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IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 3, JULY 2005 2073

Parameter Determination for Modeling SystemsTransientsPart V: Surge Arresters

IEEE PES Task Force on Data for Modeling System Transients of IEEE PES Working Group on Modeling and Analysis

of System Transients Using Digital Simulation (General Systems Subcommittee)

J. A. Martinez and D. W. Durbak

AbstractThe performance of surge arresters during elec-tromagnetic transients on power systems can be simulated withElectromagnetic Transient Program (EMTP)-type computerprograms. This paper discusses the steps to be performed forderiving the parameters needed to represent gapless metal-oxidesurge arresters in transient simulations. The paper includes asummary of the mathematical representation, guidelines forchoosing appropriate parameters, and the conversion proceduresused to obtain parameters.

Index TermsModeling, power system transients, simulation,surge arresters.

I. INTRODUCTION

THE functions of a surge arrester are to do nothing, which

is to conduct little or no current for normal operating volt-

ages, or conduct current during overvoltages, without causing

a fault. Thus, the surge arrester must have an extremely high

resistance during normal system operation and a relatively low

resistance during transient overvoltages. In other words, it must

have a nonlinear voltage versus current (V-I) characteristic.

Early overvoltage protective devices used spark gaps con-

nected in series with discs made with a nonlinear silicon-car-

bide (SiC) material. The spark gaps provide the high impedance

during normal conditions while the SiC discs impede the flow of

current following sparkover. The V-I characteristic of SiC-type

surge arresters is a combination of both the SiC disc and the gap

behavior.

The metal-oxide (MO) varistor material used in modern high-

voltage surge arresters has a highly nonlinear voltage versus

current characteristic as shown in Fig. 1. This characteristic ob-

viates the need for series spark gaps. Therefore, the electrical

characteristics are determined solely by the properties of the

MO blocks. A higher voltage rating is achieved by adding disks

in series. Higher energy ratings are achieved by using larger di-

ameter discs or parallel columns of discs.

Several manufacturers of medium-voltage applications also

market MO surge arresters with spark gaps. MO surge arresters

Manuscript received March 1, 2004. Paper no. TPWRD-00107-2004.Task Force Members: J. A. Martinez (Chairman), D. W. Durbak, B. Gus-

tavsen, B. Johnson, J. Mahseredjian, B. Mork, R. Walling.Digital Object Identifier 10.1109/TPWRD.2005.848771

Fig. 1. MO varistor nonlinear voltage versus current characteristic.

with series or parallel spark gaps can also be represented with

the model described below where the device has two curves:

1) prior to sparkover, and 2) after sparkover.

MO varistor materials have a temperature dependence that is

evident only at low current densities. Temperature dependence

does not need to be represented in simulations for typical over-voltage studies where the arrester currents exceed 10 A. The

temperature dependence factors into the selection of arrester rat-

ings for steady-state and temporary overvoltages. The tempera-

ture-dependent V-I characteristic is important only for the eval-

uation of energy absorbed by the surge arrester, and should not

influence the insulation protective margins.

The V-I characteristic depends upon the waveshape of the

arrester current, with faster rise times resulting in higher peak

voltages. Table I shows modeling guidelines derived from

CIGRE WG 3302 [1]. The commonly used frequency-inde-

pendent surge arrester model is appropriate for simulations

containing low and most switching frequencies (Groups I andII). However, a frequency-dependent model should be used

when very high frequencies are simulated (Groups III and IV);

such a model has to incorporate the inherent inductance of the

surge arrester. A lumped inductance of about 1 H per meter

for the ground leads should also be included in models for high

frequencies.

The subsequent sections present the rationale for models rep-

resenting MO surge arresters in low- and high-frequency tran-

sients simulations. Model characteristics, parameter determina-

tion, if needed, and an illustrative example are presented for

each model.

0885-8977/$20.00 2005 IEEE

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2074 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 3, JULY 2005

TABLE IGUIDELINES TO REPRESENT METAL-OXIDE SURGE ARRESTERS

II. MODELS FOR LOW-FREQUENCY AND SLOW

FRONT TRANSIENTS

A. Model Mathematics

The V-I characteristic of a surge arrester has several exponen-

tial segments [2], where each segment can be approximated by

(1)

where is the exponent, is the multiplier for that segment, and

is an arbitrary reference voltage that normalizes the equa-

tion and prevents numerical overflow during exponentiation.

The first segment can be approximated by a linear relation-

ship to avoid numerical underflow and speed the simulation.

The resistance of this first segment should be very high since

the surge arrester should have little effect on the steady-state

solution of the network. Surge arrester currents during normal

steady-state operation should be less than 0.1 A. The second

segment is defined by the parameters , and , which is

the minimum voltage for that segment. Multiple segments are

typically used to enhance the accuracy of the model since the

exponent decreases as the current level increases. Each segment

has its own values for , and .

B. Model Construction

The following data must be obtained from the manufacturers

literature to construct a surge arrester model

manufacturer's ratings and characteristics;

manufacturer's versus curves.

Manufacturers test each disc with a current pulse and record a

reference voltage. A typical test current pulse has a 10 kA peak

with an 8/20- s waveshape. The resulting peak voltage is the

reference voltage , the voltage at 10 kA for a single column

surge arrester. The V-I curves often use the value as the

1.00-p.u. value. The V-I curve can be determined by multiplying

the per-unit arrester voltages by the for that rating.

The next step is to select

reference voltage proportional to the arrester rating ;

number of parallel columns of discs;

voltage versus current (V-I) characteristic in per unit of the

reference voltage.

The choice of arrester V-I characteristic depends upon the

type of transient being simulated since current waveshapes with

faster rise times will result in higher peak voltages. Manufac-turers often publish several curves.

Fig. 2. Sample V-I characteristic for a 36/90- s wave.

The 8/20- s characteristic applies for typical lightning

surge simulations.

The front-of-wave (FOW) characteristic applies for tran-

sients with current rise times of less than 1 s.

The 36/90- s characteristic applies to switching surgesimulations.

The 1-ms characteristic applies to low-frequency phe-

nomena.

Manufacturers may supply minimum and maximum curves

for each test waveshape. The maximum curve is generally used

since it results in the highest overvoltages and the most conser-

vative equipment insulation requirements. The minimum curves

are used to determine the highest energy levels absorbed by the

arrester. Fig. 2 shows the set of six V-I points selected from a

sample V-I characteristic for a 36/90- s wave.

An EMTP supporting routine converts the set of manufac-

turers V-I points to a set of , and values. A different

curve should be created for each waveshape and manufac-

turing tolerance (maximum or minimum). The voltages are

usually given in a per-unit fashion where the reference voltage

(1.00 p.u.) is either the voltage rating or , the peak voltage

for a 10-kA, 8/20- s current wave.

C. Model Testing

The surge arrester model can be tested in the test circuit of

Fig. 3 prior to its use in a realistic power circuit. The current

source is a ramp function with a peak magnitude equal to the

largest current point of the V-I characteristic. The parallel re-

sistor is in place for computational reasons and has a large value

(e.g., 1E9). The results from the printed output can be comparedto the manufacturers data.



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MARTINEZ AND DURBAK: PARAMETER DETERMINATION FOR MODELING SYSTEMS TRANSIENTS PART V 2075

Fig. 3. Test circuit for a surge arrester model.

Fig. 4. Example simulation. (a) Test circuit. (b) Surge arrester V-I

characteristic with the units of kilovolts and kiloamperes. (c) Voltages andcurrent.

D. Example

The simple circuit of Fig. 4(a) demonstrates the function of a

surge arrester. The surge voltage has an arbitrary triangle wave-

shape that peaks at 100 kV. The 300- linear resistance repre-

sents the surge impedance of an overhead line. Fig. 4(b) shows

the V-I characteristic of the surge arrester, which has a rating

typical for 34.5-kV applications with a of 67.7 kV. Fig. 4(c)

shows the surge voltage, the arrester voltage, and the arrester

current.

The surge arrester draws little current until the voltagereaches about 45 kV. Until that time, the surge arrester voltage

Fig. 5. MOV surge arrester model for fast front surges [6].

is approximately the same as the surge voltage because the

voltage drop across the surge impedance is nearly zero.

When the surge arrester draws significant current, the voltage

drop across the surge impedance increases, resulting in a lower

voltage at the arrester. At 5 s, the peak current of 162.3 A

results in a voltage drop across the resistor of

kV and a peak arrester voltage of kV.

III. MODELS FOR FAST FRONT TRANSIENTS

The surge arrester model described above does not incorpo-

rate time or frequency dependence. With reference to Fig. 4(b),

the instantaneous V-I characteristic for the period between 0 and

5 s is the same as the period between 5 and 10 s. Therefore,

these waveshapes have symmetry about the 5- s point in time.

The surge arrester waveshapes would be skewed if they were

physically measured in a laboratory. The peak of the arrester

voltage would occur before the peak of the current. For a given

peak current, the peak voltage increases as the front time de-

creases. The percentage increase is only slightly proportional tothe current magnitude. The fast front phenomenon appears to be

an inductive effect, but it is not a simple linear inductance.

The dynamic performance of MO surge arresters was de-

scribed in the late 1970s [3]. Since then, several models have

been developed to account for a frequency-dependent behavior

[4][13]. Basically, all of these models incorporate a nonlinear

resistor to account for the V-I characteristic of MOV materials,

and an inductor to include frequency-dependent behavior. The

model used in this paper is that proposed by D. W. Durbak [ 6]

and adopted by the IEEE, including committee papers [11] and

standards [14].

A. Arrester Model

It is shown in Fig. 5 that it incorporates two time independent

nonlinear resistors ( and ), a pair of linear inductors (

and ) paralleled by a pair of linear resistors ( and ) and a

capacitor . The V-I characteristic of is slightly lessthan the

8/20- s curve while is 20% to 30% higher. and form

a lowpass filter that sees a decaying voltage across it. A lumped

inductance of about 1 H per meter for the ground leads should

also be included in series with the model.

In transients simulations, the nonlinear resistors should be

modeled as exponential segments as described above. Fig. 6

shows V-I characteristics of and , see also Table II, where

voltage values are in per unit of . is presented as five seg-ments and as two segments.



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Fig. 6. V-I characteristics for nonlinear resistors [6].

TABLE IIVALUES FOR

A

ANDA

IN FIG. 6 [6]

Note that values presented in Fig. 6 and Table II have beenscaled from those presented in [6], by using the factor 1.6 pro-

posed in the original reference.

Formulas to calculate parameters of the circuit shown in

Fig. 5 were initially suggested in [6]. They are based on the

estimated height of the arrester, the number of columns of MO

disks, and the curves shown in Fig. 6.

The information required to determine the parameters of the

fast front model is as follows:

height of the arrester (in meters);

number of parallel columns of MO disks;

discharge voltage for a 10 kA, 8/20 s current (in

kilovolts); switching surge discharge voltage for an associated

switching surge current (in kilovolts).

Linear parameters are derived from the following equations:

(2)

(3)

(4)

These formulas do not always give the best parameters, but

provide a good starting point. The procedure proposed by the

IEEE Working Group to determine all parameters can be sum-marized as follows [11].

Fig. 7. MO surge arrester model for fast front surges [12].

Fig. 8. Simplified MO surge arrester model for fast front surges [13].

1) Determine linear parameters from

the previously given formulas, and derive the nonlinear

characteristics of and .

2) Adjust and to match the switching surge discharge

voltage for current with a time-to-crest of about 45 s.

3) Adjust the value of to match the voltages.

B. Other Models

Interested readers should also consult other models presented

in the literature, see [4][13]. All models incorporate an in-

ductor to represent a frequency-dependent behavior.

One of the first models was presented in [4]; the equivalent

circuit consisted of a series combination of a nonlinear

resistor and a nonlinear inductor (Fig. 7). An alternative

approach for parameter determination was later presented

in [12].

The model initially presented in [9] was later simplified

and adopted by a CIGRE Working Group [10]. The equiv-

alent circuit wasreduced to a series combination of a linear

resistor, a nonlinear resistor, and a linear inductor.

A simplified version of Durbaks model was proposed in

[13] (Fig. 8). According to the authors of this model, the

capacitance can be eliminated since its effect is negli-gible, and the two resistances and can be replaced

by a single resistance of about 1 M , placed between

model terminals.

A procedure to determine parameters was presented for all of

the above models.

C. Parameter Determination From Field Measurements

The estimation of parameters to be specified in the above ar-

rester models is usually based on manufacturers data and ar-

rester geometry. A technique based on the measured residual

voltage derived from 8/20- s input current test was presented

in [15]. The proposed optimization procedure was applied tomodels presented in [6], [11][13] (Figs. 5, 7, and 8).



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MARTINEZ AND DURBAK: PARAMETER DETERMINATION FOR MODELING SYSTEMS TRANSIENTS PART V 2077

Fig. 9. Fast front arrester model with IEEE example parameters [11].

Fig. 10. Test results with a sinusoidal surge current waveshape. (a) 10-kA,

2- s time-to-crest surge. (b) 10-kA, 4- s time-to-crest surge.

D. Example

A summary of the example included in [11] is presented

below; readers are referred to the original paper for more

details. The procedure to calculate parameters of the fast front

model will be applied to a one column arrester, with an overall

height of 1.45 m, being kV, and kV

for a 3-kA, 300/1000- s current waveshape. The nonlinear

resistances and were deduced from values shown in

Table II, and no adjustment was necessary since the voltage

peak for the switching surge resulted in good agreement with

that provided by the manufacturer for the associated surge

current. After some adjustments of , the final model was that

shown in Fig. 9.

Figs. 10 and 11 show the performance of the model. Simu-lated results depict the discharge voltage developed across the

Fig. 11. Test results with a concave lightning surge current waveshape.(a) 10-kA, 8/20-

s time-to-crest current surge. (b) 10-kA, 2/20-

s time-to-crest

current surge.

MO surge arrester for different discharge current waveshapes.

The test circuit in all cases was similar to that shown in Fig. 4.

Simulations with a concave current source were performed

by using the Heidler model [15]. If the definition of the light-

ning surge parameters is according to [16]; an adjustment of

values is previously needed to derive the parameters of the con-

cave waveshape. Therefore, some care is advisable when using

this waveshape. Voltage waveshapes shown in Fig. 11 were de-

duced by assuming that the time to crest of the current surges

was 8 and 2 s, respectively. However, this time should not be

used as a measurement of the rise time. Fig. 12 shows the re-

sults obtained, respectively, with a time to crest of 2 s and a

rise time of 5 kA/ s; one can observe that

the difference between voltage peaks is about 2%, and that the

peak corresponding to the maximum slope current surge is in

advance.

IV. MODELS FOR VERY FAST FRONT SURGES

Limited experience is presently available on modeling and

validation of an MO surge arrester for very fast front transients

simulation. An interesting discussion on this subject was pre-

sented in [9]. Basically, the recommended models are similar to

those proposed for modeling surge arresters in fast front surge

simulations, but representing frequency-dependent behavior bymeans of distributed parameter components (e.g., lossless line).



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Fig. 12. Influence of the current slope. (a) Current surges. (b) Arrestervoltages.

V. ELECTROTHERMAL MODELS

All previous models were mainly developed to determine

residual voltages between arrester terminals. The energy ab-

sorption capability is another important issue when selecting

an arrester. The thermal behavior can therefore be of concern.

Several models based on an analog electrical equivalent circuit

have been proposed to include the thermal part of the arrester,

see, for instance, [5] and [18]. Parameter determination for

these models is based on experimental measurements.

VI. CONCLUSION

An adequate model of an MO surge arrester for low-fre-

quency and slow front overvoltages can be described by its

nonlinear V-I characteristic. The implementation of such a

model in a transients program is straightforward from the

manufacturers ratings and characteristic curves.

A more sophisticated representation is needed to duplicate ar-

rester performance in high-frequency transients, due to its fre-

quency-dependent behavior. Several models have been devel-

oped to date. This paper has detailed that proposed by Durbak,

which was adopted by the IEEE, and summarized the proce-

dure required to adjust the parameters of its equivalent circuit.

This model provides good enough results for surge currents withtimes to crest in the range of 0.5 to 45 s. However, it has also

some limitations as too much drop is shown in the tail of the dis-

charge voltage. This performance can be unimportant in some

insulation coordination studies, but it can be of limited applica-

tion when the energy discharged by the arrester is of concern.

Simplified models can also be considered in some applications.

REFERENCES

[1] CIGRE Working Group 33.02, Guidelines for representation of net-work elements when calculating transients, CIGRE Brochure 39, 1990.

[2] H. W. Dommel, Electromagnetic Transients Program Manual (EMTPTheory Book). Portland, OR: Bonneville Power Administration, 1986.

[3] E. C. Sakshaug, Influence of rate-of-rise on distribution arrester pro-tective characteristics, IEEE Trans. Power App. Syst., vol. PAS-98, no.2, pp. 519526, Mar./Apr. 1979.

[4] S. Tominaga etal., Protectiveperformanceof metaloxide surgearresterbased on the dynamic v-icharacteristics,IEEE Trans. PowerApp. Syst.,vol. PAS-98, no. 6, pp. 18601871, Nov./Dec. 1979.

[5] M.V. Lat, Analytical method for performance prediction of metaloxidesurgearresters,IEEE Trans. PowerApp. Syst., vol. PAS-104, no. 10, pp.26652674, Oct. 1985.

[6] D. W. Durbak, Zinc-oxide arrester model for fast surges, EMTPNewslett., vol. 5, no. 1, Jan. 1985.

[7] C. Dang, T. M. Parnell, and P. J. Price, The response of metal oxidesurge arresters to steep fronted current impulses, IEEE Trans. Power

Del., vol. PWRD-1, no. 1, pp. 157163, Jan. 1986.[8] D. W. Durbak, The choice of EMTP surge arrester models, EMTP

Newslett., vol. 7, no. 3, Sep. 1987.

[9] W. Schmidt et al., Behavior of MO-surge-arrester blocks to fast tran-sients, IEEE Trans. Power Del., vol. 4, no. 1, pp. 292300, Jan. 1989.[10] A. R. Hileman, J. Roguin, and K. H. Weck, Metal oxide surge arresters

in AC systems. Part IV: Protection performance of metal oxide surgearresters, Electra, no. 133, pp. 132144, Dec. 1990.

[11] IEEE Working Group on Surge Arrester Modeling, Modeling ofmetal oxide surge arresters, IEEE Trans. Power Del., vol. 7, no. 1, pp.302309, Jan. 1992.

[12] I. Kim et al., Study of ZnO arrester model for steep front wave, IEEETrans. Power Del., vol. 11, no. 2, pp. 834841, Apr. 1996.

[13] P. Pinceti and M. Giannettoni, A simplified model for zinc oxide surgearresters, IEEE Trans. Power Del., vol. 14, no. 2, pp. 393398, Apr.1999.

[14] IEEE Guide for the Application of Metal-Oxide Surge Arresters for Al-ternating-Current Systems, IEEE Std. C62.22, 1997.

[15] H. J. Li, S. Birlasekaran, and S. S. Choi, A parameter identificationtechnique for metal-oxide surge arrester models, IEEE Trans. Power

Del., vol. 17, no. 3, pp. 736741, Jul. 2002.[16] F. Heidler, J. M. Cvetic, and B. V. Stanic, Calculation of lightning cur-

rent parameters, IEEE Trans. Power Del., vol. 14, no. 2, pp. 399404,Apr. 1999.

[17] IEEE TF on Parameters of Lightning Strokes, Parameters of lightningstrokes: A review, IEEE Trans. Power Del., vol. 20, no. 1, pp. 346358,Jan. 2005.

[18] A. Petit, X. D. Do, and G. St-Jean, An experimental method to de-termine the electro-thermal model parameters of metal oxide arresters,

IEEE Trans. Power Del., vol. 6, no. 2, pp. 715721, Apr. 1991.

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