High Voltage Engineering - KUET

High Voltage Engineering

Md. Alamgir HossainAssistant ProfessorDepartment of Electrical and Electronic EngineeringKhulna University of Engineering & Technology

Transient Analysis

Surge on Transmission Lines

Due to a variety of reasons, such as a direct stroke of lightning onthe line, or by indirect strokes, or by switching operations or byfaults, high voltage are induced on the transmission line which isknown as surge.

Consider a small section of transmission line of length dx

Surge on Transmission LinesThe voltage drop across PQ and the corresponding current throughit are given by the following equations.


Eliminating dx we get

Diff. equn (1) w. r. to x and inserting equn (2) in that equation, we get

)(2

2

ti

xl

xir

xe

)(2

2

ti

xl

xir

xe

)(2

2

xi

tl

xir

xe

)()(2

2

tecge

tl

tecger

xe

)lg 2

2

2

2

telc

te

tercrge

xe

rgeteglcr

tecl

xe

)..(. 2

2

2

2


A very similar partial differential equation can be obtained for i.In practical power lines, the resistance r is much less than theinductance l, and the conductance g is negligible and hence,

2

2

22

2

2

2 1.te

atecl

xe

2

2

2

22

te

xea


Thus the general solution of this partial differential equation is

where f and F are two arbitrary functions of (x-at) and(x+at). These two functions can be shown to be forwardand reverse traveling.

Surge Impedance

Consider the forward wave e = f(x-at). The correspondingcurrent wave i be obtained as follows,

)( atxfxe

til

tatxfl

i )(1

aleatxf

ali )(1

impedanceSurgecll

clalZ

ie _.

.1

0

Energy Stored in Surge

The energy stored in a traveling wave is the sum of theenergies stored in the voltage wave and in the current wave.

It is seen that half the energy of the surge is stored in theelectrostatic field and half in the electromagnetic field.

22 lice 22

21

21 lice

We know,

Squiring, OR,

Reflection of Travelling waves

Reflection of Traveling waves at a Junction

1Z 2Z

EEZZZZER

12

12 EEZZ

ZET

12

22

If the line is short at far end, then Z2 is Zero and then

EEZZER

1

1

00

EE

ZZ

ZZ

ER

2

1

2

1

1

1

If the line is open at far end, then Z2 is infinity and then


When a voltage surge Earrives at the junction J,which is on open circuit, itis reflected without achange in sign (i.e. E)

Also, a current surge (- I)of opposite sign to theincident (I) is reflected sothat the transmitted currentis zero.


Open circuited line fed from a infinite source

If the line is fed from aconstant voltage source E,then as the reflected voltagesurge (E) arrives at thegenerator end, since thegenerator maintains thevoltage at its end at voltageE, it send a voltage surgeof -E back to the line so asto keep its voltage at Eaccompanied by a currentsurge - I.

Open circuited line fed from a infinite source


Open circuited line fed from a infinite sourceThe surge voltage -E as itreaches the open junction J, isreflected again without achange in sign, andaccompanied by a current + Iso as to make the transmittedcurrent again zero. Once thesevoltage and current wavesreach the generator, theinstantaneous voltage &current will be zero, and theline would once again beuncharged. The generator nowsends a voltage surge Eaccompanied by a currentsurge I, and the whole processdescribed repeats again



Short Circuit Line fed from an infinite source

When a voltage surge Earrives at the junction J,which is on short circuit, it isreflected with a change insign (- E), so as to cancel theincoming surge. Also, acurrent surge I of the samesign as the incident (I) isreflected so that thetransmitted current isdoubled (2I).


If the line is fed from aconstant voltage source E,then as the reflected voltagesurge (- E) arrives at thegenerator end, it send avoltage surge of E back to theline so as to keep its voltageat E. The voltage surge E isagain accompanied by acurrent surge I so that thetransmitted current becomes3I.

Short Circuit Line fed from an infinite source


Bewly Lattice Diagram

This is a convenient diagram devised by Bewley, which shows at aglance the position and direction of motion of every incident,reflected, and transmitted wave on the system at every instant oftime.

For a transmission, then the magnitude and phase of the wave as it reaches any section distance x from the sending end is Exgiven by.

When a voltage surge of magnitude unity reaches a junction between two sections with surge impedances Z1 and Z2, then a part α is transmitted and a part β is reflected back. In traversing the second line, if the attenuation factor is k, then on reaching the termination at the end of the second line its amplitude would be reduced to kα

Reflection of Travelling wavesAnalysis of an open-circuit line fed from ideal source

Thus the voltage at the open end after the nth reflection is given by

Reflection of Travelling wavesLet us now consider a line terminated through a resistance R. Thecorresponding reflection coefficient at the receiving end would beβ=(R-Z1)/(R+Z1).


The ends of two long transmission lines, A and C are connectedby a cable B of length 1 km. The surge impedances of A, BandCare 400, 50 and 500 Ω, respectively. A rectangular voltage waveof 25 kV magnitude and of infinite length is initiated in A andtravels to C. Determine the first and second voltages impressedon C.

Solution


Transmitted voltage


Transmitted voltage

Reflection at 3 Substation System

Reflection at 3 Substation System

3 substations A, B and C are spaced 75 km apart as shown in figure 4.10. B and C areconnected together by a cable (velocity of propagation 2 x 108 m/s), and the remainingconnections are all overhead lines (velocity of propagation 3 x 108 m/s). The attenuation factorsand the surge impedances of the lines are shown alongside the lines. The overhead lines beyondA and C on either side are extremely long and reflections need not be considered from their farends. Determine using the Bewley lattice diagram the over voltages at the 3 substations, at aninstant 1 ms after a voltage surge of magnitude unity and duration 3/4 ms reaches thesubstation A from the outside.


τAB= 75 x 103/3 x 108= ¼ms, τBC= 75 x 103/2 x 108= 3/8 ms

The single transit times of the two lines connecting the substations are


Reflection & Transmission at T-Junction

As far as the voltage wave is concerned, thetransmitted portion will be the same for bothbranches, i.e.,v2 = v3 = v, since they are parallel to eachother.

Reflection & Transmission at T-Junction

Insulation Co-ordination

Insulation Co-ordination:The term Insulation Co-ordination was originally introduced toarrange the insulation levels of the several components in thetransmission system in such a manner that an insulationfailure, if it did occur, would be confined to the place on thesystem where it would result in the least damage, be the leastexpensive to repair, and cause the least disturbance to thecontinuity of the supply.

Factor of Earthing:This is the ratio of the highest r.m.s. phase-to-earth powerfrequency voltage on a sound phase during an earth fault to ther.m.s. phase-to-phase power frequency voltage which would beobtained at the selected location without the fault.

A system is said to be effectively earthed if the factor of earthingdoes not exceed 80%

Terminology

Conventional Impulse Withstand Voltages:This is the peak value of the switching or lightning impulsetest voltage at which an insulation shall not show anydisruptive discharge when subjected to a specified number ofapplications of this impulse under specified conditions.

Conventional Maximum Impulse Voltage:This is the peak value of the switching or lightningovervoltage which is adopted as the maximum overvoltage inthe conventional procedure of insulation co-ordination.

Terminology

Statistical Impulse Withstand Voltage:This is the peak value of a switching or lightning impulse testvoltage at which insulation exhibits, under the specifiedconditions, a 90% probability of withstand. In practice, there is no100% probability of withstand voltage. Thus the value chosen isthat which has a 10% probability of breakdown.

Terminology

Statistical Impulse Voltage:This is the switching or lightning overvoltage applied toequipment as a result of an event of one specific type on thesystem (line energising, reclosing, fault occurrence, lightningdischarge, etc), the peak value of which has a 2% probability ofbeing exceeded.

Terminology

Conventional method of insulation co-ordinationIn order to avoid insulation failure, the insulation level of differenttypes of equipment connected to the system has to be higherthan the magnitude of transient overvoltages that appear on thesystem. Thus the insulation level has to be above the protectivelevel by a safe margin. Normally the impulse insulation level isestablished at a value 15-25% above the protective level.

Terminology

Statistical Method of Insulation Co-ordination:At the higher transmission voltages, the length of insulatorstrings and the clearances in air do not increase linearly withvoltage but approximately to V1.6

Terminology

Length of Overhead Shielding Wire

Consider a surge e approaching the terminal equipment. Whenthe surge magnitude exceeds the critical voltage e0, coronawould occur, distorting the surge wavefront, as it travels. Theminimum length of earth wire should be chosen such that intraversing that length, all voltage above the maximum surgethat can arrive at the terminal has been distorted by corona.

For reasons of economics, the same degree of protection isnot provided throughout a transmission line. Generally, it isfound sufficient to provide complete protection against directstrikes only on a short length of line prior to the substation

Length of Overhead Shielding WireCorona reduces the steepness of the wavefront above the criticalvoltage, as the surge travels down the line.


If the voltage is above corona inception, it would not remain at this value but


Thus corona causes a loss of energy of

The energy to create a corona field is proportional to the square of the excess voltage. i.e k(e-e0)2

Thus the energy required to change the voltage from e to

Length of Overhead Shielding WireThe loss of energy causing distortion must be equal to the change in energy required. Thus,

Rearranging and simplifying gives the equation

Wave propagation under ideal conditions is written in the form

The wave velocity of an increment of voltage at e has a magnitude given by

Thus the time of travel for an element at e when it travels a distance x is given by

is the time lag ∆t to the voltage element at e. Thus


A transformer has an impulse insulation level of 1050 kV and is tobe operated with an insulation margin of 15% under lightningimpulse conditions. The transformer has a surge impedance of1600Ω and is connected to a transmission line having a surgeimpedance of 400Ω. A short length of overhead earth wire is to beused for shielding the line near the transformer from direct strikes.Beyond the shielded length, direct strokes on the phase conductorcan give rise to voltage waves of the form 1000 e-0.05tkV ( where tis expressed in µs).If the corona distortion in the line is represented by the expression

µs/m , where B = 110 m/µs and e0= 200 kV,

determine the minimum length of shielding wire necessary inorder that the transformer insulation will not fail due to lightningsurges.

Example

Thus maximum permissible incident surge = 892.5/ 1.6 = 557.8 kV

Therefore,

Substitution in equation gives, 11.67/x = 1/110(1-200/557.8)

This gives, x = 2002m = 2.0kmThus the minimum length of shielding wire required is 2 km.

Surge ProtectionElectrical Surge:In general a surge is a transient wave of current, voltage orpower in an electric circuit. A power surge can occur for severalreasons. For example, high-power electrical devices can create aspike in the electrical current when they're switched on or whentheir motors kick on. Refrigerators, air conditioners andeven space heaters can cause a power surge strong enough todamage electrical systems.

The simplest and cheapest form of protection is the spark gap.The selected gap spacing should no only be capable ofwithstanding the highest normal power frequency voltage butshould flash-over when overvoltages occur, protecting theequipment.

Expulsion Tube Lightning Arrestor

The purpose of the external gap isto isolate the fiber tube fromnormal voltages thus preventingunnecessary deterioration. When anovervoltage occurs, spark overtakes place inside the fibrous tubecauses some fibrous material of thetube to volatile in the form of thegas, which is expelled through avent from the bottom of the tube.Thus, extinguishing the arc just likein circuit breakers.

Such protection may either be done by diverting the major partof the energy of the surge to earth (surge diverters), or bymodifying the waveform to make it less harmful (surgemodifiers). Surge diverters generally consist of one or morespark gaps in series, together with one or more non-linearresistors in series.

Silicon Carbide (SiC) was the material most often used in thesenonlinear resistor surge diverters. However, Zinc Oxide (ZnO) isbeing used in most modern day surge diverters on account of itssuperior volt-ampere characteristic.

When a series spark gap is required for eliminating the followcurrent, it is preferable to have a number of small spark gapsin series rather than having a single spark gap having anequivalent breakdown spacing. This is because the rate of riseof the recovery strength of a number of series gaps is fasterthan that of the single gap.

Rated VoltageThe designated maximum permissible r.m.s. value of powerfrequency voltage between line and earth terminals.

Discharge CurrentThe surge current that flows through the surge diverter afterspark over.

Discharge Voltage (or Residual voltage)The Discharge voltage is the voltage that appears between theline and earth terminals of the surge diverter during thepassage of discharge currents. The discharge voltage of theselected arrestor should be 15~25% below the BIL of theprotected equipment.

Power frequency spark over voltageThe power frequency spark over voltage is the r.m.s. value ofthe lowest power frequency voltage, applied between the lineand earth terminals of a surge diverter, which causes spark-overof all the series gaps.

Impulse spark over voltageThe impulse spark over voltage is the highest value of voltageattained during an impulse of a given wave shape and polarity,applied between the line and earth terminals of a surge diverterprior to the flow of discharge current.

Example 10.2A lightning arrestor is required to protect a 5 MVA, 66/11 kVtransformer which is effectively earthed in the system. Thetransformer is connected to a 66 kV, 3 phase system which has aBIL of 350 kV. Select a suitable lightning arrestor.

For 66 kV, maximum value of system rms voltage = 72.5 kV

Therefore, voltage rating for effectively earthed system =72.5 x 0.8 = 58 kV

The selected voltage rating is usually higher by a margin of about 5%. Selected voltage rating = 1.05 x 58 = 60.9 =60 kV Protective level of selected arrestor = 250 kV Margin of protection (crest value) = 350 - 250 = 100 kV which is more than the required margin of 15 to 25%.

100/250 x 100 % = 40%

Check the power frequency breakdown voltage. Power frequency breakdown voltage of arrestor =60x1.5 = 90 kV

Assuming the dynamic power frequency overvoltage to belimited to 25% above maximum voltage at arrestor location,

Dynamic phase-to-neutral voltage = 1.25 x 72.5 x 0.8 = 72.5 kV

This voltage is less than the withstand voltage of the arrestor.Thus the chosen arrestor is satisfactory.

Best protection is obtained for terminal equipment by placingthe arrestor as near as possible to that equipment and isusually located adjacent to the transformer. The maximumvoltage at the terminal of a line as a result of the firstreflection of a travelling wave may be expressed as

up to a maximum of 2 βEa. The factor 2 arises from thereturn length from arrestor to transformer, and the factor300 is based on a travelling wave velocity of 300 m/µs in theoverhead line. l is the separation between the arrestor andthe transformer location, β the reflection coefficient at thetransformer location, Ea is the discharge voltage at thearrestor, and de/dt is the rate of rise of the wavefront.

Example 10.3A 500kV steep fronted wave (rate of rise 1000kV/µs) as shownin following figure reaches a transformer of surge impedance1600Ω through a line of surge impedance 400Ω and protectedby a lightning arrestor with a protective spark-over level of650kV, 90m from the transformer. Sketch the voltage waveformsat the arrestor location and at the transformer location. Sketchalso the waveforms if the separation is reduced to 30m. Whatwould have been the maximum separation permissible betweenthe transformer and the lightning arrestor, if the BIL of thetransformer was 900 kV and a protective margin of 25 % isrequired.

SolutionIf the separation is 90 m, travel time of line t= 90/300 = 0.3 µs Transmission coefficient α= 2 ×1600/(1600+400)= 1.6 Reflection coefficient β= 1.6 - 1 = 0.6

The voltage waveforms at the arrestor location

The voltage waveforms at the transformer location

The voltage waveforms at the arrestor location

If the separation is 30 m, travel time of line t= 30/300 = 0.1 µs

The voltage waveforms at the transformer location

The maximum value of the voltage Et at the terminal for eachcase can be determined from

For 90m, Etmax -> 650+0.6x1000x90x 2/300 =1010 kV >1.6x500 Therefore maximum Et= 800 kV

For 30m, Etmax -> 650+0.6x1000x30x2/300 = 770 kV < 1.6 x 500 Therefore maximum Et= 770 kV

For a protective margin of 25 %, maximum permissible surge at transformer = 900/1.25 = 720 kV Therefore 720 = 650 + 0.6 x 1000 x 2 L / 300 This gives the maximum permissible length L = 17.5 m.

If the maximum rate of rise was taken as 500 kV/µs, the maximum length would have worked out at 35 m.

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