Failure Risk of UHV AC Transmission Line Considering ... - IEEE Xplore

IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 28, NO. 3, JULY 2013

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Failure Risk of UHV AC Transmission Line Considering the Statistical Characteristics of Switching Overvoltage Waveshape Yang Li, Jinliang He, Fellow, IEEE, Jun Yuan, Chen Li, Jun Hu, and Rong Zeng, Senior Member, IEEE

Abstract—The sizes of ultra-high-voltage (UHV) towers and substations are related to the air clearances which are usually determined by switching overvoltage. Based on electromagnetic transient simulation of the first 1000-kV UHV ac transmission line in China, this paper extracted the effective wave information in accordance with the concept of the active part of the waveshape from calculated main types of switching overvoltage. Moreover, based on test results of switching impulse flashover voltages, a practical and accurate method to calculate the risk of failure was presented, which considered the variable characteristics of the insulation strength of the transmission line under different switching overvoltage waveshapes. Evaluation of the results focused on the comparison between two new methods and the traditional simplified method considering the effect of the front time. Index Terms—Failure risk, switching overvoltage, transmission line, ultra-high-voltage (UHV) AC system, wavefront time, waveshape.

I. INTRODUCTION

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EVERAL ultra-high-voltage (UHV) ac and dc transmission projects in China have been put into operation in recent years to solve the imbalance of energy distribution. One of the critical technical problems facing UHV transmission projects is how to effectively suppress the switching overvoltage (SOV). Because of the high base voltage, the severest stress on system insulation is often generated by uncontrolled switching overvoltages that determine the insulation levels of the UHV system. Meanwhile, the saturation characteristics of air dielectrics in long gaps indicate that a lower level of insulation withstand voltage can reduce the sizes of UHV towers and power apparatuses and the costs of construction [1]. That is to say, the insulation coordination of UHV systems, especially the Manuscript received October 04, 2012; revised February 13, 2013 and March 04, 2013; accepted March 06, 2013. Date of publication April 25, 2013; date of current version June 20, 2013. This work was supported in part by the National Natural Science Foundation of China under Grant 5073001, in part by the National Basic Research Program of China (“973” Project) under Grant 2009CB724504), and in part by the China State Power Grid. Paper no. TPWRD01062-2012. Y. Li, J. L. He, C. Li, J. Hu, and R. Zeng are with the State Key Lab of Power Systems, Department of Electrical Engineering, Tsinghua University, Beijing 100084, China (e-mail: [email protected]; [email protected]). J. Yuan is with the Construction Department of State Grid Corporation of China, Xicheng District, Beijing 100031, China. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPWRD.2013.2252238

clearance of external insulation for transmission lines (TLs), is mainly based upon the insulation strength characteristics of typical air gaps. It is impossible to make a complete protection of the transmission line against all types of overvoltages. Therefore, the cost-effective UHV transmission line design should depend on a probabilistic procedure which considers the statistical characteristics of overvoltages. Switching surge occurring on a power system is irregular, which depends on parameters and length of the transmission line, and configuration of the substation (SS). Since the waveshape has a considerable effect on the insulation strength, it is crucially important to emulate the switching impulse with the equivalent laboratory switching impulse for the purpose of test or design, which can approximate the shape of the severest or the most frequently occurring switching impulses [2]. The switching impulse strength of an air gap is characterized by 50% flashover voltage and the coefficient of variation . Studies of switching impulse strength began in the 1960s simultaneously with the increasing rated voltage of transmission lines. Various researchers showed that the 50% flashover voltage and coefficient of the variation both depend on time and on gap to crest [3]–[5]. The relation between spacing can be represented as a U-shaped curve. Since switching surges in UHV systems have very long fronts, the strength of air insulation increases by 20% or more [6]. It is of great benefit and necessary to take into account an alternative equivalent switching impulse that can match the characteristics of UHV power systems in the insulation design. However, there are few statistical studies of the actual distribution characteristics of switching surges in UHV systems and quantitative data are not sufficient. The coefficient of variation is defined as the ratio of the standard deviation to 50% flashover voltage, which is also affected by the wavefront time [7], [8]. The value of standard deviation of long air gaps is difficult to be measured precisely in laboratories. Although there are quite different values of the coefficient of variation, it is essential to consider the approximate relation between the coefficient of variation and the time to crest. Usually, the effect of waveshape variation is always disregarded in the design of insulation coordination. The switching impulse waveform is on the assumption of having the same shape with an equivalent time to crest relating to the waveform of the lowest strength, which is called the critical wave [9]. This simplification leads to a conservative estimation of the risk of failure. The risk of failure generally provides an index for the assessment of insulation design. In the probabilistic method, an

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TABLE I PARAMETERS OF THE WIRES

Fig. 1. Schematic diagram of the Jindongnan–Nanyang–Jingmen UHV system.

acceptable risk of failure should depend on the actual power system operation experience [9]. The times to crest of most switching surges are much longer than the critical wave, and it is important to develop new approaches for calculating the risk of failure according to the UHV transmission-line parameters. In this paper, a more sophisticated and accurate approach to the calculation of risk of failure is provided, which considers the variation of switching overvoltage distribution along the transmission line under different system conditions and the variable behavior of insulation strength under different switching overvoltage waveshapes. II. OVERVIEW OF THE UHV SYSTEM MODELING APPROACH

Fig. 2. Structure of main UHV towers (unit: in millimeters). (a) Cup tower. (b) Cat-head tower.

TABLE II PARAMETERS OF THE SURGE ARRESTER

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A. Description of the 1000 kV UHV System for Simulation All subsequent simulation and analyses are based on the Jindongnan–Nanyang–Jingmen UHV system, which is the first 1000-kV UHV single-circuit transmission system in China connecting the North China Power Grid and Central China Power Grid, which has been put into commercial operation since 2009. The schematic diagram of the studied UHV transmission system is shown in Fig. 1. The rated voltage of the system is 1000 kV, and the base value is 898 kV. B. Parameter Setting and Modeling Approach The modeling approaches [10] for all components are as follows. Overhead transmission lines: they are modeled frequency dependently, and their basic parameters are shown in Table I. Phase conductors are set to transpose ideally, and there are two ground wires: LBGJ-150-20AC and OPGW-150 with directly tower grounding. The soil resistivity is 100 . The tower: IVI insulator string configuration (V-string for middle phase and I-string for two side phases) is used for most suspension towers along the entire line in order to reduce the tower window size and cross-arm length. The Jindongnan–Nanyang (JN) section adopts the cup tower and the Nanyang–Jingmen (NJ) section adopts the cat-head towers, as shown in Fig. 2 [11].

and in Fig. 1 are UHV autotransTransformer: formers, with a rated capacity of 3000/3000/1000 MVA, a rated voltage of 1050/525/110 kV, and a short-circuit impedance of 18.15%/61.7%/37.37%. The transformers are modeled as inductance. Surge arrester: the rated voltages of all arresters on either the line side or bus side are selected as 828 kV, whose parameters are shown in Table II. Circuit breaker (CB): it is modeled as a non-ideal switch with inner resistors. To suppress switching overvoltages, each CB has closing resistors without opening resistors. The closing resistor is 600 in the Jindongnan substation, 580 in the Nanyang switch substation and 560 in the Jingmen substation. The insertion time of the closing resistor in CBs is 8 ms. Operation condition: the bus voltages of the Jindongnan, Nanyang, and Jingmen substation are 1053, 1044, and 1042 kV, respectively. The power flow from Jindongnan to Nanyang is Mvar and from Nanyang to Jingmen, it is Mvar. C. Waveshape Parameter Definition and Processing Method The waveshape of a switching impulse is characterized by four parameters [12]: 1) polarity; 2) time to peak ; 3) time to

LI et al.: FAILURE RISK OF UHV AC TRANSMISSION LINE

half-value ; and peak value of the test voltage . For convenience, the waveform of the switching impulse generally uses to characterize the wavetail. Although the waveshape has a definite effect on the air insulation strength, 50% flashover voltage is not decided by the entire waveform. Tests have shown that during the flashover developing process, the leader inception and propagation occur at voltage from 60%–75% to 100% of the peak value of impulses, resulting in 50% probability of flashover [2], [13]. It is generally agreed that the active part of the waveshape can be defined as that between 70% and 100% of the impulse peak value [13]–[16]. Since the time to half-value changes with the variation of time to crest at the same time, it is quite difficult to distinguish the influence of wavetail from the wavefront effect. A few studies of the wavetail effect investigated that for a given gap and a constant time to crest, 50% flashover voltage increases with the reduction of the time to half-value, particularly when the test time to half-value is less than 60 s or time to crest is less than 10 s [17], [18]. Therefore, the wavetail effect has a slight influence on the UHV switching flashover because of the long wavefront. In analysis, the maximum absolute value of the recorded data is the peak of the studied wave, and the time when the voltage is 70% of the peak value , the time when the voltage is 85% of the peak value , and time to half-value are calculated.

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Fig. 3. Typical waveforms of the switching overvoltage.

TABLE III PHASE-TO-GROUND SWITCHING OVERVOLTAGE FRONT TIME STATISTICAL PROFILES

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III. CHARACTERISTICS OF SWITCHING OVERVOLTAGE WAVESHAPE A. Simulation Scenarios and Conditions The SOV level of the UHV transmission line is mainly associated with the following events, and the corresponding typical waveforms are shown in Fig. 3. 1) Line energizing: SOVs caused by the operation of line energizing are the most frequent occurrence among all types of overvoltages. It occurs when the state of CB changes from open to close. 2) Line single-phase reclosing: the initial conditions of the transmission line have trapped charge that may stimulate higher overvoltage. The reclosing operates after fault clearing. 3) Single-line-to-ground (SLG) fault initiation: it is the only fault type considered that the transient occurs on the sound phases when the CBs at two terminals do not operate. 4) Fault clearing: the severe overvoltages are produced by clearing all types of faults on sound phases of adjacent lines and faulted lines. The worst case is usually on adjacent lines. Fault types including single line-to-ground, double line-to-ground (DLG), two-phase short-circuit (TSC), and the three phase line-to-ground (TLG) fault are considered. To derive the SOV probabilistic distribution, it is necessary to take into account the randomness of several factors, including the instants of closing, reclosing, or fault times, which all are distributed uniformly over the full cycle of power system voltage. For energizing overvoltage, the closing times of the three phases are described by follows the uniform distribution over one 50-Hz period and all times follow independent Gaussian distributions with standard deviations of

2 ms over the range of 5 ms. For reclosing overvoltage, the instants of reclosing operations at two terminals are nonsimultaneous that are supposed to be uniformly distributed over the range of 5 ms. Fault-location randomness is also considered. B. Characteristics of Wavefront Time Distribution Different types of phase-to-ground statistical switching overvoltage and the corresponding front time profiles along the Jindongnan–Nanyang–Jingmen line, in different cases, are shown in Table III. A three-phase line-to-ground fault clearing of the Jindongnan–Nanyang section at the Nanyang side produces the maximum 2% phase-to-ground overvoltage (1.97 p.u.) on the adjacent line. The front times range from 0.30 to 10.37 ms. The most frequent overvoltages, which are energizing and singleline-to-ground fault clearing, have a longer minimum front time (1.83 ms along the line and 1.54 ms on the bus side). According to the Jarque-Bera test of the 5% true level, the front times along the line in different operation cases reject the Gaussian distribution hypothesis. And the front times at each position, which meet the Gaussian distribution, have a probability of 13% and for the substation side, a higher probability of 30% exists. As for phase-to-phase switching overvoltage, the statistical results are shown in Table IV. A two-phase short-circuit fault clearing of the Jindongnan–Nanyang section at the Nanyang side produces the maximum 2% phase-to-phase overvoltage (3.23 p.u.) on the adjacent line. In most cases, the maximum

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TABLE IV PHASE-TO-PHASE SWITCHING OVERVOLTAGE FRONT TIME STATISTICAL PROFILES

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to UHV insulation strength; thus, a statistical method is particularly applicable to reduce the line insulation strength and tower dimensions for saving cost. A rigorous calculation of the risk of failure requires the frequency distribution of the transmission-line insulation strength and switching overvoltage stresses [9] (1) where is the flashover rate; is the probability density of the switching overvoltage is the flashover probability under switching overvoltage and the front time is the minimum switching overvoltage; and is the maximum switching overvoltage. The factor 1/2 means that only the flashover probability of positive polarity overvoltages is considered because the negative polarity switching surge strength is much higher than that of the positive polarity [2]. A. Determining the Flashover Probability For practical design purpose, the flashover probability distribution is defined by Gaussian distribution (2)

Fig. 4. Distributions of along the transmission line of energizing overvoltage. (a) JN line closing at the Nanyang side, (b) NJ line closing at the Nanyang side.

2% phase-to-phase overvoltage occurs on the bus side below 2.8 p.u. For insulation design, the distribution of front time at one point of the transmission line can be approximately regarded as Gaussian distribution. For a more sophisticated way, each front time corresponding to simulated overvoltages may be considered, respectively, to calculate the 50% flashover voltage. C. Characteristics of Wavetail Time Distribution The cumulative distribution and probability distribution of for energizing at the Nanyang side along the entire line are shown in Fig. 4. When reaches the maximum frequency, the cumulative frequency of is about 50%. From the statistical data of for each type of switching overvoltage, in most cases, the ratio is less than 3. Thus, in the following calculation of failure risk, it is set as 3. IV. CALCULATION METHOD OF THE RISK OF FAILURE The risk of failure caused by the switching surges is always viewed as the switching impulse flashover rate, which is the probability that an unwanted stress along the line exceeds the insulation strength. For self-recovering insulation (e.g., air gap), the overvoltages and the insulation strength show probabilistic behaviors. Switching overvoltage is the primary control factor

is the 50% flashover voltage, and is the standard where deviation. According to IEC 60071-2 recommendation of the statistical method [9], it is assumed that the waveform of maximum voltage is the same as that of the standard switching impulse, neglecting the relation between flashover probability and waveshape. However, and vary with time to crest. The waveshape effect for calculating the risk of failure was considered in [19], but which did not cover parameters in the actual UHV system. The further study on the effect of characteristics of waveshape in an actual UHV system is discussed as follows. 1) 50% Flashover Voltage-Related Geometry Factor: The 50% flashover voltage depends on the geometry of the insulation, meteorological parameters, and waveshape. Influence of geometry is not only decided by the gap length but also the gap configuration. The strength of any gap configuration with a given length is described by the gap factor , which is the ratio between the positive polarity 50% flashover voltage of the configuration and that of a rod-plane configuration. For any given actual gap configuration, the accurate gap factor can only be measured by experiments [9]. The main types of UHV tower gap configuration are conductor-crossarm for the side phase and conductor window for the middle phase. Based on the test results of 50% flashover voltages on 1000-kV towers given in Table V [20], which are suitable for altitude below 500 m above sea level, the gap factors are determined as 1.26 for conductorcrossarm configuration and as 1.17 for the conductor-window configuration, which weakly deviates from the EPRI defined value 1.2 [2]. The lowest in the U-shape curve corresponding to the critical time to crest is a nonlinear function of the gap length. The critical 50% flashover voltage can be obtained with three different methods [2], [21]–[23]. The switching impulse


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TABLE V RESULTS OF TESTS PERFORMED ON SIDE PHASE AND MIDDLE PHASE WITH DIFFERENT WAVEFRONT [20]

strength formula suggested by CRIEPI [23] is intermediated to that of the other two methods with the same gap length. As IEC and China have recognized the legitimacy of the CRIEPI method, this study uses the CRIEPI equation (3) to express the relation between the and the gap length

Fig. 5. Relation between the gap factor and 50% flashover voltage.

(3) where is expressed in kilovolts and is in meters; and is a gap factor . The equation is valid for positive polarity switching impulse with a gap length of 1 to 25 m. is the altitude correction factor and can be calculated by , where is the altitude above sea level (in meters) and 0.39 [20]. 2) Front Time Related to 50% Flashover Voltage: The waveshape effect is mainly dependent of the time to crest. The critical time to crest, which yields the , is decided by (4) [24] and 50% flashover voltage applied for any time to crest is given by (5) [24] (4) (5) , and is the where equivalent time to crest (in microseconds) and is the critical time to crest (in microseconds). The equation is applicable in the range m, and . If is not within the range, the time to crest effect is negligible and [24]. Fig. 5 shows the 50% flashover voltage changes with the gap factor between 1 and 2 when s. Since the definition of gap factor, which was mentioned before under different gap configurations, the relation between 50% flashover voltage and the gap factor should be linear. But the equation is not appropriate for a gap factor larger than 1.9. In comparison with the experimental flashover data from the USA–USSR investigation [15], the 50% flashover voltages calculated by fitting (5) ( m) approximately match the test result in Fig. 6. For various switching impulses, it is common practice to use curve fitting based on the actual shape to determine an equivalent double exponential testing impulse. Using the active part of waveshape equivalent assumption, when , the equivalent time to crest can be given by (6) or (7) (6) (7)

Fig. 6. Relation between the front time and 50% flashover voltage [15].

where or is the time to crest of equivalent double exponential waveforms based on 70% to 100% or 85% to 100% of the peak value of actual waveform. 3) Coefficient of Variation-Related Front Time: For the IREQ tests [7], [25], the coefficient of variation with the front time that is less than the critical value increases rapidly to about 0.08 at 50 s. The lowest coefficient of variation (about 0.04) occurs at the critical time to crest and it slightly increases to 0.05 for the longer time to crest ( s). BPA tests showed that the coefficient of variation with front times from 400 to 900 s is about 0.05–0.06 [7]. The USA-USSR investigated the effect of a wide range of front times from 100 to 6000 s on the coefficient of variation [15], it increases from 0.045 to 0.09 before 2200 s, then decreases to 0.065 at 6200 s. In China UHV tests [20], [26], the coefficient of variation can reach a value of 0.08 for the front time larger than 1000 s. But the value of is 0.051 at 5000 s. A conservative value of 0.06 is generally used for UHV transmission lines with 1000 s front time. The effect of the time to crest on the coefficient of variation has been reported but still needs further investigations for UHV projects. According to the laboratory results listed before, the approximate relation between and is shown in Table VI. If more precise relation between the coefficient of variation and longer wavefront is more than 1000 s is achieved, it will be much better.

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TABLE VI DEPENDENCE OF THE COEFFICIENT OF VARIATION ON FRONT TIME

TABLE VII SOV MINIMUM CLEARANCES FOR 1000-kV SINGLE CIRCUIT TRANSMISSION LINES [27]

B. Determining the SOV Probability Density Function As the switching surges are different in each operation, the voltage peak of every recorded wave can be extracted. Thus the switching overvoltage probability for an overvoltage peak in can be expressed by (8) where

is the number of simulated operations.

C. Methods Determining the Switching Surge Flashover Rate Equation (2) combining with (8), can be used to determine the risk of failure for single insulation element: (9) is the equivalent front time of the waveform under where one operation. There are 11 positions along each line for simulation, and each position is assumed to have 100 parallel insulation gaps. When the switching overvoltage distributions and flashover probability are known, the risk of failure for all three phases of the entire UHV line is derived by (10) where is the number of phases, is the number of divided positions, and is the number of parallel insulation gaps. The minimum air gap clearances are shown in Table VII [27]. The parameters and results in the following are all corrected for the altitude of 1000 m above sea level. For a better insulation design criterion, all types of switching overvoltages with expected number of operations per year and three approaches to the risk of failure for switching overvoltages are considered: 1) Simplification method (Approach I): this is recommended in IEC 60071-2. Fixed time to crest and the coefficient of variation are used: or 2000 s and , where 2000 s is the equivalent time to crest of this system considering all possible switching failures, which is related to the UHV system structures and parameters. 2) Fixed and variable (Approach II): 50% flashover voltage is calculated by (5) and the coefficient of variation is fixed to 0.06. The minimum gap distance for middle

Fig. 7. Risks of failure for middle phase of entire transmission lines dependent on the coefficient of variation using fixed U50%, min.

phase is 7.2 m and for side phase is 6.2 m at the altitude of 1000 m above sea level. 3) Variable and (Approach III): the coefficient of variation changes with according to Table VI and is calculated by linear interpolation method. Other parameters are the same as Approach II. It is noticeable that the influence of the coefficient of variation on the risk of failure should be taken into account, as shown in Fig. 7. China national standard GB/Z 24842 permits no more than one flashover per 100 years for the entire line insulation caused by switching overvoltage [27]. According to the EHV and UHV system operation experience, assuming 4-5 energizing operations per year [28], 1-5 single line-to-ground faults per year and no more than one other fault types per year [29], the limits of risks of flashover per year are obtained: is less than for an energizing operation. is in the range from to for a single phase reclosing, fault initiation or fault clearing operation. is higher than for a two-phase or three-phase reclosing, fault initiation or fault clearing operation. V. COMPARISON OF SWITCHING IMPULSE FLASHOVER RATE A. Difference Between Middle and Side Phases By the simplification method (Approach I), Table VIII shows the differences between middle phase and side phase on the risk of failure. It is clear that the risk of failure for middle phase


TABLE VIII THE RISKS OF FAILURE FOR SINGLE PHASE BY APPROACH I ( UNIT: PER 100 SWITCHING OPERATIONS)

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S,

TABLE IX THE POSITIONS OCCURRING MAX. SOV AND MAXIMUM RISKS OF FAILURE FOR MIDDLE PHASES, AND RESPECTIVE RISKS OF FAILURE BY APPROACH II (UNIT: PER 100 SWITCHING OPERATIONS)

TABLE X THE RISKS OF FAILURE FOR THREE PHASES ALONG THE LINE BY APPROACH I (UNIT: PER 100 SWITCHING OPERATIONS)

TABLE XI THE RISK OF FAILURE FOR THREE PHASES ALONG THE LINE BY APPROACH II AND III (UNIT: PER 100 SWITCHING OPERATIONS)

D. Comparison of Different Failure Types is always lower than that for side phase, the reason is that the middle phase has a higher 50% flashover voltage generated by a longer gap distance as shown in Table VII. B. Correlation Between Max. SOV and Failure Risk Positions From analysis, if the front time distribution is considered, the maximum phase-to-ground 2% overvoltage (Max. SOV) and the maximum risk of failure (Max. FR) will occur in two different positions along the line. Usually there are two different positions, one results in the maximum phase-to-ground 2% overvoltage and the other has the maximum risk of failure. But if Approach I with fixed front time is chosen to do the analysis, both Max. SOV and Max. FR will occur in the same position. Table IX shows the positions occurring Max. SOV and Max. FR, and the respective risks of failure on both positions by Approach II, under . In general, the highest overvoltage should lead to the severest risk, but this method adopts a Gaussian distribution for flashover probability with variable front time. The risk of failure is positive correlated with the integral value of (2), which is decided by switching overvoltage, 50% flashover voltage and the coefficient of variation. Even if the position does not occur the maximum value of SOV, it can result in a higher risk of failure by a lower 50% flashover voltage. Because the time to crest and the peak value of SOV do not have strict negative correlation. C. Effect of Variable Front Time For the traditional simplification method (Approach I) in Table X, the risk of failure decreases with higher front time. Two different active parts of waveform in Approach II are considered: 70% above and 85% above. In this case, the risks of failure calculated by are lower than by as shown in Table XI, also owing to the longer equivalent time to crest of 70% above.

Tables IX and X show the risks of failure for the JindongnanNanyang-Jingmen line in the highest overvoltage case for each type. We can see the failure risks of the last three types of overvoltages are much higher than others, the three-phase line-toground fault (TLG) clearing switching operation results in the maximum risk of failure. Only double line-to-ground (TSC) and three-phase line-to-ground (SLG) fault clearing operations probably result in risks of failure greater than the limits listed above. E. Comparison of Three Approaches From Tables IX and X, the accuracy of results calculated by Approach I is decided by the equivalent front time of the analyzed UHV system. It shows that 250 s is no longer appropriate for UHV power system and 1000 s as the standard front time of UHV switching impulse may be conservative. Even if 2000 s, which is the equivalent time to crest of this system considering all possible switching failures, is applied in this system, differences between Approach I and III are at least two orders of magnitude. From Table XI, taking into account that the variable behavior of the coefficient of variation influences the insulation strength, the risks of failure for the former four types of overvoltages by Approach III are higher in two to five orders of magnitude than those by Approach I for lack of considering variable coefficient of variation. But the flashover rates of DLG, TSC and TLG fault clearing by Approach III are usually smaller than those by Approach II, but keep the same order of magnitude. But, the last three types of overvoltages occur at a very small probability so that they can be ignored in insulation coordination. Some of the reasons for this effect can be stated as follows. Since the coefficient of variation increases with longer wave front, the standard deviation of switching flashover voltage for longer wave front is higher than that for shorter wave front,

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RISK

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TABLE XII FAILURE FOR PHASE TO PHASE ALONG THE LINE (UNIT: PER 100 SWITCHING OPERATIONS)

2)

3)

4)

which will lead to higher flashover rate. However, the switching insulation strength augments with longer wave front, i.e., a higher 50% flashover voltage, which leads to a lower risk of failure. As a result, a large variety of the coefficient of variation offsets the effect of the increase of 50% flashover voltage due to long wave front of switching impulse. Consequently, whether the flashover rates increase or decrease compared with Approach II depends on the front time distributions. So Approach III will be the best one which considers the actual panorama of the system including both front time and coefficient of variation. F. Comparison of Phase-to-Ground and Phase-to-Phase Failures To calculate the switching surge flashover rate between phases, the gap factors are determined as 1.75 for the conductor -conductor configuration based on the test results of 50% flashover voltages, and the minimum gap distance between phases is 9.2 m at the altitude of 1000 m above sea level [20]. It is assumed that the phase-to-phase and the phase-to-ground insulations have no common electrode so that the risk of failure for these two can be determined separately [9]. Table XII shows the risks of failure between phases for the Jindongnan–Nanyang–Jingmen line in the highest overvoltage case for each type. It shows that only the failure risks of double line-to-ground fault clearing operations are much higher than the others, but still lower than the upper limits listed before. The risks of failure between phases are lower on at least one order of magnitude than those for phase to ground except for energizing operations. The phase-to-phase switching overvoltage has a negligible impact on the risk of failure along the line. Since the highest overvoltage between phases occurs at the substation side, it should be only considered for the substation insulation design. VI. CONCLUSION Based on an actual UHV system and test results of switching impulse flashover voltages, the effect of the switching overvoltage waveshape on the risk of failure is discussed. The results obtained by three different approaches are compared. Several conclusions are drawn as follows. 1) Three-phase line-to-ground fault clearing switching overvoltage will result in the severest flashover rate. The risk of failure for energizing or single-line-to-ground

5)

6) 7)

fault clearing is no more than per 100 switching operations. Middle phase with the long gap distance will result in lower failure risk than the side phase with short gap distance due to different 50% flashover voltage. The risk of failure, which has the highest 2% overvoltage, is not always the maximum. When the fixed coefficient of variation and switching overvoltage distribution is the same, the risks of failure calculated by the long front time are lower than by the short one. A longer time to crest than 1000 s might be more appropriate for the actual case, since 1000 s is currently recommended in the standard results in the risks of failure that are greater than the considered longer time to crest. The coefficient of variation has a significant influence on the risk of failure. A higher value of coefficient of variation increases the risk of failure. The risk of failure along the line can be mainly determined by the phase-to-ground overvoltages. In comparison, Approach III, which considers the actual switching overvoltage distribution and provides the most precise results, should be suggested in actual engineering analysis. REFERENCES

[1] J. K. Dillard, J. M. Clayton, and L. A. Kilar, “Controlling switching surges on 1100-kV transmission systems,” IEEE Trans. Power App. Syst., vol. PAS-89, no. 8, pp. 1752–1762, Nov. 1970. [2] R. J. Lings, EPRI AC Transmission Line Reference Book-200 kV and Above, 3rd ed. Palo Alto, CA: Electric Power Research Institute, 2005, ch. 3, 5. [3] Y. Watanabe, “Switching surge flashover characteristics of extremely long air gaps,” IEEE Trans. Power App. Syst., vol. PAS-86, no. 8, pp. 933–936, Aug. 1967. [4] A. J. Kachler, J. J. Laforest, and L. E. Zaffanella, “Switching-surge flashover of EHV-UHV towers,” IEEE Trans. Power App. Syst., vol. PAS-89, no. 8, pp. 1762–1771, Nov. 1970. [5] J. K. Dillard and A. R. Hileman, “UHV transmission tower insulation tests,” IEEE Trans. Power App. Syst., vol. PAS-89, no. 8, pp. 1772–1784, Nov. 1970. [6] G. Carrara, L. Dellera, and G. Sartorio, “Switching surges with very long fronts (above 1500 s): Effect of front shape on discharge voltage,” IEEE Trans. Power App. Syst., vol. PAS-89, no. 3, pp. 453–456, Mar. 1970. [7] C. Menemenlis and G. Harbec, “Coefficient of variation of the positiveimpulse breakdown of long air-gaps,” IEEE Trans. Power App. Syst., vol. PAS-93, no. 3, pp. 916–927, May 1974. [8] E. M. Bazelian et al., “Switching impulse shape and dielectric strength of external EHV/UHV insulation,” in Proc. CIGRE Session, Paris, France, 1976, paper 33-02. [9] Insulation Coordination—Part 2: Application Guide, IEC 60071-2, 1996. [10] C. Li, J. L. He, J. Hu, R. Zeng, and J. Yuan, “Switching transient of 1000-kV UHV system considering detailed substation structure,” IEEE Trans. Power Del., vol. 27, no. 1, pp. 112–122, Jan. 2012. [11] Z. Y. Liu, UHV Power Grid. Beijing: China Economic Publishing House, 2005. [12] High-Voltage Test Techniques—Part 1: General Definitions and Test Requirements, IEC 60060-1, 2010. [13] C. Menemenlis and K. Isaksson, “The front shape of switching impulses and its effect on breakdown parameters,” IEEE Trans. Power App. Syst., vol. PAS-93, no. 5, pp. 1380–1389, Sep. 1974. [14] J. J. LaForest, Transmission Line Reference Book: 345 kV and Above, 2nd ed. Palo Alto, CA: Electric Power Research Institute, 1982, ch. 11. [15] F. S. Young, H. M. Schneider, Y. M. Gutman, and N. N. Tikhodeyev, “USA-USSR investigation of 1200-kV tower insulation,” IEEE Trans. Power App. Syst., vol. PAS-99, no. 2, pp. 462–470, Mar. 1980.


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Yang Li was born in Yichuan City, Shaanxi Province, China, in 1991. He received the B.Sc. degree in electrical engineering from Tsinghua University, Beijing, China, in 2012. Currently, he is a graduate student in the Department of Electrical Engineering, Tsinghua University. His research interests include overvoltage statistical analysis in power systems and dielectric materials.

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Jinliang He (M’02–SM’02–F’08) was born in Changsha, China, in 1966. He received the B.Sc. degree in electrical engineering from Wuhan University, Wuhan, China, in 1988, the M.Sc. degree in electrical engineering from Chongqing University, Chonqing, China, in 1991, and the Ph.D. degree in electrical engineering from Tsinghua University, Beijing, China, in 1994. Currently, he is the Professor of Tsinghua University. His research interests include overvoltages and electromagnetic compatibility in power systems, grounding technology, and dielectric material.

Jun Yuan was born in Wuhan City, Hubei Province, China, in 1971. He received the M.Eng. degree in electrical engineering from Huazhong University of Science and Technology, Wuhan City, in 1997. Currently he is a Senior Engineer with the Construction Department, State Grid Corporation of China (SGCC), Beijing. He is engaged in the management of construction of ultra-high-voltage projects of SGCC.

Chen Li was born in Lanzhou City, Gansu Province, China, in 1988. He received the B.Sc. and M.Eng. degrees in electrical engineering from Tsinghua University, Beijing, China, in 2010 and 2012, respectively, and is currently pursuing the Ph.D. degree at Stanford University, Stanford, CA, USA. Currently, he is with the Department of Electrical Engineering, Stanford University. His research interests include magnetic materials, transient analysis, and protection of power systems and electronic systems.

Jun Hu was born in Ningbo City, Zhejiang Province, China, in 1976. He received the B.Sc., M.Sc, and Ph.D. degrees in electrical engineering from Tsinghua University, Beijing, China, in 1998, 2000, and 2008, respectively. Currently, he is an Associate Professor in the Department of Electrical Engineering, Tsinghua University. His research fields include overvoltage analysis in power systems, dielectric materials, and surge arrester technology.

Rong Zeng (M’02–SM’06) was born in Shaanxi, China, in 1971. He received the B.Sc., M.Eng., and Ph.D. degrees in electrical engineering from Tsinghua University, Beijing, China, in 1995, 1997, and 1999, respectively. After graduation, he was a Lecturer in the Department of Electrical Engineering, Tsinghua University, Beijing, in 1999 and an Associate Professor and Professor in the same department in 2002 and 2007, respectively. Currently, he is the Vice Dean of the Electrical Engineering Department, Tsinghua University. He is presently working in the fields of long air-gap discharge, lightning protection, and electric-field measurement by electro-optical sensors. He is the author and coauthor of many scientific papers and, so far, more than 40 papers have been published in IEEE TRANSACTIONS.