New mathematical formulations for calculating residual resistance in a static arc model of ice-covered insulators

Cold Regions Science and Technology 117 (2015) 34–42

Contents lists available at ScienceDirect

Cold Regions Science and Technology journal homepage: www.elsevier.com/locate/coldregions

New mathematical formulations for calculating residual resistance in a static arc model of ice-covered insulators Babak Porkar ⁎,1, Masoud Farzaneh 1 NSERC/Hydro-Quebec/UQAC Industrial Chair on Atmospheric Icing of Power Network Equipment (CIGELE) Chicoutimi, QC, Canada Canada Research Chair on Engineering of Power Network Atmospheric Icing (INGIVRE), Chicoutimi, QC, Canada Université du Québec à Chicoutimi (UQAC), Chicoutimi, QC, Canada

a r t i c l e

i n f o

Article history: Received 25 November 2014 Received in revised form 2 May 2015 Accepted 31 May 2015 Available online 5 June 2015 Keywords: Calculating residual resistance Static arc model Ice-covered insulators

a b s t r a c t This paper develops two new mathematical formulations for calculation of the residual resistance in a static arc model to predict ac and dc flashover voltages of heavy ice-covered insulators. In the first formulation, appropriate for dc with a small insulator string, the residual resistance is considered as a resistance between a small circular conductor where it models the arc root and the ground electrode. It is shown that using this new formula for a static dc arc model with heavy ice-covered insulators leads to an improved model to predict flashover voltage. In the second formulation, appropriate for ac and dc with long insulator strings, the residual resistance is considered as a resistance between two small circular conductors modeling two arc roots where the arcs are on air gaps formed near the high voltage and ground electrodes. The method of image charges is used in both formulations. The capability of this improved static arc model is confirmed when it is compared to that of previous static and dynamic models. This improved arc model has a better correspondence with the experimental results than the previous static and dynamic models. It can be used as a powerful tool for the design and selection of insulators subjected to ice accretion. © 2015 Elsevier B.V. All rights reserved.

1. Introduction In many cold climate regions, a most important challenge is the decrease in outdoor electrical insulation strength of power network insulators under ice and snow conditions. This can sometimes lead to flashover and consequent power outages which have been reported in North America (Charneski et al., 1982; Cherney, 1980; Farzaneh and Kiernicki, 1995; Kawai, 1970; Schneider, 1975) as well as in many cold climate countries of Europe (Fikke et al., 1993, 1994; Meier and Niggli, 1968) and Asia (Fujimura et al., 1979; Matsuda et al., 1991). A detailed industry survey (Yoshida and Naito, 2005) reported that 35 utilities in 18 countries had ice- and snow-related electrical flashover problems. In particular, a total of 83 such events (69 on lines, and 14 in stations) occurred on transmission lines from 400- to 735-kV in relatively clean conditions. From January 2006 to June 2007 only, icecovered insulators flashovers in China caused failures of 500-kV lines four times (Su et al., 2012). A recent power outage lasting for a long period of time happened in thirteen provinces of southern China early in 2008 where more than 30,000 transmission lines and 8000 towers were damaged, with a direct economic loss of nearly 10 billion RMB ⁎ Corresponding author at: NSERC/Hydro-Quebec/UQAC Industrial Chair on Atmospheric Icing of Power Network Equipment (CIGELE), Chicoutimi, QC, Canada. E-mail address: [email protected] (B. Porkar). 1 www.cigele.ca.

http://dx.doi.org/10.1016/j.coldregions.2015.05.007 0165-232X/© 2015 Elsevier B.V. All rights reserved.

(1.6 billion dollars) (Deng et al., 2012; Su et al., 2012). Furthermore, it should be noticed that there were 61 trippings caused by flashover of iced insulators in China in 2012 while the flashovers trippings caused by pollution happened only 11 times (Guan et al., 2014). Therefore, a great deal of research including field and laboratory tests in controlled conditions and the development of mathematical models has been carried out to understand the flashover process on ice and snow-covered insulators (Farzaneh, 2014). To the best of our knowledge, Farzaneh and Zhang (2000), Farzaneh et al. (1997), and Zhang and Farzaneh (2000) provided the first attempts to model AC and DC arc discharge on an ice surface in order to calculate the flashover voltage of heavy ice-covered insulators where ice accretion, t, on a reference rotating cylinder is t N 10 mm (Farzaneh and Chisholm, 2009). Based on a number of tests carried out on ice-covered insulators during the flashover process it was observed that several violet arcs first appeared across the air gaps followed by the extension of one of the arcs along the ice surface forming a white arc. When the white arc reached a certain length, a flashover occurred suddenly. Therefore, the electrical flashover process on an ice surface can be described adequately by adapting the Obenaus approach (Obenaus, 1958) for the polluted insulators as described in Farzaneh and Zhang (2000), Farzaneh et al. (1997), and Zhang and Farzaneh (2000), including the arc discharge on an air gap in series with an ice layer. Direct laboratory measurements of arc constants, surface conductance, and reignition conditions in Farzaneh and Zhang (2000),

B. Porkar, M. Farzaneh / Cold Regions Science and Technology 117 (2015) 34–42

Farzaneh et al. (1997), and Zhang and Farzaneh (2000) lead to values that differed systematically from those found for flashovers on polluted surfaces. In Farzaneh et al. (2004) and Shu et al. (2012), static arc models were adapted to take into account the influence of air pressure on ac and dc flashover voltage of ice-covered insulator strings. Moreover, static arc models were elaborated in order to model ac and dc flashovers on long-rod ice-covered composite insulators taking into account the influence of different shed configurations and low atmospheric pressure in Hu et al. (2007, 2011, 2012), Jiang et al. (2011), and Shu et al. (2014). The above mentioned static models, as well as the dynamic models (Farzaneh et al., 2003b; Taheri et al., 2014; Tavakoli, 2004) and the finite element method (FEM) based models (Volat et al., 2011; Yang et al., 2007) were developed, providing powerful tools to predict AC and DC flashover voltage, thus minimizing time consuming experimental laboratory tests (Farzaneh et al., 2003a; IEEE std., 1783, 2009) and the use of equipment. Although dynamic models can predict the whole temporal evolution of the flashover process, the parameters of a modeled equivalent electrical circuit need to be calculated. Some parameters of the model, particularly the capacitance between the arc tip and the opposite electrode, C, as well as the arc channel inductance, L, may be influenced in service conditions by the presence of corona rings, arcing horns, phase conductors, towers and other metallic structures. So, more complex closed-form formulas or numerical calculations are needed to take those into account. Moreover, the value of the heat dissipation rate, P0, used in Mayr's equation (Mayr, 1943) to calculate the arc channel resistance should be adjusted for different geometries and different freezing water conductivities in order to obtain good agreement between the simulation and the laboratory test results (Taheri et al., 2014; Tavakoli, 2004). FEM models need commercial FEM software, like COMSOL Multiphysics®, to compute the electric field and the leakage current (Volat et al., 2011; Yang et al., 2007). The equation used for calculating the residual resistance both for the static (Farzaneh and Zhang, 2000, 2007; Farzaneh et al., 1997; Zhang and Farzaneh, 2000) and dynamic models (Farzaneh et al., 2003b; Taheri et al., 2014; Tavakoli, 2004) is based on the formula developed by Wilkins (1969) for a flat model of polluted insulators. In this paper, two new equations are formulated for the residual resistance. As compared to the present static and dynamics models, the improved static model developed in the present paper, where these new equations are used instead of Wilkins's equation, provides a better fit with laboratory test results. 2. Static model description The mathematical model for analyzing the flashover on ice-covered insulating surfaces (Fig. 1) is given by: V ¼ AxI−n þ V e þ IRp ðxÞ

ð1Þ

where V(V) and I (A) are the applied voltage and leakage current (in AC case there are peak values), A and n are the arc constants, x (cm) is the

35

length of the arc, Ve is the electrodevoltage drop, and Rp(x) (Ω) is the residual resistance of ice section not bridged by the arc. Under AC conditions, in order to maintain an arc burning on a dielectric surface, another equation with regards to arc reignition condition must also be satisfied: V¼

kx

ð2Þ

Ib

where k and b are reignition constants. Experimental investigations at CIGELE established the parameters of Eqs. (1) and (2) as those presented in Table 1 (Farzaneh and Zhang, 2000, 2007; Farzaneh et al., 1997; Farzaneh-Dehkordi et al., 2004; Zhang and Farzaneh, 2000). Since the ice layer only covers the windward side of insulator string, as reported in (Drapeau and Faraneh, 1993), the ice deposit was considered as a half cylinder with rectangular surface of length L(cm)and width W(cm) given by: W¼

πðD þ 2εÞ 2

ð3Þ

where D is the insulator diameter and ε is the thickness of the ice layer. Then, the residual resistance Rp(x) can be calculated from the following equation for a narrow ice layer (W ≪ L) as developed first in Wilkins (1969): Rp ðxÞ ¼


 106 π ðL−xÞ W þ ln ðΩÞ W 2πr πγe

ð4Þ

where r is the radius of the arc root on an ice surface (cm) and γe (μ S) is the equivalent surface conductivity. The relation between the arc channel radius and leakage current can be expressed by Wilkins (1969) rffiffiffiffiffiffi I r¼ πB

ð5Þ

where the values of B for both inner and outer AC and DC arcs were estimated experimentally (Farzaneh and Zhang, 2000; Zhang and Farzaneh, 2000) as presented in Table 2. As well, γe may be calculated as a function of conductivity of the water (σ(μ S/cm)) at 20 °C used to form the ice (Farzaneh and Zhang, 2000; Farzaneh et al., 1997; Zhang and Farzaneh, 2000): γe ¼ 0:0675σ þ 2:45 f or AC arc

ð6Þ

γe ¼ 0:0599σ þ 2:59 f or DC− arc

ð7Þ

γe ¼ 0:082σ þ 1:79 f or DC þ arc:

ð8Þ

Using Eqs. (1)–(8) the critical flashover voltage can be calculated by a trial and error numerical method used in Farzaneh and Zhang (2000), Farzaneh et al. (1997), and Zhang and Farzaneh (2000) or by the following theoretical formulae developed by Wilkins in Wilkins (1969): Vc ¼ A

1=ðnþ1Þ

rp

n=ðnþ1Þ

W BW 2 ln Lþ 2π 4πic

! þ Ve

ð9Þ

f or a narrow layer

Table 1 Arc discharge parameters on an ice surface.

Fig. 1. Physical model of an arc on an ice surface.

Arc type

A

n

k

b

AC (60 Hz)

204.7

0.5607

0.5277

DC− DC+

84.6 208.9

0.772 0.449

1118 (for the arc propagation upward) 1300 (for the arc propagation downward) – –

– –

Ve 0

526 799

36

B. Porkar, M. Farzaneh / Cold Regions Science and Technology 117 (2015) 34–42

Table 2 The values of B. Arc type

B

AC

Inner Outer Inner Outer Inner Outer

DC− DC+

Vc ¼

106  ic 4L2 B L −n ln þ Aic þ Ve πic 2 2πγ e

2.439 0.875 1.759 0.624 1.643 0.648

ð10Þ

f or a wide layer

where rp and ic are resistance per unit length (Ω/cm) and critical current, respectively, given by rp ¼

106 ð11Þ γe W

ð11Þ

 1=ðnþ1Þ ic ¼ A=r p f or a narrow layer

ð12aÞ

ic ¼ ðAγ e LÞ1=ðnþ1Þ f or a wide layer:

ð12bÞ

Eqs. (9) and (10) are for a narrow layer (W ≪ L) and a wide layer (W N 3L), respectively. The model in Zhang and Farzaneh (2000) was applied to a string of 5 units of IEEE standard insulators with ε = 2 cm and the critical flashover was calculated and validated by experimental results. The geometry and electrical characteristics of the insulator are presented in Table 3. Fig. 2 shows the simulation results. From these simulations, it can be seen that: • The calculation results from the trial and error numerical method have the same values as those obtained from Eq. (9). • The experimental results are closer to the calculation results for a wide ice layer (Eq. (10)) by using Eq. (12a) than those for a narrow ice layer (Eq. (9)). In Zhang and Farzaneh (2000) a wide ice layer formula (Eq. (10)), with Eq. (12a) instead of Eq. (12b), was used for Rp(x) which was in good agreement with the laboratory tests. Residual resistance Rp(x) for a wide ice layer (W N 3L) is given by Wilkins (1969) 
 πx  106 2L − ln tan RðxÞ ¼ ln ðΩÞ: πr 2L πγ e

ð13Þ

Fig. 2. Calculated and experimental results of AC flashover voltage with 5 units of IEEE standard insulators.

temperature values. He assumed that f = 1.8 with a mean value of the results for a narrow and wide layer to obtain good agreement between the simulation model results and the laboratory results for a 10 × 10 cm flat polluted strip. However, it can be seen from Fig. 2 that this conductivity factor of 1.8 leads to more errors for icecovered insulator cases. Fig. 3 shows the simulation results reported in Farzaneh and Zhang (2000) for DC arc flashover voltages for 5 units IEEE standard insulators with ε = 1.5 cm. From these simulations, it can be seen that: • In Farzaneh and Zhang (2000), to be in agreement with the experimental results, a coefficient k = 1.3 was introduced in Eq. (1) to take in account the fact that the actual arc length in air is longer than the insulator arcing distance, as follows: V ¼ AkxI−n þ V e þ IRp ðxÞ:

ð14Þ

However, it should be noted that this coefficient was not considered for AC arc flashover voltages in Farzaneh et al. (1997) and Zhang and Farzaneh (2000). In addition, there was only one experimental result for each polarity, at σ = 80 μS/cm.

However, since here L = 80.9 cm and W = 46.18 cm, the wide ice layer assumption (W N 3L) was not respected in Zhang and Farzaneh (2000). • To obtain correspondence with the experimental results, Wilkins (Wilkins, 1969) introduced a conductivity factor, f justifying this by the fact that the surface conductivities plotted as abscissas are measured before the test using a low voltage, thus corresponding to room temperature conductivities. However, when the test voltage is applied, the pollution film heats up, and reaches boiling point in the regions where the dry bands form. Hence, the conductivity of the film when the discharge appears is much higher than room

Table 3 Geometry and electrical characteristics of the insulator. Diameter of shed, D, (mm)

Shed spacing (mm)

Leakage distance (mm/unit)

Arcing distance for 5 units, L, (mm)

254

146

308

809 Fig. 3. Calculated and experimental results of DC flashover voltage with 5 units of IEEE standard insulators.

B. Porkar, M. Farzaneh / Cold Regions Science and Technology 117 (2015) 34–42

Therefore, it is not clear whether k = 1.3 can be used for other values of σ and for other types and dimension of insulators with various ice deposits. Further research is needed to address these issues, both mathematically and experimentally. • Fig. 3 shows calculation results for k = 1.3 and k = 1.0, taking into account a narrow ice layer formula (Eq. (9) while using Eq. (12a)) for Rp(x) as in Farzaneh and Zhang (2000). However, it can be seen that the curve for k = 1.0 is well below that for k = 1.3 and that the errors, when compared to the experimental results, are important.

The potentials of the two conductors are given by V2 ¼

ρl a ln d 2πϵ0

V1 ¼ −

ð16Þ

ρl a ln : d 2πϵ0

ð17Þ

The capacitance per unit length is given by C¼

3. Model description The residual resistance Rp(x) in Farzaneh and Zhang (2000) and then in Farzaneh and Zhang (2007) was calculated based on the formula developed by Wilkins (1969) by assuming a flat model and using Laplacian fields for two cases: 1) narrow strip, when W ≪ L and 2) wide strip, where W N 3L. In this section two new formulations for Rp(x) are developed. The electric field level can influence the distribution of ice along a line insulator string or a post type insulator. It was found in Farzaneh and Chisholm (2009) and Phan and Matsuo (1983) that an air gap was formed between the lowest insulator unit and the HV terminal for a suspension insulator string and at the top of the insulator near the HV terminal for a post type insulator. Because the arc channel radius is much smaller than the dimension of the ground electrode, Rp(x) between the arc root and the ground electrode may be considered as a resistance between a small circular conductor located at a distance D/2 from a large plane conductor which is at zero potential, as shown in Fig. 4. The ground plane conductor can be removed and replaced by an image circular conductor using the method of image charges, as shown in Fig. 4. The equipotential surfaces of the two circular cylinder conductors of radius a can be considered to have been generated by a pair of line charges, ρl, and, −ρl, separated by a distance of (D–2di) = d–di by using the method of image charges, where di is given by Cheng (1983) as

37

ρl πϵ ¼ ln ðd=aÞ V 1 −V 2

ð18Þ

where d ¼ D−di ¼ D−

a2 d

ð19Þ

which yields to d¼

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1 D þ D2 −4a2 : 2

ð20Þ

Substituting Eq. (20) in Eq. (18), we obtain C¼

πϵ πϵ0  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ −1 2 csch ðD=2aÞ ln ðD=2aÞ þ ðD=2aÞ −1

ð F=mÞ

ð21Þ

The resistance between two the conductors can be obtained by
  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ϵ 1 106 ¼ ln ðD=2aÞ þ ðD=2aÞ2 −1 γe C πγe 106 −1 ¼ csch ðD=2aÞ ðΩÞ: πγe

Rp ¼

ð22Þ

For a = r and D = 2(L − x), Rp(x) can be obtained by  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 106 ln ðL−xÞ=r þ ððL−xÞ=r Þ2 −1 πγe 106 −1 ¼ csch ððL−xÞ=r Þ ðΩÞ: πγe

Rp ðxÞ ¼ di ¼

a2 : d

ð15Þ

Fig. 4. The proposed model to calculate RP(x).

ð23Þ

38

B. Porkar, M. Farzaneh / Cold Regions Science and Technology 117 (2015) 34–42

Formula (23) is the first formulation mentioned in the abstract for calculating the residual resistance which is appropriate under dc voltage with small insulator strings. During an arc propagation process along an ice-covered insulator besides an air gap near the HV terminal, another air gap may be formed close to the ground electrode mainly due to the heating effects of increased leakage current density near the ground electrode. This particularly occurs when the time lag to flashover increases, for example for long insulators used in UHV and EHV applications or in AC condition where the arc is weakened due to its cyclical extinction and reignition. In these conditions, the residual resistance, Rp(x), can be expressed between two arc roots near the HV and ground electrodes where D = L − x and thus Rp(x) is given by  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 106 ln ðL−xÞ=2r þ ððL−xÞ=2r Þ2 −1 πγe 106 −1 csch ððL−xÞ=2r Þ ðΩÞ: ¼ πγe

Rp ðxÞ ¼

ð24Þ

Formula (24) is the second formulation mentioned in the abstract for calculating the residual resistance which is appropriate under dc voltage with long insulator strings as well as under ac voltage. 4. Simulation results In this section the simulation results of Eqs. (23) and (24), labeled “New Model”, are compared with those labeled “Previous Model”. In Fig. 5 which is for dc flashover voltage with 5 units of IEEE standard insulators, “New Model” refers to (23) whereas for Figs. 6–9 which stand for ac flashover voltage, “New Model” refers to (24). “Previous Model” refers to Eq. (4) used in Farzaneh and Zhang (2000), Farzaneh et al. (1997), and Zhang and Farzaneh (2000) for calculating the residual resistance Rp(x). Fig. 5 shows the simulation results with the same conditions as those of Fig. 3, considering k = 1.0 for DC −. It can be observed that the simulation result with “New Model” is closer to the experimental result than those obtained with the “Previous Model”, as presented in Table 4. Fig. 6 and Table 5 show the simulation results of AC flashover voltage with the same conditions as those for Fig. 2. It can be seen that the “New Model” results are in better agreement with the experimental results than those of the “Previous Model”. From Table 5 it can been seen that the RMS error decreases from 27.01% for “Previous Model” to 15.78%

Fig. 5. Calculated results of DC-flashover voltage with 5 units of IEEE standard insulators obtained from “New Model” and “Previous Model”.

Fig. 6. Calculated results of AC flashover voltage with 5 units of IEEE standard insulators obtained from “New Model” and “Previous Model”.

for “New Model”, an improvement of 42% in prediction of the critical flashover voltage. For further evaluation of the proposed equations for calculating Rp(x), the simulation results are compared with the other experimental results carried out at CIGELE. Fig. 7 shows the experimental test results from Farzaneh and Kiernicki (1997) with ε = 2 cm for variation of the maximum withstand stress (kV/m), VWS/m, for IEEE standard insulators as a function of freezing water conductivity for AC condition. An empirical power curve, VWS/m = 165.3σ−0.18, was proposed in Farzaneh and Kiernicki (1997) to express the variation of the maximum withstand stress. As seen in Fig. 7 and Table 6, the simulation results from “New Model” are in better agreement with the experimental test results than those of the “Previous Model”. From Table 6 it can been seen that the RMS error decreases from 31.02% for the “Previous Model” to 22.04% for the “New Model”, an improvement of 30% in prediction of the critical flashover voltage. Fig. 8 shows another evaluation of the model in comparison to test results on a post type insulator reported in Farzaneh and Drapeau (1995). In that paper, an empirical power curve, VWS = 80.8σ− 0.092, was proposed to approximate the maximum withstand voltage, VWS, as a function of σ which is valid up to a value of 80 μS/cm. Table 7

Fig. 7. Calculated results of AC flashover stress with IEEE standard insulators obtained from “New Model” and “Previous Model” and experimental results in Farzaneh and Kiernicki (1997).

B. Porkar, M. Farzaneh / Cold Regions Science and Technology 117 (2015) 34–42

39

Table 4 Experimental and calculated results for DC−. Model type for Rp(x)

New model Previous model

V50% flashover voltage (kV) From model

Test results

53.87 52.00

60 60

Error (%) −10.22 −13.34

Table 5 Experimental and calculated results for AC.

Fig. 8. Calculated results of AC flashover voltages with a post-type insulator obtained from the “New Model” and “Previous Model”, and experimental results in Farzaneh and Drapeau (1995).

shows the rms of the error between the “New Model”, “Previous Model” and test results. From Table 7 it can been seen that the RMS error decreases from 36.73% for the “Previous Model” to 19.39% for the “New Model”, an improvement of 47% in predicting the critical flashover voltage. The mentioned difficulty was dealt with in Farzaneh et al. (2003b), Taheri et al. (2014), and Tavakoli (2004) through the creation of artificial air gaps after ice deposition without voltage application. Although there is good agreement between the laboratory tests and the simulation results obtained from the developed models in Farzaneh et al. (2003b), Taheri et al. (2014), and Tavakoli (2004), these models may fail to predict accurately the flashover voltage, particularly for high values of freezing water conductivity at service voltage for the whole icing period, as recommended in Farzaneh et al. (2003a) and IEEE std. (1783, 2009). In Fig. 9 and Table 8, the performance in calculating Rp(x) is compared between the equations developed in this paper as a static model and the dynamic model developed in Tavakoli (2004) where a 40-cm post insulator was tested under uniform wet-grown ice. It can be seen that the improved static model developed in this paper works

Model type for Rp(x)

Error (%) (RMS)

New model Previous model

15.78 27.01

much better for predicting flashover voltage than the dynamic model. From Table 8 it can been seen that the RMS error decreases from 25.18% for dynamic model to 9.30% for “New Model”, a significant improvement of 63% in predicting the critical flashover voltage.

5. Experimental investigations To validate the proposed model, the experimental investigations carried out at CIGELE for the present study are presented in this section.

5.1. Test facilities and experimental arrangement Glaze ice (wet-grown ice), known as the most dangerous type of ice, and associated to the highest probability of flashover on energized insulators (Farzaneh, 2014; Farzaneh and Drapeau, 1995; Farzaneh and Kiernicki, 1995; IEEE std., 1783, 2009), was used for the present study. This type of ice formed from supercooled droplets having a mean diameter of 80 μm was deposited artificially on an insulator string placed in a uniquely designed 4.8 m(w) × 2.8 m(1) × 3.5 m(h) cold room at an ambient temperature of −12 °C at the CIGELE laboratories using a pneumatic spray nozzle system at a average wind velocity of 3.3 m/s. Air pressure in the chamber is normalized to ambient by mechanical flaps, but with no pressure difference. Four units of porcelain IEEE standard insulators with a dimension of 254 mm (unit diameter) × 146 mm (unit spacing)–305 mm (leakage distance) formed the string. This number of units corresponds with what is being used in 69 kV Hydro-Quebec transmission lines (Farzaneh and Kiernicki, 1997). The tests were carried out for two different freezing water conductivities of 60 and 100 μS/cm adjusted by adding sodium chloride (NaCl) to deionized water feeding the nozzles, which was verified before and after each test. Table 6 Experimental and calculated results for AC. Model type for Rp(x)

Error (%) (RMS)

New model Previous model

22.04 31.02

Table 7 Experimental and calculated results for AC condition.

Fig. 9. Calculated results of AC flashover voltages obtained from “New Model”, dynamic model and experimental results in Tavakoli (2004).

Model type for Rp(x)

Error (%) (RMS)

New model Previous model

19.39 36.73

40

B. Porkar, M. Farzaneh / Cold Regions Science and Technology 117 (2015) 34–42 Table 8 Experimental and calculated results for AC condition. Model type for Rp(x)

Error (%) (RMS)

New model Dynamic model

9.30 25.18

“Melting regime” test procedure as described in IEEE Std. 1783 (IEEE std., 1783, 2009) that is more representative of natural conditions was applied to evaluate icing performance of the insulator strings. In this test procedure, the melting sequence was started immediately after complete hardening of the ice. The “critical moment” in the melting phase was considered when water droplet ejection from icicles was initiated. At this point, the voltage was increased at a rate of 3% per second, based on service voltage, until the test voltage was achieved. The test voltage was maintained at a constant level until there was a flashover,

a 15 min withstand or a significant shedding of the ice deposit. Since similar results were obtained from “melting regime” and “icing regime” test procedures for laboratory tests reported in Farzaneh (2000) and following the general advice proposed in IEEE std. (1783, 2009), the tests based on the “icing regime” procedure were not carried out in the present study. The maximum withstand voltage method, VWS, was used to evaluate the icing performance of the insulator strings as described in Farzaneh and Kiernicki (1997), Farzaneh et al. (2003a), and IEEE std. (1783, 2009). The VWS is defined as the maximum voltage at which flashover does not occur in at least three tests out of four. The VMF corresponds to a voltage level 5% higher than the VWS at which two flashovers out of a maximum of three tests are produced. The high-voltage system consisted of a 300-kV, 600-kVA DC source with an associated voltage regulator. This system was specially designed for flashover tests on insulators under icing conditions.

(a)

(b)

(c)

(d) Fig. 10. Physical configuration of the insulator string.

B. Porkar, M. Farzaneh / Cold Regions Science and Technology 117 (2015) 34–42

A National Instruments digitizer card was used to sample the line voltage and leakage current. The leakage current was monitored across a 10-Ω high-power resistor in the ground return to the transformer. The current was sampled at a rate of 1200 samples per seconds, transferred to a data buffer and stored through LABVIEW application software. The signals were optically isolated for equipment protection using an Analog Devices 5B41 device. The voltage and current signals and computer were enclosed in a Faraday cage, powered by an isolation transformer. Real-time display of the line voltage, the leakage current, the averaged leakage current over ten cycles as well as the Lissajous figure of the line voltage (horizontal axis) versus line current (vertical axis) were monitored, along with the readouts of the line voltage and leakage current parameters. The leakage current values for the Labview monitoring system were compared with reference rms values measured using a Keithley 51/2 digit volt/ammeter. The values agreed within 1% for a wide range of sine and pulse signals, generated using a bipolar Avtech instrument. Arc propagation was observed by a high-speed video camera (FASTCAM SA1, Photron Inc.) with recording capacity up to 675,000 frames per second. 5.2. Experimental results Fig. 10(a)–(d) shows the physical configuration considered for the tests, as seen from different directions. In order to produce a uniform accumulation of ice on the insulator units according to the spray system position in the climate room, seven insulator units were considered for the string placed in vertical position. However, after the ice accretion period and hardening sequence in the “melting regime”, an air gap was artificially created to separate the four units of IEEE standard insulators from other units, as shown in Fig. 10. This eliminated possible effects of the upper three units of insulators on the icing performance of the tested sting. It can be seen from Fig. 10 that the ice layer only covers the windward side of the insulator string as reported in Drapeau, and Faraneh (1993) and Farzaneh and Chisholm (2009). Service voltage was applied to the test insulator string during the whole icing period as recommended in Farzaneh et al. (2003a) and IEEE std. (1783, 2009). It was considered to be 41.8 kV for DC and the RMS value for AC according to the typical maximum phase-ground voltage in 69-kV Hydro-Quebec transmission lines where the typical maximum service voltage is 72.5 kV (Farzaneh and Kiernicki, 1997). Fig. 11 shows the simulation results obtained from the “New Model” (Eq. (23)) and the “Previous Model” (Eq. (4)) in comparison to the test

Fig. 11. Calculated results of DC-flashover voltage obtained from “New Model” and “Previous Model”.

41

results carried out in the present study for DC−. It can be seen that the “New Model” can predict the critical flashover voltage more accurately than the “Previous Model”. There is an improvement of 23% in predicting the critical flashover voltage by the “New Model” instead of the “Previous Model”. As shown in the paper the simulation results from new formulations for calculating the residual resistance are in better agreement with the experimental results than those of the “Previous Model” as well the Dynamic Model. However, further research is needed to implement new formulations in multiple arc models. 6. Conclusion In this paper, two new equations were formulated to calculate the residual resistance of ice-covered insulators. The equation for DC with small insulator strings considers a small circular conductor and a large plane electrode. The other equation for AC or DC with long insulators considers two small circular conductors modeling two arc roots on an ice surface where the two arcs occur near the high voltage and ground electrodes, respectively. The method of image charges was used to obtain the new equations for the residual resistances. The simulation results from the improved model were compared with those of the present static model and a dynamic model and it was shown that the improved model is in better agreement with the experimental results. Acknowledgment This work was carried out within the framework of the NSERC/ Hydro-Quebec/UQAC Industrial Chair on Atmospheric Icing of Power Network Equipment (CIGELE) and the Canada Research Chair on Engineering of Power Network Atmospheric Icing (INGIVRE) at Université du Québec à Chicoutimi. The authors would like to thank the CIGELE partners (Hydro-Québec, Hydro One, Réseau de Transport d'Électricité (RTE), General Cable, K-Line Insulators, Dual-ADE, and FUQAC) whose financial support made this research possible. References Charneski, M.D., Gaibrois, G.L., Whitney, B.F., 1982. Flashover tests of artificially iced insulators. IEEE Trans. Power Appar. Syst. 101 (8), 2429–2433. Cheng, D.K., 1983. Field and Wave Electromagnetic. Addison-Wesley Publishing Co. Cherney, E.A., 1980. Flashover performance of artificially contaminated and iced long-rod transmission line insulators. IEEE Trans. Power Appar. Syst. 99 (1), 46–52. Deng, Y., Jia, Z., Wei, X., Su, H., Guan, Z., 2012. Mechanism of salt mitigation in icicles during phase transition and its impact on ice flashover. IEEE Trans. Dielectr. Electr. Insul. 19 (5), 1700–1707. Drapeau, J.F., Faraneh, M., 1993. Ice accumulation characteristics on Hydro-Quebec HV insulators. The 6th International Workshop on Atmospheric Icing of Structures, Hungary, pp. 225–230. Farzaneh, M., 2000. Ice accretion on high-voltage conductors and insulators and related phenomena. Phil. Trans. R. Soc. 358 (1776), 2971–3005. Farzaneh, M., 2014. Insulator flashover under icing condition. IEEE Trans. Dielectr. Electr. Insul. 21 (5), 1997–2011. Farzaneh, M., Chisholm, W.A., 2009. Insulators for Icing and Polluted Environments. IEEE Press Series on Power Engineering. IEEE/John Wiley, New York. Farzaneh, M., Drapeau, J.F., 1995. AC flashover performance of insulators covered with artificial ice. IEEE Trans. Power Deliv. 10 (2), 1038–1051. Farzaneh, M., Kiernicki, J., 1995. Flashover problems caused by ice build-up on insulators. IEEE Electr. Insul. Mag. 11 (2), 5–17. Farzaneh, M., Kiernicki, J., 1997. Flashover performance of IEEE standard insulators under ice conditions. IEEE Trans. Power Deliv. 12 (4), 1602–1613. Farzaneh, M., Zhang, J., 2000. Modeling of dc arc discharge on ice surfaces. IEE Proc. Gener. Transm. Distrib. 147 (2), 81–86. Farzaneh, M., Zhang, J., 2007. A multi-arc model for predicting ac critical flashover voltage of ice-covered insulators. IEEE Trans. Dielectr. Electr. Insul. 14 (6), 1401–1409. Farzaneh, M., Zhang, J., Chen, X., 1997. Modeling of the ac arc discharge on ice surfaces. IEEE Trans. Power Deliv. 12 (1), 325–338. Farzaneh, M., Baker, T., Bernstorf, A., Brown, K., Chisholm, W.A., Tourreil, C., Drapeau, J.F., Fikke, S., George, J.M., Gnandt, E., Grisham, T., Gutman, I., Hartings, R., Kremer, R., Powell, G., Rolfseng, L., Rozek, T., Ruff, D.L., Shaffner, D., Sklenicka, V., Sundararajan, R., Yu, J., 2003a. Insulator icing test methods and procedures, a position paper prepared by the IEEE task force on insulator icing test methods. IEEE Trans. Power Deliv. 18 (3), 1503–1515. Farzaneh, M., Fofana, I., Tavakoli, C., Chen, X., 2003b. Dynamic modeling of dc arc discharge on ice surfaces. IEEE Trans. Dielectr. Electr. Insul. 10 (3), 463–474.

42

B. Porkar, M. Farzaneh / Cold Regions Science and Technology 117 (2015) 34–42

Farzaneh, M., Li, Y., Zhang, J., 2004. Electrical performance of ice-covered insulators at high altitudes. IEEE Trans. Dielectr. Electr. Insul. 11 (5), 870–880. Farzaneh-Dehkordi, J., Zhang, J., Farzaneh, M., 2004. Experimental study and mathematical modeling of flashover on extra-high voltage insulators covered with ice. Hydrol. Process. 18, 3471–3480. Fikke, S.M., Hanssen, J.E., Rolfseng, L., 1993. Long range transported pollutants and conductivity of atmospheric ice on insulators. IEEE Trans. Power Deliv. 8 (3), 1311–1321. Fikke, S.M., Ohnstad, T.M., Telstad, T., Förster, H., Rolfseng, L., 1994. Effect of long range airborne pollution on outdoor insulation. Nordic Insulation Symposium, Paper 1.6: 1, Vaasa, Finland, (June 13–15). Fujimura, T., Naito, K., Hasegawa, Y., Kawaguchi, T., 1979. Performance of insulators covered with snow or ice. IEEE Trans. Power Appar. Syst. 98 (5), 1621–1631. Guan, Z., Wang, X., Bian, X., Wang, L., Jia, Z., 2014. Analysis of causes of outdoor insulators damages on HV and UHV transmission lines in China. Electrical Insulation Conference (EIC), Philadelphia, USA, (June 8–11). Hu, J., Sun, C., Jiang, X., Zhang, Z., Shu, L., 2007. Flashover performance of precontaminated and ice-covered composite insulators to be used in 1000 kV UHV AC transmission lines. IEEE Trans. Dielectr. Electr. Insul. 14 (6), 1347–1356. Hu, J., Sun, C., Jiang, X., Yang, Q., Zhang, Z., Shu, L., 2011. Model for predicting DC flashover voltage of pre-contaminated and ice-covered long insulator strings under low air pressure. Energies 4 (4), 628–643. Hu, Q., Shu, L., Jiang, X., Sun, C., Zhang, Z., Hu, J., 2012. Effects of shed configuration on AC flashover performance of ice-covered composite long-rod insulators. IEEE Trans. Dielectr. Electr. Insul. 19 (1), 200–208. IEEE std. 1783, 2009. IEEE Guide for Test Methods and Procedures to Evaluate the Electrical Performance of Insulators in Freezing Conditions. Jiang, X., Chao, Y., Zhang, Z., Hu, J., Shu, L., 2011. DC flashover performance and effect of sheds configuration on polluted and ice-covered composite insulators at low atmospheric pressure. IEEE Trans. Dielectr. Electr. Insul. 18 (1), 97–105. Kawai, M., 1970. AC flashover tests at project UHV on ice-coated insulators. IEEE Trans. Power Appar. Syst. 89 (8), 1800–1804. Matsuda, H., Komuro, H., Takasu, K., 1991. Withstand voltage characteristics of insulator strings covered with snow or ice. IEEE Trans. Power Deliv. 6 (3), 1243–1250. Mayr, O., 1943. Beitrag zur Theorie der Statischen und der Dynamischen Lichtbogens. Arch. Elektrotech. 37, 588–608.

Meier, A., Niggli, W.M., 1968. The influence of snow and ice deposits on supertension transmission line insulator strings with special reference to high altitude operations. IEEE Conf. Publ. 44, London, UK, pp. 386–395. Obenaus, F., 1958. Fremdschichtüberschlag und Kriechweglänge. Deut. Elektrotech. 4, 135–136. Phan, C.L., Matsuo, H., 1983. Minimum flashover voltage of iced insulators. IEEE Trans. Electr. Insul. 18 (6), 605–618. Schneider, H.M., 1975. Artificial ice tests on transmission line insulators—a progress report. IEEE/PES Summer Meeting, San Francisco, USA, Paper No. A75-491-1, pp. 347–353 (July 20–25). Shu, L., Shang, Y., Jiang, X., Hu, Q., Yuan, Q., Hu, J., Zhang, Z., Zhang, S., Li, T., 2012. Comparison between AC and DC flashover performance and discharge process of ice-covered insulators under the conditions of low air pressure and pollution. IET Gener. Transm. Distrib. 6 (9), 884–892. Shu, L., Wang, S., Jiang, X., Hu, Q., Liang, J., Yin, P., Chen, J., 2014. Modeling of AC flashover on ice-covered composite insulators with different shed configurations. IEEE Trans. Dielectr. Electr. Insul. 21 (6), 2642–2651. Su, H., Jia, Z., Sun, Z., Guan, Z., Li, L., 2012. Field and laboratory tests of insulator flashovers under conditions of light ice accumulation and contamination. IEEE Trans. Dielectr. Electr. Insul. 19 (5), 1681–1689. Taheri, S., Farzaneh, M., Fofana, I., 2014. Improved dynamic model of dc arc discharge on ice-covered post insulator surfaces. IEEE Trans. Dielectr. Electr. Insul. 21 (2), 729–739. Tavakoli, C., 2004. Dynamic modeling of ac arc development on ice surfaces (Ph.D. Thesis). Université du Québec à Chicoutimi (UQAC), Chicoutimi, Canada. Volat, C., Farzaneh, M., Mhaguen, N., 2011. Improved FEM models of one and two arcs to predict AC critical flashover voltage of ice-covered insulators. IEEE Trans. Dielectr. Electr. Insul. 18 (2), 393–400. Wilkins, R., 1969. Flashover voltage of high-voltage insulators with uniform surfacepollution films. Proc. IEEE 116 (3), 457–465. Yang, Q., Sima, W., Sun, C., Shu, L., Hu, Q., 2007. Modeling of DC flashover on ice-covered HV insulators based on dynamic electric field analysis. IEEE Trans. Dielectr. Electr. Insul. 14 (6), 1418–1426. Yoshida, S., Naito, K., 2005. Survey of electrical and mechanical failures of insulators caused by ice and/or snow CIGRE WG B2.03. Electra (222), 22–26. Zhang, J., Farzaneh, M., 2000. Propagation of ac and dc arcs on ice surfaces. IEEE Trans. Dielectr. Electr. Insul. 7 (2), 269–276.