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Experimental study and mathematical modelling fo flashover on extra-high voltage


HYDROLOGICAL PROCESSES Hydrol. Process. 18, 3471– 3480 (2004) Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/hyp.5807

Experimental study and math

ematical modelling of ?ashover on extra-high voltage insulators covered with ice
J. Farzaneh-Dehkordi* J. Zhang and M. Farzaneh
NSERC/Hydro-Quebec/UQAC Industrial Chair on Atmospheric Icing of Power Network Equipment (CIGELE) and Canada Research Chair on Engineering of Power Network Atmospheric Icing (INGIVRE), Universit? e du Qu? ebec a ` Chicoutimi, 555 boulevard de l’Universit? e, Chicoutimi, Qc G7H 2B1, Canada

Abstract:
Using a test method developed at the high-voltage laboratory of the NSERC/Hydro-Quebec/UQAC Industrial Chair on Atmospheric Icing of Power Network Equipment (CIGELE), the relation between the minimum ?ashover voltage V MF and the insulator dry arcing distance for standard porcelain station post insulators, as typically used in Hydro-Quebec substations, was investigated under icing conditions. The experimental results show that, under wet-grown ice, known as the most dangerous type of ice for power transmission systems, the V MF increases nonlinearly with an increase in insulator length. Based on these results, an improved mathematical model for predicting the critical ?ashover voltage versus length of ice-covered insulators is presented. This model is helpful for understanding the ?ashover phenomenon on ice-covered insulators and presents a powerful tool for choosing the proper length of outdoor insulators in cold climate regions. Copyright ? 2004 John Wiley & Sons, Ltd.
KEY WORDS

atmospheric icing; arc; ?ashover; insulator; modelling

INTRODUCTION In cold climate regions, one of the major problems for power systems is atmospheric icing due to freezing rain or drizzle, in-cloud icing, icing fog, wet snow, or frost. In addition to mechanical damage due to excessive ice accumulation and dynamic loads caused by wind, the presence of ice and snow on insulators may lead to ?ashover faults. Flashover of insulators is a phenomenon associated with the failure of insulation under electrical stress. It will short-circuit the electrodes and result in consequent outages in power networks. For example, on 18 April 1988 at the Hydro-Quebec Arnaud substation, a series of six ?ashovers occurred on insulators covered with wet snow and resulted in a major power interruption for a large part of the province of Quebec (Hydro-Qu? ebec, 1988). Also, power outages caused by ice and snow accretion have been reported by many studies in Canada (Chisholm et al., 1996; Cherney, 1980), the USA (Cherney, 1980), Japan (Matsuda et al., 1991), Norway (Fikke et al., 1992), China (Su and Hu, 1998), and the UK (Forrest, 1969). This problem has received a great deal of attention from many researchers, and a large number of investigations and theoretical studies have been carried out in several laboratories (Farzaneh, 2000). Reviews of most of these investigations were reported in previous work (Farzaneh and Kiernicki, 1995, 1997) and recent papers by IEEE (Farzaneh et al., 2003a) and International Council on Large Electric Systems (CIGRE) (CIGRE TF 33 04 09, 1999, 2000) task forces. The ?ashover phenomenon on ice-covered insulators has also been studied for over 25 years in the high-voltage (HV) laboratories of Universit? e du Qu? ebec a ` Chicoutimi (UQAC; Phan et al., 1974) and, subsequently, of the CIGELE. A mathematical model has been established
* Correspondence to: J. Farzaneh-Dehkordi, Universit? e du Qu? ebec a e, Chicoutimi, Qc G7H 2B1, Canada. ` Chicoutimi, 555 blvd de l’Universit? E-mail: jalil farzaneh@uqac.ca

Copyright ? 2004 John Wiley & Sons, Ltd.

Received 28 April 2004 Accepted 10 September 2004

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for predicting the critical ?ashover voltage of ice-covered insulators, and this has been successfully applied to a short insulator string covered with a wet-grown ice layer (Farzaneh et al., 1997). Such a model may be used by researchers and power companies to study the ?ashover phenomenon and for designing the insulation level of transmission lines in cold regions. However, mainly due to limited laboratory conditions, very few experimental results for the ?ashover voltage of full-scale extra-HV (EHV) insulators under icing conditions are available. This situation makes it dif?cult to apply this model to long, ice-covered insulators for engineering purposes. The main objectives of the present study are to evaluate the critical ?ashover performance of a standard post insulator, as typically used in 735 kV Hydro-Quebec substations, under icing conditions and, based on the experimental results, to improve the mathematical model for application to long, ice-covered insulators. FLASHOVER MECHANISM OF ICE-COVERED INSULATORS Flashover on ice-covered insulators is a very complex phenomenon. An arc is not only an electrical process, but also involves thermal and electrochemical processes. Figure 1 shows an example of a ?ashover on standard line insulators covered with ice. The ?ashover of ice-covered insulators includes the following steps: 1. Atmospheric ice accretion on the insulator surface due to hoar frost, in-cloud icing, or precipitation icing. Precipitation icing can occur in several ways, including by freezing rain and drizzle, as well as by wet and dry snow. Glaze with icicles is the most dangerous type of atmospheric icing because to its high probability of producing ?ashovers (Farzaneh et al., 1992; Farzaneh and Kiernicki, 1995). 2. The distribution of ice on insulators is seldom uniform. The leeward side is usually free of ice. Also, for long insulators, no accretion usually occurs in areas of high electric stress, i.e. air gaps. These air gaps are caused by the melting or shedding of ice from some parts of the insulator. 3. Dry ice has high resistivity and does not reduce signi?cantly the electrical properties of insulators. However, owing to the effects of sunshine, a rise in air temperature, condensation, and/or the heating effect of leakage current, a water ?lm will form on the ice surface. This water ?lm has very high conductivity and may cause predictably large voltage drops across the air gaps. Therefore, the initial corona discharges and the consequent local arcs will develop at these sections of the insulator. 4. If the applied voltage is high enough, then the local arc will change to a white arc and extend along the ice surface. When the local arc reaches the critical length, it will result in complete ?ashover.

Figure 1. Flashover on ice-covered insulators

Copyright ? 2004 John Wiley & Sons, Ltd.

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Therefore, the ?ashover process is a local arc propagation process on an ice surface. It may be considered as local arcs in series with the residual ice layer.

TEST FACILITIES AND PROCEDURE In order to determine the minimum ?ashover voltage of the EHV insulators under icing conditions, a series of tests was carried out in one of the CIGELE climatic rooms. This room, 6 m w ? 6 m l ? 9 m h , is equipped with an HV SF6 composite bushing, as well as a sophisticated water-droplet generator for physical simulations of cold precipitations. The ammonia cooling system and computer-controlled regulators allow for rapid cooling to temperatures as low as 30 ? 0?2 ° C. The water-droplet generator is comprised of a system of six oscillating pneumatic nozzles located in front of a diffusing honeycomb panel. Behind the panel, a set of fans in a tapering box produces adjustable wind velocities. The speci?c design of the water-droplet generator can produce a very uniform ice deposit on the test object. Figure 2 shows the inside of the climatic room, featuring the water-droplet generator (1), the insulators under test (2) and the HV bushing (3). The HV system is composed of a 350 kV, 700 kVA transformer and its associated voltage regulator (Figure 3), specially designed for ?ashover tests on insulators under icing conditions. This system, with its two tap switches, has a minimum short-circuit current of 10 A at 130 kV, and maximums of 42 A at 240 kV and 32 A at 350 kV. Standard porcelain insulators, which are typically used in Hydro-Qu? ebec 735 kV substations, were tested in this study. Figure 4 shows one unit of the insulators tested and some of its characteristics. At CIGELE, two test procedures for evaluating the electrical performance of ice-covered insulators, i.e. an icing regime and a melting regime, were developed according to a systematic investigation program undertaken jointly by Hydro-Qu? ebec and UQAC since 1989. Under a careful control of test conditions, these two methods present similar results (Farzaneh et al., 2003b). Compared with the melting regime, the icing regime method is more time ef?cient and, therefore, is used in this study. This method is summarized as follows. This procedure includes two sequences, i.e. ice accretion and evaluation of the maximum ?ashover voltage (Figure 5). During the ice accretion sequence, water with a conductivity of 80 ?S cm 1 (at 20 ° C) was used to build up a uniform wet-grown ice layer on the entire length of the vertically installed insulators, energized at 80 kVrms m 1 . Once the desired 15 mm ice thickness, measured on the rotating monitoring cylinder, was reached, the water spraying system and the voltage applied to the insulator were turned off. This ice thickness

3

1

2

Figure 2. Interior of the UQAC climate room used in this study (see text for description)

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Figure 3. UQAC 350 kV alternating HV system

Height 1540 mm Arc distance 1390 mm Leakage path 3500 mm Higher part Interior diam. 154 mm Exterior diam. 246 mm Middle part Interior diam. 168 mm Exterior diam. 262 mm Skirts Number Spacing 26 50 mm

Figure 4. 735 kV porcelain station post insulator with normal glaze and standard shed pro?le

was chosen based on the fact that the ice at 15 mm thick will completely bridge the space between the insulator sheds and lead to ?ashover voltage saturation. The details of test conditions for the ice accretion period are summarized and listed in Table I. Then, the icing process is stopped and the insulator is photographed. This period ?t0 takes less than 2 min to ensure the existence of a water ?lm on the ice surface. Then, the voltage is immediately applied to the insulators and raised from zero to an estimated test value VE , corresponding to the start-up of the evaluation sequence, at a rate of 3?9 kV s 1 . Using a method based on and developed from that used for pollution tests, as described in the international standard IEC60507 (International Electrotechnical Commission, 1991), the maximum withstand voltage VWS was determined as the maximum level of applied voltage at which ?ashover did not occur for a minimum of three tests out of four, under similar experimental conditions. For each withstand test, the insulators were kept at the test voltage for a period of at least 15 min to ensure that no ?ashover occurred during this period. The minimum ?ashover voltage VMF corresponds to a voltage level ?5% higher than VWS at which two ?ashovers out of a maximum of four tests was produced.
Copyright ? 2004 John Wiley & Sons, Ltd. Hydrol. Process. 18, 3471– 3480 (2004)

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Figure 5. Sequences of the icing regime test procedure

Table I. Test parameters for the ice accretion sequence Test parameters Air temperature (° C) Average water droplet size (?m) Freezing water conductivity at 20 ° C (?S cm 1 ) Precipitation intensity (mm h 1 ) Incidence angle (° ) Wind velocity (m s 1 ) Voltage gradient (kVrms m 1 ) Ice thickness on reference cylinder (mm) Ice amount on insulator per dry arcing distance (g cm 1 ) Parameters values 12 ? 0?2 80 80 34 ? 7 53 ? 5 3?3 80 15 60

EXPERIMENTAL RESULTS AND DISCUSSION Using these facilities and procedure, a series of tests was carried out. The minimum ?ashover voltage VMF was determined for different insulator lengths. In this study, ?ve insulator lengths, corresponding to dry arcing distances of 1?39, 2?02, 3?07, 3?51, and 4?17 m, were chosen. The last length corresponds to the full-scale insulators used in 735 kV power substations. The results are shown in Table II and Figure 6. It can be observed that VMF increases with the increase in insulator dry arcing distance. However, the ?ashover stress decreases as the insulator dry arcing distance increases, which suggests that the minimum ?ashover voltage shows a slightly nonlinear increase with the increase in insulator dry arcing distance. Under the test conditions, i.e. freezing water conductivity of 80 ?S cm 1 and ice layer thickness of 15 mm, the
Table II. Flashover performance of standard porcelain post insulator Dry arcing distance (m) 1?39 2?02 3?07 3?51 4?17 VMF (kVrms ) 120 150 216 266 304 VMF /m (kVrms m 1 ) 86?3 74?3 70?4 75?8 72?9

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350 300 250 VMF (kV) 200 150 100 50 0 VMF (kV) VMF/m (kV/m) VMF =68(L + 0.3)

350 300 250 200 150 100 50 0 VMF/m (kV/m)

0

1

2 3 4 Dry arcing distance, L (m)

5

Figure 6. Minimum ?ashover voltage and stress as a function of dry arcing distance

?ashover stress of the insulators tested is only about 70% of the service voltage stress (105 kVrms m 1 ) of 735 kV substations.

PREDICTION OF MINIMUM FLASHOVER VOLTAGE OF ICE-COVERED INSULATORS In-?eld or laboratory investigations for determining the minimum ?ashover voltage of ice-covered insulators are generally costly and time consuming. Therefore, the use of a mathematical model is one way of overcoming these constraints for estimating the critical ?ashover voltage of ice-covered insulators. As mentioned previously, one such model has been developed at CIGELE, but it needs to be improved for predicting the ?ashover voltage of large-scale, ice-covered insulators, i.e. longer than 1 m. In the ?ashover tests carried out in this study, it was observed that, in the case of long insulators, the electric arcs were usually established at both ends of the insulator, i.e. the HV and ground ends (Figure 7). This phenomenon will change the current distribution along the ice surface and, consequently, bring some modi?cation into the existing mathematical model (Chaarani, 2003). Therefore, in this case, the ?ashover can be modelled as the result of two local arcs, one at each electrodes, in series with a residual ice layer in the middle section of the insulator (Figure 8). The equation for this circuit model can be expressed as follows (Farzaneh et al., 1997): Vm D AxImn C Im R x 1 where x (cm) is the total length of the two arcs, Vm (V) and Im (A) are the peak values of applied voltage and leakage current, A and n are the arc constants, and R(x ) ( ) is the residual resistance of that part of the ice not bridged by the arc. For an insulator string covered with a semi-cylindrical ice layer and two local arcs, one at each end, R(x ) can be calculated as follows (Chaarani, 2003): Rx D 1 2
e

4L x C 2 ln D C 2d

D C 2d 4r

2

where e (?S) is the surface conductivity of the ice layer, L (cm) and D (cm) are the length and diameter of the insulator respectively, d (cm) is the thickness of the ice layer, and r (cm) is the arc root radius.
Copyright ? 2004 John Wiley & Sons, Ltd. Hydrol. Process. 18, 3471– 3480 (2004)

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Figure 7. Two arcs are established, one at each end of the ice-covered insulator

Arc

Arc

H.V

Residual-Resistance
Figure 8. Model of ?ashover on an ice surface with two arcs

Under AC conditions, in order to maintain an arc propagating on a dielectric surface, not only Equation (1), but also the arc reignition conditions, which can be expressed by Equation (3), must be satis?ed (Farzaneh et al., 1997): kx Vm D b 3 Im where k and b are reignition constants. This arc reignition condition represents the maximum length x that the arc can reach under the applied voltage Vm and the corresponding leakage current Im . In the existing mathematical model (Farzaneh et al., 1997; Zhang and Farzaneh, 2000), using a triangular ice sample, all the necessary parameters in Equations (1)–(3) have been determined as follows: A D 204?7 n D 0?5607 Im 0?875 D 0?0675 C 2?45 rD b D 0?5277
Copyright ? 2004 John Wiley & Sons, Ltd.

4 5 6 7 8
Hydrol. Process. 18, 3471– 3480 (2004)

e

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k D 1118

9

where (?S cm 1 ) is the freezing water conductivity at 20 ° C. The arc constants A and n, the arc root radius r , and the arc reignition constant b are independent of insulator dimensions, but the arc reignition k is affected by the insulator parameters such as diameter (Chaarani, 2003). Therefore, keeping the value of k as a constant will bring some error into the calculation results when applying this model to the insulators with different parameters. The relation between the value of k and the insulator diameter was determined experimentally in a previous study (Chaarani, 2003). Based on the experimental results of the present study, it was found that the value of k should be modi?ed to 1300 for the insulators tested. Thus, the mathematical model, i.e. Equations (1) and (3), can be used for predicting the ?ashover voltage of full-scale EHV insulators covered with ice. It should be noted that results calculated present the critical ?ashover voltage Vc of ice-covered insulators, whereas the experimental results give their minimum ?ashover voltage VMF . However, these two voltages are comparable, since the difference between them is less than 2% for ice-covered insulators under AC conditions (Farzaneh and Kiernicki, 1997). As an application, this improved model was validated by the experimental results obtained with the standard porcelain post insulators used in this study (Figure 4), with ?ve different lengths. The results are shown in Table III and Figure 9. From these results, it may be observed that there is good concordance, from the viewpoint of engineering application, between the experimental results and those calculated from the improved model. The maximum error is 6?7%. It is interesting to compare the results calculated from the present model with those suggested in a recent IEEE Task Force paper (Farzaneh et al., in press), in which the icing stress product (ISP) approach was used to estimate the ?ashover strength of post insulators, fully bridged with ice: Flashover strength under melting conditions kV m
1

D 396 ISP

0?19

10

where ISP is the product of ice amount (g cm 1 ) and the conductivity ?S cm 1 of melting water of the ice layer. In our case, the ice amount is 60 g cm 1 and the conductivity of water is 80 ?S cm 1 (at 20 ° C). Thus, the ?ashover strength from Equation (10) is 396 4800 0?19 D 79 kV m 1 , whereas the values from the present model are shown in Table III. It can be seen that there is an acceptable concordance between them. This model is helpful for understanding the ?ashover phenomenon on ice-covered insulators, and it is a powerful tool for design of outdoor insulators in cold climate regions. It may be used by power company researchers to estimate the ?ashover probability of insulators under icing conditions, and to establish some procedures, e.g. choosing a proper length of outdoor insulators, or de-icing, to ensure reliable operation.
Table III. Comparison of experimental results and those from the model for the standard porcelain post insulator Dry arcing distance (m) Vc kVrms 1?39 2?02 3?07 3?51 4?17 118 160?8 230 260 303?5 Model results Vc /m kVrms m 84?9 79?6 74?9 74?1 72?8 Experimental results VMF kVrms 120 150 216 266 304 VMF /m kVrms m 1 86?3 74?3 70?4 75?8 72?9 1?7 6?7 6?1 2?6 0?2 Difference between Vc and VMF (%) Difference between Vc /m and IEEE Task Force paper (%)

1

7?5 0?6 5?2 6?2 7?2

Copyright ? 2004 John Wiley & Sons, Ltd.

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Experimental results of Vc Experimental results of Vc/m 350 300 250

Calculted results of Vc Calculted results of Vc/m 120 100 80 Critical Flashover Strength (kV/m)

Critical Flashover Voltage (kV)

200 60 150 40 100 50 0 0 1 2 3 4 5 Insulator Length (m) 20 0

Figure 9. Experimental results and those calculated from the model

CONCLUSIONS An improved and validated mathematical model for predicting the ?ashover voltage of ice-covered insulators is presented. From the results obtained, the following conclusions may be drawn: 1. The electrical performance of standard 735 kV station post insulators with arcing distances up to 4?17 m for full scale was evaluated under severe icing conditions. The VMF increases with an increase in insulator dry arcing distance. The ?ashover stress decreases as the insulator dry arcing distance increases. This suggests that the VMF presents a slight nonlinear increase with the increase in insulator dry arcing distance. 2. For a freezing water conductivity of 80 ?S cm 1 and ice layer thickness of 15 mm, the minimum ?ashover stress of the 735 kV station insulators tested is about 30% lower than that of the service voltage stress of 105 kVrms m 1 . 3. There is good concordance between the ?ashover voltage calculated from the improved mathematical model and the experimental results. Also, the results calculated from the model agree with those suggested by the IEEE Task Force paper (Farzaneh et al., in press). 4. This model is useful for understanding the ?ashover phenomenon on ice-covered insulators, and it is a powerful tool for design of outdoor insulators in cold climate regions. It may be used by power company researchers to estimate the ?ashover possibility of insulators under icing conditions and to establish some procedures to ensure reliable power network operation.

ACKNOWLEDGEMENTS

This research was carried out within the framework of the NSERC/Hydro-Quebec/UQAC Industrial Chair on Atmospheric Icing of Power Network Equipment (CIGELE) and Canada Research Chair on Engineering of Power Network Atmospheric Icing (INGIVRE) at Universit? e du Qu? ebec a ` Chicoutimi. We would like to thank all the partners of CIGELE/INGIVRE for their ?nancial support.
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REFERENCES ? Chaarani R. 2003. Etude de l’in?uence des caract? eristiques des isolateurs sur leurs performances e ? lectriques dans des conditions de givrage . PhD thesis, University of Quebec in Chicoutimi. Cherney EA. 1980. Flashover performance of arti?cial contaminated and iced long rod transmission line insulators. IEEE Transactions on Power Apparatus and Systems (PAS) 99: 46–52. Chisholm WA, Tam YT, Erven CC, Melo TO, Ringler, Green MA, Nigol O, Kuf?e J, Boyer A, Pavasars IK, Macedo FX, Sabiston JK, Caputo RB. 1996. The cold fog test. IEEE Transactions on Power Delivery 11(4): 1874– 1880. CIGRE TF 330409. 1999. In?uence of ice and snow on the ?ashover performance of outdoor insulators—part I: effects of ice . Electra No. 187; 91–111. CIGRE TF 330409. 2000. In?uence of ice and snow on the ?ashover performance of outdoor insulators—part II: effects of snow . Electra No. 188; 55–69. Farzaneh M. 2000. Ice accretion on high-voltage conductors and insulators and related phenomena. Philosophical Transactions of the Royal Society 358(1776): 2971– 3005. Farzaneh M, Kiernicki J. 1995. Flashover problems caused by ice build-up on insulators. IEEE Electrical Insulation Magazine 11(4): 5–17. Farzaneh M, Kiernicki J. 1997. Flashover performance of ice-covered insulators. IEEE Canadian Journal of Electrical and Computer Engineering 22(3): 95–109. Farzaneh M, Kiernicki J, Drapeau JF. 1992. Ice accretion on energized line insulators. International Journal of Offshore and Polar Engineering 2(3): 228– 233. Farzaneh M, Zhang J, Chen X. 1997. Modeling of the AC arc discharge on ice surfaces. IEEE Transactions on Power Delivery 12(1): 325–388. Farzaneh M, Baker T, Bernstorf A, Brown K, Chisholm WA, de Tourreil C, Drapeau JF, Fikke S, George JM, Gnandt E, Grisham T, Gutman I, Hartings R, Kremer R, Powell G, Rolfseng L, Rozek T, Ruff DL, Shaffner D, Sklenicka V, Sundararajan R, Yu, J. 2003a. Insulator icing test methods and procedure. A position paper prepared by the IEEE Task Force on Insulator Icing Test Methods. IEEE Transactions on Power Delivery 18(4): 1503– 1515. Farzaneh M, Drapeau JF, Zhang J, Roy M, Farzaneh J. 2003b. Flashover performance of transmission class insulators under icing conditions. In Proceedings of the World Conference Exhibition on Insulators, Arresters, Bushings (INMR), Marbella, Spain; 306– 316. Farzaneh M (Chairman), Baker T, Bernstorf A, Burnham, JT, Carreira T, E. Cherney E, Chisholm WA, Christman R, Cole R, Cortinas J, de Tourreil C, Drapeau JF, Farzaneh-Dehkordi J, Fikke S, Gorur R, Grisham T, Gutman I, Kuffel J, Phillips A, Powell G, Rolfseng L, Roy M, Rozek T, Ruff DL, Schwalm A, Sklenicka V, Stewart G, Sundararajan R, Szeto M, Tay R, Zhang J. 2004. Selection of station insulators with respect to ice or snow—part I: technical context and environmental exposure. A position paper prepared by the IEEE TF on Icing Performance of Station Insulators. IEEE Transactions on Power Delivery in press. Fikke SM, Hanssen JE, Rolfseng I. 1992. Long range transported pollutants and conductivity of atmospheric ice on insulators. In IEEE/PES Summer Meeting, Seattle, WA, USA; 1–9. Forrest JS. 1969. The performance of HV insulators in polluted atmospheres. In IEEE Winter Meeting, New York; paper no. 69 CP7-PWR. Hydro-Qu? ebec. 1988. Analysis of the Hydro-Qu? ebec system blackout on April 1988 . Of?cial Hydro-Qu? ebec Report, Montreal. International Electrotechnical Commission. 1991. Arti?cial pollution tests on high-voltage insulators to be used on A.C. systems . International Standard 60507. Matsuda H, Komoro HK, Takasu K. 1991. Withstand voltage characteristics of insulator strings covered with snow or ice. IEEE Transactions on Power Delivery 6: 1243– 1250. Phan CL, Pirotte P, Trinh NG. 1974. A study of corona discharges at water drops over the freezing temperature range. IEEE Transactions on Power Apparatus and Systems (PAS) 93(2): 724–734. Su F, Hu S. 1998. Icing on overhead transmission lines in cold mountainous districts of southwest China and its protection. In Proceedings of 4th International Workshop on the Atmospheric Icing of Structures, Paris, France; 354– 357. Zhang J, Farzaneh M. 2000. Propagation of AC and DC arcs on ice surfaces. IEEE Transactions on Dielectrics and Electrical Insulation 7(2): 269– 276.

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Hydrol. Process. 18, 3471– 3480 (2004)


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