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MODELING GUIDELINES FOR FAST FRONT TRANSIENTSReport Prepared by the Fast Front Transients Task Force

of the IEEE Modeling and Analysis of System Transients Working GroupContributing Authors: Ali F. Imece, Daniel W. Durbak, Hamid Elahi, Sharma Kolluri, Andre

Lux, Doug Mader,Thomas E. McDermott, Atef Morched, Abdul M. Mousa, Ramasamy Natarajan, Luis Rugeles,

and Eva Tarasiewicz

1. INTRODUCTION

1.1. Objective

The fast front transients in power systems cover afrequency range from 10 kHz up to 1 MHz. One of the pri-mary causes of such transients is the lightning strokes to thetransmission lines and associated backflashovers. The objec-tive of this task force is to develop modeling guidelines forthe digital simulations involving fast front waveforms.

2. BACKGROUND

Power system studies involving lightning surgephenomena are performed to design transmission lines andsubstations, and for the protection of power system equip-ment [1]. Substation voltage uprating and transmission linecompacting are some of the specialized studies that requirelightning surge analysis [2,3]. The objectives of these stud-ies are to characterize the magnitude of the lightning over-voltages for insulation requirements, and/or to find thecritical lightning stroke current that causes insulation flash-overs.

Specific study objectives for transmission linesmay be to:

-Determine transmission or distribution LineFlashOver Rates (LFOR).

-Establish line arrester application guidelines. For substations the objectives may be to: -Establish/verify surge arrester ratings. -Find optimum location for surge arresters for

lightning surge protection. -Determine minimum phase-to-ground and phase-

to-phase clearances. -Calculate Mean Time Between Failure (MTBF)

for the substation. -Determine optimum location of capacitances to

reduce steepness of surges. The lightning overvoltages are caused by either

shielding failures or backflashovers of the tower insulationon the transmission lines. Direct strokes to the phase con-ductors may also become a concern if the transmission lineand/or substation is not shielded due to relatively low light-ning activity in the area. Direct strokes to the substations aregenerally ignored, since it is commonly assumed that thesubstation is perfectly shielded, via shield wires or lightning

masts.

2.1.Direct Strokes to Phase Conductors

Direct strokes to the phase conductors of ashielded transmission line occur typically when lightningstrokes of low magnitude (a few kA) bypass the overheadshield wires (shielding failure). Traditionally, the electro-geometric model based upon strike distance has been used todetermine the maximum prospective peak lightning currentwhich can bypass the shielding and terminate directly onphase conductors. This electrogeometric model has beenmodified recently to include the concept of attractive radius.A detailed discussion of the use of this model can be foundlater in this report. It is sufficient now to indicate that theusual approach has been to design the transmission line insu-lation to withstand the maximum shielding failure currentpredicted by the electrogeometric model without an outageto the line. Overvoltages produced by currents equal to orless than this maximum shielding failure current shouldtherefore be considered when they occur within a few spansof a substation terminal when performing insulation coordi-nation studies for that substation terminal.

More then 90% of the total number of flashes-to-ground are of negative polarity. According to Reference [4],55% of negative downward lightning flashes contain morethan one stroke. The mean number of strokes per flash isthree, typically separated by less than 50 millisecondsbetween strokes. In the shielding failure current range, thereis about 12% probability that the peak current of a subse-quent stroke will exceed that of the first stroke with veryweak correlation between the amplitudes of the two. Factorsof up to 200% have been observed (i.e., subsequent stroke of24 kA for 12 kA first stroke). No subsequent stroke ampli-tudes in excess of 80 kA have been observed within theavailable sample of records for negative downward flashes.In general, the rate-of-rise of current for subsequent strokesis higher than that for first strokes.

The above observations are significant for shield-ing failures since it is possible in the shielding failure rangeto have a higher peak current amplitude in a subsequentstroke than in the first stroke. In most cases, where the sub-sequent stroke is significantly higher in amplitude than thefirst stroke, line flashover will result.

For overhead lines terminated on GIS or cables,detailed studies should be performed due to consideration

DRAFT Dec. 97

5-2

for potential overvoltage build-up at the termination. Thedetails of these phenomena are outside the scope of thispaper, but in-depth discussion can be found in a companionreport by IEEE Very Fast Transients Task Force.

2.2. Backflashovers

The event of greater concern is backflashovers,since direct strokes to the phase conductors due to shieldingfailures are relatively less likely. Backflashover occurs whenlightning strikes the tower or the shield wire, and the result-ant tower top voltage is large enough to cause flashover ofthe line insulation from the tower to the phase conductor.When backflashover occurs, a part of the surge current willbe transferred to the phase conductors through the arc acrossthe insulation strings. Usually, the backflashover causes atemporary line-to-ground fault that will be cleared by a cir-cuit breaker. A line outage results until the circuit breaker isreclosed.

The voltage surge as a result of the backflashover isvery steep, and generally dictates the modeling requirementsof the study. Note that direct strokes to the phase conductorswill create relatively less steep voltage waveforms. Thesteepness and the magnitude of the voltage decrease as thesurge propagates along the line, depending upon the lineparameters. Corona is another important factor that reducesthe steepness of the incoming voltage surge.

The lightning performance of the transmission linesis characterized by the outage rate which may dictate theinsulation requirements of the line. In the design studies, theminimum lightning stroke current (i.e., critical current) thatcauses insulator backflashover is determined. The probabil-ity of occurrence for the lightning currents exceeding the crit-ical current is described by a log-normal distribution, and canbe calculated by using basic probability tables. This proba-bility is the same as the probability of flashover given that alightning stroke is terminated on the line. The number ofstrokes to the line per year depends on the keraunic level ofthe region and exposed area of the shield wire. By multiply-ing the probability of the flashover and the number of thestrokes to the shield wire, the LFOR for the line can be calcu-lated.

For substation design studies, lightning is assumedto hit a nearby tower or the shield wire of the incoming linecausing a backflashover. The resultant lightning surge entersthe substation and propagates inside depending upon the sub-station layout. A discontinuity exists at junction pointswhere a change in height or cross section of the busbar takesplace, and at equipment terminals. The discontinuity pointsinside the substation, status of circuit breakers/switches(open/close), and location of lightning arresters are espe-cially important for the overvoltage characterization at thesubstation. These overvoltages will provide the data requiredfor detailed arrester specifications. Then, the insulation lev-els (i.e., BIL) of the substation equipment can be coordinatedwith the protective level of the arresters. The magnitude ofthe lightning stroke current in connection with the number of

strokes per year to the incoming line will determine the rateof noncatastrophic flashover as well as the rate of possiblecatastrophic failures of the equipment (i.e., MTBF).

2.3. Analysis Tools

Digital transient programs are almost exclusivelyused in lightning studies, as opposed to the Transient Net-work Analyzer (TNA) due to the range of frequenciesinvolved. Although time scaling is possible in the TNA, thedigital approach is still preferred because of better modelingcapabilities. The Electro-Magnetic Transients Program(EMTP) is one of the most widely used digital transient pro-grams for lightning simulations. Although the informationpresented in this document generally refers to EMTP, themodeling requirements are general enough to be equallyapplicable to the other digital transient programs.

3. MODELING GUIDELINES

The main emphasis of this section is to identify themodels of power system components to be used in digitallightning studies. For each component, the important modelparameters will be described, and typical values will be pro-vided. The general trends and rules of thumb that should befollowed in the model development will also be addressed.Finally, the sensitivity of the study results with respect tomodel parameters will be discussed.

Before presenting the details of modeling require-ments for the individual power system components, the gen-eralized assumptions in lightning studies will be discussed.One of the initial questions is whether to have a multi-phaseor single-phase equivalent representation of the power sys-tem for lightning studies. The models discussed in this docu-ment are based on a multi-phase approach, since neglectingground mode of the incoming surge may introduce consider-able error in transient calculations. The other critical ques-tion is the extent to which the power system will be modeled.The transmission line and source sections of this documentpresents more details for different types of studies such assubstation design or transmission line design studies.

The accuracy involved in lightning studies is sub-ject to controversy, since the lightning related surge voltagesand currents cannot be easily measured or verified. Ratherthan embarking on a philosophical discussion of how muchmodel accuracy is needed in lightning studies, the answer isleft to the judgment of the user. The models presented in thisdocument should be treated as the recommended approach inrepresenting the behavior of the power system componentswithin the specified frequency range.

3.1.Overhead Transmission Lines

The overhead lines are represented by multi-phasemodels considering the distributed nature of the line parame-

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ters due to the range of frequencies involved. Phase conduc-tors and shield wires are explicitly modeled between towersand only a few spans are normally considered. Tower modelsinclude the effects of tower geometry and tower groundingresistance with special emphasis on its lightning current mag-nitude dependent characteristics due to soil ionization. Insu-lators are also modeled with their flashover characteristics.All incoming lines to the substation should be represented insubstation design studies, although the worst case tends to bewith only one line in service due to voltage doubling effectfrom open circuit breakers. Depending upon the relativeposition of open circuit breakers inside the substation, theovervoltages may be higher for specific line outages, thusrequiring the evaluation of different line contingencies. Fig-ure 3.1 shows the model of transmission line and tower usedfor lightning studies.

Fig. 3.1 Overhead Transmission Line, Tower and Insulator Representations

3.1.1 Phase Conductors and Shield Wires

The overhead lines are represented by multi-phaseuntransposed distributed parameter line sections for eachtower span. The necessary line parameters for this represen-tation are modal surge impedances for each phase conductorand shield wire (traveling wave models), velocity of propaga-tion for each mode, and modal current and voltage transfor-mation matrices. Note that there is one mode of propagationfor each conductor and shield wire. Bundled phase conduc-tors are represented by one equivalent conductor. The lineparameters can be determined by a line constants routine,using the tower structure geometry and conductor data asinput. The parameters are generally calculated at 500 kHzfor lightning studies with skin effect considered in calcula-tions. Typical values for model surge impedances range from250 ohms to 500 ohms for line modes, while the groundmode surge impedance is generally around 700 ohms. Veloc-ity of propagation for aerial modes are close to the speed oflight. However, for the ground mode, velocity is muchslower. In general, transformation matrices are complex and

frequency dependent. EMTP uses only the real part of thesematrices in the time step simulation. This seems to be anacceptable approximation in transient simulations, since thecomplex part is generally much smaller than the real part.

Comparative EMTP studies for single circuit trans-mission lines showed that computer simulation results withfrequency dependent line models are very similar to thoseobtained with constant parameter line models in lightningstudies. A constant parameter line model with parameterscalculated at 500 kHz gives satisfactory performance, elimi-nating the extra CPU time burden associated with frequencydependent line models.

Line Length and Termination - In transmissionline design studies, the peak voltage at the struck tower maybe influenced by reflections from the adjacent towers. A suf-ficient number of adjacent towers at both sides of the strucktower should be modeled to determine the overvoltages accu-rately. This can be achieved by selecting the number of linespans modeled such that the travel time between the strucktower and the farthest tower is more than one-half of thelightning surge front time. The number of line spans mod-eled must be increased when the effects due to the tail of thelightning surge are considered, especially while evaluatingthe insulator flashovers with the leader propagation method.

In substation design studies, a similar approach canbe followed provided that all the line spans and towersbetween the struck tower and the substation are modeled indetail.

Furthermore, it may be desirable to determine thefirst reflections of overvoltages accurately at any point insidethe substation. This criteria may require detailed modelingof additional towers further away from the substationdepending upon the distance from the struck tower and sub-station layout. The rule of thumb is that the distance betweenthe last tower and the struck tower should be larger than thedistance from the struck tower to the farthest discontinuitypoint inside the substation.

In both transmission line and substation designstudies, the line extended beyond the last tower can be repre-sented with a matrix of self and mutual resistances equal tothe corresponding line surge impedances. This results inalmost no reflections from the matched termination. Theresistance matrix can be determined by a line constantsroutine [19].

3.1.2 Towers and Footing Impedance

Steel Towers - The steel towers are usually represented as a single conductor distributed parameter line terminated by a resistance representing the tower footing impedance. The surge impedance for the tower depends on the structure details, and is determined according to the procedure outlined in Reference [1]. Typical values range from 100 to 300 ohms, and the velocity of propagation can be assumed to be equal to the speed of light.

The peak overvoltage occurring on the tower is

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y y pp g preflections from the tower base will arrive much sooner at thetower top then reflections from adjacent towers. The influ-ence of the apparent tower footing impedance on the towertop voltage is determined by its response time and currentdependence. The response time is usually only important incases where counterpoise is installed covering distancesgreater than 30m from the tower base. In that case, the fre-quency dependent model shown in Fig. 3.2 can be utilized assuggested in [6].

Fig. 3.2

Within 30m of the tower base, the time response cangenerally be neglected and the tower footing impedance isdetermined by using the current dependence of the towerfooting resistance as follows [5].

(3.1)

where:

RT=Tower footing resistance, ohm

Ro=Tower footing resistance at low current and low

frequency, ohm

Ig=the limiting current to initiate sufficient soil ionization, A

I=the lightning current through the footing impedance, A. The limiting current is a function of soil ionization and is given by:

(3.2)

where:

ρ=Soil resistivity, ohm-m

Eo=Soil ionization gradient (about 300 kV/m) [4,17]

In most of the studies, it is recommended to con-sider the waveshape dependence of tower foundation andcounterpoise grounding. Lumped footing resistance may notbe adequate as compared to more detailed models of counter-poise grounding. The counterpoise can be represented as anonlinear resistance with values calculated by Eq. (3-1), or asdistributed parameter lines at ground level with dispersedconductive connections to earth. The typical tower ground-ing resistance is between 10 and 100 ohms.

Wood Poles and Crossarms - Wood poles andcrossarms can be modeled by a parallel combination of aresistor and a capacitor. Figure 3.3(a) shows a combinationof a wood cross-arm and a string of suspension insulatorssupported on a grounded structure. In the case of woodpoles, the structure is also modeled in a similar fashion to thecrossarm. Since the leakage resistance across the insulators,Ri, is normally much greater than that of the wooden arms or

poles, it may be neglected. Similarly, the stray capacitanceof the insulator to wood and to ground, Cs, may be neglected.

Figure 3.3(b) shows the simplified model which has beencommonly accepted as the equivalent circuit for wood-insu-lator combination. Some typical values of the capacitanceand resistance of wood are given in Reference [26]. Notethat the values of the capacitance and resistance are very sen-sitive to moisture contents.

The flashover characteristics of wood can be mod-eled by a voltage-controlled switch as indicated in Fig.3.3(b). Reference [26] shows the characteristic per-unit volt-time curve with its upper and lower limits for a wood cros-sarm subjected to a 1.2/50 µs voltage waveshape. Theimpulse flashover voltage of wood as a function of its lengthfor different moisture contents is also provided in the samepaper.

3.1.3 Insulators

The insulators are represented by voltage-depen-dent flashover switches in parallel with capacitors connectedbetween the respective phases and the tower. The capacitors

RR

I

I

To

g

=+1

IE

Rg

o

o

=π

•1

2 2

ρ

5-5

simulate the coupling effects of conductors to the towerstructure. Typical capacitance values for suspension insula-tors are of the order of “some 10 pF” [29,30], while for pininsulators, the capacitance is around 100 pF/unit. Ten sus-pension insulators in a string has an equivalent capacitance of8/10 = 80 pF/string. The value of 80 pF per unit was used ina study conducted by several of the authors in which transientstudy calculations were compared with high voltage impulsetests. The tests were performed on a full-scale substationmock up consisting of strain and rigid bus work, disconnectswitches and suspension and post insulators [2,32]. With theselected capacitance values, good agreement was obtainedbetween the test and computer simulation results [2]. Capaci-tance values for non-ceramic insulators are an order of mag-nitude less for comparable ceramic insulators.

The backflashover or flashover mechanism of theinsulators can be represented by volt-time curves. The volt-time characteristics of insulators can be represented as afunction of insulator length [1]. The insulator flashover volt-age can be calculated using Eq. (3-3) during the simulation,and compared to the actual insulator voltage. If the insulatorvoltage exceeds this voltage, a flashover occurs across theinsulator. The front time for the arcing can be quite steep,(around 20 ns) and is determined by the physics of air gapbreakdown. For a simplified analysis, a detailed arcingmodel for flashover is not necessary, and a short-circuit (idealswitch) representation will be adequate.

(3.3)

where:Vv-t=Flashover voltage, kV

K1=400*L

K2=710*L

L=Insulator length, mt=Elapsed time after lightning stroke, µs In EMTP, the volt-time characteristics are modeled

using Transient Analysis of Control Systems (TACS) routine,for the insulators that are likely to flashover at each tower.These insulators have a voltage controlled switch across thecapacitor in their EMTP models which is closed automati-cally when the insulator voltage exceeds the flashover volt-age calcula ted f rom volt - t ime curve, s imulat ing abackflashover or a flashover. The start-up time (i.e., zerotime) for the volt-time characteristics must be synchronizedto the instant that lightning stroke hits the shielding wire orthe tower top. Note that multiple flashovers at consecutivetowers are also possible, which are likely to reduce the peakovervoltages. It is recommended to represent all the insula-tors that are on the path of lightning surge with their volt-timecharacteristics for accurate calculation of the overvoltages.

Breakdown volt-time characteristics of air gaps andinsulator strings have been of interest to many researchersand a large volume of experimental work has been reported,as described above. The problem, however, is that knowl-edge of the performance of insulation under the stress of the

standard impulse is not sufficient to predict the performanceof insulation exposed to any non-standard l ightningimpulse. Furthermore, it is inaccurate to assume that flash-over will occur when a voltage wave just exceeds the volt-time curve at any time. The experimental volt-time charac-teristic is only adequate for relating the peak of the standardimpulse voltage to the time of flashover. In order to obtaincorrect results at all times to flashover, further modificationsto volt-time curve would be required. Other factors whichcall for investigation beyond volt-time curve are given in [1].Additional information on Volt-Time Curves are given in thediscussions and closure of a paper published by Front Tran-sients Task Force[35].

Generally, when producing hand calculations addi-tional exploration and modifications of volt-time curves maynot be worth the effort if some corrective multipliers can beused instead. In complex programs, like EMTP, accurate rep-resentation of the short and long air gap (insulator strings andspark gaps) breakdown subject to standard and non-standardlightning impulses is necessary for insulation coordinationstudies. Two alternatives are possible to overcome the short-comings of volt-time characteristics. The first is to produceexperimentally flashover characteristics for surges of allkinds and shapes that may occur in practice. The second is todevelop an analytical procedure to predict the performance ofinsulation as a function of impulse voltage waveform, time toflashover, gap configuration and others. The first alternativemay be difficult, if not impossible, simply because the light-ning overvoltages may be too large for available generators toreproduce them. Therefore, the second alternative seems tobe more attractive especially if the EMTP type models devel-oped can be validated by tests performed in the high voltagelaboratories.

Fig. 3.3 Impedance Model of a Wood-Porcelain Combination. (Switches close after flashover)

The Integration Methods - Various approacheshave been proposed to evaluate the strength of the insulation

V KK

tv t− = +1

2

0 75.

5-6

under the lightning overvoltages. The approaches may begrouped into two main categories. The first is the integrationmethods which employ the equal-area criterion to determinethe time to breakdown. The basic principles is to integratethe difference between the applied voltage and a constantvoltage in time. Breakdown is assumed to take place whenthe integral reaches a fixed value depending on gap configu-ration and voltage polarity. As seen from Eq. (3-4) describ-ing the integral, this approach enables to take into accountthe applied voltage waveform of any shape.

(3.4)

The values DI, U’ and k (in most cases k is differentfrom unity) need still to fit the standard 1.2 ?s x 50 ?simpulse volt-time curve in the following manner. Threepoints on the volt-time curve have to be known, and thenparameters DI, U’ and k are determined by solving a nonlin-ear system of three equations with three unknowns. Refer-ence voltage U’ corresponds approximately to the voltagedefining the dielectric withstand of an air gap subjected to astandard lightning impulse of positive polarity defined in[21]:

(3.5)

where U50 is the mean value of breakdown voltage

and σ is the standard deviation. The EMTP model based on this method has some

limitations. It has been reported that for longer gaps (2m orlonger) parameters DI, U’ and k cannot be determinedbecause the algorithm for solving the system of three nonlin-ear equations with three unknowns no longer converges [21].Therefore, the model is suitable only for shorter gaps. Fur-thermore, various studies show that Eq. (3-4) is valid only forlimited conditions [22,23]. For example, it cannot take intoaccount the geometry of the electrodes, whereas, it is wellknown that different overvoltages are obtained for rod-rodand rod-plane gaps. Experimental results reported in [25]indicate that 50% breakdown voltage U50, obtained for wave-

form similar to standard impulse, is 60% lower than thebreakdown voltage produced with identical impulse butchopped at certain level. The 60% ratio (for standard wave-form and chopped one) applies to positive rod-plane gaps,decreases with negative polarity to 24% and again is differentfor rod-rod gap configuration (40% and 33% for positive andnegative impulses, respectively).

The Leader Development Method - The secondmethod, classified as a physical approach, is the leader devel-opment method. Special consideration is given to breakdownparameters and to physical aspects associated with the dis-charge mechanism. The method is partially based on experi-mental results which, in turn, lead to some analyticalformulations.

By solving a set of differential equations leader

development is calculated, and then volt-time breakdowncharacteristic is obtained in a numerical process which fromphysical standpoint can be described as follows. When theapplied impulse attains a certain value, streamers developfrom the rod into the gap space. Once the streamers cross thegap, ionizing waves propagate along the streamer channeluntil they reach the relatively high conductive zone near theelectrode. At that time the leader starts to develop and pro-gressively bridges the whole gap. Depending upon gaparrangement and polarity, both phases (streamer and leader)can develop only from one or either electrodes. When thegap is closed by the leader and the applied voltage is stillhigh enough, intense ionizing waves lead to the arc develop-ment which completes the breakdown.

In the numerical algorithm, first the leader velocityis empirically formulated as a function of the applied voltage,leader length, gap length, gap geometry and electric fieldintensity with two contributing factors, i.e., leader core andcorona cloud. Then this equation is combined with the cir-cuit equation determined by the experimental condition andsolved numerically in a time step loop until the breakdown asdescribed below.

From [4], the t ime to breakdown (tc) can beexpressed as:

tc = ti + ts + tl (3.6)

where:ti=Corona inception time, assumed zero

ts=Streamer propagation timetl=Leader propagation time

For ts:

(3.7)

where:ts=Streamer propagation time, ?sec

E=Maximum gradient in gap before breakdown,kV/m

E50=Average gradient at CFO voltage, kV/m

For tl:

(3.8)

where:V(t)=Voltage across gap, kVL=Leader length, mg=Gap length, mand

DI ty U t U dtk

to

td

= −∫ ( ( ) ' )

U U U' ( . ) .= − =50 501 2 5 0 96σ

1125 0 95

50t

E

Es

=

−. .

( ) ( )dL

dtK V t

V t

g LEo=

−−

5-7

Using the differential equation of (3-8), the leaderlength can be solved as a function of time. The breakdownoccurs when the leader length “L” is equal to gap length “g”and the corresponding time specifies the tl in Eq. (3-6).

This method can yield the breakdown volt-timecharacteristics of a long gap with any impulse wave inextremely short time (e.g., less than 1 ?sec impulse rise time).It can be applied to a very wide range of experimental condi-tions such as gap configuration (rod-plane and rod-rod),impulse voltage polarity (positive and negative), any impulsevoltage waveform, and a gap length up to 7m. It has beenreported [24, 26] that calculations of leader development andbreakdown volt-time characteristics were carried out andresults were compared with experimental results obtained byauthors, as well as, previously published by other research-ers. Very good agreement was obtained for various gap con-figurations with various voltage waveforms. Furtherinvestigation of associated physical phenomena is expectedin the future.

3.1.4 Corona

It has been well known for some time that coronahas a significant effect on overvoltage surges associated withlightning strikes to overhead lines [5, 7-11]. The important

work carried out by Wagner, Cross and Lloyd [7] resulted inthe following important conclusions concerning coronaeffects:

1.For high magnitude positive surges, the corona effect isindependent of the conductor size and geometry. The sameapplies for negative polarity surges except for one conductorsize (24 millimeter diameter).

2.For low voltages, the effect differs due to different corona-inception voltages.

3.Weather conditions have no significant impact on coronadistortion.

4.The coupling factor between phases increases withincreasing surge voltage.

5.The tail of the surge is not influenced by corona.

The essence of the corona effect on the impulse is the introduction of a time delay to the front of the impulse corresponding to the loss of energy necessary to form the

corona space charge around the conductor. The time delay introduced by corona takes effect above the corona-inception voltage (Vi) and varies with surge magnitude. This variation

with voltage can be expressed as a voltage-dependent capacitance (Ck) which is added to the geometrical capacitance

of the transmission line.

The corona-inception voltage (Vi) for a single conductor

above earth is given by the streamer approach as follows [1]:

(3.9)

where:

r = Conductor radius, cm

h = Conductor height, cm The modeling details of corona can be expressed by curves of charge (q) versus impulse voltage (V). These q/V curves can be divided into three parts:

1.Below corona inception, the q/V curve is a straight linedetermined by the geometrical capacitance. 2.Above corona-inception Vi, the q/V curve shows an initial

capacitance jump (Ci) plus an increase in capacitance which is

voltage dependent as long as the voltage is increasing. 3.For decreasing voltages, the q/V curve again is practicallydetermined by the geometrical capacitance.

The excess capacitance (Ck) to be added during the second stage of the q/V curve is given by [4]:

(3.10)

where:

Ci=Initial capacitance jump, constant

K=Corona constantVi=Corona inception voltage, kV

V=Instantaneous impulse voltage, kV and the sum of the excess capacitance (Ck) and geometric

capacitance (Cg) is the dynamic capacitance (Cdyn):

Cdyn = Ck + Cg (3.11)

The corona constant K varies with conductor diameter and the number of subconductors as well as the polarity of the applied surge voltage. For a 31mm conductor diameter, the constant

varies from 4.8 x 10-3 pF/kVm for a single conductor and

positive polarity surges to 2.4 x 10-3 pF/kVm for 8

Configuration Polarity Km

kV

2

2 sec

E

kV

mo

Air Gaps, PostInsulators

PositiveNegative

0.81.0

600670

Cap and PinInsulators

PositiveNegative

1.21.3

520600

( ) ( ) [ ]V r rh

rkVi = +

23 1 12220 37. ln.

( )C C K V Vk i i= + −

5-8

subconductors and positive polarity surges. For negative polarity surges, the constant is approximately half of these values.

Fig. 3.4 Linear Corona Model

The coupling factor between phases increases due to corona and is given by:

(3.12)

In this equation, Kc is the coupling factor in corona, Kg is the geometric coupling factor, and Cg is the geometric capacitance

[4]. Kg is calculated using the method in [1].

Corona models such as the linear one suggested in Figure 3.4 can be used to model the dynamic capacitance region of the q/V curve in a piecewise linear fashion [8,9]. However, a number of problems remain:

1.The model is constructed of lumped elements and must,therefore, be lumped at sufficiently small intervals along theline that error introduced by the discretization is minimal. Aminimum interval length of 50 meters has been suggested,however, smaller intervals are likely necessary. 2.The model does not adequately address corona in a multi-phase calculation. Here, the voltage dependence of the coronashould be transformed into a charge dependence, becausecorona depends on the electric field around the conductor.

3.The available data on corona parameters of actual three-phase overhead lines is insufficient to enable general practicalapplication of these type of models.

Until better data is available along with complete models in such programs as the EMTP, the approach of Weck can be used to estimate the variation of the steepness of lightning overvoltages impacting on substations with travel length [5]. His approach relies upon the observation that for voltages substantially higher than the corona-inception level, the time delay as a function of travel distance, becomes linear, that is, in this region, the steepness of the overvoltage is independent

of the voltage value. This yields the following relationship:

(3.13)

where So is the original steepness of the overvoltage, S is the new steepness after the waveform travels for a distance d, and A is a constant. The constant A is a function of a line geometry only and is dependent as well on surge polarity. Typical values are given in Reference [5].

Although corona effects may reduce the peak of lightning related overvoltages by 5 - 20% [9], in some studies corona is neglected in order to be on the pessimistic side. The complexity of corona modeling and associated burden on the computer CPU time are the other reasons for such an approach.

3.2. Substation

The overall substation models are derived from the substation layout drawings. The views from all three ordinal directions are very beneficial to locate the exact position of substation equipment.

3.2.1 Buswork and Conductors

The buswork and conductors between the discontinuity points inside the substation, and connections between the substation equipment are explicitly represented by line sections. These line sections are modeled by untransposed distributed parameter sections with modal surge impedances, if they are longer than 3m; otherwise, a lumped parameter inductance of 1.0 ?H/m is used. The line parameters can be calculated using a line constants EMTP routine. Note that the minimum conductor length with distributed parameter representation dictates the simulation time step. In some studies, busbar sections longer than 15m are modeled with distributed parameters to increase the simulation time step. However, caution must be exercised when performing lightning overvoltage calculations for Gas-Insulated Substations (GIS). Since the surge impedance of the gas-insulated buswork (GIB) is considerably smaller than the surge impedance of the air-insulated line or buswork, typically about 60 ohms, traveling wave reflection at the GIB entrance could rapidly result in sizable overvoltages at the open disconnect position within the GIB (i.e., due to multiple reflections). In such scenarios it is critical not to assume a lumped model for the GIB, regardless of the length.

Cables are represented by distributed parameter line sections. Typical surge impedance valves are between 30-60 ohms with velocity of propagation equal to 1/3 to 1/2 of speed of light.

K K C Cc g k g/ /= +1

S

SA d

o

=+ •

11

5-9

Fig. 3.5 Circuit Breaker Representations and Capacitance to Ground Valves for Various Substation Equipment

3.2.2 Substation Equipment

The substation equipment, such as circuit breakers,substation transformers, and instrument transformers, arerepresented by their stray capacitances to ground. The capac-itance of CVTs should also be represented. Figure 3.5 sum-marizes circuit breaker circuit diagrams and minimumcapacitance values used in lightning studies for differenttypes of substation equipment, when the actual data is notavailable. These data are based on supplier information, andonly the lowest values are reported as a pessimistic assump-tion. If the disconnect switches or breakers have more thanone support, appropriate capacitances should be added to themodel. Furthermore, if some of the substation equipment areclose to each other, such as closer than 3m to 5m, their capac-itances can be grouped together for simplification. The open/close status of circuit breakers/switches should be consid-ered, and can be represented by ideal switches.

Line traps are not necessarily found on every phase.Most line traps have a small distribution arrester in parallelwith protection, which pass through a lightning surge.

In lightning studies, conducted to design trans-former protection at the terminals against high voltage, high

frequency disturbances, the most conservative and thereforepessimistic approach would be to represent the transformeras an open circuit. To increase the level of accuracy whensetting up a terminal model of a transformer, it is recom-mended to account for the capacitance of the winding and thecapacitance of the bushing to which the winding is con-nected. Values of the winding capacitance, supplied by IEEEWorking Group on Transient Recovery Voltages, togetherwith capacitance values for outdoor bushings are presented in[28]. A resistance equal to the surge impedance of the wind-ing can be placed across the capacitance.

The model can be enhanced by adding the inductivetransformer model and relevant capacitances between wind-ings, windings to core and windings to ground as well asbushing capacitances. The winding and core capacitancesconstitute together a crude potential divider in which the volt-age divides inversely to the capacitance. Capacitances can bedetermined from the geometry of the coil and core structure,or from manufacturers and tables. The model is used to cal-culate the surge transfer from winding-to-winding as in thecase of generator (or motor) protection studies.

Recently developed transformer model, describedin [16], can accurately determine how a voltage applied toone set of terminals is transferred to another set of terminals.This model duplicates the transformer behavior, over a widerange of frequencies and acts like a filter suppressing somefrequencies and passing others. The use of frequency depen-dent transformer model is important when determining thesurge that appears on a generator bus when a steep-frontedsurge impinges on the high voltage terminals of the generatorstep-up transformer. The model presented in [28] allows thesimulation of any type of multi-phase, multi-winding trans-former as long as its frequency characteristics are knowneither from measurements or from calculations based on thephysical layout of the transformer.

The substation modeling approach outlined aboveis much easier and quicker to implement as compared to asimplified approach described in literature in which the bus-work is represented by distributed parameter lines betweenmajor discontinuities inside the substation, and the lineparameters are modified to include the capacitance of thesubstation equipment, if the total capacitance is less than1000 ?F. In this approach, if the total equipment capaci-tances are larger than 1000 ?F, explicit lumped capacitancerepresentation for the power system equipment must be used.

3.2.3 Insulators and Bus Support Structures

The bus support structures are represented by a dis-tributed parameter model with surge impedances calculatedfrom the structure geometry, and with velocity of propagationequal to the speed of light, similar to the transmission linebus tower models [1]. Typical bus support configurations areshown in Fig. 3.6. The representative grounding resistanceinside the substations is usually between 0.1 to 1 ohms.Comparative simulations showed that the support structuresdo not have much impact on the simulation results, and can

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be neglected. However, the capacitance to ground of all insu-lators should be represented, since the substation capacitanceis one of the critical parameters that modify lightning surgewaveshapes.

Fig. 3.6 Insulator and Bus Support Structure Representation. Bus Support Structure: a. Common to All Phases. b. Individual for Each Phase.

3.3. Surge Arresters

The voltage-current characteristics of metal-oxidesurge arresters are a function of incoming surge steepness.Protective characteristics for surge arresters showing crestdischarge voltage versus time-to-crest of discharge voltagesare available from manufacturers [12]. The arresters can bemodeled as nonlinear resistors with 8 x 20 ?s maximum volt-age-current characteristics. An iterative non-linear resistor ispreferable. The pseudo non-linear resistor should be avoidedif possible, especially in simulations that involve high fre-quencies or backflashovers. This is due to the fact that thesolution algorithm allows for an incorrect operating point forone time-step while switching from one segment to anotheron the piecewise linear representation of the current versusvoltage characteristics. Note that the nonlinear arrester char-acteristics need to be modeled up to at least 20 to 40 kA,since high current surges initiated by close backflashoverscan result in arrester discharge currents above 10 kA. Thearrester lead lengths at the top and at the bottom must be con-sidered to account for the effects of additional voltage riseacross the lead inductance. A lumped element representationwith an inductance of 1.0 ?H/m will be sufficient.

It is a well known fact that, unlike the resistive ele-ments, experimentally obtained arrester terminal voltage andcurrent do not reach their peak values at the same time. Thefrequency dependent characteristics of arresters may be ofsignificant importance when excited by fast transient surges.There have been few attempts to produce frequency depen-dent surge arrester models such as the model suggested byIEEE Surge Arrester Committee which is fairly accurate for awide range of surge wavefronts [13,33]. The drawbacks ofthis model are the increased computational time due to sev-eral nonlinear elements, and the difficulty in choosing theparameters of the model.

A new surge arrester model which can reproducemetal oxide surge arrester characteristics over a wide rangeof frequencies such as lightning, switching, and temporaryovervoltage curves is described in Reference [2]. The modelincludes only one nonlinear element, thereby, expected to becomputationally efficient. The detailed circuit diagram alongwith typical parameters for this model is provided in [2].

The high voltage terminals of transformers are gen-erally protected by surge arresters. Additional arresters maybe necessary at the line entrance and at intermediate loca-tions inside the substation depending upon the BIL require-ments. In substation design studies, the optimum location ofthe arresters inside the substation is one of the outcomes ofthe study. In all studies, the energy through the arrestersmust be monitored, and verified that the maximum allowedenergy dissipation is not exceeded. Furthermore, if thearrester current increases beyond 40 kA, it may create hotspots in the blocks due to high rate of rise times associatedwith backflashovers.

3.4. Sources

3.4.1 Initial Conditions

The instant of lightning stroke with respect to theinstantaneous steady-state ac voltage must be coordinated tomaximize its impact for worst case conditions. This can beachieved by properly selecting the magnitude and phasing ofthe three-phase sinusoidal voltage sources at the terminatingpoint of the transmission lines.

In transmission line design studies, one of theobjectives is to determine the highest line outage rate whichis generally maximized by finding the minimum criticallightning current that causes insulator backflashovers. Theinsulator stress is a combination of the voltage due to light-ning current and the power-frequency voltage. If the light-ning hits the tower when the contribution of ac powerfrequency voltage to the insulation stress is maximum, thebackflashover can occur with a smaller lightning current.Since smaller magnitude lightning currents are more proba-ble, the possibility of line outage due to backflashoversincreases. In general, the outer conductors in a transmissionline will experience the highest insulation stress since thecoupled voltage on these conductors are lower than the inner

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conductors. Thus, while setting the initial magnitude andangle of the ac power frequency voltage, the phase which ismost likely to flashover due to relative conductor positionmust be selected. For a negative polarity lightning stroke,+1.05 pu (opposite polarity) ac voltage will maximize theinsulation stress and thereby the line outage rate. The slopeof the insulator voltage versus time characteristics togetherwith the front time of the lightning stroke are some of theparameters that may cause slight deviations in this recom-mended voltage to obtain the worst case conditions.

In substation design studies, it is desirable to maxi-mize the steepness and magnitude of the line-to-ground volt-age surges toward the substation. The steepness is directlyrelated to the arcing mechanism across the flashing insulatorwhile the magnitude jumps up to the tower top voltage afterthe backflashover. Thus, if the tower voltage has sufficienttime to build up before the backflashover, the worst caseovervoltages can be observed. Setting the magnitude of thepower frequency voltage to +0.5 pu for a negative polaritylightning strike will minimize the insulator stress and delaythe backflashover which will maximize the voltage surge.Other power frequency voltages will cause earlier backflash-overs on the other phases. Note that under these conditions,two of the phases may backflashover at the same time due tosimilar voltages across the insulators, and give the impressionof reduced current and/or energy at the substation arrestersdue to current sharing which may not be the case in reality.

3.4.2 Lightning Stroke

The lightning stroke is represented by a currentsource of negative polarity. The parameters of a lightning,such as crest, front time, maximum current steepness, andduration, are determined by a statistical approach consideringthe ground flash density at the location. These parametersare all statistical in nature, and are also used in calculation ofLFOR and MTBF. They are generally characterized by log-normal distributions. Note that the peak current is statisti-cally related to the steepness or time to crest of the currentwave form. The steepness increases as the peak currentincreases, however, the front time increases as well with peakcurrent. The detailed calculation procedure for these parame-ters is shown in the CIGRE Guide, Reference [4].

A rigorous approach would require the front of thelightning current source to be upwardly concave, however,for practical purposes, a linearly rising front at the selectedmaximum current steepness is sufficient. In this case, a nega-tive triangular wave shape for the lightning current sourcecan be selected. Note that the double exponential impulsemodel given in EMTP should be used only with caution sincethis model does not accurately reflect the concave waveshape of the wave front. Typical lightning current values forbackflashovers and direct strokes are discussed below.

Backflashover - Lightning strokes of high magni-tude, in the range of 20 kA up to values rarely exceeding 200kA, cause the backflashovers. In this current range, median

front times (30% - 90%) range from about 3 ?s at 20 kA toabout 8 ?s at 200 kA. Maximum current steepness rangesfrom about 20 kA/?s at 20 kA to about 48 kA/?s at 200 kA [4,20].

Direct Lightning Stroke - Lightning strokes ofamplitude below the critical shielding current, generally lessthan 20 kA, can bypass the overhead shield wires and strikedirectly on the phase conductors. The maximum lightningcurrent that can strike the phase conductors of any givenoverhead transmission line can be predicted by using themethods recommended by the IEEE Working Group on theEstimation of Lightning Performance of Overhead Lines[14]. The recommended method employs a modified electro-geometric model for the case of perfect shielding. As dis-cussed in Reference [1], it can be shown that the maximumshielding failure current is equal to:

(3.14)

where:

(3.15)

and

Yo= (YG + YC)/2

As=m2 - m2 β2 - β2

Bs=β (m2 + 1)

Cs=(m2 + 1)

m=(XC - XG)/(YG - YC)

Coefficient β is less than 1.0 and its value isreduced when the height of the phase wires is increased. InReference [1], the adopted values are expressed in terms ofthe voltage of the line β=0.8 for EHV lines and β=0.67 forUHV lines. In Reference [34], β is taken as a continuousfunction of the height of the phase wires:

β=.36 + .168 1n (43 - YO) for YO < 40m(3-16)

where XC and XG are the horizontal positions, and

YC and YG are the vertical positions for the phase conductor

and ground wire, respectively. For the unshielded lines, insulation coordination

studies are generally performed with the highest direct strokecurrent that a phase conductor can receive without creating aflashover of the tower insulation (CFO + 3σ).

In regard to the typical current amplitudes involvedin backflashovers and in direct strikes, the following shouldbe noted:

I Smax..= 0 029 1 54

S YB B A C

Aos s s s

s

=− − +

2

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a)Regardless of mechanism by which a lightningvoltage surge is generated (backflash or direct strike), themaximum amplitude of the surge may be taken equal to 1.2 xCFO, where CFO is the critical flashover voltage of the insu-lation. The 1.2 multiplier accounts for two effects:

i)the fact that the CFO is a median value and hencethe insulation can carry higher voltages 50% of the time, and

ii) the CFO is based on the standard 1.2 x 50 ?simpulse waveform. The withstand voltage will hence behigher for steeper fronts and may also be higher for somenon-standard waveforms.

b) In determining the maximum stroke currentwhich can cause shielding failures, References [1] and [34]use a model in which the striking distance to ground is takenequal to ßS, where S is the striking distance to the wires, andß= 1.0 is a factor which is a function of either the voltage orthe height of the phase wires. As noted in the discussion of[14] by A. Mousa, varying ß with voltage (or height of theconductors) produces results which are inconsistent with thephysics of the problem. Reference [31] presents a revisedelectrogeometric model in which the striking distance toground is kept constant. This second approach is more con-sistent with the physics of the problem.

3.5.Time Step and Simulation Time

The accuracy of the digital simulation can be affected by the use of a time step that is too large or too small. The timestep selection depends upon the steepness of the surge, the minimum length of traveling wave models, plus the use of flashover gaps and surge arresters with significant lead lengths. As a general guide:

range of time step = 1 to 20 ns; typical = 5 ns

range of simulation length = 20 to 50 µs, typical 40 µs

4. MODEL VALIDATION

4.1. Field Tests

One of the specific goals of an EPRI investigation was to study and model the type of transient which is generated during a backflashover of transmission line insulation in close proximity to a substation [2,18]. The flashover initiates a steep-fronted surge, the existence of which is important to the insulation design of substation in the voltage range up to 242 kV. A full-scale mockup of a 115 kV rated (550 kV BIL) substation was constructed at EPRI’s High Voltage Transmission Research Center (HVTRC) in Lenox, Massachusetts, to investigate the behavior of nonstandard voltage impulses on substation insulation [2,18]. In the substation, the phase-phase and phase-ground clearances, amount and type of insulation was reproduced according to standard design procedures of a utility which participated in

the study. The substation contained a combination of 795 kcmil aluminum strain bus and 5" diameter aluminum rigid bus with various types of insulators, cap-and-pin switches, station post insulators, and 7 standard 5.75" suspension insulators on strain bus dead-ends. The switches were installed to provide reflections under different operating modes as well as realistic substation equipment gap configurations. Other typical substation air gaps (rod-rod, ring-ring, and conductor-structure) were also incorporated into the substation design.

High voltage flashover tests were conducted by applying phase-to-ground and phase-to-phase impulses. The impulses were generated by discharging a bank of capacitors into the tertiary winding of a single-phase autotransformer and then through a peaking gap and capacitor which resulted in an impulse having a shape of 0.2/200 ?s applied to the test object.

4.2. Substation Modeling and Model Validation

Computer simulations of several flashover testswere performed for benchmarking the substation modelusing EPRI version 1.0 of the EMTP. The substation mockupand test circuit were modeled based on guidelines similar tothe ones described in this paper. Modeling of the individualelements was as detailed as possible. For example, even theshortest connections between two insulator supports wererepresented by distributed parameters; ground mode attenua-tions were modeled; the stray capacitance of each insulatorwas also modeled.

The phase conductors were represented using a linemodel which takes into account the distributed nature of thephase conductors. It also reflects the dependence of the line-to-ground coupling and of the earth’s damping on the spec-tral contents of the surge. The insulators are represented bycapacitances, and three different types of insulators wereused in the substation (cap-and-pin, station post, and suspen-sion), each of which has a different stray capacitance. Thenodes, where the insulators are connected together on thesupport structure, are connected to the grounding cable bycopper conductors. This cable was part of the line setup;therefore, it was represented as distributed parameter linesegments. The grounding cable was solidly grounded at thesubstation entrance. The grounding conductors, which con-nected the towers to the grounding cable, were representedwith lumped linear elements. More detailed informationconcerning the model is available in Reference [2].

The incoming voltage surge waveshape was mod-eled in as much detail as possible. The substation stress isgiven by the voltage impinging on the substation from anincoming line. The steep voltage entering the substation isassumed to be the result of a backflashover of the line insula-tion in close proximity to the substation. The magnitude ofthe voltage is limited by lightning arresters at the substationentrance. These conditions were represented in the computerstudy.

Good agreement was found between the calculated

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voltage waveforms, as determined by EMTP, and oscillo-grams obtained by direct measurements of the impulses inthe substation. Therefore, it was concluded that the bench-marking was satisfactory. More detailed information con-cerning the comparison between measurements andcalculations is available in Reference [2].

5. CASE STUDY

The modeling guidelines described in this paper areapplied in a system study where a lightning surge analysis ofan uprated substation is performed. The substation is upratedfrom 115 kV to 230 kV maintaining 550 kV BIL insulation.The specific objectives of the study are to evaluate the sever-ity of lightning overvoltages stressing the substation, and toestablish the extent of the overvoltage control required toachieve the desired lightning performance. Overvoltage con-trol consists of selecting optimum rating and location for thesurge arresters inside the substation.

Previous work has shown that steep lightning over-voltages, caused by line insulation backflashovers close tothe substation, typically define the limiting scenarios forinsulation design of compact and uprated HV (i.e., up to242 kV) substations. Computer simulations were performedto investigate the overvoltages due to lightning strike at anearby tower. An enhanced version of the BPA’s M39 EMTPis used for the simulations described in this section.

5.1. Computer Model

Based on the guidelines described in this paper andusing the substation layout drawings, an EMTP model for the230 kV, 550 kV BIL substation and its incoming transmis-sion lines were developed as shown in Figs. 5.1 and 5.2. Inthe computer simulations, the lightning is assumed to strikethe first tower outside the substation on 230 kV line #2 attower T2. The lightning stroke is captured by the shield wireat the point of connection to the tower (i.e., its highest point)and is represented as a current source with a negative triangu-lar waveshape. The parameters of the lightning stroke, suchas crest, rise time, and duration, are determined consideringthe line dimensions and lightning incidence data for the siteof the substation [3,4]. The lightning stroke parameters usedin this study are given below.

Peak Current=110 kATime to Crest=3 µsHalf Time= 75 µs

These parameters are based on the MTBF rate of200 years for the substation. This assumes that substationwould fail, if a lightning more than 110 kA would strike thefirst tower of either of the two incoming lines. The strikesfurther away from the substation are less severe.

After the lightning stroke hits the shield wire, towertop voltage increases, resulting in voltage rise across theinsulator strings supporting the phase conductors. There is a

50% probability of insulator flashover, if its voltage reachesthe critical flashover voltage (CFO). It is well recognizedthat the flashover voltage is also dependent upon the steep-ness of the voltage; that is, insulator flashover voltage hasvolt-time dependency.

When the insulator flashover occurs, a surge with avery steep front propagates through the multi-conductortransmission line toward the substation. The severity of theovervoltages at the substation depends on how far the strucktower is away from the substation. Further distances result inless severe overvoltages due to stronger distortion and attenu-ation effects due to corona and ohmic resistance. In thisstudy, corona effects are neglected. This assumption was jus-tified since the lightning is assumed to have stricken the firsttower outside the substation for the base case. Also, protec-tive levels for line entrance arresters are below conductorcorona starting voltage.

TABLE 5.1 CRITICAL PARAMETERS FOR

LIGHTNING ANALYSIS• Base Case• Struck Tower; 1st, 2nd, or 3rd from the substation• Tower Resistance; 15-50 ohms• Arrester Placement• Line Outages• Substation Equipment Outages, Transformer, Breaker,• etc.• Lightning Current Magnitude and Rise Time• Strike to shield for backflashover or simulate direct • strokes

The total EMTP simulation time was chosen to besufficiently large to observe the decaying of overvoltages andreflections from the incoming lines. In this study, the maxi-mum simulation time is set to 20 µs. The simulations areperformed with a 5 ns time step. Decreasing the time stepdown to 1 ns gives almost identical results, indicating that theselected time step is sufficiently small for the transients ofinterest.

5.2. Case List

In order to cover various substation operating conditions, a simulation case list is formed considering the system contingencies and substation equipment outages for the worst scenarios. A base case is defined for a comparative analysis of system parameter variations. In the base case, surge arresters are located at all 230 kV line entrances and at all transformer locations; however, there are no bus arresters. Furthermore, all incoming lines are assumed to be in service without any substation equipment outages. Several simulations are performed with different magnitudes and rise times of lightning strokes hitting different towers away from the substation entrance. The effects of tower footing resistance variations are also considered. Table 5.1 shows a list of important parameters to be considered in general

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lightning analysis. Sensitivity studies with respect to these variables within the applicable range of values are strongly recommended.

5.3 Simulation Results

The simulation results are given in terms of plots of waveforms for the important system variables, such as line insulator voltages, phase-to-ground and phase-to-phase voltages at towers, tower top voltages, and tower grounding resistance voltages. Inside the substation, phase-to-ground and phase-to-phase voltages at all equipment locations, at minimum clearance points, and at midway between arresters are provided, in addition to arrester voltage, current and energy duties. Sample waveforms for the base case are provided in Figs. 5.3 through 5.6.

A comprehensive set of lightning overvoltage studies are performed to establish the minimum insulation requirements. The effects of the lightning overvoltages on the equipment BIL, minimum phase-to-ground and phase-to-phase clearances, and surge arrester energy duties are evaluated for several contingencies. In some of the cases simulated, it has been observed that the BIL rating of the substation could be

exceeded. Additional simulation results showed that by placing line entrance arresters overvoltage control inside the substation can be accomplished. In overall conclusion, application of 180 kV rated metal oxide arresters at both line entrance and all transformer locations makes it feasible to uprate the 550 kV BIL substation from 115 kV to 230 kV.

The following power system components may be the subject of further research for possible improvements in the existing models:

•Corona Models for Transmission Lines

•Frequency Dependent Models for Double-Circuit Lines

•Frequency Dependent Models for Cables

•Models for Tall Towers

Fig. 5.1 Substation EMTP Model - Transmission Line Details.

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Fig. 5.2 Substation EMTP Model - Substation Details

5-16

Fig. 5.3 230 kV Line Voltage Waveforms

Fig. 5.4 Struck Tower Voltage Waveforms

Fig. 5.3 230 kV Line Voltage Waveforms

Fig. 5.5 Phase-to-Ground Voltage Waveforms Inside the Substations

Fig. 5.6 Arrester Voltage, Current and Energy Waveformss

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6. CONCLUSIONS

Modeling philosophy, simplified mathematical rela-tionships and typical data are presented for various powersystem components in studies of fast front transients.Although emphasis has been on lightning surge analysis oftransmission lines and substations, modeling guidelines areapplicable for similar phenomena having the same frequencyrange (i.e., 10 kHz up to 1 MHz).

Examples where such modeling guidelines areapplicable include:

a) selection of surge arrester location and rating forprotection of transmission lines, as well as air-insulated andgas-insulatedsubstation,

b) selection/verification of clearances within sub-stations and transmission towers (i.e., phase-to-ground andphase-to-phase),

c) calculation of flashover rates or MTBF, etc Fur-ther illustration of the modeling guidelines has also beendemonstrated through a “case study”. Note that field test val-idation of the modeling guidelines is reported in Ref. [2].

Altogether, this report provides a working referencedocument for engineers involved in electromagnetic tran-sients simulation of transmission and distribution systems.

7. REFERENCES

[1]Transmission Line Reference Book, 345 kV and Above,Second Edition, Electric Power Research Institute, Palo Alto,California, 1982.[2]EPRI Substation Voltage Uprating, Volumes I and II, EPRIEL-6474, April 1992.[3]EPRI Substation Voltage Uprating Seminar, Denver, CO,March 3-5, 1992.[4]“Guide to Procedures for Estimating the LightningPerformance of Transmission Lines,” CIGRE Working Group33-01 (Lightning) of StudyCommittee 33 (Overvoltages and Insulation Coordination),Paris, October, 1991.[5]A.J. Eriksson and K.H. Weck, “Simplified Procedures forDetermining Representative Substation Impinging LightningOvervoltages,” Paper 33-16, CIGRE, Paris, 1988.[6]M. Khalifa, High Voltage Engineering, Marcel Dekker Inc.,New York, 1990.[7]C.F. Wagner, I.W. Cross, and B.L. Lloyd, “High VoltageImpulse Tests on Transmission Lines,” AIEE Transactions onPower Apparatus and Systems, Vol. PAS 73, pp. 196-209,1954.[8]A. Ametani, and H. Motoyama, “A Linear Corona Model,”EMTP Newsletter, 1987. [9]H. Elahi, M. Sublich, M.E. Anderson, and B.D. Nelson,“Lightning Overvoltage Protection of the Paddock 362-145kV Gas Insulated Substation,” IEEE Transactions on PowerDelivery, Vol. PWRD-5, pp. 144-149, January 1990.[10]K. C. Lee, “Non-Linear Corona Models in theElectromagnetic Transient Program,” IEEE Transactions on

Power Apparatus and Systems, Vol. PAS-102, No. 9, pp.2936-2942, September 1983. [9]H. Elahi, M. Sublich, M.E.Anderson, and B.D. Nelson, “Lightning OvervoltageProtection of the Paddock 362-145 kV Gas InsulatedSubstation,” IEEE Transactions on Power Delivery, Vol.PWRD-5, pp. 144-149, January 1990.[10]K. C. Lee, “Non-Linear Corona Models in theElectromagnetic Transient Program,” IEEE Transactions onPower Apparatus and Systems, Vol. PAS-102, No. 9, pp.2936-2942, September 1983.[11]M.M. Suliciu, and I Suliciu, “A Rate Type ConstitutiveEquation for the Description of the Corona Effect,” IEEETransactions on Power Apparatus and Systems, Vol. PAS-100, No. 8, pp. 3681-3685, August 1981.[12]GE Tranquell XE Station Surge Arresters, Product andApplication Guide, 1986.[13]IEEE Working Group 3.4.11, Application of SurgeProtection Devices Subcommittee, Surge Protection DevicesCommittee, “Modeling of Metal Oxide Surge Arrester,” IEEETransactions on PWRD, Vol. 7, No. 1, January 1992.[14]IEEE Working Group on the Estimation of LightningPerformance of Overhead Lines, “A Simplified Method forEstimating Lightning Performance of Transmission Lines,”IEEE Trans. on PAS, Vol.PAS-104, No. 4, pp. 919-932, 1985.[15]G.W. Brown, “Lightning Performance I; ShieldingFailures Simplified,” IEEE Transactions on Power Apparatusand Systems, Vol. 97, pp. 33-38, January/February 1978. [16]M. G. Lauby, “Detailed Transformer Model for EMTP,”EMTP Review, October 1989.[17]A.M. Mousa, “The SoilIonization Gradient Associated With Discharge of HighCurrents Into Concentrated Electrodes,” IEEE Trans. onPWRD, Vol. 9, No. 3, pp 1669-1677, 1994.[18]J. Panek, et. al., “Substation Voltage Uprating,” CIGRE,Paper No. 33-207, 1992.[19]H.W. Dommel, Electromagnetic Transients ProgramReference Manual (EMTP Theory Book), Report Prepared forBonneville Power Administration, Portland, Oregon, August1986.[20]R.B. Anderson, and A.J. Ericksson, “LightningParameters for Engineering Application,” Electra, No. 69, pp.65-102.[21]M. Rioual, et. al., “Short and Long Air Gaps (InsulatorStrings and Spark Gaps) Modeling for Lightning Studies withthe EMTP Program,” EPRI, Palo Alto, California, 1989.[22]C. F. Wagner and A. R. Hileman, “Mechanism ofBreakdown of Laboratory Gaps,” AIEE Transactions, Vol. 80,pp. 604-622, 1961.[23]T. Harada, et. al., “V-T Characteristics of Air Gaps forSteep Front Impulses,” ISH-Milan, 52.06. 1979.[24]T. Shindo and T. Suzuki, “A New Calculation Method ofBreakdown Voltage Time Characteristics of Long Air Gaps,”IEEE Transactions on PAS, Vol. PAS 104, pp. 1556-1563,June 1985.[25]A. Pigini, et. al., “Performance of Large Air Gaps under

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