Modeling of flashover arcs in medium voltage networks due to direct lightning strikes

Electrical Power and Energy Systems 65 (2015) 59–69

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Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes

Modeling of flashover arcs in medium voltage networks due to direct lightning strikes Farhan Mahmood a,⇑, Nagy I. Elkalashy b, Matti Lehtonen a a b

Department of Electrical Engineering and Automation, Aalto University, P.O. Box 13000, 00076 Aalto, Finland Department of Electrical Engineering, Faculty of Engineering, Minoufiya University, Sehbin Elkom 32511, Egypt

a r t i c l e

i n f o

Article history: Received 21 January 2014 Received in revised form 18 September 2014 Accepted 23 September 2014

Keywords: Lightning overvoltages Medium voltage line Flashover arc Dynamic arc model ATP-EMTP

a b s t r a c t Distribution line faults in many cases are caused by direct lightning strokes to overhead lines resulting in a disruption between phase and ground in the form of flashover arc. Therefore, it is important to accurately simulate the lightning behaviour for the protection studies of distribution networks. This paper investigates the influence of considering the dynamic arc model and the actual volt–time characteristics of line insulators in the evaluation of lightning overvoltages. A full-scale experimental set-up was installed in the high voltage laboratory to study the dynamic interaction between fault arc and power system with grounded and ungrounded cross arm configurations. The least square method has been used to extract the arc parameters from the experimental results for modeling purpose. The model of experimental set-up has been implemented in Alternative Transients Program–Electromagnetic Transients Program (ATP–EMTP) software and the experimental results have been reproduced by computer simulations with reasonable accuracy. Based on the comparison of experimental and simulation results, it is concluded that the actual volt–time curves and the arc model that characterize the behaviour of line insulators should be considered during the simulation of the lightning performance of overhead distribution networks. Ó 2014 Elsevier Ltd. All rights reserved.

Introduction MEDIUM voltage (MV) distribution lines up to 20-kV do not have a shield wire and are thereby prone to lightning strikes. Field statistics have shown that the majority of direct lightning discharges to unshielded lines result in single-phase as well as multi-phase faults [1,2]. This can produce a fault arc from phase to ground on the surface of insulator through air. Consequently, the fault arc appears in the form of flashover causing a fault on the power system. In Finland, most of the 20-kV distribution networks are singlecircuit wood pole construction with ungrounded steel cross-arms. However, at the same time, the cross arm of wood pole is grounded at some locations for protection purposes. The benefit of grounding the cross arm is to suppress the fault currents into ground produced by lightning strikes. However, in this case, the flashover path is simply between the phase conductor and the earthed cross arm causing a single-phase fault. Therefore, the total critical flashover voltage (CFO) for the flashover path is provided by the insulator alone i.e. 136-kV in case of 24-kV pin type insulator. For

⇑ Corresponding author. http://dx.doi.org/10.1016/j.ijepes.2014.09.036 0142-0615/Ó 2014 Elsevier Ltd. All rights reserved.

ungrounded cross arm configuration on MV wood poles, direct lightning strike to the phase conductor always results in a multiphase fault. For example, in case of two-phase fault, the flashover occurs over the line insulator between the struck phase and cross arm and then from cross arm to the neighbouring phase. The reason is that the wood pole has very high lightning impulse strength so that the weakest flashover path is always across the two neighbouring insulators through metallic cross arm. Now, the total CFO for the flashover path is provided by the series combination of two insulators, which, of course, is higher, compared to the case of an earthed cross arm [3]. This means that the lightning impulse strength required to produce a flashover in ungrounded cross arm is higher than the earthed one. Previous studies have analyzed the transient performance of MV overhead networks due to direct lightning strikes [4–11]. In such studies, the flashover criterion for the insulators is usually modeled by the closing of a parallel switch when the voltage across it exceeds 1.5 times the line CFO [3]. Once, the switch closes, the arc appearing during flashover is represented by a linear resistance, for which more accurate arc models are needed. The consideration of such simplified criterion of flashover and arc appearing during flashover can result in significant error in the calculation of lightning overvoltages [12]. Therefore, the models of important

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1m

1m

Lead Wire

0.5 m

(1)

7m

(2)

(a) Dimensions of the medium voltage wood pole overhead line with (1) cross arm grounded with lead wire (2) cross arm ungrounded by removing lead wire Lightning Impulse Generator

20 kV Insulators

R1' 720 Ω

R1 720 Ω

Potential Divider

R2 720 Ω

R2' 720 Ω

CT

CT

Potential Divider

Digital Impulse Analyzer

(b) Complete experimental set-up Fig. 1. Full scale experimental set-up consisting of a test distribution line with measurement system and impulse generator (a) dimensions of the medium voltage wood pole overhead line with grounded and ungrounded cross arm configurations, and (b) complete experimental set-up.

phenomena associated with flashover arc behaviour should be incorporated in order to accurately estimate the lightning performance of overhead distribution lines. The aim of this paper is to investigate the influence of considering the dynamic arc model along with the actual volt–time

curves of the insulation in the calculation of lightning overvoltages. The full-scale lightning flashover experiments were performed in the high voltage laboratory at Aalto University, Finland. The measurements have been conducted with grounded and ungrounded cross arm configurations to investigate single-phase

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Flashover Period

Induction Period

Arcing Period

Pre-arc Period

Fig. 2. Experimental lightning impulse voltage applied to one phase of a three-phase distribution line for grounded cross arm configuration under wet air-condition.

Induction Period

Pre-strike Period

Arcing Period

Pre-arc Flashover Period Period

Fig. 3. Experimental lightning impulse voltage injected to one phase of a three-phase distribution line under wet air-condition for ungrounded cross arm configuration.

Pre-arc Period

Arcing Period

Induction Period

Flashover Period

Fig. 4. Experimental lightning induced voltage on the neighbouring phase for grounded cross arm configuration under wet air-condition.

and two-phase flashover faults in MV distribution lines. The parameters of the dynamic arc model (stationary arc voltage Uarc and arc time constant s) have been estimated from the experimental results using the closed form of least square error methods. Based on experimental results, a complete model of MV distribution line is simulated for both cross arm configurations by incorporating the dynamic arc model and the actual volt–time characteristics of the insulators. The model has been implemented in Alternative Transients Program–Electromagnetic Transients Program (ATP–EMTP) software and the experimental results have been validated by computer simulations with reasonable accuracy.

High voltage laboratory experiments Fig. 1(a) illustrates the full-scale experimental setup for the investigation of lightning flashover in a MV wood pole distribution line stroked by lightning impulse generator. The laboratory tests were performed on a 20-kV distribution line supported on a 7 m high wood pole with metallic cross arm. The power conductors were insulated from the ground by 24-kV pin- type porcelain insulators. The positive critical flashover voltage (CFO) of the insulator has been calculated as 136-kV using up-and-down experimental test. The length of power conductor was 22 m, diameter = 6 mm and Rdc = 0.509 X/km. The conductors were grounded at both ends

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F. Mahmood et al. / Electrical Power and Energy Systems 65 (2015) 59–69 Pre-arc Period

Flashover Period

Arcing Period

Induction Period

Pre-strike Period

(b)

(a)

(c)

Fig. 5. Experimental lightning induced voltage on the neighbouring phase for ungrounded cross arm configuration under wet air-condition (a) complete waveform, (b) partial arc period, and (c) flashover period.

Fig. 6. Lightning flashover observed with (a) grounded (single-phase flashover), and (b) ungrounded (two-phase flashover) cross arm configuration during artificial rainfall.

through terminating resistances as shown in Fig. 1(b) to simulate an infinitely long line to some extent. It should be noted that the experiments were performed with grounded and ungrounded cross arm configuration causing a single-phase and two-phase fault on the system respectively. The metallic cross arm was grounded by connecting the cross arm brace to ground by a lead wire. The experiments were performed under dry air (laboratory weather conditions) and wet air conditions (artificial raining condition). The weather conditions for the dry-air and wet-air conditions were recorded as: T = 22 °C, RH = 55.7%, P = 1007.4 hPa and T = 22 °C, RH = 61.5% and P = 1019 hPa respectively. Water spraying equipment was used for producing artificial rain in the laboratory to perform the tests in rainy conditions. The conductivity of the distilled water used for artificial rainfall was 0.01 S/m. The equipment was placed at a height of 2 m and 3 m away from the test set-up and consists of a number of nozzles to give the precipitation of rain at a rate of 1 mm/min. Standard lightning impulse voltages (1.2/50 ls) of different amplitudes were produced by an impulse generator (Haefely:

800 kV, 20 kJ). High Volt MIA Digital Impulse Analyzer was used with four measurement channels. Channel 1 was used to measure the applied impulse voltage to one phase (side phase conductor) of a three- phase distribution line through a resistive voltage divider with a scale factor of 1633; Channel 2 was used to measure the induced voltage across neighbouring phase (centre phase conductor) through RCT 2000 damped capacitive voltage divider with a scale factor of 2018; Channels 3 and 4 were used to measure the current flowing into ground through the two terminating resistances of the neighbouring phase by a set of Pearson CTs Model 110 and 110A respectively (bandwidth 20 MHz). However, in ungrounded cross arm configuration, the current flowing into ground through the lead wire was measured by Channel 4. The impulse voltage applied to one phase of a 3-phase wood pole distribution line was gradually increased so that a singlephase and two-phase flashover occurred in grounded and ungrounded cross arm configuration respectively. The tests were performed with positive polarity and visual camera inspection to observe the flashover phenomenon. The experimental measurements were repeated 10 times to confirm the dynamic interaction

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Fig. 7. Experimental arc voltage and arc current for grounded cross arm configuration under wet air conditions.

Fig. 8. Experimental arc voltage and arc current for ungrounded cross arm configuration under wet air conditions.

Fig. 9. Experimental V–I characteristics of the arc for a lightning struck wood pole distribution line for wet air conditions (a) grounded cross arm and (b) ungrounded cross arm.

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Fig. 10. Volt–time characteristics of the line insulators for grounded and ungrounded cross arm configuration.

between fault arc and power system. It was also observed that the waveforms of different parameters show similar trend under wet and dry air conditions, so the experimental and simulated results reported in this paper are only for wet air conditions. A brief discussion on the experimental results is given as following. Recorded measurements The recorded waveforms of the applied impulse voltage and the induced voltage in the neighbouring phase are shown in Figs. 2–5 for grounded and ungrounded cross arm configuration under wet air conditions. For modeling purpose, the waveforms are divided into four periods, namely, the induction period, pre-arc period, flashover period and the arcing period [6]. However, a pre-strike period also exists between pre-arc and flashover periods for ungrounded cross arm configuration. During the rising front of the applied voltage, an induced voltage of 5–12 kV is observed in the neighbouring phases in both cross arm configurations as shown in Figs. 4 and 5. The magnitude of the induced voltage mainly depends on the front time, peak value of the applied impulse voltage and the spacing between phase conductors. This period is called as induction period. When the applied voltage reaches its peak value and starts to fall gradually, the induced voltage drops to zero. This period is known as prearc period. In ungrounded cross arm configuration, multiple pre-strikes of the partial arc occur across the insulator directly under stress. Partial arc occurs when the applied voltage exceeds the reduced withstand voltage of the insulator but does not completely flash over its surface. This period is known as pre-strike or partial arc period [13]. It should be noted that partial arc period is not observed in grounded cross arm configuration. Next comes the flashover period. In grounded cross arm configuration, the flashover occurs over the insulator under stress and the fault current flows into ground through the lead wire. Flashover induces a relatively low voltage of few kVs across the neighbouring phase with grounded cross arm configuration as shown in Fig. 4. For ungrounded cross arm configuration, since both insulators are supported on the metallic cross arm, the flashover on the insulator first occurred from the struck phase to the cross arm and then from the cross arm to the other phase. Therefore, a relatively high voltage is observed across the neighbouring phase at the time of flashover as shown in Fig. 5. Also, a high frequency oscillation is observed in the induced voltage waveform as shown in Figs. 4 and 5 due to the interaction between cross arm inductance and stray capacitance of insulators and measurement system.

Finally, the applied voltage continues to drop from the instant of flashover of insulator. This period is known as arcing period. The luminous discharge channel shown in Fig. 6 explains the path through which the flashover takes place over single and two insulators causing a single-phase and two-phase fault on the power system. Figs. 2 and 3 also show that the source voltage waveform is affected due to the arc conduction over the surface of insulators. Experimental arc characteristics Electric arcs in free air commonly occur during direct lightning strikes to overhead distribution lines [13,14]. A detailed understanding of the interaction of lightning initiated arcs on distribution lines with the power system is very important for the transient analysis of the power system. For the grounded cross arm configuration, the voltage drop across the arc channel, Uarc(t), and the arc current, Iarc(t), are calculated using Eqs. (1) and (2) as,

U arc ðtÞ ¼ U in ðtÞ

ð1Þ

Iarc ðtÞ ¼ Ip ðtÞ

ð2Þ

where Uin(t) is the applied impulse voltage in kV and Ip(t) is the current flowing into ground through down conductor in amperes. However, for ungrounded cross arm configuration, the equations for Uarc(t) and Iarc(t) are modified as,

U arc ðtÞ ¼ U in ðtÞ  U 2 ðtÞ

ð3Þ

Iarc ðtÞ ¼ I1 ðtÞ þ I2 ðtÞ

ð4Þ

where U2(t) is the induced voltage in the neighbouring phase in kV, I1(t) and I2(t) are the currents flowing into ground through terminating resistances R1 and R2 respectively. Generally, the electric arcs are described by arc conductance that relates the arc voltage and arc current. With known Iarc and Uarc as shown in Figs. 7 and 8 respectively, the corresponding V–I characteristics of the arc can be plotted as depicted in Fig. 9. The arc conductance, g, one of the important parameter in arc modeling is obtained from the experimental measurements by,

g¼

Iarc ðtÞ U arc ðtÞ

ð5Þ

The role of arc conductance in modeling arc characteristics is discussed in Section ‘Modeling of arc characteristics’.

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Fig. 11. Arc parameters as a function of arc conductance during flashover period for ungrounded cross arm configuration (a) arc time constant s, and (b) arc stationary voltage Uarc.

Table 1 Arc model parameters, Uarc and s, during flashover and arcing period for both cross arm configurations. Cross arm configuration

s (s)

Uarc (V)

Grounded Ungrounded

Flashover period

Arcing period

Flashover period

Arcing period

2000 7000

10,000 21,000

1  109 1  108

50  103 1  108

Fig. 12. Block diagram for the sequential implementation of dynamic arc model during flashover and arcing period.

Experimental volt–time characteristics To assess the voltage withstand strength of insulation, volt– time curve should be established. The procedure is to apply a series of standard lightning impulse voltages with progressively higher peak values and recording the time to flashover [15]. The crest of

lightning impulse voltage is plotted against the time to flashover. The volt–time curve tends to flat out and the asymptotic value is equal to the CFO of insulation. The volt–time curves for both cross arm configurations are shown in Fig. 10. For grounded cross arm configuration, the flashover occurs over single insulator, so the volt–time curve represents

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the insulation strength of only one insulator. However, for ungrounded cross arm configuration, the flashover occurred over two insulators supported on the same metallic cross arm, so volt–time curve represents the combined insulation strength of two insulators.

In Eq. (6), there are two unknown parameters in the dynamic arc model, namely, Uarc and s. The experimental V–I characteristics of the arc shown in Fig. 9 are used to calculate these parameters. To determine Uarc and s, Eq. (6) can be re-written as,

Modeling of arc characteristics The accurate modeling of the lightning initiated arcs becomes a complex task due to irregular behaviour of arc parameters. A number of stationary and dynamic arc models have been employed by the researchers for modeling breaker arcs, long arcs and high impedance arcing faults [16–23]. However, more accurate model of the arc should be used in lightning studies. One of the main tasks of this work is to understand and model the arc creation process during single-phase and two-phase flashover in overhead distribution lines. The physical behaviour of lightning triggered arcs depends on parameters like the applied impulse voltage Uin, induced voltage U2, arc voltage Uarc and the arc propagation current Iarc. In order to represent the arcing phenomenon across the insulators, a variable resistance controlled by the dynamic arc model is introduced in series with the switch that closes on the occurrence of flashover. The dynamic arc model is a form of Mayr’s differential equation based on energy balance in the arc column and is given by [17],

dg 1 ¼ ðG  gÞ dt s

dg jiarc j g ¼  dt U arc s s

ð7Þ

dg ¼ C 1 jiarc j  C 2 g dt

ð8Þ

where C1 = 1/(Uarcs) and C2 = 1/s. It is proposed to calculate these two unknowns, C1 and C2, using the well-known closed form of least square error as follows. For the kth sample, Eq. (7) can be discretized as,

g kþ1  g k ¼ C 1 jiarc jk  C 2 g k Dt

ð9Þ

For a certain number of n-samples taken at sampling period Dt, Eq. (9) can be written in a matrix form as,

2 gkþ1 gk

3

2 jijk 7 6 7 6 jijkþ1 7 6 7 ¼ 6. 7 6 .. 5 4 g kþn g kþn1 jijkþn Dt Dt

6 gkþ2 gkþ1 6 Dt 6 6. 6. 4.

3 g k 7 g kþ1 7 C  7 1 7 .. 7 C2 . 5 g kþn

ð10Þ

In equation (10), the vector at left-hand side represents the rate of change of the arc conductance. It is ascertained from substituting the experimental arc characteristics in (5) at the end samples of the measurements. The right-hand side contains the measurement matrix of the absolute current and conductance. There is also the unknown vector of C1 and C2. In order to find this vector, the left pseudo-inverse is applied on the measurement matrix. Therefore, Uarc and s can be easily estimated by evaluating the least square error estimation of C1 and C2. Using the above procedure, the

ð6Þ

where g is the instantaneous arc conductance, G = |i|/Uarc is the stationary arc conductance, |i| is the absolute value of instantaneous arc current, Uarc is the stationary arc voltage and s is the arc time constant.

G Rd

V

V

Impulse Generator U(0)

+

Cs

Re

LCC

Cb

LCC

V

Volt-time Curves Distribution Line Model with Insulators and cross arm

S2

S5

Variable Arc Resistance S1

S4

R CTRL

I

T

S3 I

=1.0

T

54

Uarc-1

Two Dynamic Arc Models

CTR_2

ABS_I

Uarc-2

T

CTR_1

T

G TAW-1

G

G

TAW-2

Fig. 13. ATP-EMTP network of the experimental set-up for ungrounded cross arm configuration.

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relation between the arc parameters (Uarc and s) and arc conductance is determined using experimental results. The values of the parameters Uarc and s were found different during flashover and arcing period. Based on this observation, it was decided to use two dynamic arc models sequentially for the flashover and arcing periods. The final arc conductance computed at the end of flashover period is considered as the initial arc conductance at the start of arcing period. For ungrounded cross arm configuration, Uarc and s, as a function of arc conductance during flashover period are shown in Fig. 11. Using the above procedure, the arc parameters, Uarc and s, were calculated during flashover and arcing period for both cross arm configurations. Table 1 shows the values of Uarc and s calculated from the experimental results during flashover and arcing period. The concept of universal arc representation [24] has been used to compute the arc conductance during flashover and arcing periods by sequentially executing the dynamic arc models. The algorithm for the sequential execution of dynamic arc model is implemented by Transient Analysis Control System (TACS) feature of ATP-EMTP software [25]. As shown in Fig. 12, two controlled Integrators Type 58 are used to solve the dynamic arc model during flashover and arcing periods. When the flashover occurs, the control signal of controlled Integrator-I becomes high whereas the control signal of controlled Integrator-II is still low. The control signal of controlled Integrator-I is synchronized with the closing of the switch across insulator which is directly under stress at the instant of flashover. In this case, the dynamic arc model during flashover period is solved and outputted by the controlled Integrator-II through its reset signal. Next, the control signal of controlled Integrator-II becomes high at the start of arcing period. The time interval between flashover and arcing period is estimated by calculating its mean value from all the measurements. Now, the controlled integrator solves the dynamic arc model for the arcing period. In both cases, the output of controlled Integrator-II is the arc conductance, the reciprocal of which is the arc resistance. This variable arc resistance is fed to TACS controlled resistance connected in series with the switch that closes when the voltage across it exceeds insulator voltage withstand capability characteristic curve.

Component modeling in ATP-EMTP According to the configuration of experimental set-up shown in Fig. 1, the components modeled in ATP-EMTP software are the

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impulse generator, pin-type insulators, metallic cross arm, overhead distribution line and the arc interactions during single-phase and two-phase flashover. The details of the component modeling are given as following. Modeling of impulse generator In order to accurately reproduce the experimental conditions, the applied impulse voltage was represented by a complete model of single-stage impulse generator [15]. Standard lightning impulse voltage (1.2/50 ls) is generated in the laboratory with the component values as Rd = 320 O, Re = 1120 O, Cs = 62.5 nF and Cb = 800 pF and it is simulated using the ATP-EMTP circuit presented in Fig. 13. Modeling of MV distribution line A frequency dependent parameter model of the overhead line has been used because the frequencies of lightning surge span a large bandwidth (typically 100 kHz to 3 MHz) and the line parameters also significantly vary within this range. In this study, J. Marti’s frequency dependent model (Line/Cable Constants subroutine) is selected because it calculates the line parameters over a wide user-defined frequency range [25–27]. Modeling of insulators The line insulators are represented by capacitors in parallel with resistors between the phase conductor and cross arm. The values of capacitance and resistance for pin- type insulators have been tuned to 80 pF and 25 MO respectively considering the effect of wet air conditions [26]. The flashover phenomenon is represented by the closing of parallel switch when the voltage building up across line insulation exceeds the flashover voltage (Uf) of the insulator. During the simulation, the flashover voltage is calculated using the simplified volt–time model given in [27–31].

Uf ¼ K 1 þ

K2 t0:75

ð11Þ

where K1 = 400  L, K2 = 710  L, L = insulator length (cm) and t is the elapsed time after lightning stroke (ls). For the tested insulator, L = 18 cm and the computed K1 and K2 were utilized as initial values. Then, the parameters K1 and K2 have been tuned to obtain reasonable match between the experimental and simulated volt–time curves as shown in Fig. 10.

Fig. 14. Comparison between experimental and simulated (a) arc voltage and (b) arc current for grounded cross arm configuration.

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F. Mahmood et al. / Electrical Power and Energy Systems 65 (2015) 59–69

Fig. 15. Comparison between experimental and simulated (a) applied impulse voltage and (b) induced voltage across neighbouring phase for ungrounded cross arm configuration.

Fig. 16. Comparison between experimental and simulated (a) arc voltage and (b) arc current for ungrounded cross arm configuration.

Modeling of wood pole and metallic cross arm

Comparison of experimental and simulation results

The concept of single conductor above ground plane is used to approximate the inductance of the metallic cross arm as [9],

After modeling the experimental system shown in Fig. 1 in ATPEMTP program as described in Sections ‘Modeling of arc characteristics’ and component modeling in ATP-EMTP, a comparison of the experimental and simulated waveforms is conducted using the proposed method as follows.

Lxarm ¼ 2  107 ln

  2hxarm rxarm

ð12Þ

Grounded cross arm configuration where hxarm is the height of the cross-arm above earth and rxarm is the equivalent radius of the cross-arm with oblong cross-section. The complete ATP-EMTP network of the experimental set-up for ungrounded cross arm configuration is shown in Fig. 13. The models of different components, i.e. impulse generator, MV overhead line with insulators and cross arm, and the TACS based implementation of dynamic arc models are labeled and shown by dashed line box. The sequential execution of the network events is attained by controlling the switches S1, S2, S3, S4 and S5. During the induction period, S1, S3 and S4 are closed while S2 and S5 are opened. The transition from pre-arc period to the flashover period is controlled by the volt–time characteristics of the insulator. Accordingly, the flashover and arcing period is modeled by opening the switches S1, S3, S4 whereas switches S2 and S5 are closed so that the dynamic arc model is sequentially implemented and controls the value of variable arc resistance. However, the pre-strike period is modeled by delaying the closing of switch S5 with S2 closed and S3 opened.

Fig. 14 compares the experimental and simulated waveforms of the arc voltage (or applied impulse voltage) and arc current for the grounded cross arm configuration. The comparison confirms that the proposed model accurately reproduces the experimental results in terms of the peak value. The parameters of the arc model, Uarc and s, were tuned based on experimental characteristics to match the simulated and experimental results. It can be observed that the peak of arc voltage and arc current is well simulated till the end of flashover period. However, a discrepancy from the measured results is found during the arcing period till 30 ls. This disagreement is possibly due to the interaction of the measurement system with the stray capacitances of the power system. Ungrounded cross arm configuration A comparison of experimental and simulated applied impulse voltage and the induced voltage across neighbouring phase is

F. Mahmood et al. / Electrical Power and Energy Systems 65 (2015) 59–69

shown in Fig. 15. It can be observed that simulated applied voltage and the voltage across neighbouring phase during flashover agree reasonably well with the experimental results. The comparison of experimental and simulated waveforms of the arc voltage (or applied impulse voltage) and arc current for ungrounded cross arm configuration is shown in Fig. 16. It should be noted that the only disagreement in the experimental and simulated arc currents for both cross arm configurations is due to modeling of terminating resistances and grounding system. This requires further investigation of the modeling method for terminating resistances along with the grounding system.

Conclusions An evaluation of incorporating the dynamic arc model and the actual volt–time characteristics of the line insulation to estimate the lightning performance of overhead distribution line is carried out in this paper. Experiments were performed to ascertain the features of lightning initiated flashover with grounded and ungrounded cross arm configurations. Instead of assuming that the flashover occurs when the voltage across the line insulators exceeds 1.5 times line CFO, actual volt–time characteristics of the line insulators are considered. Once the flashover occurs, the variable arc resistance is being controlled by the two sequential arc models because the experimental characteristics indicate that the parameters of the dynamic arc models are different during flashover and arcing periods. Therefore, the dynamic arc model was sequentially implemented in the simulation with different arc parameters (Uarc and s). The obtained results have shown that the proposed method can accurately predict the lightning overvoltages during single-phase and two-phase lightning initiated flashover. The proposed method is much closer to the actual condition due to the arc dynamics modeled as a variable parameter. However, some disagreement is observed in the simulated and experimental arc current waveforms possibly due to the modeling method used for terminating resistances and the grounding system. To conclude, the models of important phenomena associated with flashover must be considered during the estimation of lightning performance of overhead distribution lines. Although, the dynamic arc model has been applied to single-phase and twophase flashover only, but it can also be applied to model threephase flashover in overhead distribution lines. The dynamic arc models along with the actual volt–time curves of the line insulators are needed to accurately estimate the lightning overvoltages and probabilities of flashovers to the other phases. Furthermore, the model reported in this paper is helpful for in-depth understanding of flashover phenomenon in distribution lines since the assumption of simplified 1.5 times CFO flashover criterion and the constant arc resistance may lead to erroneous results on the predicted lightning overvoltages. Therefore, the methodology presented in this paper can be employed to optimally design the protection scheme against lightning overvoltages in a power network.

Acknowledgements The first author is thankful to the Department of Electrical Engineering at Aalto University for the financial support provided by RIMA project. The authors also acknowledge the assistance of Jouni Mäkinen and Tatu Nieminen for the experimental set up.

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