern China, (b) the northern key area, (c) the western key area, and (d) the southern key area calculated by the OIT (blue dotted line; mm) and TLIT (black, solid line; mm) data.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0172.1
In southern China as a whole, the average icing thickness during the 67 events was 3.7 (3.2) mm, the maximum icing thickness was 16.3 (17.3) mm, and there were 12 (12) events where the icing thickness was over 6 mm based on the TLIT (OIT) data. In the three key areas, the average icing thickness in the northern key area was the smallest at 1.3 (1.8) mm, the average icing thickness in the western key area was the largest at 5.9 (5.5) mm, and the average icing thickness in the southern key area was 3.7 (2.8) mm based on the TLIT (OIT) data. The TLIT data could reconstruct most of the events observed at stations, although some events with minor ice thicknesses were not considered for analysis. The correlation coefficients for the relationship between icing thickness calculated by the TLIT and OIT data were 0.648, 0.384, 0.565, and 0.599, respectively. The results indicated that the TLIT data can describe the icing location and icing thickness for icing events in southern China. In addition, there are some differences in icing event frequency, icing thickness, duration of icing event, and circulation situation for southern-type, northern-type, and western-type icing events, and these results will be analyzed in future work.
5. Discussion and conclusions
Using ERA-Interim data, gauge observations, transmission line icing observational data, and the hindcasted predictors from the NFSTLI, a new dataset of transmission line icing thickness was constructed. Its reliability was analyzed by case studies and studies of climate data. The main results can be summarized as follows.
There were three icing events in the southern China, which occurred in January 2018, January 2016, and February 2014. They were described using TLIT data and the accuracy of the descriptions was analyzed using transmission line icing observational data from electric power companies. The results showed that the evolution of transmission line icing events described by the NFSTLI was consistent with the actual observations. The icing thickness difference between observational data and data calculated by the NFSTLI was less than 2 mm.
The spatial distributions of annual icing days and icing thickness calculated by the OIT and TLIT data were similar. Most annual icing days were concentrated in the western part of southern China, where the maximum number exceeded 5 days, while there were fewer than 2 icing days in the eastern part of southern China. The largest icing thickness occurred in the western part of southern China, where the annual icing thickness exceeded 10 mm. There were two areas of larger icing thicknesses in the southern and northern parts of southern China, where the annual icing thickness exceeded 5 mm. The annual icing thickness in most of the eastern part of southern China was less than 3 mm. The correlation and NRMSE analyses indicated that the trend in the TLIT and OIT data was consistent, and the differences in the numerical values between the TLIT and OIT data were small.
A REOF decomposition was conducted for the TLIT data and the OIT data for 67 transmission line icing events in southern China. The spatial distributions of the first three characteristic vectors of TLIT data and OIT data were similar. The correlation coefficients for the time coefficients of the first three characteristic vectors were 0.801, −0.443, and 0.576, respectively, all of which were significant at the 5% confidence level. Based on the spatial distribution of the first three characteristic vectors for the TLIT data, the three regions at 25.5°–26.5°N, 111°–115.5°E; 30.5°–32°N, 111.5°–116.5°E; and 26.5°–29.5°N, 109°–112°E were identified as the southern key area, northern key area, and western key area, respectively, for transmission line icing events. The icing thickness of 67 transmission line icing events in southern China and the three key areas were calculated using the TLIT and OIT data. The correlation coefficients for the relationship between the icing thicknesses calculated using the TLIT and OIT data were 0.648, 0.384, 0.565, and 0.599, respectively.
In conclusion, the results indicated that the TLIT data can reflect the temporal and spatial variations of ice thickness in southern China. The construction of the TLIT dataset solves the problem of missing data in transmission line icing historical data, and provides a basis for further research.
However, the correlations of the TLIT and OIT data are low at a few high-mountain stations because of topographical impacts. According to the observations of transmission line icing thickness by electric power companies, topography has a significant impact on the formation of microscale area icing, severe icing often occurs in some microscale areas (such as high mountains), and the TLIT data cannot easily reflect the heavy icing that occurs in some high-mountain stations due to the mesh size. The impact of topography and the refined forecasting technology of transmission line icing thickness in microscale topographic areas will be analyzed in a future study. Moreover, the uncertainty associated with ERA-Interim fields and manual automatic measurements of icing may affect the results of the study and will be analyzed in follow-up work.
Acknowledgments
The authors thank the editor and anonymous reviewers who provided valuable suggestions for improving our manuscript. This work was jointly supported by two Science and Technology Projects of the State Grid Corporation of China (5216A0180004 and 5216A01700UF).
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