An ATP-EMTP Monte Carlo Procedure for

Backflashover Rate Evaluation

F.M. Gatta, A. Geri, S. Lauria, M. Maccioni, A. Santarpia Dept. of Astronautic, Electric and Energetics Engineering (DIAEE)

"Sapienza" University of Rome

Rome, Italy

Abstract-The paper presents the ATP-EMTP implementation of

a Monte Carlo procedure aimed at evaluating the backflashover

rate (BFOR) of an HV overhead line (OHL). The ATP-EMTP

circuit model of the OHL includes detailed line insulation and

lightning representation; spatially extended and/or involved

grounding systems are represented by a new, simplified model

which reproduces the effects of propagation and soil ionization

phenomena; statistical input data concerning lightning polarity,

lightning stroke parameters (peak current, front and tail times),

lightning location, line insulation and phase angle of the supply

voltage. An external software engine generates all the required

statistically-oriented ATP-EMTP input data, sequentially

launches and manages ATP simulations and post-processes all

results. An application on a 150 kV - 50 Hz typical Italian OHL

is reported and discussed.

Backflashover rate; HV overhead line; grounding system; ATP­

EMTP; Monte Carlo (key words)

I. INTRODUCTION

Lightning strokes are the main cause of overhead transmission line (OHL) outages at HVIEHV level. These OHLs are practically immune from indirect lightning overvoltages; faults are due to direct lightning strokes, either to phase conductors (i.e. "shielding failures") or to shield wires and tower peaks (in the latter case, line insulation breakdown is called "backflashover"). Correct installation of shield wires reduces drastically the occurence of flashover due to shielding failures, so that backflashovers account for the majority of lightning-originated faults: as the phenomenon is caused by the interaction of lightning, line tower, grounding system and line insulation, the time-domain simulation of direct lightning strokes to overhead transmission lines by means of circuit­oriented, EMTP-like programs, requires the assembly of a number of different sub-models, namely: the transmission line itself (conductors and towers), line insulation breakdown processes, lightning current waveforms and the transient response of tower grounding systems.

The ability of the resulting system model to reproduce the lightning response of the line under study depends on the degree of accuracy of the various sub-models: in particular, the backflashover is largely governed by the tower grounding transient response, which includes propagation as well as non­linear ionization phenomena. Grounding system modeling

varies widely, from a simple linear resistance to a large equivalent network including non-linear elements. Transmission lines built on low-resistivity soils typically adopt physically small grounding systems, for which computationally efficient models [1], including soil ionization, are available. An assessment of the backflashover rate (BFOR), due to the random nature of lightning (and, to a lesser extent, of line insulation withstand), must be carried out by a statistical simulation, typically following a Monte Carlo approach. The latter requires a large number of simulations in order to attain stable results (convergence), which is a problem when using detailed modeling, in particular of tower grounding systems. The CIGRE model has been used to this purpose [2]; however, backflashovers usually occur at towers with higher footing resistances, i.e. those on medium/high resistivity soils, where spatially extended tower grounding systems are used. In these cases, Monte Carlo time-domain simulation requires a drastically simplified, yet accurate model of the grounding system: the authors recently presented a reduced model for time domain simulation of spatially extended grounding systems, able to reproduce the lightning response, including soil ionization, at a modest computational cost [3-6].

The present paper deals with the ATP-EMTP implementation of a Monte Carlo BFOR evaluation procedure: section II recalls the authors' and CIGRE approaches to BFOR calculation; section III describes the ATP-EMTP system components' models and in particular the grounding system model; section IV presents the Monte Carlo procedure and the related statistical assumption; lastly, results of the application to a sample 150 kV - 50 Hz OHL are presented and discussed in section V.

II. BFOR CALCULATION

A simple but approximate deterministic formulation available in literature [1] for the estimation of the BFOR (backflashovers per 100 km-years) is:

28ho6 + S BFOR=O.6·Ng

g P(1c) 10

(1)

where Ng is the ground flash density (flashes/km2 -year), h is the

tower height (meters), Sg is the horizontal distance between the ground wires (meters) and P(lc} is the cumulative probability that a lightning stroke current 1 equals or exceeds the critical

978-1-4673-1897-6/12/$31.00 ©20121EEE

current Ie, which is the lowest current value causing a flashover. The numerical multiplicative coefficient 0.6 takes into account the fact that backflashovers are mostly caused by strokes to the tower whereas the ones to shield wires along the span practically do not cause failures and thus are negligible in the BFOR calculation. This approach, however, disregards some crucial questions which, in some cases, may lead to a wrong computation ofBFOR:

• At tower footing, the 50 or 60 Hz resistance is considered instead of the "impulse" impedance.

• Soil ionization is neglected.

• Only one phase conductor is assumed.

• Standard critical flashover (CFO) is used to estimate the critical current Ie, while the waveshape of the voltage across line insulation may significantly differ from the standard 1.2/50 �s test impulse.

• When a stroke occurs, the pre-existing power frequency voltage is not taken into account.

In order to take into account these issues, the authors developed a full statistical procedure, based on Monte Carlo A TP-EMTP simulations, for the BFOR evaluation. The Monte Carlo procedure generates a large population of N lightnings, assumed to fall within a 1 km-wide swath centered on the OHL: among these, the large sample of NL flashes that actually hit the line (only strokes to tower are assumed) is extracted by means of an electrogeometric model [7] and the attendant strokes are simulated by the A TP-EMTP system model, including statistical modeling of line insulation breakdown, yielding Ndisc total flashovers out of N strokes. The BFOR (referred to 100 km of line-year) is then calculated as

(2)

where the numerical multiplicative coefficient 0.6, as in (1), accounts for the strokes terminating within the span.

III. SYSTEM MODELING

A. OHLModel

The simulated 150 kV - 50 Hz OHL is 10 km long (25 line spans, each 400 m long), and it has been simulated in A TP­EMTP by means of the "JMarti" frequency-dependent model. At each end of the simulated line stretch, the OHL model is connected to the line surge impedances: phase conductors are then terminated on a three-phase 150 kV - 50 Hz voltage system with one of the phases always at the maximum

operating voltage to ground (i.e. 170· % kV), whereas the

shield wire is solidly grounded. Corona was not simulated. Segments and crossarms of the OHL towers have been simulated by means of lossless, single phase transmission line; at each tower, the shield wire is connected to the tower peak.

B. Line Insulation Model

Line insulation breakdown has been simulated with the CIGRE Leader Progression Model (LPM), implemented with A TP-EMTP by means of the embedded "Models" programming/simulation language [8]:

dl = k. U(t)[ u(t) -Eo] (3)

dt dG-I(t)

where l(t) (m) is the leader length; de (m) is the gap length; u(t) (kV) is the voltage across the gap. Eo (kV/m) and k (m

2 kV-

2

S-I) depend on gap configuration and impulse polarity. The gap length de is 1.46 m. Numerical integration is carried out by means of a trapezoidal algorithm.

C. Lightning Model

The classic "Heidler" impulse current source available in A TP-EMTP has been used in all simulations:

t I p k; --;-

i(t)=-.--.e 2 17 1+ k;

(4)

where Ip is the peak current, '1 is the correction factor of the peak current, ks=t/II, II and I2 are time constants determining current rise- and decay-time, respectively, and n is the current steepness factor.

D. Simplified Grounding System Model

All towers except the one struck by lightning are grounded via a constant resistance depending on the soil resistivity, i.e. the 50 Hz tower grounding system equivalent resistance. The struck tower grounding system is modeled in detail and is a typical grounding system configuration used by the Italian Transmission System Operator (Terna S.p.A.), named Type2, with soil resistivity pg=1000 Dm, soil relative permittivity

£r=35 and RSOHz""" 19 D [3], shown in Fig. 1; values of Pg and lOr

are assumed as constant along the line.

The authors have recently proposed [5,6] to use the simple pi-circuit in Fig. 2 for the transient simulation of spatially extended grounding systems. The pi-circuit model is obtained by synthesis of a full circuit model [9], able to reproduce the transient impedance of extended grounding systems also in non-linear conditions, i.e. when soil ionization is taken into account. At first, the linear components of the pi-circuit (shunt resistors and capacitors RJ, R2, CJ, C2, longitudinal resistor and inductance R, L) are estimated by comparing the input impedances of the full circuit model (ATP-EMTP frequency scans without considering ionization) and of the pi-circuit, switching off the ideal voltage-controlled current sources G, and G2. A �GA-based [10] optimization procedure minimizes the standard deviation between the input impedances in the frequency range (1 Hz -7 1 MHz). In the model, ideal voltage­controlled current sources Gl and G2 simulate the non­Iinearities due to soil ionization, which are caused by large current pulses. The analytical functions assigned to Gland G2 are:

·co ·DO

llml A'l

., .

being

GIiOUNl)ltlG S'I' 5'1 fu I vrr,

"

Figure I. Sketch of Type2 grounding system

Figure 2. Simplified pi-circuit model

G(t)=V (t).R;-F;(t)

, i=I,2 I R; R,F,(t) (5)

with F, E [1O-4 ;R;] (6)

and V R; (t) the voltage across R,. Parameters of G I (a I and � a

and G2 (a2 and �2) are again obtained by a IlGA procedure which minimizes the standard deviation between transient input "impedances", i.e. time plots of ground potential rise (GPR). The full circuit model GPR is found by ATP-EMTP time-domain simulation (with ionization now taken into account), while a dedicated FORTRAN routine solves the circuit in Fig. 2. Computations are performed on a wide range of impulsive current wave-shapes (simulated by the Heidler functions) varying the current peak, Ip, the time-to-front, tF, and the tail time, tT' Numerical values of parameters of Type2 simplified equivalent pi-circuit are reported in [6].

IV. MONTE CARLO PROCEDURE

Given the number of random variables involved, the BFOR of the OHL under study is estimated by means of the Monte Carlo procedure detailed in the flow chart of Fig. 3. In the flow chart, N,o, is the total number of samplings, N is the number of the current simulation, Nun is the number of simulations with lightnings actually striking the OHL, Nd,sc is the number of discharges (backflashovers) presently occurred, TgN is the

calculated Nd;sjN ratio and eN is the attendant convergence error. The random input variables sampled by the algorithm

C..,.I.:;uI01tion of" OnSI01YOmont by Eloctr�goDmctric modo'

NO

NO

RD-sults

End

Figure 3. Flow-chart of the procedure

are: polarity of lightning; lightning stroke parameters (peak value of the lightning current, Ip, front time of the current wave, tF, tail time of the current wave, tT); lightning location; line insulation (LPM) parameters; phase angle of impressed (power frequency) voltages.

The procedure is implemented in a Linux environment, whereas the program generating statistical distributions of the various inputs is written in Scilab; if the sampled lightning "strikes the line", a Linux script updates the A TP-EMTP file with relevant input data and runs the simulation in order to check the occurrence ofBFO.

A. Lightning Polarity

Assuming that 90% of flashes to ground are negative [1], lightning polarity is associated to a random variable uniformly distributed between 0 and 1: if the random number exceeds 0.9 the flash is positive, otherwise it is negative. Polarity is sampled first, as it influences the generation of the other inputs.

B. Lightning Stroke Parameters

The statistical variation of lightning stroke parameters (peak current Ip, front time tF and tail time tT) has been assumed to follow a log-normal distribution, with probability density function p(x)

() 1 [ 1 (lnX-lnxm

J

2 . p x = exp --.J2;X(Jlnx 2 (JInx

(7)

where Oinx is the standard deviation of Inx and Xm is the median

value of x, in accord with [11]. Values of Xm and Ohm both for positive (+) and first negative (-) strokes, are reported in Table I.

TABLE I. STATISTICAL PARAMETERS OF FIRST NEGATIVE AND POSITIVE RETURN-STROKES CURRENT

Median value Standard deviation Parameter

+ - + -

Ip 35 kA 31.1 kA 1.21 0.48

IF 221lS 3.83 IlS 1.23 0.55

tT 230llS 77.5 IlS 1.33 0.58

C. Lightning Location

To check the actual occurrence of a lightning stroke to the OHL, the position of the lightning in a 1 km wide strip, centered on the OHL (implicitly, its initial distance from the line, assuming a vertical channel), is generated as a random, uniformly distributed variable. From the peak current value of the given lightning stroke, the attractive radius Ra of the OHL, according to the Ericksson electrogeometric model [7], is calculated as

Ra =O.67.Ho6 '!pO.74 (8)

being H the tower height (m) and Ip the peak current (kA): if the initial lightning position falls within the attractive radius of the line, then the sampled lightning is assumed to hit OHL.

D. Line Insulation Parameters

Statistical data for the critical field Eo are extracted from [1] and summarized in Table II.

E. Phase Angle of the Supply Voltage

The phase angle of the three-phase system of impressed voltages (supposed symmetrical, with positive phase sequence) is assumed as a uniformly distributed variable between 0° and 360°.

V. RESULTS

A. Output of the Procedure

For the case under study, the total number of simulations is NIOI=686570, in order to obtain N"n=lOOOOO strokes on the line. Fig. 4 plots the peak current distribution of the generated 686570 lightning strokes, whereas in Fig. 5 and Fig. 6 the peak current distributions of the lightnings that hit the line and that caused backflashover, respectively, are reported. The smallest peak current causing backflashover is Ip=39.5 kA, being

trO.34 IlS and t7=64.34 IlS. Fig. 7 shows the plot of TgN vs. Nlol: the obtained value of TgN is l.553, while the convergence

error &N, expressed in percent, is lesser than 1.6 % for N>8000 and lesser than 0. 15 % for N>300000. By using (2) and

considering Ng=4 flashes/km2-year, BFOR"""3.73; by using (1),

instead, BFOR"""3.l9.

B. Validation of Results

Since the grounding system behavior plays a key role in the evaluation of the BFOR, an a posteriori validation of the performance of the simplified pi-circuit model was carried out and reported in Fig. 8.

TABLE IT. LINE INSULATION PARAMETERS

Polarity Median value Standard deviation (kJ.') (kJ.')

+ 560 16.80

- 605 18.15

O�,-----�----��----�----�----__, pCI)

00'"

0.010

0<10.

, , I I --- -- ----po -----------,.-----------,. -----------,.-----------· , , , , I I I I I I I , I I I I I I I I , I I to _________ , ___________ 1 ___________ 1 __________ _ , I I I , I I I • I I I I I I I , , I I , , I I _ _ _ _ ___ _ . '- ___________ '- ___________ L.. __________ L. __________ _ I I I I I I I I , I I I • I I I • , I I I I I I ---- , ---------_ .. ---------_., -----------, , ,

, , , , , , , , , , , , , , , , ------, ---------_.' -----------, , , , , , , , , , , , , , ,

'00

, ,

' '''' "" I lkA) ""

Figure 4. Peak current distribution of the generated lightnings

O��--"'�------�----�----�------' P(II 0,00>0

0,""""

OMOS

am I [kA] �

Figure 5. Peak current distribution of the lightnings that hit the line

..,.()g.....Q.,------,-------,--------,-----�------, 1'(11

---- ---- ---.. -----

2.0..0. -----------.. ---

I.�.

,00 ,'" 3D I [kAJ 2'"..£J

Figure 6. Peak current distribution of the lightnings causing backflashover

Figure 7. NdlsJN ratio vs. N.o•

800-�----------------------------------------,

(kV) a) 650 -

500 -

350 -

200 -

4 8

1,2 -(MV)

1,0 -

0,8 -

0,6 -

0,4 -

0,2 -

0,0 -

-0,2 -0 4 8

full model simplified model

12 16

••• , full model _ simplified model

12 16

(l1s) 20

c)

700-�-------------------------------------------

� � 600-

500-

400-

300-

200-

full model simplified model

1 OO-"""'----�--�--�--�----�--�--�--�--�--_____J o 4 8 12 16

700 -

(kV) 600 -

500 -

400 -

300 -

200 -

100 -0 4 8

8

full model simplified model

12

full model simplified model

12

b)

16 (�LS) 20

d)

16

1,2 -,------------------------------------------------------:::lf� (MV) �

1,0 -

0,8 -

0,6 -

0,4 -

0,2 -

0,0 -

full model simplified model

-0,2 -I---_,__--�--___,_---,---____,----c__--_,__----,---___,_--__! o 10 20 30 40

Figure 8. Voltage across phase insulator for sample Monte Carlo generated strokes: full grounding system model vs. simplified model. a) Ip=56.5 kA, tF2.l ms, h=42.6 ms; b) Ip=64.1 kA, tF=7.3 ms, t-F19.4 ms; c) Ip=42.1 kA, tF=1.1 ms, t-F147.1 ms; d) Ip=77 kA, tF2.2 ms, h=13.1 ms; e) Ip=33.2 kA, tF1.8 ms,

h=1 0.4 ms; t) Ip=150 kA, tF7.1 ms, t-F350 ms

Fig. 8 shows an A TP-EMTP comparison between full and simplified model, in terms of voltage across the insulator, for a wide range of lightning strokes that hit the line, in order to check differences related to the occurrence of back flashover.

Six tests are reported (only the higher phase voltage is plotted). Cases from 1 to 5 show that the simplified model has a very good behavior for lightning strokes in the range 30kA -7 80kA, that are the most numerous strokes that hit the line, as inferred from Fig. 5. Lastly, case 6 reports a comparison for lightning current out of this range (namely, 150 kA), again

evidencing a good agreement between simplified and complete model.

VI. CONCLUSIONS

The implementation of a Monte Carlo procedure (based on A TP-EMTP time-domain transient simulations) to evaluate the BFOR of a given overhead line was presented. The use of a simple accurate model, proposed by the authors, for complex tower grounding arrangements allows the study of "difficult" lines, i.e. those built on medium/high resistivity soil. An

external software "engine" allows to represent relevant parameters as statistical variables, namely:

• Lightning location.

• Lightning current waveshape and polarity.

• Overhead line insulation (via a lightning progression model).

• Phase angle of impressed operation (power frequency) voltage.

The main results can be summarized as follows:

• The proposed Monte Carlo approach achieves convergence in reasonable times.

• The computational burden of the single lightning stroke simulation is negligible (about 2 s).

• Results are very accurate: the backflashover evaluation by using the simplified pi-circuit model is in very good agreement with backflashover evaluation by using the full circuit model.

• A comparison between (1) and (2) evidences that (1), when applied to extended tower grounding systems, may underestimate the backflashover rate (for the studied case, about 20%).

In order to check the performance of the proposed procedure, further investigations will include the comparison with the operational records of an existing HV OHL.

REFERENCES

[I] ClGRE Working Group 01 of SC 33, "Guide to Procedures for Estimating the Lightning Performance of Transmission Lines," ClGRE Brochure n° 63, October 1991.

[2] J. A. Martinez, and F. Castro-Aranda, "Lightning performance analysis of overhead transmission lines using the EMTP", IEEE Trans. Power Del., vol. 20, no. 3, pp. 2200--2210, July 2005.

[3] F. M. Gatta, A. Geri, S. Lauria, and M. Maccioni, "Equivalent lumped parameter 1!-network of typical tower grounding systems for linear and non-linear transient analyses", in Proc. IEEE PowerTech Con f., Bucharest, Romania, June 28th-July 2nd, 2009.

[4] F. M. Gatta, A. Geri, S. Lauria, and M. Maccioni, "Equivalent lumped parameter pi-network of standard grounding systems under surge conditions", in Proc. of 30th International Conference on Lightning Protection (ICLP), Cagliari, Italy, September 20 I O.

[5] F. M. Gatta, A. Geri, S. Lauria, and M. Maccioni, "Simplified HV tower grounding system model for backflashover simulation", in Proc. of 30th International Conference on Lightning Protection (TCLP), Cagliari, Italy, September 20 I O.

[6] F. M. Gatta, A. Geri, S. Lauria, and M. Maccioni, "Simplified HV tower grounding system model for backflashover simulation", Elect. Power Syst. Res., vol. 85, pp. 16-23, April 2012.

[7] A. J. Eriksson, "An improved electrogeometric model for transmission line shielding analysis", IEEE Trans. Power Del., vol. 2, no. 3, pp. 871-886, July 1987.

[8] "Alternative Transients Program (ATP) Rule Book", Canadian/American EMTP User Group, 1995.

[9] A. Geri, "Behavior of grounding systems excited by high impulse currents: the model and its validation", IEEE Trans. Power Del., vol. 14, no. 3, pp. I008-I017, JulyI999.

[10] D. L. Carroll, FORTRAN Genetic Algorithm (GA) Driver, http://cuaerospace.comicarrolllga.html.

[II] Lightning and Insulator Subcommittee of the T&D Committee, "Parameters of Lightning Strokes: A Review", IEEE Trans. Power Del., vol. 20, no. I, pp. 346-358, January 2005.