Transient overvoltages on power systems

IEE REVIEW

Transient overvoltages on powersystems

J.P. Bickford, M.Sc.(Tech)., Ph.D., C.Eng., M.I.E.E., and A.G. Heaton, B.Sc.Ph.D., C.Eng., M.I.E.E.

Indexing terms: Power systems and plant, Transients, Overvoltages

Abstract: Power systems are subjected to many forms of transient phenomena brought about essentially bysudden changes in the steady state values of voltages or currents. Such changes may be the result of a lightningstroke, some malfunction of the system or be brought about by the switching of a circuit either to clear a faultor as a normal operational procedure. To be practical the scope of the review has had to be restricted. Neverthe-less it has been found possible to cover a wide range of transient voltages from those which pose problems intransmission systems operating at the highest levels of system voltage down to those which can appear in thedomestic situation. Apart from mentioning nonlinear elements in systems, the review is, in the main, restricted tophenomena which are essentially linear in nature and no attempt has been made to include the more compli-cated phenomena associated with ferroresonance or the production and propagation of harmonic voltages andcurrents. The review does not claim to be exhaustive but it is hoped that the major causes of transient overvol-tages have been considered. In addition to dealing with the causes of transient overvoltages, the review indicatesthe range of analytical methods that are now available for their analysis and assessment.

1 Introduction

1.1 Scope of the reviewThis review covers a wide dynamic range of transient volt-ages, from those which pose problems in the distributionand supply of power down to effects of low-voltage tran-sients in the domestic situation.

The source of the transient in the case of lightning maybe difficult to characterise; nevertheless, the inducedvoltage waveforms may be determined from theoreticalconsiderations. The order of magnitude of such waveformscan be calculated using numerical values attached tomathematical models of the structure of the stroke. It isevident that the majority of transient conditions in electri-cal circuits are initiated by the action of closing or openinga switch or circuit breaker. The switching operation isessentially mechanical, where power system voltages areconcerned, and the effect on any circuit is to change theimpedance of the circuit by altering the interconnection ofcircuit elements and to apply voltage or current shocks tothe circuit. With the advent of solid-state switching devicesthere has been a tremendous increase in the use of cyclecontrol of loads in industrial and domestic situations.These devices operate in low voltage circuits and oftenproduce sequences of transients manifesting themselves asbursts of radio interference (RFI) which add to the back-ground of 'man-made static', a term used in earlier days todescribe radio interference caused mainly by AC com-mutator motors and motor starter relays.

It is intended that the review should indicate the rangeof analytical methods available to solve problems arisingfrom transient overvoltages in existing systems and in theassessment of performance of projected systems at thedesign stage. The effectiveness of such methods depends onthe detailed formulation of the physical situation and aknowledge of the characteristics of the plant involved, overa wide frequency range.

Paper 4533C, received in final form 23rd January 1986

IEE Commissioned Review

The authors are with the Department of Electrical Engineering & Electronics, Uni-versity of Manchester Institute of Science and Technology, PO Box 88, ManchesterM60 1QD, United Kingdom

7.2 Historical backgroundThe invention of the electric lamp by Swan and Edison inthe late 1870s led to a rapid expansion in the use of elec-tricity. Generating equipment increased in size and theswitching of machines in parallel became necessary tocater for the build-up of loads which varied widely overthe working day and night. Some 90 years ago Ferranticonstructed a 10 kV link from Deptford, Kent to NewBond Street in London which was probably the first majorpower transmission system. Ferranti found a significantrise of voltage along the unloaded cable. This 'Ferrantieffect' constitutes a steady-state overvoltage which dependson source impedance, the surge impedance of the cableand its electrical length which, in this case, would havebeen a fairly small fraction of a wavelength. This type ofovervoltage did not cause problems until the advent ofEHV systems which used shunt reactors to control steady-state overvoltages under light-load conditions. Overvol-tages caused by lightning discharges on overhead lineshave been limited by the use of rod gaps, earth wires andlightning arresters from as early as 1905. Air-breakswitches in which a long arc was drawn were used onsystems up to 10 kV by the turn of the century. The long-arc provided a simple and commonsense means by whichthe current could be gradually interrupted to prevent tran-sient overvoltages. From the turn of the century to the late1920s there had been a gradual increase in machinevoltage up to 11 kV. In 1928 the first 33 kV machine wascommissioned at Brimsdown power station. The conduc-tor bars were made in the form of cables having 3 conduc-tors giving a maximum insulation stress equivalent to thatof an 11 k V machine.

During 1920-29, the importance of the transientrecovery voltage appearing across a circuit breaker duringopening was recognised. This led to a realistic assessmentof circuit-breaker duties and to the introduction ofopening resistors to control this voltage. Following theSecond World War, the severe transient recovery voltageassociated with a short-line fault was identified. From 1946the projected demands for electricity called for a massiveexpansion of the electricity supply industry and, followingthe Electricity Act (1947), the British Electricity Authority

IEE PROCEEDINGS, Vol. 133, Pt. C, No. 4, MAY 1986 201

was set up to bring together some 561 separate supplyundertakings having many different supply voltages. Theincreased requirement for switchgear in the integratedsystem called for the best and most economic designs, andstandardisation and rationalisation played an essentialrole in achieving this objective. The surge voltages pro-duced on closing a circuit breaker had been well knownfor most of this period, but the need to limit insulationlevels on UHV systems stimulated a thorough study ofsuch overvoltages in the early 1960s. This resulted in theintroduction of circuit breakers with closing resistors tolimit switching-surge overvoltages. It soon became evidentthat severe transients could be generated within powertransmission systems by switching lines and cables in anunrestricted sequence. At the higher transmission voltagesthis could produce overvoltages greater in magnitude thanthose produced by lightning strikes. This was brought tolight in 1960 when rod-gap flashovers were experienced ona 230 kV system in North America [1] where a 4.5 mileline was terminated in a voltage regulating transformer,with series and shunt windings, connected as part of theline. Switching tests carried out on this system indicatedthat closure on to the line produced a peak transient, onthe busbar side of the transformer, 2.6 times the peaknormal frequency phase-to-ground voltage, i.e. 488 kV.The predominant frequency of the transient was found tobe 9 kHz which is close to the quarter-wave frequency ofan air-spaced line 4.5 miles long, i.e. 10.3 kHz. The rod-gapsettings were 36 inches when flashovers were consistentlyexperienced. The rod-gaps were increased to 40 inches andno flashovers occurred subsequently. Flashovers of arcinghorns on a 132 kV system in the UK was investigated indetail in 1964 [2]. The system consisted essentially of a 3.8mile length of overhead line, energised by an air circuitbreaker, terminated in a fault limiting inductor at the farend. Arcing-horns at the remote end of the inductorflashed over on energisation of the line. The predominantfrequency of the transient was found to be 12 kHz which isvery close to the quarter-wave frequency of the air-spacedline 3.8 miles long. The high-voltage bushings and the dis-tributed capacitance of the fault limiting inductor werefound to have resonant properties around 12 kHz whichinteracted with reflections on the line to build up a peaktransient of 4.6 per unit, i.e. 485 kV. The arcing-horns werefound to be set to 38.5 inches when flashovers were experi-enced. At the time of this flashover, which was the result ofpre-arc at peak of the supply voltage onto the line/inductor combination by an air blast circuit breaker, thecharacteristics of plant were specified only at power fre-quency. Subsequently, inductors supplied to the samespecification were tested and found to have widely differentcharacteristics in the kilohertz frequency range, largely dueto the type of screen used in the construction, e.g. iron oraluminium. The analysis of this particular problem wascarried out in detail by a Fourier analysis technique inwhich the frequency dependent parameters of the line, i.e.the propagation constant and attenuation, were used alongwith the measured frequency-dependent inductor charac-teristics.

2 Lightning overvoltages

A great deal of statistical information concerning elec-tricity distribution system faults due to lightning has beencollected at the ERA and elsewhere in the past. NotablyGosden [3] presented the following statistics of faults onBritish systems during 1967/68 to 1970/71 from the

National Fault and Interruption Reporting Scheme of theBritish Electricity Boards:

(i) at least 32% of all faults affecting the supply systemoperating at voltages between 650 V and 66 kV were dueto lightning, causing a loss of 4.4 million consumer hoursduring 2.7 million consumer interruptions per annum

(») 89% of these faults occurred on the 11 kV system,causing a loss of 3.1 million consumer hours during 1.6million consumer interruptions per annum

(Hi) 77% of those in (ii) were of a transient naturecausing no damage to the supply equipment, and theyresulted in a loss of 1.3 million consumer hours during 0.7million consumer interruptions each year.

The significance of transient non-damage faults on the11 kV system is apparent from these figures and it is clearthat a major improvement in supply reliability is possibleif interruptions arising from this cause could be reduced.

A direct lightning stroke to a line can result in per-manent damage, either to line insulators after flashover, orto terminal equipment, although some protection can beprovided for the latter by surge diverters and spark gaps.However, the incidence of direct strokes is very small. Onaverage, one direct stroke occurs per 100 km on the British11 kV system each year. Therefore, direct strokes do notcontribute significantly to the transient faults on the 11 kVsystem. On the other hand, voltage surges on 11 kV linesinduced by lightning strokes to earth near line routes causethe vast majority of the supply interruptions arising fromnatural phenomena.

2.1 Induced voltages due to indirect lightning strokesLightning strokes to earth in the vicinity of an overheadline induce voltages on the line conductors. Golde's theory[4] of bound charges on the line only accounted forseveral hundreds of faults on the 11 kV system per annumwhereas the fault statistics indicate that 10000 per annumis a realistic figure for fault incidence due to lightning.Recordings made by Cornfield and Stringfellow [5] showthat induced-voltage waveforms are bipolar with a firstpeak of up to 200 kV of negative polarity. One typicalwaveform, recorded on a 33 kV line, is shown in Fig. 1.

100h

50

1 °2 -50>-100

-150

0 10 20 30 40 50 60 70 80 90 100time, jis

Fig. 1 Typical recorded bipolar induced-voltage waveform

The impulse withstand voltages of plant on the 33 and 11kV systems are 200 and 95 kV, respectively. Hence, in-direct strokes could result in a very significant number oftransient non-damage faults on the 11 kV system and onlyoccasional faults on the 33 kV system. This is, in fact, con-firmed by the fault statistics. In addition, indirect strokesup to 500 m from a line can induce significant voltage onit. This wider collection area results in a very much greaterprobability of line overvoltages due to indirect strokesthan direct strokes. The probability is further enhanced bythe large number of spurs on 11 kV lines (compared with,for instance, 33 kV lines).

Chowdhuri and Gross [6] developed a theory which

202 IEE PROCEEDINGS, Vol. 133, Pt. C, No. 4, MAY 1986

gave unipolar and bipolar waveforms of induced voltage,depending on the parameters of the stroke and its positionrelative to the line. This theory considered to be negligiblethe components of induced voltage on the line due to anybound charges. The leader was also assumed to produceno significant induced voltage, as the total time taken forthe leader to reach the ground from the cloud wasassumed to be too great for any induced charge on the lineto accumulate to produce a significant voltage. Theinduced voltage was attributed solely to the return strokecharge and current. The electric field intensity £, at anypoint along the line and at any time was expressed in theform

where (f> is the inducing scalar potential created by thecharge of the return stroke and A is the vector potentialcreated by the current of the return stroke, (j) and A weregiven by Maxwell's field equations in terms of chargedensity and current density, respectively. The height h ofthe line is insignificant compared with that of the cloudabove the ground, thus permitting a linear calculation ofthe value of the inducing voltage Vt at any point of the lineat any time from

The speed at which the return stroke moves upwardsapproaches the velocity of light. The electromagneticeffects, which produce the inducing voltage, of the chargeand the current, travel toward the line at the velocity oflight. Therefore, the equations for the inducing potentialsA and <j) were modified to indicate that, at a given point onthe line at a given time, the potentials are determined bythe charge and the current which existed at the stroke atan earlier time. The difference in time is that required totravel the distance between the stroke and the field pointat the velocity of light.

One conductor of the line was then represented by dis-tributed series inductance and shunt capacitance. Theeffect of the inducing voltage V{ was represented by con-necting a voltage source at each point on the line as shownin Fig. 2.

OfVi r>jv,*i

Fig. 2 Equivalent circuit of line with inducing voltage

The induced voltage V at any point x on the line at anytime t was then obtained from the solution of

d2vdx2

d2v -dt2 ~ c2 dt2

where c is the velocity of light.In computing the induced voltage on a doubly-infinite

single conductor, a linearly rising return-stroke currentwas assumed with time. The theory produced bipolarwaveforms with a few exceptions, the first peak of negativevoltage arising due to the rate of change of the current.The polarity is then reversed by the effect of the charge inthe return stroke. The waveform becomes unipolar wheneither the electrostatic effect or the magnetic effect solely

predominates, being of negative or positive polarity,respectively. The results also indicated that the maximumvalue of the induced voltage occurs on the line at a pointwhich is remote from the stroke, and that strokes as nearas 500 m to the line can induce voltages in excess of100 kV. The induced voltage at any point consists of twosuperimposed components: (i) a travelling wave and (ii) anelectrostatically induced voltage. The results also indicatedthat the electromagnetic effect predominates nearer thestroke whereas the electrostatic effect is predominantremote from the stroke.

Chowdhuri and Gross were unable to match the ampli-tudes of computed waveforms with the waveforms record-ed by Cornfield and Stringfellow, even with allowance fornon-uniform distribution of charge in the leader. Singa-rajah [7] explained the initial negative excursion of theinduced voltage by accounting for the effect of the leader.The effect of the charge in the leader had previously beenneglected, as, in computing the average velocity, the pausesbetween the leader steps were included in the total time ofthe leader. However, if significant charge is transferredduring steps, then the voltage induced by the leader duringthe last step to ground or by the connecting streamer maynot be negligible, due to its high speed and proximity tothe line. Singarajah's theory predicted bipolar waveformswhich resembled recorded voltages more than any pre-vious theory.

To verify the postulated theories, Stringfellow [8]recorded the variation of the inducing electric field inten-sity at a point near the surface of the earth and close to anartificially triggered lightning stroke to ground. A typicalrecording is shown in Fig. 3. The final increase in field

r10

-10 10time, ̂

20 30

Fig. 3 Recorded electric field near the ground

intensity due to the last step of the leader is followed by arapid collapse of the field during the return stroke. It wasfound that each stroke consisted of multiple discharges.The initial triggered stroke was followed by successivedownward-moving dart leaders and upward-movingreturn strokes. A theoretical model of the stroke structurewas adopted to be able to calculate the magnitude ofinduced voltages on a line. The model assumes that,during the leader process, charge is deposited uniformlyalong the channel as the leader descends, and that the


return stroke comprises a zone of high conductivity risingfrom the ground and neutralising the leader charge. Thenet charge, therefore, during both the leader and the returnstroke is a negative column extending from the clouddown to some point. The electric field intensity at the mea-suring point due to this column of negative charge wascalculated for various values of height of the base of thecolumn above ground and for various charge densities.Correlation of the measured field intensity/time curves andthe calculated field intensity/height curves gave an estimateof the distribution of the leader at return stroke charge atvarious heights and times, i.e. a new boundary condition.

The theory of Chowdhuri and Gross was thenemployed with the new boundary condition to computethe inducing electric field intensity, and then the inducedvoltage at any point along a doubly-infinite line at anytime. Examples of the calculated variations of electric fieldintensity and induced voltage are shown in Figs. 4 and 5,

n

ty,

kV/m

in

a>•£-20

ield

u-30uQj

0)

-40

-80

_

;

-

-

-

time, jis-60 -40 -20 0 20 40

• . .

\\

leader \

V

r\1 return1 stroke

1Fig. 4 Calculated variation of inducing electric field intensity with time

for an indirect stroke 100 mfrom the lineCharge density = 2.5 x 10~* C/mCurrent = 12.5 kA

600

>400

| 2 0 0

uced

ind c

-200

-

-

_

-

- 4

\\

/ i I i

/ 0 4/ time, us

/

Vi i i i

8 12

Fig. 5 Calculated variation of induced voltage with time for an indirectstroke 50 mfrom a 10 m-high overhead lineCharge density = 1.25 x 10"3 C/mCurrent = 60 kA

respectively. The consideration of the leader during thetime before the commencement of the return stroke, andthe realistic expression for charge-density movement, pro-duced close agreement with recorded bipolar waveforms ofinduced voltage, and hence verified that the leader isresponsible for the first negative excursion. The magneticeffect due to the current was found to have little effect, thechange of the electric field being almost entirelyresponsible for the induced voltage waveform. However,the induced voltage on the line is composed of a travellingwave and an additional electrostatically-induced voltage.The theory confirms that the maximum value of voltageoccurs on the line at a point which is remote from thestroke.

2.2 Response of unprotected 11 kV line to inducedvoltage

Baker [9] describes the response of an 11 kV overheadnetwork to the induced voltage waveforms. The inducedvoltage to earth is approximately equal on each of thethree conductors of the line. It will be superimposed on the50 Hz rated AC voltage to earth. When, at some earthedpoint on the line, the total voltage to earth exceeds theimpulse withstand value of 120 kV of a line insulator itflashes over. This flashover will occur, during the negativeexcursion of the surge voltage, on the one conductor whichis more negative, due to the 50 Hz voltage, than the othertwo. The flashover results in reflected surges.'

The surge impedance of one conductor when connectedto earth was calculated to be 443 Q by substitution oftypical parameters of an 11 kV line in Schlatter's [10]theory for a multi-conductor system. Therefore, the reflec-tion coefficient at the flashover is of the order of 0.8 toalmost unity and is negative. The resulting positive reflec-tion from the flashover is shared by all three conductorsafter travelling a short distance. Baker [9] then describesthe creation of a second flashover. It is possible that, in along distribution line with no spurs, the positive surgewhich is reflected by the first flashover during the negativeexcursion of the induced voltage would cause a secondflashover when meeting the incident positive excursion ofthe induced voltage. This flashover would occur if the sumof the amplitudes of the positive excursion and the re-flected positive surge exceeded 120 kV. It would mostlikely occur on the conductor which had the most positive50 Hz voltage to earth at that time, i.e. a different conduc-tor to the one which flashed over first. For a typical timebetween negative and positive peaks of induced voltage of20 fis, the two flashovers would occur approximately 6 kmapart.

There are many earth points on a practical 11 kV dis-tribution line. It is, therefore, more likely that the firstflashover will occur at two earthed poles near to and ateach side of the point nearest the stroke. The two positivereflections which travel back toward the point nearest theflash will meet and, if of sufficient combined amplitude,will produce the second flashover. This will occur beforethe positive excursion of the incident induced voltage canmake any contribution, and at some point near the stroke.

A typical 11 kV distributor also has many spurs. Trav-elling wave components of voltage on a main line arereduced, on passing a spur, to two-thirds of their originalvalue. However, voltage doubling at the end of a spur linecan also result in sufficient increase of surge amplitude toproduce flashover. There are, then, various possible sitesfor flashover on an 11 kV distribution network. However,they all result in a first flashover to earth which is followedby a second flashover to earth in a second conductor.Therefore, this presents a line-line-earth fault for power-frequency follow-through current, the two earth resistanceslimiting the current magnitude. This occurrence agreeswith the fault recording results of Seed [11] who notedthat 78% of faults due to lightning are multiphase to earth.Plant connected to the line is vulnerable to incident andreflected induced voltages, if the plant impulse withstandvoltage is exceeded. It is, therefore, essential to divert theseinduced voltages to earth to avoid plant replacement.

2.3 Overvoltage protection of 11 kV overhead system

2.3.1 Protection of plant: 'Duplex' rod gaps and surgediverters are employed extensively on 11 kV systems toprotect transformers and cables from overvoltages. The

204 1EE PROCEEDINGS, Vol. 133, Pt. C, No. 4, MAY 1986

reliability, as shown from experience of surge diverters inservice, is unsatisfactory [161, 162]. Baker [163] notedthat duplex gaps have a relatively poor wavefront per-formance when subjected to typical surges appearing aftera direct lightning stroke. Attenuation due to insulatorfiashover is also poor. The triggered gap of Baker [9, 163]achieves a much faster wavefront performance than duplexgaps, offering protection to plant against direct strokes.

Baker [9] claims almost complete protection to plantagainst induced voltages by connection of a single trig-gered gap between the centre conductor and earth. Flash-over of the gap results in discharge of the outerconductor-to-earth capacitances, reducing the voltages toearth of the outer conductors by approximately 50%.Resistance of the earth electrode reduces this percentage.The insulation of terminal plant can withstand the 95 kVsurge, which would remain after fiashover of the gap whensubjected to an induced voltage surge of 190 kV. Very fewinduced voltages exceed 190 kV in practice, as demon-strated by the recordings of Cornfield and Stringfellow [5].The relative economy of installing one triggered gap (at analready earthed terminal pole), to protect the systemagainst induced surges, justifies the omission of morecostly surge diverters (possibly with a separate earthelectrode) necessary to protect the network against therelatively rare direct strokes. Breakdown of a spark gap isfollowed by conduction of power-frequency current toearth.

3 Overvoltages caused by interruption ofcurrents

In power systems the switching of circuits as part of thenormal operating procedure and the clearance of faults areperformed by circuit breakers. Previous reviews [12, 13,14] and an IEE monograph [15] have dealt extensivelywith the subject of circuit breakers. Interruption of currentin a circuit by means of a circuit breaker normally occursat a current zero of the AC wave and results in a voltageappearing across the contacts of the circuit breaker. Thisvoltage contains a transient component, and is known asthe transient recovery voltage (TRV) and, for low powerfactor circuits, may attain values substantially in excess ofthe system nominal voltage. The peak value of the TRVand the rate of rise to this peak exert a considerable influ-ence on circuit breaker performance.

3.1 Mechanism of circuit interruptionThe phenomenon of circuit interruption is illustrated inFig. 6. On receipt of a trip signal, the contacts separate at

Fig. 6 Illustrating current interruption

point A and an arc is drawn between them. The arc, whichhas a small voltage drop Va, continues until the current / isinsufficient to maintain it. This occurs as the current passesthrough zero, at which point the arc extinguishes and thetransient recovery voltage appears across the circuitbreaker contacts. To achieve successful interruption the

dielectric strength between the separating contacts must beestablished at a higher rate than the build-up of the TRVand, furthermore, the peak value of the TRV must notexceed the breakdown strength of the gap between thecontacts. If these conditions are not satisfied the arc will bere-established and current interruption will be delayeduntil a subsequent current zero. When the current ceasesto flow, the voltage between the contacts undergoes achange from virtually zero (the arc voltage) to the instanta-neous value of the power frequency voltage. Such a changecannot take place instantaneously, overshoot occurs andthe voltage approaches its steady state value by means of atransient oscillation whose frequency is determined by thevalues of the circuit inductances and capacitances adjacentto the circuit breaker. The amplitude of the TRV oscil-lation may have a value of twice the steady state voltagechange but, in practice, its value is usually something lessthan this due mainly to the damping produced by thelosses of the system.

The instantaneous value of the recovery voltage at theinstant of current interruption depends upon the powerfactor of the circuit. The amplitude of the voltage changewhich takes place will depend also on whether load orfault current is being interrupted and, if the latter, on thecircuit impedance between the circuit breaker and thefault. The form of the TRV under various system condi-tions is dealt with in References 16 and 17. Under faultconditions, power systems are mainly inductive so that thepower factor of the circuit as seen from the circuit breakeris effectively zero lagging and the power frequency com-ponent of the TRV has its maximum value at the instant ofcurrent interruption.

Because of the displacement that exists between the cur-rents in the phases of a three phase system, current zeroand hence interruption occurs earlier in one phase than inthe other two. As a consequence, clearance of a three-phase unearthed fault on an earthed neutral system leadsto a power frequency component of the TRV having avalue of 1.5 times the peak phase to neutral voltage at theinstant of interruption. Without system damping, over-shoot can double this so that the TRV across the circuitbreaker under this condition can reach a value of threetimes the peak value of the phase to neutral voltage.

3.2 Severity of the transient recovery voltageInformation about the transient recovery voltage that acircuit breaker is expected to encounter in service is ofgreat importance in the design of the circuit breaker. Thishas led to TRV surveys [18-22, 27, 28] of power systemnetworks being carried out based on both computer calcu-lations and field measurements. An assessment of the TRVunder the most severe conditions is required, and for lowervoltage networks has led to surveys being based on thecondition of the first phase to clear a three-phaseunearthed fault. For systems operating at voltages inexcess of 362 kV a three-phase unearthed fault is a rareoccurrence and has resulted in recommendations [20, 21]that, for such systems, the TRV should be assessed on thebasis of a three-phase earthed fault with a multiplyingfactor of 1.3 rather than the 1.5 associated with anunearthed fault.

The severity of the duty on a circuit breaker dependsupon the magnitude of the fault current interrupted, sothat to obtain the most onerous condition the three-phasefault is located at the substation with the highest faultlevel. To maximise the fault current interrupted, the fault isassumed to occur on the terminals of a circuit breaker of acircuit with either no fault infeed or minimum fault infeed.


The value of the stray shunt capacitance on the terminalsof such a circuit breaker is likely to be comparatively highas, by necessity, to obtain a high fault level many circuitsmust be connected to the substation, each contributing tothe total shunt capacitance. The severity of the circuitbreaker duty increases with the rate of rise of the TRV. Ahigh rate of rise implies that the transient waveform con-tains a high frequency component which is obtained whenthe shunt capacitance at the circuit breaker terminals islow. Thus, in addition to considering substations with highfault levels, TRV surveys must also examine those systemconditions which lead to low values of shunt capacitanceoccurring at the circuit breaker terminals as they canproduce high rates of rise even though the fault currentinterrupted may be comparatively low.

The switching condition so far considered is the clear-ance of a terminal fault, i.e. a fault on the terminals of thecircuit breaker. Although this produces a large faultcurrent and for this reason must always be taken into con-sideration, other switching situations exist which can leadto undesirable transient conditions being imposed both onthe circuit breaker and on the system as a whole. Promi-nent amongst these are the short line fault, the interruptionof low inductive currents and the interruption of thecapacitive currents of open lines and capacitor banks.

3.3 Short line faults [23-26, 29-37]This is the situation which exists when a fault occurs ashort distance along a transmission line from the circuitbreaker. If the length of line between the fault and thecircuit breaker is less than about 10 km, the fault isreferred to as a short line fault and its clearance is capableof producing conditions which may impose a severe stresson the circuit breaker.

Under these conditions the TRV has two components.The frequency of the first of these is governed by theparameters of the circuits connected on the source side ofthe circuit breaker. The second component is due to thelength of line between the circuit breaker and the fault.

supply reactanceline reactance

fault

The voltage profile under fault conditions is shown in Fig.7 with the voltage decreasing from the open circuit valuebehind the source impedance to zero at the fault point.The voltage at the circuit breaker is at an intermediatevalue V determined by the length of the line and theimpedance of the circuits connected on the source side ofthe circuit breaker. When the fault is cleared, the voltageon the source side returns to the open circuit value bymeans of an oscillation whose frequency is determined bythe source side inductances and capacitances. The voltageon the line side returns to zero by means of a high fre-quency oscillation which has a triangular waveform,caused by the distributed parameter effect of the line.From Fig. 7 it may be seen that the effect of the line is tocause a sharp increase in the rate of rise during the initialstages of the TRV at a time when contact separation issmall and the insulation strength is just beginning to buildup. It is for this reason that the short line fault is of impor-tance.

As the line has distributed parameters, the frequency ofthe line component is dependent on the time taken by awave to travel between the circuit breaker and the fault, i.e.it is inversely proportional to the length of line. The ampli-tude of the line side component is directly proportional tothe fault current and to the length of line between thecircuit breaker and the fault. Thus, as the length of linebetween the circuit breaker and the fault is reduced, theeffect is to reduce the amplitude and to increase the fre-quency.

Under short line fault conditions the inherent character-istic to the first peak of the line side component of theTRV may be obtained from a knowledge of the faultcurrent and the effective surge impedance of the line. Therate of rise of the transient recovery voltage is given by

dV Zdidt ~ dt

where Z is the surge impedance of the line and di/dt is theslope of the fault current wave at current zero.

As the fault current i is given by

i = sin cot

0 timeFig. 7 Short line fault

then

— = J2 Ico cos cot = J21codt v

as cot is small and, hence, cos cot « 1.Thus the rate of rise to the first peak of the line side

component is given by

dV

where

/ = system frequency, Hz

/ = RMS value of the fault current interrupted, A

The amplitude of the first peak of the line side componentis given by

dV ,V = t —- volts

dt

where t is the time taken for a surge to travel twice thelength of line between the circuit breaker and the fault.

The effective value of the surge impedance dependsupon the sequence of fault clearance and upon the positionon the tower of the particular phase being cleared. Its


determination involves the calculation of the surge imped-ance matrix for the line configuration being studied andthe modification of this matrix, if necessary, to suit thephase clearing (i.e. first, second or third phase to clear).The required matrix modification is determined by substi-tution of the appropriate voltages and current conditionsin the matrix equation relating the voltages, currents andsurge impedances of the three phases.

The single-phase earth fault is the most common faulton high voltage systems and the most severe short linefault duty is encountered when such a fault is cleared. Thisoccurs under third or last phase to clear conditions whenthe last phase is the faulty phase. This is so, first, becausefor the length of line considered, the fault current is usuallygreatest in the case of a single phase fault and, secondly,because the effective value of surge impedance is alsogreatest under these conditions.

The calculation of the surge impedance matrix can belaborious and the use of a digital computer is of greatassistance. This is particularly true if it is desired to includeearth penetration effects. For low values of earth resistivityand if earth wires are present, a sufficiently accurate assess-ment of the short line fault duty may be obtained if theearth is assumed to be a perfect conductor and earth pen-etration effects neglected. However, for high values of earthresistivity and in the absence of earth wires, accountshould be taken of the change with time of the depth ofpenetration [25] into the earth of the surge currents. Thechanging depth of penetration implies a surge impedancewhich is varying with time so that a mean value over thetime of interest should be used.

The steep rate of rise of the TRV introduced by the lineside component is moderated by the presence of lumpedcapacitance at the line terminal of the circuit breaker. Thiscapacitance [30, 31] is due to current and voltage trans-formers connected to the line and its effect is to increasethe time to peak of the line side component. The presenceof a short length of cable connecting the circuit breaker tothe line has a similar effect. The influence of such capaci-tance becomes progressively greater as the distancebetween the circuit breaker and the fault is reduced. Theeffect of such capacitance is to ease the duty on the circuitbreaker. Further reduction in the stress on the circuitbreaker can be obtained by an increase in the number ofbreaks in series or, alternatively, by the use of resistorswitching [23, 32]. The effect of the resistor is to reduce theamplitude and hence the steepness of the line side com-ponent; a reduction in the rate of rise of the order of 50%being obtained when the resistor has a value equal to thesurge impedance of the line.

3.4 Interruption of small inductive currents [38-41 ]Current interruption in a circuit breaker does not alwaysoccur at a natural current zero. When the circuit breaker isused to de-energise transformers, shunt reactors andmotors the current interrupted may be very small com-pared to the fault current which the circuit breaker iscapable of interrupting. Instability can occur in the circuitbreaker arc with the possible consequence that the arcextinguishes and the current falls virtually instantaneouslyto zero. This phenomenon is known as current chopping[38] and will normally occur on a falling current, i.e.before rather than after a natural current zero.

Although the current in the circuit breaker is forced tozero by the current chop, the current in the inductive loadcannot change instantaneously and continues to flow intoany capacitance, stray or otherwise, which exists at the ter-minals of the load. The current in the inductive load rep-

resents magnetic energy which is converted intoelectrostatic energy in the terminal capacitance. If thecapacitance is small the process results in an overvoltageappearing at the terminals. In the case of a single phasecircuit, the magnitude of the overvoltage is determinedmainly by the value of the current chopped and the induc-tance and capacitance of the load. It can be evaluatedapproximately by equating the magnetic and electrostaticenergies which give

where V is the voltage across the capacitance, Ic is thevalue of current chopped and L and C are the inductanceand terminal capacitance of the load circuit. The overvol-tage V is oscillatory with a frequency dependent on thevalues of L and C. The phenomenon is extremely complexbut it has been found experimentally [39] that the value ofthe current chopped is dependent on the effective capaci-tance of the circuit. Thus although the equation above sug-gests that the overvoltage might be reduced by increasingthe terminal capacitance, this is only true provided thatthe value of the chopped current is not increased to suchan extent that the measure becomes ineffective. In threephase circuits the process is further complicated by mutualeffects between phases.

3.4.1 Re-ignitions: If the oscillatory overvoltage whichappears as a consequence of a current chop, instan-taneously exceeds the withstand voltage of the gapbetween the circuit breaker contacts, the arc will re-ignite.As a result, a high frequency current will flow through thecircuit breaker with a magnitude determined initially bythe difference between the voltages on the source and loadsides of the circuit breaker. Subsequently the current mayagain be interrupted and it is possible for a chain ofcurrent interruptions and re-ignitions to occur. Underthese circumstances large values of overvoltage may beproduced and the condition known as voltage escalationcan develop. A detailed description of re-ignition pheno-mena is given in References 40 and 41. The effects ofcurrent chopping and re-ignitions can be minimised by theuse of switching resistors.

3.4.2 Virtual current chopping [42-45, 47]; A re-ignition of the circuit breaker arc causes a transientcurrent to flow which is superimposed on the power fre-quency current, and may cause the total current in thecircuit breaker to pass through zero. As a consequence, thecircuit breaker may interrupt before the power frequencycurrent zero and, if the load circuit is inductive, the inter-ruption appears to the load as if power frequency currenthas been chopped. This phenomenon is referred to asvirtual current chopping and has occurred mainly inindustrial type systems where vacuum switches are fre-quently used for the switching of medium voltage motorsand arc furnace transformers. The vacuum switch is attrac-tive in such applications because of its ability to endure alarge number of operations without maintenance but,because of its high interrupting capability, it is able tointerrupt the current flowing as a consequence of a re-ignition at a high frequency current zero.

The phenomenon is not current chopping in the truesense and can occur in a circuit where the load beingswitched is inductive with some capacitance to earth at itsterminals. The capacitance may be that of a short length ofcable or of a surge capacitor. If the load current is being


interrupted, the contacts of all three poles of the switchwill separate and arcing will take place. A current zero willoccur first in one phase and interruption will take place. Ifthis phase is unable to withstand the resulting recoveryvoltage, because of the relatively small contact gap, a re-ignition will occur and cause a high frequency transientcurrent to flow. This current is superimposed on the powerfrequency current in the phase that has re-ignited andreturns via the other two phases and the neutral connec-tion. It is thus superimposed also on the power frequencycurrents in the other two phases. As a consequence, highfrequency current zeros can appear in all three phases sothat virtual current chopping is not restricted to the phasethat has re-ignited but can also occur in the other twophases. Such interruptions can lead to repetitive re-ignitionand voltage escalation, the whole process being extremelycomplex. As discussed in the literature [42, 46, 47] virtualcurrent chopping is dependent on the values of the circuitparameters and the configuration of the circuit, andvarious measures can be adopted to prevent its occurrence.

3.5 Interruption of capacitive current [1 6, 17,48-50]

3.5.1 Single phase circuits: When interrupting capacitivecurrent associated with a transmission line or a portion ofa capacitor bank, arc extinction occurs at current zero anda trapped charge voltage is left on the line or capacitor asshown in Fig. 8 for the single phase case. This trapped

As shown in Fig. 9 the voltage on the capacitor under-goes a change of 2V from + V to — V so that, neglectinglosses, the oscillation can attain a peak value of 3V with

2V

- V

voltage acrossthe contact gap

supply sidevoltage

time

capacitor side/voltage

Fig. 8 Interruption of capacitor current

charge voltage is equal in magnitude to the peak value Vof the supply voltage, so that initially the voltage appear-ing across the circuit breaker is relatively small. Becauseconditions for interruption are therefore easy, arc extinc-tion occurs at the first current zero after contact separa-tion. The voltage on the supply side is varying at powerfrequency so that the voltage across the circuit breakerbuilds up sinusoidally until a half cycle after interruption itattains a value of 2V. For successful interruption to takeplace it is necessary for the gap between the contacts towithstand 2V, twice the peak value of the supply voltage,half a cycle after arc extinction.

If the gap between the contacts cannot withstand thevoltage across it a restrike will occur. Assuming this occurshalf a cycle after arc extinction, the voltage across the con-tacts will collapse to zero almost instantaneously from avalue of 2V. This is accompanied by a discharge of thetrapped charge on the capacitor through the system induc-tance. The voltage on the capacitor then attempts to buildup to the voltage on the source side by means of an oscil-lation at a frequency determined by the capacitance andthe system inductance.

c wD V

4V

volta

ge<

<

<

0

-V

-2V

-3V

arcextinction

_

arc.extinction

/ restrike/ S

\\

X

-

/Jy

arc ^extinction

\\

X

yrestrike

restrike

/ time

y

Fig. 9 Interruption of capacitor current with restrikes

respect to earth. When the voltage reaches its peak value,the transient current associated with it passes throughzero and an opportunity for interruption is thus provided.In practice, some damping will be present and the voltagestress which then develops across the contacts may not beas great as that before the restrike and interruption underthese conditions is possible. If interruption takes place, thecapacitor is left at a voltage of — 3 V and half a cycle laterthe source side voltage becomes + V so that the voltageacross the contacts is 4V. During this period the contactshave been moving further apart, thereby enabling the gapto withstand a larger voltage, so that a further restrikemay or may not occur depending upon the dielectricstrength of the gap. If a restrike should occur under theseconditions, the capacitor will attain a voltage of 5V withrespect to earth as shown in Fig. 9. If the associated highfrequency current is interrupted the voltage of 5V will betrapped on the capacitor.

Theoretically the voltage can continue to build up inodd multiples of V but in practice damping will be presentand restrikes are likely to occur before the supply voltagereaches its peak values. In a circuit breaker which is proneto multiple restriking the build-up of voltage will not be asrapid as suggested by Fig. 9 because the contact gap actsas its own voltage limiter. The conditions can be alleviatedby the use of switching resistors.

3.5.2 Three-phase circuits: Three-phase transmissionlines and three-phase capacitor banks with an earthedneutral can be considered to behave as three independentsingle-phase circuits and the description given in Section3.5.1 applies. In the case of three-phase capacitor bankswith an unearthed neutral, conditions are more complex. Itcan be shown [16] that the recovery voltage VR for the firstphase to clear has a value given by

VR = 1.5F [1 - cos co(t - tj]

where V is the peak phase to neutral voltage and ta is thetime at which interruption takes place in the first phase toclear. The peak of the recovery voltage has a value of 3Vwhich occurs half a cycle after time ta. This compares withthe value of 2 V which occurs in the single-phase and three-phase earthed neutral cases.


4 Overvoltages caused by energisation

At transmission voltage levels of 400 kV and above, tran-sient overvoltages caused by the energisation of transmis-sion lines become of increasing importance in fixing theamount of insulation required [51, 70-85]. Basically, theproblem is that of a voltage surge travelling along a trans-mission line. Travelling wave theory shows that when sucha surge reaches an open-circuited termination it is reflectedwith the same sign, and the voltage at the terminationobtains a value twice that of the incident surge. As a result,if a line is energised at a peak of the supply voltage wave(1 p.u.), then 2 p.u. voltage will be produced at the openend of the line. In practice the magnitude of the voltage isinfluenced by the particular system conditions whichprevail at the instant of energisation and under some cir-cumstances the voltage may exceed 2 p.u. by a largemargin.

4.1 Factors influencing the magnitude of lineenergisation overvoltages

Many factors exist which influence the magnitude of theline energisation overvoltages and have been dealt with inthe literature [52-63].

4.1.1 Source: The source from which a transmission lineis energised has a considerable effect on the magnitude ofthe transient voltage produced when a line is energised, asthis determines the shape of the voltage wave applied tothe line and governs the sending end reflection coefficientas encountered by waves returning from the open end ofthe line. In practice, the source characteristics are veryvariable and range from that of a pure inductance in thecase of source busbars fed only by generation and trans-formers, to a source which has a resistive characteristicwhich is obtained with the source busbar is fed only bytransmission lines and cables. Between these two extremesa variety of combinations can exist.

When a transmission line is energised from an inductivesource, the waveforms and magnitudes of the transientvoltages produced on the line are dependent upon threetime factors [59, 63]. This is illustrated by the waveformsof Fig. 10 which show the sending and receiving end volt-

2 = 20) a.

oTJ OC ±ZOi O</> >

8 10 12

-2

? . 2 -

16 18 20time, ms

I'. T- 2 <

J

. 1

\ 6 I 8/"~^> Li* / " 20

time, ms

Fig. 10 Sending and receiving end voltagesinfinite busbar source0.1 H inductive source

ages produced on a line when energised at a peak of thesupply voltage wave, from an inductive source. The corre-sponding waveforms for energisation from an infinitebusbar source are shown for comparison. First, when theline is energised, the voltage at the sending end does notexhibit an initial step-change as in the case of an infinitebusbar source but rises exponentially to the power fre-quency voltage with a time constant determined by theinductance of the source and the surge impedance of the

line. This initial exponential rise occurs also at the receiv-ing end of the line and in fact due to multiple reflections,exponential changes are apparent throughout both thewaveforms. The intervals at which these exponentialchanges occur are determined by the second time factor,namely the propagation time of the line. The peak A in thesending end waveform is due to the first reflection from thereceiving end arriving at the sending end and impinging onthe source inductance. This peak itself is transmitted to thereceiving end and appears as a peak B in the receiving endwaveform. Thereafter due to multiple reflections thesepeaks reappear in the waveforms at intervals equal totwice the propagation time of the line and in between themthe exponential changes referred to above occur. Thewhole is superimposed upon the power frequency voltagewaveform whose variation with time provides the thirdtime factor. The waveforms of Fig. 10 are calculatedwithout losses being represented and, in practice, the lossesof the system ensure that the transients die out leavingonly the power frequency voltage. For a line of given con-struction and hence fixed surge impedance, alteration ofthe source inductance will alter the time constant of theexponential changes and alteration of the line length willvary the interval at which the peaks A and B occur. Suchchanges will therefore alter the waveforms of the sendingand receiving end voltages and produce changes in themagnitude of the transient voltages. For a given line lengthbeing energised, it is found that if the source inductance isincreased above a particular value the magnitude of thereceiving end voltage commences to increase continuouslywith increasing inductance values. This continuous rise inovervoltage may be attributed to the fact that conditionsare approaching resonance at the power frequency. Theresonance is due to the fact that the natural frequencygiven by the source inductance and the shunt capacitanceof the line is low and approaches the power frequencyvalue more closely the longer the line length energised andthe greater the source inductance. Under conditions ofnear power frequency resonance, preinsertion resistorsbecome virtually ineffective and to reduce the large over-voltages (which are sustained overvoltages rather thantransient overvoltages), it is necessary to compensate theline capacitance by means of shunt reactors. The overallpicture is often clarified if the maximum overvoltages arepresented in the form of contours of overvoltages plottedon axes of source inductance and line length [59, 60].

In the case of energisation of a line from a sourcebusbar to which only transmission lines are connected thesource will initially appear resistive, but this situation willonly prevail until reflections return from the remote endsof the source lines. The duration of this initial period obvi-ously depends upon the lengths of the lines on the sourceside and the nature of their remote terminations.

Assuming that the transmission lines on the source sideand the line being energised all have the same surgeimpedance Zc, and if Re is the equivalent surge impedanceof the source lines then when the circuit breaker closes theinitial step of voltage applied to the line being energised isgiven by

V, = Z

Re + Zc

and the step voltage transmitted into the source is

V - y Re

where V is the voltage across the circuit breaker imme-diately before closure.


The initial step of voltage applied to the line depends onthe number of lines on the source side and will be smallestwhen there is only one source line in which case Re = Zc

and VL = 0.5V. This step voltage travels to the receivingend of the line where it is reflected with a coefficient of + 1(because of the open circuit) and returns to the source. Thecircuit breaker is now closed so it will again be reflectedwith a coefficient KR, whose value depends upon thenumber of source side lines. With one source line, KR iszero and with two lines on the source side

- Z, 0.5Z, - Z,

R< 0.5Zc

The coefficient KR becomes more negative as more linesare added to the source side and tends to — 1 which is thecase of an infinite busbar, where Re is zero.

More generally, the source consists of a mixture of localgeneration, transformers and transmission lines. Initially,in such cases, the effect is of an inductance in parallel witha resistance whose value is given by the parallel com-bination of the surge impedances of the lines. During theinitial portion of the transient, the inductance has littleeffect, the voltage waveform on the line having an initialstep similar to that produced by an infinite source ratherthan the exponential rise associated with an inductivesource. The effect of the remote terminations of the sourcelines will eventually affect the waveform in a mannerdepending on the nature of the termination.

4.1.2 Reactive compensation: To satisfactorily operatelong high voltage lines under steady state conditions, it isnecessary to compensate the capacitive reactive power theyproduce by shunt reactors. At the higher voltages above400 kV, these reactors are often connected directly to thehigh voltage line rather than to the tertiary of a trans-former. Shunt reactors act to reduce energisation overvolt-ages [52, 59, 63] if they are connected directly to the linewhen it is energised. The amount of reduction obtaineddepends upon the size of shunt reactor in relation to theline length and on its position in the system. In general, agreater reduction might be expected when the reactor isconnected at the receiving end of the line.

For weak sources (large inductance) preinsertionresistors become increasingly ineffective in reducing ener-gisation overvoltages as the natural frequency of thesource and line approaches the power frequency value.Under these conditions the overvoltages may be reducedby compensating the line capacitance by means of shuntreactors. This situation is most likely to occur when verylong lines are being energised and it is probable that shuntreactor compensation would, in any case, be employed insuch cases for other reasons.

Investigations have shown that for a line having onlyseries capacitor compensation [56], the effect on themaximum value of energisation overvoltage is small.Where both series capacitor and shunt reactor com-pensation is employed, conditions of resonant and ferro-resonant oscillations may arise. Such oscillations are of amore permanent nature and are normally classed as tem-porary overvoltages.

4.1.3 Residual charge: The clearance of transmission linefaults which do not involve all three phases may result inthe healthy phases being left charged to a voltage of theorder of the peak phase to neutral voltage of the system.The subsequent restoration of supply to such a line canproduce overvoltages on the healthy phases which under

certain conditions may be large enough to cause flash-overs. The magnitude of the overvoltages produced byreclosure depends on the magnitude of the voltage trappedon the line and also on the point on the supply voltagewave at which the line is reclosed. Maximum overvoltagewill occur when the circuit breaker is reclosed [63] at thesupply voltage peak and the line is charged to the oppositepolarity. With 1 p.u. trapped charge, a step voltage of2 p.u. is applied to the line on energisation under this con-dition. A 2 p.u. voltage wave travels to the open end of theline and doubles to give a voltage to earth of 3 p.u. Theline may remain charged practically to peak voltage formany seconds after current interruption, which is a timemuch greater than those used in high-speed auto-reclosureschemes. The line will discharge eventually throughleakage paths across insulators etc., but the rate at whichthe discharge occurs is governed by the prevailing climaticconditions. The time constant of the discharge is usually inthe range 20 to 60 seconds giving times of the order of twoto five minutes to effectively discharge the line completely,but under extremely dry conditions this time may beincreased to more than 15 minutes. A very real possibilityexists, therefore, even in the case of manual reclosure, ofclosing on to a line with a large trapped charge voltage.

The discharge time of the line may be modified con-siderably if the circuit breaker is fitted with openingresistors or if shunt reactors or magnetic voltage trans-formers are connected to the line. The effect of a circuitbreaker opening resistor in reducing the discharge time ofthe line and the trapped voltage on the line depends uponits resistance, the length of line and the time the resistor isin circuit. The resistor and the time it is in circuit are func-tions of the circuit breaker design. Opening resistors usedare of the order of tens of thousands of ohms, and thecontacts of the resistor break may separate at times of theorder of 30 to 60 milliseconds after the main break. Theresistor may, however, be in circuit for times longer thanthis owing to arcing of the contacts, and times of the orderof 120 to 150 milliseconds may well hold. The time con-stant of the discharge may be calculated from the resist-ance and the shunt capacitance of the line. As an example,with 266 miles of line having a shunt capacitance of 5microfarads and a 25 000 ohm resistance, the time constantof the discharge is given by 25 x 5 = 125 milliseconds.Thus, if the resistor is in circuit for only 30 milliseconds,the residual charge voltage is reduced to about 80% of itsinitial value, and if, owing to arcing, it is in circuit for 120milliseconds, the reduction is to about 38% of the initialvalue. Once the resistor is out of circuit, the charge will, ofcourse, continue to decay, but at a much slower rate.

When a line is compensated by a shunt reactor, it willdischarge through the reactor in a oscillatory manner. Thefrequency of the oscillation is determined by the reactorinductance and the line capacitances, and the oscillationwill decay at a rate determined by the losses of the line andreactor. The frequency is low, often of the same order asthe supply frequency, and in general a difference in the fre-quencies of the voltages on either side of the circuitbreaker will exist. There is therefore always a possibility ofreclosing the supply on to the line in antiphase to theinstantaneous residual charge voltage.

4.1.4 Non-simultaneous closure of the three phases: Inpractice, transmission line energisation overvoltages areincreased by virtue of the mutual effects between the threephases and the fact that the three phases of the circuit donot close simultaneously. The maximum receiving endvoltage varies considerably with the time intervals between


closure of the first phase and the closures of the secondand third phases. The total time elapsing between theclosure of the first and last phases depends upon the circuitbreaker design, but for prediction purposes it is frequentlyassumed that all phases will close within a period of 5 ms.This is more than adequate for many pressurised gas typesof circuit breaker, but times in excess of this are sometimesexperienced with older equipment in which closure iseffected by means of a rotating arm in air at atmosphericpressure.

The increase in overvoltages can be significant and,because of the wide variations which can occur with differ-ent pole closing sequences, statistical methods [55, 61, 64,65, 66] are frequently employed to assess the situation.The overvoltages are computed for a large number of ran-domly generated closing sequences and the results plottedas frequency distribution curves from which the probabil-ity of a particular magnitude of overvoltage occurring canbe assessed.

Such curves constitute one of the factors to be con-sidered in determining a suitable insulation level for thesystem. The effect of non-transposition [53-55, 57, 67, 68]of the conductors of an overhead line is normally com-paratively small, but under some conditions may be of sig-nificance. Likewise, the effects of nonhomogeneous earthreturn paths have been considered by a number of authors[53, 57, 68, 69].

4.2 Energisation of composite circuitsThe simplest composite feeder consists of two componentshaving different characteristics and which may be regardedas two oscillatory circuits. In the case of a line and a cable,the parameters of the circuits are distributed and eachcircuit has a frequency which is determined by its lengthand velocity of propagation. With a transformer feeder,one circuit is distributed and the other may be regarded asa lumped series inductance capacitance circuit at theinstant of energisation from the line end of the feeder.Under these circumstances the inductance is the leakageinductance of the transformer and the capacitance is thatseen at the open circuited transformer secondary and ismade up of the transformer stray capacitance to earthtogether with the capacitance of any short length of cableused to connect the transformer to its circuit breaker. Thenatural frequency of this circuit is determined by thevalues of the inductance and capacitance.

When a circuit is being energised, the actual instant ofenergisation may occur when the voltage across the circuitbreaker is at or about its maximum value and this resultsin the application of a voltage step, of the order of peakphase, to neutral voltage, to the circuit being energised. Inthe case of a composite feeder this step of voltage isapplied to the first circuit of the feeder and produces atransient voltage in this circuit which may exceed the orig-inal step by a considerable margin. The first circuit thenacts as a source and its transient voltage is applied to thesecond circuit of the feeder to produce an even larger tran-sient in that circuit. This phenomenon is sometimesreferred to as 'surge magnification' and under some cir-cumstances much larger overvoltages are produced than ifone of the circuits is energised on its own. The magnitudeof the overvoltage produced depends upon the energyinterchange between the two circuits which, in turn,depends upon the values of their parameters.

4.2.1 Overhead line and cable: The simplest example of acomposite feeder is probably that of a length of cable con-nected in series with a length of overhead line to form a

transmission circuit, the whole being switched as a singleunit. Such combinations are common at all voltage levelsalthough at the highest voltages the cable length is oftenvery short compared with that of the overhead line,whereas at the lower levels the cable is quite likely to be aslong as, if not longer than, the overhead line.

Consideration of the conditions at the junction of theline and cable will show that because the surge impedanceof the line is much larger than that of the cable, a largeproportion of any incoming wave from the cable will bereflected back to the source. The associated transmissioncoefficient at the junction will have a value greater thanunity and may approach a value of 2.

Consequently, if the feeder is energised at peak voltagefrom the cable end, a travelling wave of almost 2 p.u. maybe transmitted into the overhead line at the line/cablejunction. On arrival at the open circuited end of the line,doubling will occur and produce a voltage approaching4 p.u. at that point. On the other hand, if the feeder isenergised from the overhead line end, the transmissioncoefficient for waves travelling from the line into the cablewill be much less than unity, with the result that thevoltage at the open circuited end of the feeder will have amuch slower wavefront than in the previous case. There isthus a best end from which to energise the feeder. Theabove is a simple example of best end switching and inpractice the voltage waveforms are modified by a numberof factors. The relative lengths of the cable and overheadline can be critical and losses will, of course, be presentand act to reduce these overvoltages. The presence oftrapped charge on the feeder at the instant of energisationincreases the severity and can lead to large voltages beingproduced at the open end of the feeder, particularly in thecase of energisation from the cable end. In practice, partic-ularly at the lower voltage levels, a feeder may consist ofmore than one length of overhead line and one length ofcable and may also include fault limiting reactors. In suchcases the magnitude of the energisation overvoltagedepends upon the arrangement of the components of thefeeder, their lengths and characteristics. Although, ingeneral, there is a best end for switching under these cir-cumstances, its determination must be the subject of anindividual study.

4.2.2 Reactively terminated feeders [2, 86-89, 91 ] : Thetransformer terminated line has already been mentioned asan example of a composite feeder. Similar conditions alsoexist in the case of an underground cable terminated in atransformer and in the case of an overhead line or cableterminated in a fault limiting reactor [2]. An explanationof the basic phenomena associated with a reactively ter-minated feeder has been given [87] as follows.

Energisation of an overhead line alone from a zeroimpedance source results in the generation of a squarewave voltage at the open end of the line due to the reflec-tion at the line terminations of the initial energisationvoltage step. Neglecting losses, the amplitude of thissquare wave is twice that of the energising step and itsfrequency is | T , where T is the propagation time of theline. If the line is terminated by an oscillatory circuit con-sisting of inductance and capacitance in series (such as isprovided by a transformer or series reactor and its associ-ated capacitance), this circuit is excited by the square wavevoltage and, due to overswing, the voltage across the reac-tive elements may exceed the amplitude of the square wavevoltage. The voltage produced on the secondary side of thetransformer, i.e. across the capacitance, is dependent uponthe length of the line. If the line is short the line frequency


may be higher than the transformer frequency, in whichcase the voltage building up across the capacitor may notachieve its maximum value before a reflected wave of theopposite polarity returns from the source end of the line. Ifthe line length is such that the line frequency and thetransformer frequency are equal, a state of resonance existsand large overvoltages are produced across the capac-itance on the secondary of the transformer.

Both the natural frequency and the effective surgeimpedance of the transformer are important factors indetermining the magnitude of the overvoltage. A survey[87] has indicated the existence pf a very wide range offrequencies depending on the voltage, rating and design oftransformer. For windings in the range 132 kV to 400 kVand ratings of 50 to 1000 MVA the appropriate naturalfrequencies of transformers alone (not including the sec-ondary connections) are in the range 3 kHz to 15 kHz. Theeffective surge impedances of transformers were found torange from below 1 kfi to in excess of 10 kQ dependingupon the capacitance of the secondary connections.

An initial assessment may be made on the basis of asingle phase representation of the system [91]. The resultsof Fig. 11 indicate that a valid result may be obtained if

Fig. 11 Energisation of a transformer feeder

Voltage waveforms at the transformer terminals calculated using a single phase rep-resentation with saturation neglecteda, c, e and g voltage on the transformer secondaryb, d,f and h voltage on the line side of the transformera and b compensation methodc and d lumped parameter methode and /lattice diagram methodg and h transient network analyser representation

the transformer is represented simply by its leakage induc-tance. For the system shown, the Figure shows a compari-son of the voltage waveforms on both sides of thetransformer calculated by the compensation method [91]with those calculated by three other methods, in all caseswith transformer saturation neglected. The other resultsare obtained by a lumped parameter method with thetransmission line represented by cascaded 7r-sections, alattice diagram method and a transient network analyser

model in which the transformer is represented by a modeltransformer. Comparing the voltage waveforms on the lineside of the transformer, a difference may be noticedbetween the results obtained with a distributed parameterrepresentation of the line and those obtained with alumped parameter representation. On the other hand, thesecondary voltage waveforms calculated by all fourmethods are in good agreement with each other. The maindifference is that the magnitude of the voltage calculatedby the TNA is slightly lower than that obtained from theother methods.

4.3 Energisation of capacitor banksThe worst overvoltage condition occurs when energisationtakes place at a peak of the supply voltage wave. Fig. 12

2V

-V

voltage oncapacitor C L J

time \

cs4= c4=

supply^voltage

Fig. 12 Energisation of a single phase capacitor

shows conditions which relate to the energisation of asingle-phase bank or to one phase of a three-phase bankhaving an earthed neutral. The capacitor on the supplyside is negligible in comparison with the capacitance C ofthe bank being energised. The capacitance C is initiallydischarged so that at the instant of energisation thevoltage on the supply side of the switch drops to zerobecause instantaneously C appears as a short circuit. Thesupply side and capacitor voltages are now equal andincrease towards the peak V of the power frequencyvoltage. Because of circuit inductance, an oscillatory over-shoot occurs and, without damping, the capacitor voltagecan attain a value of 2 V as shown in Fig. 12.

The energisation of a three phase capacitor bank withan unearthed neutral is shown in Fig. 13. It is assumed

Fig. 13 Energisation of a 3-phase capacitor bank with unearthed neutral

that two phases B and C have already closed and thatphase A closes at a positive peak of the supply voltage. Atthis instant the voltages on phases B and C are both equalto — 0.5 K so that this is also the voltage on the capacitorside of the phase A switch. As a result the voltage acrossthis switch at the instant of closure is 1.5 V. Immediatelyafter closure the voltages VA = VB = Vc = 0, and subse-quently climb back to their power frequency values bymeans of an oscillation as shown in Fig. 13. Neglectingdamping, the capacitor voltage on phase A can reach avalue of 2V and the voltages on phases B and C can reacha value of - V (2 times -0.5K).

Thus in the energisation of three-phase capacitor banksthe maximum overvoltage is independent of whether or


not the neutral is earthed. Under both conditions themaximum voltage is 2V.

4.3.1 Multiple restrikes and interruptions: It is shown inSection 3.5 that restrikes can occur during the discon-nection of capacitor banks and transmission lines leadingto a succession of interruptions and restrikes. Similarmultiple restrikes and interruptions can occur during theenergisation of capacitor banks under some circumstances.This is caused by the circuit breaker prestriking beforemetallic contact has been made and the resulting high fre-quency current transient being interrupted at a high fre-quency current zero in the closing arc. Such multiplerestrikes and interruptions can lead to destructiveovervoltages being impressed on the system which,depending upon circuit configuration, can propagate,increase or decrease at circuit discontinuities and causedamage at points remote from the circuit breaker. It isperhaps ironic that the probability of this phenomenaoccurring is greatest in the case of modern circuit breakerswith improved interrupting capability.

The whole process can become quite complex and anyattempt at a detailed analysis must be capable of definingin some manner both the high frequency current zeros atwhich interruption occurs and the voltage stress at whichbreakdown of the contact gap will take place. In addition,assumptions have to be made with respect to the point onwave at which the process is initiated.

4.4 Energisation of large motors [169-172]A further problem is that of the transient overvoltagewhich may be associated with the switching of a largemotor. Normal practice is for such a motor to be con-nected to the supply busbar by a length of cable with acircuit breaker at the supply end of the cable. If the supplybusbar has other cables connected to it, then energisationof the cable supplying the motor by closure of the circuitbreaker results in a step of voltage travelling down thecable to the motor. The magnitude of this initial step ofvoltage is dependent on the number of cables already con-nected to the source busbar at the instant of energisationand will increase as the number of such cables is increased.When the step of voltage arrives at the motor terminal itwill undergo magnification due to the relatively largeimpedance of the motor. With modern types of cableshaving low loss dielectrics, very little wavefront distortionoccurs as the wave travels down the cable so that, onarrival at the motor, the motor winding insulation isstressed by a steep fronted voltage wave. Field tests [173-175] have indicated that transients with wavefronts of0.2 ̂ s and magnitude in excess of 2 p.u. are not infrequent.

Severe conditions may be expected when prestrikeoccurs during the closing operation. In these circumstances[169] the gap between the closing contacts of the circuitbreaker breaks down and a prestrike occurs. The voltageson the two sides of the circuit breaker will reach acommon voltage level very rapidly and the rapid voltagechange which occurs on the cable and motor side of thecircuit breaker is equivalent to injecting a very steepfronted wave into the cable. This wave then travels downthe cable to the motor and stresses the insulation. Thecurrent which flows in the arc during the prestrike may beinterrupted, depending upon the type of circuit breakerand, if it is, the dielectric strength of the gap between theclosing contacts recovers until a further prestrike occurs.There is therefore a possibility of obtaining a series of pres-trikes and interruptions before metallic contact is finallymade between the contacts of the circuit breaker. Each

prestrike produces a transient overvoltage at the motorterminals so that the winding insulation is subjected to aseries of steep fronted voltage waves and insulation failuremay occur.

Most motors do not have an earthed neutral, so thatthe voltage wave produced when the first phase closes canpropagate through the windings and cause voltage oscil-lations to occur at the terminals of the second and thirdphases. Depending on the oscillation frequency and thedelay between first pole closure and the closure of thesecond pole, an increased voltage wave may be initiatedwhen the second pole closes. As a consequence, evenhigher stresses may be imposed on the motor windinginsulation.

It has been shown [169, 170] that the connection ofcapacitors as close as possible to the motor terminals is aneffective way of reducing the stresses on the insulation.

5 Overvoltage caused by faults

Overvoltages in this category may arise for a number ofreasons and are dependent on the particular type of systemearthing that has been adopted. The earthing of theneutral of a power system may be achieved in a number ofways, the two extreme conditions being a solidly earthedneutral and an insulated neutral. With the neutral insu-lated from earth, although asymmetrical fault currents aresmaller, fault conditions are likely to generate higher over-voltages than on a system with a solidly earthed neutral.Conversely, with the neutral solidly earthed, asymmetricalfault currents are larger but overvoltages under fault con-ditions tend, in general, to be smaller.

A very high proportion of all faults on power systemnetworks are single phase to earth. Under this fault condi-tion, an increase in the voltages of the healthy phases takesplace, giving rise to a temporary overvoltage which per-sists until the fault is cleared. The magnitude of the over-voltage depends upon the zero sequence parameters of thefaulted network and reaches the phase to phase value inthe extreme case of an isolated neutral system. The tempo-rary overvoltages for different values of X0/Xx and K0/A

r1

and with X1 = X2 and Rl — R2 = 0 are given in Reference95 for single phase to earth faults. Earlier practice [93]was to consider a system effectively earthed whenX0/Xl < 3 and R0/Xl < 1 which meant a temporary over-voltage of less than 1.4, but this definition has now beenabandoned. Earthing conditions are now characterised byan 'earth fault factor' which is the ratio of the highestpower frequency voltage in any phase during a fault to thenormal phase to earth voltage without fault.

A similar temporary overvoltage caused by imbalancewill occur in the healthy phase under double phase toearth fault conditions. The variations of the magnitudes ofthe voltages on the healthy phases under asymmetricalfault conditions with system constants are given in the lit-erature [92, 94, 95].

5.1 Intermittent earth faultsOn transmission lines the majority of faults to earth in onephase are self clearing in the sense that the original causeof the fault, for example a lightning stroke, is of a tran-sitory nature. The arc produced by such a fault on asystem with an unearthed neutral will, however, persist ifthe capacitive current between the two healthy phasesand earth is large enough to keep the arc path between thefaulty phase and earth ionised. Such an arc, when keptalive solely by the capacitive current of the healthy phases,is often referred to as an arcing ground.


An arcing ground involves the risk of a high transientovervoltage being built up on the system due to continualextinguishing and restriking of the arc. The processinvolved is very similar to that which may occur where acircuit breaker, which is not restrike free, interrupts linecharging current. However, in the case of an arcing groundthe sequence of events during the build-up of a high tran-sient overvoltage is more fortuitous than that which mayoccur in a circuit breaker, but the length of time availablefor a dangerous sequence to occur is much longer, beingthe whole time that the arc persists. A general idea of theprocess may be obtained by ignoring all losses and bytaking into account only an inductive source, which maybe a generator or a transformer, with insulated neutral,and the capacitance to earth of the 3 phases. For a single-phase fault, the capacitance of the two healthy phasescombined with the inductance of the source decides thenatural frequency of oscillation. As the system is largelyreactive, the voltage and current are in quadrature so that,if the current is suppressed at a natural zero, the recoveryvoltage has a maximum value. The sequence of events atany time after the arc has first struck is described in theliterature [92, 96].

The situation may be avoided by earthing the systemthrough a reactor connected to the transformer neutral.Under phase to earth fault conditions a current will flowto earth through this reactor and return via the fault path.This current lags the neutral to earth voltage by 90° and isin antiphase to the capacitive current in the fault. By asuitable choice of the value of this reactor, the magnitudeof its current can be made equal to that of the capacitivefault current. Under these conditions the current in thefault is very nearly zero and insufficient to maintain an arc.The system has some resistance and a small current inphase with the voltage will continue to flow in the faultand cannot be balanced out. Such a reactor is known as an'arc suppression coil', a 'Peterson coil' or an 'earth faultneutraliser'.

An isolated neutral system gives rise to dangerousarcing fault transient voltages if the capacitive fault currentexceeds 5 to 10 amps. These conditions obtain on almostall systems of 33 kV and over and often on 11 kV systems.All such systems may therefore be provided with an arcsuppression coil if they are operated with an isolatedneutral. At voltages of 220 kV and over, corona loss andother factors cause the phase angles of the currents todepart from the 90° lag and lead, respectively, so that thereis a resultant current in phase with the voltage whichcannot be neutralised.

One important danger of arc suppression coil earthingarises when independent circuits run close together. Undersuch conditions mutual coupling exists between them andin particular between the zero sequence networks. In suchcircumstances a fault in one circuit, due to the mutualcoupling, may produce series resonance in the secondcircuit with resultant high overvoltages. The remedy [97,98] in this case is to couple the zero sequence networksdirectly through a compensating transformer, the effect ofwhich is the direct opposite of that due to the mutualcoupling.

5.2 Secondary arcs associated with single poleautoreclosure

After clearance of a single-phase fault on a transmissionline by single-pole switching, the faulty phase remainscoupled to the healthy phases. As a consequence of thiscoupling, a residual current can continue to flow in thefault arc path giving rise to a secondary arc [110-112, 116,

118]. It is important that this arc should be extinguishedwithin the dead time of the reclosure scheme for the auto-reclosure operation to be successful. The time to secondaryarc extinction is therefore of interest and this is dependenton a number of factors. Among these are the secondary arccurrent, the recovery voltage which appears when the arcextinguishes, the length of the arc and climatic conditions.In addition the construction and length of the line willaffect the amount of coupling between the faulty phase andthe healthy phases, and the fault location and positioningof the faulty phase on the tower have a bearing on thevalue of the secondary arc current. The prediction of thetime required for the arc to extinguish is not easy and anumber of papers [113-117] describe field tests and com-puter simulations. The situation is more complex if thetransmission line is reactively compensated. Depending onthe position of the fault, the presence of series capacitorsand shunt reactors can increase the current in the second-ary arc. If shunt reactors are connected to the line, somereduction in the secondary arc current can be obtained bythe adoption of remedial measures described in the liter-ature [110, 111, 118, 119]. One such measure is the use ofa shunt reactor having a fourth limb connected betweenthe reactor star point and earth, the effect being similar tothat of the arc suppression coil mentioned in the previoussection.

5.3 Transient overvoltages caused by faultapplication [99-105]

Under the unbalanced conditions caused by single line toground and double line to ground faults, a sustainedsteady state overvoltage can exist on the healthy phases.The magnitude of this overvoltage depends upon the zerosequence parameters of the faulted circuit and can reachthe line to line value in the extreme case of a line toground fault on an isolated neutral system. The steadystate overvoltage conditions is reached by means of a tran-sient oscillation so that, even for an earthed system, thevoltages on the healthy phases may achieve values of theorder of 1.8 to 2 p.u. as a transient. These conditions are,of course, of great interest from the point of view of oper-ating systems at voltage levels of 1000 kV or more as pro-posals are for maximum overvoltage levels to be restrictedto the order of 1.6 p.u. It is therefore necessary whendesigning such systems to assess the magnitude of theovervoltages produced by faults in order to take thenecessary steps to minimise their effects. The initiation of afault on one phase of a network can also produce overvolt-ages on that same phase. On the occurrence of a fault thevoltage is reduced suddenly to zero and this step changepropagates through the system as a travelling wave and issubject to transmission and reflection at circuit discontin-uities. As a result, surge magnification may take place ifthe conditions are suitable and overvoltages may occur onthe faulty phase. It must be stressed that damping willreduce the voltage steps rapidly, as there is no sustainedvoltage source behind them. Loads connected to thesystem, particularly at terminations, may prevent the over-voltages occurring or reduce their magnitudes. Neverthe-less, it is theoretically possible for such phenomena tooccur and examples have been recorded in practice.

6 Transient overvoltages in low-voltage networks

6.1 Status of transientsPrior to 1961 very little statistical information had beenpublished regarding transients in factories, laboratories,offices and domestic premises. The steady growth of the


use of semiconductors in electronic equipment, in place ofthermionic devices, caused designers to consider the ques-tion of reliability of operation of semiconductors whensubjected to transient voltages. Such considerations led tothe development of equipment for the automatic recordingof transients. Subsequently, statistical information on therelationship between amplitude and the frequency ofoccurrence of short-duration transients in low-voltagesupply mains, taken over a period of years, appeared in theliterature [106] in 1964. The equipment which was used toobtain this information was capable of responding topulses having durations exceeding 0.3 microseconds and tocount the number of transients with amplitudes greaterthan a set of predetermined voltage levels as follows: 50,100, 140, 200, 280, 400 and 560 volts.

To prevent the loss of recording of large amplitudetransients which happen to be in opposition to the instan-taneous value of the supply voltage, the recorders wereconnected between line and neutral via passive mains-frequency rejection filters. These filters provided high rejec-tion of the mains-frequency waveform by the use ofparallel T-type notch filters followed by CR high-pass filtersections. Thus, transients were measured directly with themains-frequency waveform virtually eliminated. Totalvoltage excursion recordings were carried out simulta-neously without mains rejection filters, to obtain a com-plete assessment of the transient situation.

The survey [106] indicated that transients up to 50 voltpeak occur at rates of up to 100 per day at any given siteand as a guide to the frequency of occurrence of highertransient voltages their frequency is reduced by 10 to 1 fora 2 to 1 increase in voltage amplitude.

Power supply disturbances may be classified as follows.The term 'sag' is used to indicate a definite drop in

supply voltage for a few cycles of the mains waveformwhile 'surge' indicates a rise in supply voltage for a fewcycles. The term 'normal-mode' serves to indicate tran-sients which would be observed between line and neutral;such transients may be observed between a reference earthand either the line or the neutral. In the case where suchobservations indicate time coincidence of a transient onboth line and neutral the term 'common-mode' is oftenquoted.

A typical survey, carried out in a research laboratory in1984 over a period of two days, showed 100 normal modetransients occurred which exceeded 50 volts and of the 10largest amplitudes recorded three exceeded 400 volts.

6.2 Origin of local transientsTransient voltages arising from external causes in previoussections can be detected within the associated low-voltagenetworks. For instance, under earth fault conditions, thewhole of a substation site may rise several hundred voltswith respect to a true earth. However, it is evident fromexperience that the majority of transients detected on low-voltage systems are generated within the low-voltagesystem itself, with only occasional spikes of 200 volt ampli-tude arising at the low-voltage terminals of a substationtransformer, under normal load conditions. Remote fromthe substation, local switching of loads largely determinesthe frequency of occurrence of transients. In domestic situ-ations, low-current non-inductive loads such as a 100 wattincandescent lamp when switched on to a long length ofPVC wiring can produce radio frequency damped oscil-lations in excess of 100 volt amplitude. A length of wiringmay be considered as a transmission line of characteristicimpedance of the order of 100 ohms whereas the 100 wattlamp constitutes a load of 40 ohms (cold resistance) ini-

IEE PROCEEDINGS, Vol. 133, Pt. C, No. 4, MAY 1986

tially rising to around 600 ohms under normal workingconditions. Assuming closure onto the wiring takes placeat the peak of the 240 volt mains waveform and a reflec-tion coefficient of magnitude 0.43 is presented by the 40 Qresistance to the 100 Q line, then the first reflected wavewill have an amplitude of 146 volts. Successive reflectionsproduced damped oscillations of the order of 1 MHz, thefrequency being dependent on the physical length of lineand the dielectric constant of the PVC insulation.

Switching of a fluorescent lamp can produce a fewcycles of a damped oscillatory transient of the order of 500volts amplitude in the megahertz range, such transientsbeing associated with the tube and the starting mechanismused for this type of discharge lamp. A more general causeof transients is the use of 'hard switches' which, by virtueof the high velocity of contact separation, are able to inter-rupt the current in an inductive circuit leaving energy to bedissipated as a pulse of damped sinusoidal oscillation. Themagnitude of the transient depends on the point-on-waveof the mains cycle at which the switch opens.

Inductive circuits consist mainly of lumped inductanceshaving iron cores ranging from induction motors, mainstransformers, solenoid control valves and actuators downto small AC relays. The transient condition relates to bothopening and closing operations and the simple analysisshown below follows from consideration of Figs. 14a and

50 Hzmainssupply

50 Hzmains 'v» Vpsupply

=r L

Fig. 14 Inductive circuit transients

a Opening operationb Closing operation where stray wiring inductance 'L' and ' C determine the fre-quency of the transient

b. A lumped capacitor C can be employed to ensure thetransient is kept within prescribed limits. In the absence ofthis capacitor there would be, on opening the circuit, anabrupt cessation of magnetising current through the induc-tor which would produce a large negative value of di/dtand hence an extremely high voltage would be developed,limited by the stray winding capacitance across the induc-tor. The current i which flows in the inductor immediatelyprior to opening the switch must, on opening the switch,flow into the oscillatory circuit formed by C, L and rwhere r is determined by both copper and iron circuitlosses. Ignoring r initially allows the use of the conserva-tion of energy to determine the peak voltage V to which Cwill be charged.

g i v i n g V = i j -

The rate of decay from this prospective peak depends oncoL/r where the radian frequency of the oscillation co isgiven by l/y/LC. The largest amplitude transient corre-sponds to interruption at a peak value of the mains supply

215

current such that i=Vp/cosL. On substitution, V/Vp =(o/cos which gives the transient amplitude in normalisedform and indicates that when co = co5 the transient islimited to the mains voltage peak. This resonant value ofcapacitance is seldom used in practical situations becausea fraction of this capacitance value may limit the transientto a specified value. Transients caused by switching on arefound to be of little significance when lumped capacitor Cis not used, but when C is introduced the transient isfound to increase in amplitude with increase in capacitancevalue up to a maximum of twice the peak mains voltage,assuming closure at mains voltage peak. The frequency ofthis highly damped oscillatory transient is governed by theinductance associated with the supply leads L as indicatedin Fig. 14b and is of such a high frequency that the effect ofthe impedance a>L of the inductor may be disregarded forpurposes of calculation.

With the widespread use of solid state devices which usephase control of load power by chopping off portions ofeach cycle of mains frequency, transients are generatedcontinuously. The rapid turn-on and turn-off properties ofthese waveform chopping circuits, using thyristors andtriacs, can generate harmonics of high order which causeradio interference. The interference increases with increasein load current and becomes more difficult and costly tosuppress. Electric heating which may be regarded as a loadhaving a long time constant may be controlled by the tech-nique called burst firing or integral cycle control. Theswitching is carried out at zero voltage crossing in themains waveform and results in a form of low frequencyon-off modulation of the mains waveform which is vir-tually interference free.

It is obvious that dimming of lamps by burst firingwould produce flicker effects which are undesirable and insome cases harmful, hence this technique is not applied tolighting loads. The interference generated by all forms oftransient phenomena is referred to as electromagneticinterference (EMI). Computer EMI is produced by digitalgates, switching from high to low level continuously, andFourier analysis of logic signals indicates that harmonicsof the repetition rates will be produced, with amplitudesdiminishing with frequency, up to several hundred mega-hertz.

The detonation of a nuclear device above the surface ofthe earth, exo-atmospheric, would produce an enormouselectromagnetic pulse (EMP) lasting for several hundredsof microseconds having a rise-time of less than 10 nano-seconds, which is many times faster than that of a light-ning stroke. The EMP pulse approximates to a singlerectangular pulse and covers a frequency spectrum extend-ing from the lowest frequencies to several hundred mega-hertz. It is believed that a one megaton exo-atmosphericexplosion would produce field strengths of several kilo-volts per metre over an area limited only by the earth'scurvature, and cause serious damage to power supply linesand communication equipment over a radius of 1000 kmcentred on the location of the explosion.

6.3 Reduction of transients by non-linear devicesVoltage dependent resistors or 'varistors' are used tosuppress overvoltages such as appear at relay contacts oradjacent commutator segments. The nonlinear relationshipis given as V = (const.)/** which can be expressed inlogarithmic form as log V = k + ft log /, indicating thatsome distance from the origin the relationship tends toapproximate a straight line. For small voltages and lessthan 1 W dissipation, titanium oxide beads are used with /?values in the range 0.11 to 0.3. Disc types manufactured

using ZnO have RMS working voltages from 50 to 425 V.Discs approximately 1 cm diameter can handle non-repetitive energies of 6 joules which arise from transientsand perform as spark suppressors. Test specification forsuch discs call for a discharge energy of 8 J from a capac-itor charged to 2 kV, the maximum discharge current isusually limited by a series resistor of just less than 1 Q. Thevaristor type of suppressor operates as a constant voltagedevice which reduces the transient amplitude, to protectsemiconductors, by a clamping action. The device isdesigned to have negligible drain of current under normalworking voltage conditions and as low as possible clamp-ing voltage; the physical size of the device increases withincrease in energy to be dissipated, this dissipation is oftenrelated to an idealised transient which rises linearly fromzero to maximum in 10 microseconds, thereafter falling lin-early to zero in 1 millisecond, the energy rating being injoules. As a guide, the clamping voltage is some 2.4 timesthe rated RMS operating voltage, e.g. a zinc oxide varistorof 250 V RMS maximum continuous rating will limit atransient amplitude to 600 volts when passing 100 amps,whereas at normal working voltage the current throughthe device is of the order of 1 milliamp. The varistorreverts to this low current drain condition after the tran-sient dies down to zero, provided that the energy ratingand the maximum current have not been exceeded.

The direct protection of semiconductor devices such asintegrated circuits from fast transients in low-voltage cir-cuits and, in particular, transients from DC power suppliesis achieved by the use of PN silicon transient voltage sup-pressors. Silicon suppressors are characterised by theirhigh surge handling capability and fast response time. Thesuppressors are basically Zener diodes with avalancheproperties. In the bipolar form the suppressor comprisestwo Zener diodes connected in series, back to back; suchdevices are slightly slower in operation than the single PNdevice. A typical suppressor, used on a 6.8 volt DC supplyrail, would clamp the transient voltage to 10.8 volts at amaximum peak current of 139 amps. Small computers andmicroprocessor based systems are primarily protectedfrom radio frequency interference and transients in generalby screened mains filters of the LC type followed by mainstransformers with a high degree of Faraday screening.

7 Overvoltages in cable systems

The use of buried-cable systems which utilise threeseparate coaxial cables to transmit 3-phase power over dis-tances in excess of 500 metres is common. To improve therating of the cables it is essential that the steady-statesheath currents be suppressed by means of sheath inter-rupters and cross-bonding of short section lengths, minorsections in sets of three, to form major sections. Whereinterruption and cross-bonding is used this involves thetransposition of the three phases to provide magnetic sym-metry when the cables are laid in flat formation. For pur-poses of calculation it is assumed that complete symmetryexists in the steady-state and that a sufficiently low barrier-capacitance exists to block the power frequency circulatingcurrents.

When a step voltage is applied to only one phase, thetransient overvoltages seen at the first joint of a cross-bonded system may be calculated by equivalent circuitswhich are developed in terms of the surge impedance ofthe cable (Z01) in the coaxial mode, the sheath-earth (Z02)and the sheath-sheath surge impedances [107].

The problem may be simplified by assuming that ahighly conducting earth return path is concentrated in a


thin shell at the outer surfaces of all the cable sheath insu-lation. By considering a surge voltage E to be injectedbetween red phase and its sheath only (1 to 4) shown inFig. 15, which is the connection diagram for a trefoil cross-bonded cable system with its inherent discontinuity along

hminor _Jsectionj

1 -

'- yellow phase

red phase

Fig. 15 Typical crossbanded joint in symmetrical system

a Connections of one major section of crossbonded system, showing transpositionsof phases(i) Solid bond(ii) Cross bondsb Connection diagramc Equivalent circuit in generalised formd Equivalent circuit for voltage injection between red conductor and sheath only

the line X-X, the voltage across the red-phase interrupterVAB is given on a per unit basis by

VAB

E

4Z02

4Z01 + 3Z' 0 1 02

It is accepted that the maximum sheath voltages are gener-ally those arising from the first reflection at a cross-bondedjoint. Thus, a 132 kV power cable with Z01 = 18 Q andZ02 = 7 Q gives VAB = 0.3 per unit and a voltage of 0.15per unit between sheath and earth; for earth-free condi-tions the voltage would be twice this value. On this basis, atransient of peak amplitude greater than 15 kV could arise

between earth and the lead sheath of a cable. Neoprene isused as a sheath anti-corrosion insulating jacket approx4 mm thick. This has a dielectric constant of 5.7 comparedwith that of the impregnated paper dielectric of the cablewhich is 3.5; this indicates that the velocity of wave propa-gation in the sheath material would be approx 0.8 of thatin the cable. The difference in propagation velocities wouldhave to be taken into account in the calculation of over-voltages at other cross-bonded joints along the system.Sheath jackets may not withstand such transient voltagesfor systems operating at 230 kV and above, and protectivedevices are installed to limit these transients. A cross-bonded joint with three non-linear resistors connected toearth, one from each sheath, is shown in Fig. 16 so that

7 nonlinearresistors

Fig. 16 Cross bonded joint with nonlinear resistors

two non-linear resistors in series connect each sheath toeach other. The non-linear resistors must be capable of dis-sipating some part of the energy stored in the cable whenit discharges as a result of a line-to-earth fault.

From the foregoing it is evident that the nature of tran-sient overvoltages due to switching in a cross-bondedcable system cannot readily be determined by theoreticalanalysis except for the transient voltage at the first cross-bonded joint. To investigate transients further along thesystem, high-ratio capacitance potential dividers may beused without significantly affecting the performance of theinsulation of the cable. A capacitance divider may be con-veniently incorporated in a cross-bonded joint; this con-sists of a coaxial foil inserted within the first few paperlayers close to the sheath. A hybrid type potential dividerhas been designed for use at 33 kV which employs bothcapacitive and resistive division and has a response up to2 MHz. This type of capacitance potential divider, whenbuilt into cables, has provided an effective means of moni-toring transient and power frequency voltages on cablesystems [108, 109].

8 Temporary overvoltage

Although strictly speaking they are not transient overvolt-ages, temporary overvoltages are closely akin to, and oftenassociated with, transient phenomena. A temporary over-voltage [120] is an oscillatory overvoltage of relativelylong duration which is undamped or only weakly damped.This is in contrast to lightning and switching overvoltageswhich are of short duration and usually highly damped.Both switching and temporary overvoltages occur as aresult of a switching operation or the initiation or clear-ance of a fault so that it is not always possible to make aclear distinction between the two.

Temporary overvoltages may have different effects onthe system. Among them are flashover of insulation andpuncture of internal insulation if their magnitude is high,and heating of transformer and reactor cores if they cause


saturation. In addition they can affect surge arrester resealproperties and possibly the thermal stability of thearrester.

8.1 Load rejection [121,124-1 26]When load is suddenly removed from the end of a longtransmission line, a rise in voltage occurs at the end of theline. The magnitude of this voltage rise can be considerableand depends upon the line length, the reactance of thesource and the load that is rejected [121]. Reactive com-pensation can assist in minimising the rise in voltage, butwith certain levels of series capacitor compensation, selfexcited oscillations may occur [125, 126]. A higher loadwill increase the internal voltage of the source as also willa reduction in the short circuit power of the source.

It should be noted that when the load is removed, therewill be an increase in the generator speed before the gover-nor acts. This increase in speed leads to increases in thegenerator internal voltage and the frequency, which causesan increase in overvoltage which may be as much as 7%.

8.2 Open circuit and single phase reclosureResonant conditions at power frequency can occur whenswitching a line associated with an unloaded transformer[121]. Such a situation is shown in Fig. 17 and if a delay in

Fig. 17 Resonant condition due to single phase open circuit

the closing of one phase of the circuit breaker shouldoccur, the positive sequence network is in series with theparallel connected negative and zero sequence networks asshown. For some line lengths the positive sequencenetwork is capacitive whereas the zero sequence network isinductive. A resonant condition then occurs at the linelength which makes the positive and zero sequence reac-tances equal at the power frequency. It is not essential forexact resonance to be achieved, large values of voltage canstill occur as the peak of the resonance curve isapproached.

Such a situation has occurred in Sweden [122] with a200 km length of 400 kV line terminated in an unloadedtransformer. One circuit breaker pole closed 300 ms afterthe other two due to malfunctioning and resulted in anovervoltage at the transformer which caused a surgearrester to fail. Subsequent investigation showed that theovervoltage had a magnitude of 2.25 p.u. which reduced to2.15 p.u. including the effects of saturation in the trans-former. It was found the worst case would occur with aline length of 250 km giving overvoltages of 4 p.u. withoutsaturation included and 2.15 p.u. with saturation included.

Similar conditions to those described can be producedduring single phase reclosure operations under conditionswhere the line feeds a transformer which is lightly loaded.The production of an overvoltage is conditional on reclo-sure taking place first at the transformer end, thereby

leaving one phase open circuited at the source end of theline. To avoid this situation the auto-reclosure sequenceshould be designed to reclose the circuit breaker at thesource end before the circuit breaker at the load end of theline.

8.3 Saturation and harmonic resonanceLarge temporary overvoltages may lead to saturation intransformers connected to the system. If the harmonicsproduced contain a frequency which is close to a systemnatural frequency then harmonic resonance may occur.

Loss of load and the consequent voltage rise can causesaturation in transformers and the production of har-monics. Such a condition has been reported [90] when a270 MW, 0.85 p.f. load was dropped from a 35.4 km, 420kV line connected to a generator transformer. On thisoccasion a temporary overvoltage of 1.4 p.u. was recordedand consisted of a harmonic voltage superimposed on thepower frequency voltage. Such overvoltages require atten-tion as they can have a bearing on the reseal requirementsof surge arresters.

Energisation of lines terminated in transformers canlead to temporary overvoltages caused by harmonic reson-ance. In Finland [123] a 400 kV, 520 km transformer ter-minated line was energised from a weak source and apronounced 2nd harmonic appeared resulting in an over-voltage of 2.5 p.u. which was of long duration. Such over-voltages are most pronounced in weak systems with longlines, with the most severe conditions occurring when thesystem is in resonance with one of the harmonics. Theovervoltages can last a long time, their decay being depen-dent on the slow demagnetisation of unloaded transformercores.

8.3.1 Inrush current: The nature of the inrush current canbe appreciated by finding the transient response of a linearcircuit comprising a resistance R in series with a 'fixed'inductance L. A simple linear differential equation may besolved to obtain the inrush current i(t) for the worst casewhich results from the application of the power frequencyvoltage E sin cot at t = 0. The value of i(t) after t = 0 isshown in Fig. 18 where the steady-state condition is

40 ms/di vision

Fig. 18 Inrush current for a series R and L circuit excited by E sin cotat t = 0, showing decay (e~R"L) to steady-state peak value I

approached after some twenty cycles of the power fre-quency. The initial response indicates a prospective doub-ling of the steady-state peak current. It is evident that i(t)could reasonably well represent the magnetising current inan iron-cored transformer, provided that the iron circuit isnot saturated by the peaks of the current waveform shownin Fig. 18. However, most power transformers are designedto operate near the knee of the B-H curve where the mag-netising current and the core losses are not excessive; inwhich case the transient current would produce core satu-ration on successive half cycles resulting in excessivecurrent flow into the transformer. The current waveform is


grossly distorted by the transition from non-saturation tosaturation of the core and contains significant harmonics.

The situation described above is clearly dependent onthe residual magnetism in the core prior to energisationand the point-on-wave at which the breaker closes thecircuit. The residual magnetism depends on circuit condi-tions when the transformer is disconnected from thesupply, for example the load connected to the transformerwhen the transformer is switched off. The interruption ofcurrent by a circuit breaker normally occurs at a naturalcurrent zero and reference to the hysteresis loop indicatesthe residual magnetism left in the iron core. Under theworst conditions of point-on-wave switching and residualmagnetism, inrush currents several orders of magnitudegreater than the full-load current are possible. The inrushcurrent may be limited by energisation via a series resistorin which case the flux in the core can be made to varyabout the zero value after a few cycles and the seriesresistor may be shorted out without excessive current flow.

8.3.2 Dynamically sustained overvoltages: Long dura-tion dynamic overvoltages, associated with transformerinrush currents which are large enough to produce coresaturation, have been encountered in situations wherepower factor correction capacitors or harmonic filters areused. Switching overvoltages of this type arise in HVDCsystems when a DC system is connected to a lightlydamped AC system such as isolated generation [164, 165].In this particular case the voltage ratings of convertorvalves as well as the normal equipment have to be con-sidered. The overvoltages occur during transformer ener-gisation, AC fault clearing and after DC load rejection.

In general, dynamically sustained overvoltages associ-ated with ferroresonance and inrush currents occur in ACsystems when a transformer is energised from a capacitivesource such as the end of a long transmission line or cable[164, 166, 167].

9 Method of analysis

The calculation of transient phenomena in power systemnetworks is not simple. This is because the power systemitself consists of plant whose characteristics vary widely.Overhead lines and cables have parameters which are dis-tributed in nature in contrast to those of generators andtransformers which, for many purposes, may be consideredas lumped. The power system under transient conditionsmay be subjected to voltages and currents having a widefrequency range from power frequency up to the region of100 kHz. Over this range the parameters of the system andof the earth path have values which vary with the fre-quency. As a consequence any method of calculationshould be capable of representing equally well, lumped anddistributed parameters over a wide frequency range andinclude the effects of nonlinearities such as those due tosurge arresters, magnetic saturation, corona and arcing. Inpractice such a method is not easily achieved and methodsin current use represent a compromise in some respects,the particular compromise arrived at being determined bythe specific requirements of the user.

Hand calculations are only practical for the very sim-plest of systems because the labour and complexity of suchcalculations increase rapidly with an increase in networksize. The use of analogue or digital computers is thereforenearly always essential. Some of the methods used are out-lined in the following Sections, a more complete treatmentbeing available in the literature [68, 127]. In particular, a

useful review of methods of analysis has been publishedelsewhere [168].

9.1 Analogue methodThe traditional method of calculating transient pheno-mena in power systems is that of the transient networkanalyser (TNA). This has been used since 1939 [95, 128]and essentially consists of forming a scale model of thenetwork using lumped elements of inductance, capacitanceand resistance. Both impedance scaling and frequencyscaling can be employed, the model is energised from a lowvoltage source, switching operations are performed byminiature switches and the resulting transients observedon an oscilloscope.

The TNA can be of particular advantage where theexact mechanism of the transient phenomena is unknownand where the work is of an exploratory nature. A com-bination of TNA and digital facilities can be extremelypowerful and the two approaches should be viewed ascomplementary rather than competitive. SophisticatedTNA facilities have been described [129-132] and in somecases are closely linked to digital facilities [133-136].

9.2 Lumped parameter systems-solution of differentialequations

The transient analysis of a resistively-terminated losslesstransmission line is classically performed in terms of reflec-tions at the ends of the line. Thus a series of time shiftedwaves arise at definite time intervals related to the timetaken for a unit step to travel between source and termina-tion. When a solution to the problem of a line with reac-tive terminal impedances is sought, the wave approach byLaplace transforms is severely complicated by the require-ment for inverse transformation, when many reflections areto be taken into account.

One approach which provides insight to the problem isto represent the transmission line by a finite number of n-or T-sections having fixed lumped parameters, the numberof sections being chosen to obtain minimum circuit com-plication consistent with the required high frequency per-formance of the limited representation.

Taking a single T-section to represent a fraction of theline length, leads to a requirement that the characteristicimpedance (Zo) should be reasonably constant up to thehighest frequency of interest. For the loss-free T-section

1/2

where

fc =

and

L is the total series inductance of the section and C is thetotal shunt capacitance. When the highest frequency ofinterest/is 7th of/c, the value of ZT is about 1% lowerthan Zo.

The phase delay /? produced by the T-section at any-frequency/is obtained from the equation

cosh;0 = cos $ = 1 - 2n2f2LC = 1 - 2 [ y

njLC

for small values of /?, cos /? = 1 - f}2/2 which gives /? =2nfy/LC = 2(///c) radians per section which implies that

1EE PROCEEDINGS, Vol. 133, Pt. C, No. 4, MAY 1986 219

the delay time t for the T-section is given by t = jseconds per section. Thus the number of sections requiredto represent any line or cable may be chosen so that thefrequency response of the fixed parameter sections whichform the equivalent circuit is adequate up to the highestsignificant frequency. Another physical system which maybe represented in this way is shown in Fig. 19 where one

c4= c4= C—r-

Fig. 19 One phase of an alternator winding4 coils, each having inductance L and distributed capacitance to core C representedby T-sections

phase of an alternator winding is shown as sets of coils inseries, each with self inductance L and having distributedcapacitance to the core. The step response of the typedescribed above may be solved by mesh analysis, e.g. asimple case where four meshes are involved would give riseto an eighth order polynomial in the Laplace operator p.The algebraic process associated with the derivation of thepolynomial is laborious, having obtained the correct coeffi-cients of the polynomial the four pairs of complex conju-gate roots may be obtained by digital computation. In thisway a closed form of solution for the step response of alumped-parameter system is obtained.

However, when a large number of sections are requiredfor the representation it is essential that methods involvingmodal analysis are employed to provide a feasible processof solution to such linear circuit problems, where the equa-tions are linear with constant coefficients. The reason forresorting to the lumped parameter method is that theaction of voltage dependent resistors (surge diverters) maybe taken into account in the digital computation of over-voltages [150]. A single phase general form of the lumpedparameter equivalent circuit is shown in Fig. 20 where acurrent i is assumed to flow through the surge diverterwhere v0 has exceeded a given voltage level. The circuitmay be described by a finite number of differential equa-tions which may be expressed in the form of vector differ-ential equation

x = Ax + Bv + Ci, where x =

when i = 0 this reduces to a linear form

x = Ax + Bv

The equations may be integrated by a numerical integra-tion routine which has been adapted to incorporate the

Ri Li RQ LQ

law governing the action of the non-linear element, i.e. i isa known function of v0. For example, for silicon carbidenon-linear resistors i may be taken as proportional to thefifth power of the voltage v0. The method described aboveis able to deal with circuits with other than zero initialconditions such as appertain when the line has pre-charge;also it is worth noting that a linear form of equation

x = Ax + Ci

exists which can be used to calculate transient recoveryvoltage where i is the injected current.

9.3 Travelling wave methodsThese methods are based on the solution of the transmis-sion line equations, which may be expressed as a com-bination of forward and backward travelling waves on theline. Two graphical forms of the solution exist, one due toSchnyder [137] and Bergeron [138] and frequentlyreferred to as the Schnyder-Bergeron method, and asecond known as the lattice diagram method which wasdeveloped by Bewley [139]. The advent of the digital com-puter enabled both techniques to be applied to the solu-tion of problems involving extended single phase and threephase networks. This development is described in the liter-ature for both the Schnyder-Bergeron method [140-144]and the lattice diagram method [63, 105, 145-148].

Although basically the methods are applicable to dis-tributed parameter elements such as lines and cables, thelumped parameter elements of generators, transformersand capacitor banks etc., can be approximated by shortline stubs [145, 146]. Mutual effects between the phases ofa three-phase system are included by the use of the fullimpedance and admittance matrices of the network ele-ments.

Transmission line attenuation and distortion can berepresented in both methods and allows the frequencydependence of the line parameters to be represented [63,147, 148]. In the case of the lattice diagram method, trans-mission line losses are included in the calculation by trans-forming all voltage steps, including mutually inducedvoltages, entering a line into the modal domain [149]where they are attenuated and distorted before beingtransformed back into the real or phase domain when theyarrive at the remote end of the line. The modal domain isone in which there are no mutual effects, thus enabling themodal voltages to be distorted independently of oneanother in accordance with modal step responses calcu-lated prior to the main calculation.

9.4 Fourier frequency domain method [151 -157]Any frequency domain approach which uses Fourier seriesor Fourier transforms can deal with any arbitrary inputwave only when linear system elements and operations areinvolved. The response of a linear system to a sine wave issimply another sine wave differing from the original, at themost, in amplitude and phase. This statement gives physi-cal significance to Fourier analysis and to the concepts offrequency spectra and frequency response which are intu-itive to the engineers' approach. By formulating theproblem in terms of a repetitive function any input wavecan be represented as a sum of related sine waves. The

co=fvo

220

Fig. 20 General form of line representation

IEE PROCEEDINGS, Vol. 133, Pt. C, No. 4, MAY 1986

output from any linear system will consist of the samenumber of related sine waves each modified in amplitudeand phase as determined by the frequency response of thesystem, which must be known in amplitude and phase forthe range of sine waves employed. Any one of the numberof sine waves will be transmitted through the linear systemas if it alone were present. The 'superposition' of eachoutput sine wave i.e. the sum of the output sine waves pro-vides the output waveform as a function of time.

The advantages of this method may be fully appreciatedwhen the frequency dependence of one or more circuitparameters, such as R, L, C, characteristic impedance Zoand the propagation constant (a + jfi), must be taken intoaccount in order to obtain the true representation of aphysical system [151]. Thus the time response of a linearsystem comprising both lumped and distributed frequencydependent parameters may be obtained to any desiredaccuracy, limited only by the accuracy to which the systemparameters are known [152]. For example, the response ofa stable physical system to a step input reaches a 'steady-state' for all practical purposes after a finite time intervalT. If the step is replaced by a repetitive square-wave with arepetition interval greater than T, complete informationregarding the transient behaviour of the system is availablefrom the response. To determine the response it is firstnecessary to modify, in magnitude and phase, the Fouriercoefficients of the input square-wave by the system's fre-quency response function evaluated at the fundamentaland harmonic frequencies. By summing enough of thedominant output harmonics it is possible to determine thetransient response to any desired accuracy. The outputwaveform is synthesised from the summations which aretaken at discrete intervals, the interval being chosen todelineate the highest frequency anticipated. These summa-tions are readily programmed in a high level language.

This method is always applicable as the response of anyphysical system cannot display true discontinuities. This isevident from the fact that any generator must have a smallfinite internal impedance and feeds current into cables orlines which themselves have fringe capacitances acrossjunctions and terminations. The residual mean squareapproximation error of a finite summation can thereforebe reduced to any desired value by summing a sufficientlylarge number of terms. The Fourier series for a squarewave/(t) of fundamental co0 and amplitude Vg is given by

m Y sin(2n+l)co0t

The removal of the DC term provides half wave symmetryand a series of sine waves of odd harmonics only as thedriving function for the network under consideration. Thisreplaces the usual step input in the time domain. The net-works have, as a rule, direct current paths to the pointsunder consideration and the DC term is modified, whereapplicable, and ultimately added to the full sinusoidalresponse to obtain the complete response.

The steady-state voltage response at any point x on atransmission line is given by

V(x) = Vg

where

exp (- >,- exp [-y(2/ - x)]

Zn-Z(

Z n '

This is the simplest expression to use when a single lineor cable with a complex termination is involved. Beyondthis where a cascade of lines, cables and lumped imped-ances is involved the following approach may be applied[152]. The transmission properties of any smooth line oflength / can be represented by an equivalent T- or n-section as shown in Fig. 21. The series and shunt elementsare frequency dependent via the propagation 'constant'which is, in general, a complex function of frequency. Forexample the system shown in Fig. 22a is energised by anair-blast circuit-breaker.

ZQ sinh y l

Zo coth

Fig. 21 n-section representation of a distributed parameter line of lengthI

cable

0/H line V3

V2 h Aft cable >fe

step voltageo».,,

o—in-voltage

o

are the reflection coefficients at the load and the generator,respectively.

Fig. 22 Single phase of a cable and line system energised by a stepvoltagea Schematic diagramb Smooth n-section representation for purposes of calculation of voltages generatedalong the system

The breaker is assumed to arc-through near the peakvalue of the power frequency waveform producing a steadystep voltage of value VG. For completeness the internalimpedance of the generator is represented by Zg. Thesystem may be represented, at any given frequency, by thethree 7r-sections in cascade shown in Fig. 22b. The voltageat the input Vt may be found by systematically reducingthe network to a single impedance across the generatoroutput terminals.

Thus the input voltage to the first cable is obtained.This may now be applied to the system as from an idealvoltage generator. The other voltages along the systemsuch as V2, V3 and K4 may be computed by simplyworking forward along the system from the input to theoutput of each section.

9.5 Z-transform methodsMore recently [127] the Z-transform has been applied tothe transient analysis of power systems. This is a methodwhich seeks to avoid the inverse transformation from thefrequency domain to the time domain using the inverseFourier transform with its attendant difficulties due totruncation and the necessity to use the sigma factor. Themethod proceeds from the frequency domain to the Z-domain and then directly to the time domain. It makes useof the similarity between the exponential form of the Z-transform and that of the principal transmission lineresponses in the frequency domain. The application of thismethod is described fully in the literature [158-160].

IEE PROCEEDINGS, Vol. 133, Pt. C, No. 4, MA Y 1986 221

10 Summary

It is evident that transient overvoltages take many formsand can arise in various ways. It would be rash indeed toclaim that this review is exhaustive but it is hoped that themajor causes of transient overvoltages have been covered.It must be remembered that the problems associated withsuch overvoltages have not all appeared simultaneously.Rather they have arisen sequentially as power system net-works have developed and transmission voltages haveincreased over the years. In their turn, these problems havebeen investigated and solutions found so that the literatureon the subject now represents a vast store of informationon transient phenomena. No doubt as power systems con-tinue to expand, other problems are bound to occur andthey in their turn will become the focus for investigation,research and solution.

The ever increasing range of problems arising fromtransients within electrical power systems has given rise toa multiplicity of methods of analysis and solution, particu-larly since the advent of large fast computational facilities.Consequently we are led to expect that prospectivesystems may be analysed at the design-study stage and thisshould prevent problems arising during commissioningand subsequently when the system is fully operational.Such feasibility studies depend for their success on thechoice of a method which can take into account all theavailable data relating to the performance of the systemelements. Thus, although ideally the most precise mathe-matical models of the physical system should be analysed,in practice comprehensive data is not always readily avail-able and the choice of method will be influenced by theresources, computational facilities and the limitations ofthe data in both resolution and accuracy.

11 Acknowledgment

The authors wish to express their thanks for the contribu-tion of Section 2 of this paper, which was provided by Dr.S. Littlewood and Mr. B. F. N. Briggs, Department ofElectrical Engineering, Huddersfield Polytechnic.

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65 PARIS, L.: 'Basic considerations of magnitude reduction of switch-ing surges due to line energisation', IEEE Trans., 1968, PAS-87, pp.295-302

66 VYSKOCIL, V., and FIC, J.: 'Results of statistical investigation ofovervoltages in the Czechoslovak System', CIGRE Paper 33-01,1972

67 THOMAS, C.H., WELLE, D.H., HEDIN, R.A., and WEISHAUPT,R.W.: 'Switching surges on parallel HV and EHV untransposed linesstudied by analog simulation' IEEE Trans., 1972, PAS-91, pp.180-189

68 BICKFORD, J.P., MULLINEAUX, N., and REED, J.R.: 'Compu-tation of power system transients', IEE Monograph 18 (Peter Pere-grinus, 1976)

69 BATTISSON, M.J., MULLINEAUX, N., DAY, S.J., and PARTON,K.C.: 'Some effects of frequency dependence of transmission lineparameters', Proc. IEE, 1969,116, (7), pp. 1209-1216

70 BARNES, H.C.: 'Preliminary analysis of extensive switching surgetesting of A.E.P's first 765 kV line and stations', IEEE Trans., 1971,

PAS-90, pp. 785-79871 GARRITY, T.F., HAAHR, J.C., KNUDSEN, L , and RAEZER,

M.C.: 'Experience with the AEP 750 kV system Pt V—Overvoltageand staged fault test—Analysis', ibid. 1973, PAS-92, pp. 1074-1084

72 THANASSOULIS, P., D E F R A N C O , N , CLERICI, A., andCAZZANI, M.: 'Overvoltage on a series compensated 750 kVsystem for the 1000 MW Itaipu Project', ibid., 1975, PAS-94, pp.622-631

73 STEMLER, G.E.: 'BPA's field test evaluation of 500 kV PCB's ratedto limit line switching overvoltages to 1.5 per unit', ibid., 1976,PAS-95, pp. 352-361

74 FAKHERI, A, and HAAHR, J.C.: 'Experience with the AEP 765 kVsystem Dumont-Marysville-Kammer field tests', ibid., 1978, PAS-97,pp. 109-117

75 BATTISSON, M.J., BICKFORD, J.P., CORCORAN, J.C.W.,JACKSON, R.L, SCOTT, M., and WARD, R.J.S.: 'British investiga-tions on the switching of long EHV transmission lines', CIGREPaper 13-02, 1970

76 DILLARD, J.K., and HILEMAN, A.R.: 'Switching surge per-formance of transmission systems', CIGRE Paper 33-07, 1970

77 BALTENSPERGER, P., and RUOSS, E.: 'Switching overvoltages inEHV and UHV networks', CIGRE Paper 13-14, 1970

78 DWEK, M.G., HALL, J.E., JACKSON, R.L., and JONES, B.: 'Fieldtests and analysis to determine switching transients on the BritishSystem', CIGRE Paper 13-03, 1972

79 SMITH, D.C.: 'Switching surge measurements on an uncompensated500 kV line', CIGRE Paper 33-06, 1972

80 AKOPYAN, A.A., BOURGSDORF, V.V., KUZMITCHEVA, K.I.,KYSKOV, Yu.L, RASHKES, V.S., and FOTIN, V.P.: 'Switchingovervoltages and the system of protection against them in 750 kVnetworks of the USSR', CIGRE Paper 33-07, 1972

81 CAZZANI, M, CLERICI, A., MARGARITIDIS, P., and THEL-OUDIS, J.: 'Internal overvoltages on the new Greek 400 kVnetwork', CIGRE Paper 33-03, 1974

82 LEGATE, A.C., STEMLER, G.E., REICHERT, K., and CUK, N.P.:'Limitation of phase to phase and phase to ground switching surges;Field tests in B.P.A. 500 kV system', CIGRE Paper 33-06, 1976

83 BELIAKOU, N.N., KOMAROV, A.N., and RASHKES, V.S.:'Results of internal overvoltages and electrical equipment character-istics, measurements at the 750 kV networks', CIGRE Paper 33-03,1978

84 DILLARD, J.K., CLAYTON, J.M, AND KILAR, L.A.: 'Control-ling switching surges 1100 kV transmission systems', IEEE Trans.,1970, PAS-89, pp. 1752-1762

85 AIEE Committee Report: 'Switching surge field tests on ArizonaPublic Service 345 kV system', ibid. 1968, PAS-87, pp. 1635-1643

86 WHITE, E.L.: 'Switching surges on a 275/132 kV auto-transformer',ERA Report S/Tll 1,1961

87 CSUROS, L., FOREMAN, K.F., and GLAVITCH, H.: 'Energisingovervoltages on transformer feeders', Electra, 18, pp. 83-105

88 CSUROS, L., and FOREMAN, K.F.: 'Energising overvoltages ontransformer feeder circuits', Electr. Times-, August 1972, pp. 37-40

89 DOLAN, E.J., GILLIES, D.A., and KIMBARK, E.W.: 'Ferro-resonance in a transformer switched with an EHV line', IEEE Trans,1972, PAS-91, (3), p. 1273

90 CSUROS, L., and FOREMAN, K.F.: 'Some practical aspects ofovervoltages on the CEGB transmission system', IEE Proc. C,Gener., Trans. & Distrib., 1980, 127, (4), pp. 248-261

91 DISEKO, N.L., and BICKFORD, J.P.: 'A method of simulatinglinear and non-linear resonant phenomena associated with trans-former feeders', ibid., 1980,127, (3), pp. 169-178

92 'Westinghouse transmission and distribution book' 4th Edition, p.625

93 'Surge Divertors' BS 2914: 195794 VOSPER, J.S.: 'Fundamental frequency voltages due to single phase

earth faults on HV lines with resistance earthing', Proc. IEE, 1963, p.1990

95 PETERSON, H.A.: 'Transients in power systems' (Wiley, 1951)96 BEEMAN, D.: 'Industrial power systems handbook' (McGraw Hill,

1955)97 MORTLOCK, J.R, and DOBSON, CM. : 'Neutral earthing of three

phase systems with particular reference to large power systems', J.Inst. Electr. Eng., 1947, (2), pp. 549-572

98 MORTLOCK, J.R.: 'AC Switchgear Vol. 1' (Chapman & Hall, 1956)99 KIMBARK, E.W., and LEGATE, A.C.: 'Fault surge versus switch-

ing surge, a study of transient overvoltages by line to ground faults',IEEE Trans., 1968, PAS-87, pp. 1762-1769

100 CLERICI, A., SANTAGOSTINO, G. and MAGAGNOLI, A.:'Influence of fault initiation and fault clearing overvoltages on theinsulation of UHV lines', ibid., 1975, PAS-94, pp. 802-809

101 CLERICI, A., SANTAGOSTINO, G., MAGAGNOLI, A., and TAS-CHINI, T.: 'Overvoltages due to fault initiation and fault clearingand their influence on the design of UHV lines', CIGRE Paper


33-17, 1974102 BALASUBRAMANIAM, R., and GUPTA, S.: 'Calculation of tran-

sients due to fault initiation on a double circuit line' Proc. IEE, 1976,123, (6), pp. 537-542

103 CLERICI, A. and TASCHINI, A.: 'Overvoltages due to line ener-gisation and re-energisation versus overvoltages caused by faults andfault clearing in EHV systems', Trans. IEEE, 1970, PAS-89, pp.932-941

104 COLCLASER, R.G., WAGNER, C.L., and BUETTNER, D.E.:'Transient overvoltages caused by the initiation and clearance offaults on a 1100 kV system', ibid., 1970, PAS-89, pp. 1744-1751

105 BICKFORD, J.P., and ABDEL-RAHMAN, M.H.: 'Application oftravelling-wave methods to the calculation of transient-fault currentsand voltage in power-system networks', IEE Proc. C, Gener., Trans.& Distrib., 1980, 127, (3), pp. 153-168

106 BULL, J.H., and NETHERCOT, W.: 'The frequency of occurrenceand the magnitude of short duration transients in low-voltage supplymains', Radio & Electron. Eng., September 1964, pp. 185-190

107 HEATON, A.G., and ISSA, A.M.H.: 'Transient response of cross-bonded cable systems', Proc. IEE, 1970,117, (3), pp. 578-586

108 GRANT, A.E., and HEATON, A.G.: 'Capacitance potential dividersfor the investigation of transient overvoltages in crossbonded cables,ibid., 1967,114, (6), pp. 803-808

109 HEATON, A.G., and MELAS, E.: 'Determination of effective per-mittivity and loss, as functions of temperature and frequency, ofimpregnated paper insulation by measurements on lengths of 132 kVpower cables'. IEE Symposium on Dielectrics, Lancaster University,24th July 1970

110 KIMBARK, E.W.: 'Suppression of ground fault arcs on single poleswitched EHV lines by shunt reactors' IEEE Trans., 1964, PAS-83,pp. 285-290

111 HAUBRICH, H.J., HOSEMANN, G., and THOMAS, R.: 'Singlephase auto reclosing in EHV systems', CIGRE Paper 31-09, 1974

112 LAMBERT, S.R., KOSCHIK, V., WOOD, C.E., WORNER, G., andROCAMORA, R.G.: 'Long line single phase switching transientsand their effect on station equipment', IEEE Trans., 1978, PAS-97,pp. 857-863

113 KIMBARK, E.W.: 'Discussion on single pole switching—a compari-son of computer studies with field test results', ibid., 1974, PAS-93,pp. 107-108

114 EDWARDS, L , CHADWICK, J.W., REICH, H.A, and SMITH,L.E.: 'Single pole switching on TVA's Paradise—Division 500 kVline—Design concepts and staged fault test results', ibid., 1971,PAS-90, pp. 2436-2450

115 KAPPENMAN, J.G., SWEEZY, G.A., KOSCHIK, V., and MUS-TAPHI, K.K.: 'Staged fault tests with single phase reclosing on theWinnipeg-Twin Cities 500 kV interconnection', ibid., 1982, PAS-101,pp. 662-670

116 JOHNS, A.T., and AL-RAWI, A.M.: 'Digital simulation of EHVsystems under secondary arcing conditions associated with singlepole autoreclosure', IEE Proc. C, Gener., Trans. & Distrib., 1982,129,(2), pp. 49-58

117 JOHNS, A.T, AND AL-RAWI, A.M.: 'Developments in the simula-tion of long-distnce single-pole-switched EHV systems', ibid., 1984,131, (2), pp. 67-77

118 PERRY, D.E., and HASIBAR, R.M.: 'Investigations and evaluationof single phase switching on EHV networks in the United States',CIGRE Paper 39-08, 1984

119 SEKINE, Y., and ICHIDA, Y.: 'Asymmetrical four legged reactorextinguishing secondary arc current for high speed reclosing onUHV systems', CIGRE Paper 38-03, 1984

120 GERT, R, GLAVITSCH, H., SHUR, S.S., TIKHODEYEV, N.N.,and THOREN, B.: 'Temporary overvoltages, their classification,magnitude, duration, shape and frequency of occurrence', CIGREReport 33-12, 1972

121 THOREN, B.: 'Temporary Overvoltages', Symposium on PowerSystem Overvoltages, UMIST, 1974

122 KELLER-JACOBSEN, J.: 'Resonance overvoltages in the 380 kVnetwork', Eheknik, 1960,3, pp. 81-83

123 KATTELIUS, J.: 'A resonance phenomenon observed in the 400 kVsystem', Saehkoe, 1965, 38, (4), pp. 137-140

124 DANDENO, P.L., and MCCLYMONT, K.R.: 'Extra high voltagesystem overvoltages following load rejection of hydraulic generation',IEEE Trans., 1963, PAS-82, pp. 49-57

125 RUSTEBAKKE, H.M., and CONCORDIA, C : 'Self excited oscil-lations in a transmission system using series capacitors' ibid., 1970,PAS-89, p. 1504-1512

126 BALASUBRAMANIAN, R., BABU RAM, and TRIPATHY, S.C.:'Temporary overvoltages due to load rejection on a series-compensated transmission line', IEE Proc. C, Gener., Trans. &Distrib., 1983,130, (1), pp. 8-15

127 HUMPAGE, W.D.: 'Z-transform electromagnetic transient analysisin high-voltage networks'. IEE Power Engineering Series 3 (Peter

Peregrinus, 1982)128 PETERSON, H.A.: 'An electric circuit transient analyser', Gen. Elect.

Rev., 1939, p. 394129 DICKSON, J.K., HEDMAN, D.E., LEWIS, W.A., and WEBLER,

R.M.: 'A new TNA Pt. 1—Design features provide versatile capabil-ities' IEEE Conference Paper C73-390-2, 1973

130 BORGONOVO, G., CAZZANI, M., CLERICI, A., LUCCHINI, G.,and VIDONI, G.: 'Five years of experience with the new CESI TNA'IEEE Canadian Cdmmunication and Power Conference, Montreal,Canada, 1974

131 RITCHIE, W.M., and PENDER, J.T.: 'The modern transientnetwork analyser and its role in analysis and design of electricalsystems'. Proc. IEE, 1978,125, (2), pp. 129-134

132 PENDER, J.T.: 'A combined steady-state and transient AC networkanalyser'. Int. J. Elect. Eng. Educ, 1968, 6, pp. 353-361

133 BROWN, J.L, MORSZTYN, K., and WRIGHT, I.A.: 'A new tran-sient network analyser', Trans. Inst. Engrs. Aust. Electr. Eng., 1969,EE5, (2), pp. 263-270

134 MORSZTYN, K.: 'Computer Controlled Transient NetworkAnalyser' Symposium on Power System Overvoltages, UMIST, 1974

135 CLERICI, A.: 'Analogue and digitial simulation for transient over-voltage determination', Electra, 1972, pp. 111-138

136 BOWLES, J.P.: 'An integrated computing facility for power systemstudies', Canadian Communication and EHV Conference, 1972

137 SCHNYDER, O.: 'Durchstrosse in pumpensteiglectungen', Schwertz.Banztg., 1929, 94, (22), p. 271

138 BERGERON, L.J.B.: 'Etude des variations de regime dans les con-duites d'eau: Solution graphique generale', Rev. Gen. Hydraulique,1935, 1, p. 12

139 BEWLEY, L.V.: 'Travelling waves in transmission systems' (Wiley,1933)

140 FREY, W, and ALTHAMMER, P.: The calculation of electromag-netic transients on lines by means of a digital computer', BrownBoveri Rev., 1961, 48, p. 344

141 ARLETT, P., and MURRAY-SHELLEY, R.: 'The teaching of trav-elling wave techniques using an improved graphical method' Int. J.Elec. Eng. Educ, 1966, 4, pp. 213-230 & 327-349

142 ARLETT, P , and MURRAY-SHELLEY, R.: 'The use of the graphi-cal method for the solution of transients on simple symmetricalthree-phase systems', ibid., 5, p. 377-388

143 DOMMEL, H.W.: 'Digital solution of electromagnetic transients insingle and multiphase networks', IEEE Trans., 1969, PAS-88, (4), pp.388-395

144 BERGMANN, R.Ch.G., and PONSIOEN, I.J.P.J.M.: 'Calculationof electrical transients in power systems', Proc. IEE, 1979, 126, (8),pp. 764-770

145 BARTHOLD, L.O., and CARTER, G.K.: 'Digital travelling wavesolutions, single phase equivalents', Trans. Amer. Inst. Elect. Engrs.,1961, 80, Pt. Ill, p. 812

146 MCELROY, A.J. and PORTER, R.M.: 'Digital computer calcu-lations of transients in electrical networks', IEEE Trans., 1963,PAS-82, p. 88

147 AMETANI, A.: 'Modified travelling wave techniques to solve electri-cal transients on lumped and distributed constant circuits', Proc.IEE, 1973, 120, (4), p. 497

148 BICKFORD, J.P., SANDERSON, J.V.H., ABDELSALEM, M.M.,MOHAMED, S.E.T., MORAIS, S.A., and OLIPADE, O.: 'Develop-ments in the calculation of waveforms and frequency spectra fortransient fault currents and voltages'. IEE Proc. C, Gener., Trans. &Distrib., 1980,127, pp. 145-152

149 WEDEPOHL, L. M.: 'Application of matrix methods to the solutionof travelling wave phenomena in polyphase systems', Proc. IEE,1963,110, (12), pp. 2200-2212

150 ANDERSON, J.H., and HEATON, A.G.: 'Transient analysis ofpower line/cable systems—including reactive terminations with surgediverters', ibid. 1966,113, (12), pp. 2017-2022

151 HEATON, A.G., and EDWARDS, R.: 'Implementation of a numeri-cal method for transient analysis of Power Systems with lumped anddistributed frequency-dependent parameters'. IEEE Summer PowerMeeting New Orleans, La., USA, 1966, Paper 31 pp. 66-413

152 HEATON, A.G., EDWARDS, R., and HILL, R.: 'An inherentlyaccurate method for transient analysis of linear power systems', Int.J. Electr. Eng. Educ, 1969, 7, pp. 7-14

153 DAY, S.J., MULLINEUX, N., and REED, J.R.: 'Developments inobtaining transient response using Fourier transforms Pt. 1'. ibid.,1965, 3, p. 501; 'Pt. II', 1966, 4, p. 31; 'Pt. Ill', 1968, 6, p. 259; 'Pt.IV, 1972,10, p. 256

154 BATTISSON, M.J., DAY, S.J., MULLINEUX, N., PARTON, K.C.,and REED, J.R.: 'Calculation of switching phenomena in powersystems', Proc. IEE, 1967, 114, (4), p. 478

155 BATTISON, M.J., DAY, S.J., MULLINEUX, N., and REED, J.R.:'Calculation of transients on transmission lines with sequentialswitching', ibid., 1970,117, (3), p. 587


156 WEDEPOHL, L.M., and MOHAMED, S.E.T.: 'Multiconductortransmission lines, theory of natural modes and Fourier integralapplied to transient analysis', ibid., 1969,116, (9), p. 1553

157 WEDEPOHL, L.M., and MOHAMED, S.E.T.: 'Transient analysisof multiconductor lines with reference to non linear problems', ibid.,1970,117, (5), p. 979

158 HUMPAGE, W.D., WONG, K.P., NGUYEN, T.T., andSUTANTO, D.: 'Z-transform transient analysis in power systems',IEE Proc. C, Gener., Trans. & Distrib., 1980, 127, pp. 370-378

159 HUMPAGE, W.D., WONG, K.P., and NGUYEN, T.T.: 'Develop-ment of Z-transform electromagnetic transient analysis for multi-node power networks', ibid., 1980,127, (6), pp. 379-385

160 HUMPAGE, W.D., WONG, K.P., and NGUYEN, T.T.: 'Time con-volution and Z transform methods of electromagnetic transientanalysis in power systems', ibid., 1980,127, (6), pp. 386-394

161 BAKER, W.P., and OAKESHOTT, D.F.: 'Surge diverters andspark-gap protection', IEE Conf. Publ. 108, 1974, pp. 60-66

162 DARVENIZA, B.E., and MERCER, D.R.: 'Service performance ofdistribution lightning arresters and transformers', Trans. Inst. Eng.Aust. Electr. Eng., 1966

163 BAKER, W.P.: 'Spark gaps for lightning protection', Cired, 1971,Report 17

164 BOWLES, J.P.: 'AC System and transformer representation forHV-DC transmission studies'. IEEE Trans., 1970, PAS-89, (7)

165 BOWLES, J.P.: 'Overvoltages in HVDC transmission systemscaused by transformer magnetizing inrush currents', Paper T73 433-0IEEE PES Summer Meeting and EHV/UHV Conference, Vancou-ver, B.C., Canada, July 15-20, 1973

166 THIO, C.V., MCNICHOL, J.R., MCDERMID, W.M., POVH, D.,

and SCHULTZ, W.: 'Switching overvoltages on the Nelson RiverHVDC system—studies experience and field tests' IEEE Conferenceon 'Overvoltages and Compensation on Integrated AC-DC Systems',Winnipeg, Canada, July 9-11, 1980

167 HOLMGREM, B., JENKINS, R.S., and RUIBRUGENT, J.: 'Trans-former inrush current', CIGRE, International Conference on largehigh tension electric systems Paris, Session 10, 20th June 1968

168 HUMPAGE, W.D., and WONG, K.P., 'Electromagnetic TransientAnalysis in EHV Power Networks', Proc. IEEE, 1982, 70, pp.

169 CORNICK, K.J., and THOMPSON, T.R.: 'Steep-fronted switchingvoltage transients and their distribution in motor windings, part 1:System measurements of steep-fronted switching voltage transients'.IEE Proc. B, Electr. Power Appl., 1982,129, (2), pp. 45-55

170 CORNICK, K.J., and THOMPSON, T.R.: 'Steep-fronted switchingvoltage transients and their distribution in motor windings Part 2:Distribution of steep-fronted switching voltage transients in motorwindings', ibid., 1982,129, (2), pp. 56-63

171 CIGRE WG: 'Interruption of small inductive currents Chapter 3Part A. High voltage motors', Electro, March 1981, 75, pp. 5-30

172 CIGRE, WG: 13.02 'Interruption of small inductive currentsChapter 3 Pt. B' ibid., July 1984, 95, pp. 31-45

173 SHANKLE, D.F., EDWARDS, F.R., and MOSES, G.L.: 'Surge forpipeline motors' IEEE Trans. 1968, IGA-4, pp. 171-176

174 PRETORIOUS, R.E., and ERIKSSON, A.J.: 'A basic guide to RCsuppression on motors and transformers', Trans. S.Afr. Inst. Electr.Eng., 1980, pp. 201-209

175 PARROTT, P.G.: 'Switching surge measurements on two highvoltage induction motor installations' ERA report 72-159, 1972


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Transient overvoltages on power systems

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