Restricted Earth Fault Relay Project

EG/94/710

FACULTY OF ELECTRICAL ENGINEERING

Group Electrical Energy Systems

RESTRICTED EARTH FAULT

DIFFERENTIAL PROTECTION

Master Thesis of

Pierre Raphael Bermejo

EG/94/710.A.

The Faculty of Electrical Engineering of theEindhoven University of Technology does notaccept any responsibility for the contents oftraining or terminal reports.

M. Sc. graduation report coached by:Prof.dr.-ing. H. Rijanto (EUT)Ir. P. Bertrand (Group SCHNEIDER)Eindhoven, April 1994.

EINDHOVEN UNIVERSITY OF TECHNOLOGY

SUMMARY

The Restricted Earth Fault (REF) differential protection is a zone protection that has to beable to detect currents to ground (zero sequence current). The principal of the RestrictedEarth Fault is based upon the distinction between a fault current inside the protected zoneand a fault current outside the protected zone. The REF is applied to protect e.g. powertransformer.

For faults inside the protected zone the protection has to react (switch-off) and for faultsoutside the protected zone we do not want a reaction.

Further on the REF has to be able to recognise effects like saturation of a currenttransformer -in consequence of a large short-circuit current or in consequence of aninrush current from a power transformer- to avoid undesirable swith-off command of theprotection. Current transformers are used like a measuring instrument to reduce current toan acceptable level for the hard-and software inside the computer.

The quantities diffusion current (id) and through current (it) are defined to distinguish afault current inside the protected zone from a fault current outside the protected zone.

As current transformers are not perfect (the can get saturated) the proportional current(ip) is introduced.

To discover an inrush current in relation to an undesirable switch-off command of theprotection the detection of second harmoniC has been applied, however, without succes.

From measurements we learn that in case there is no inrush-effect there is a possibility todetect second harmonics only for faults inside the protected zone and not for faultsoutside the protected zone.

Another possibility to perceive the inrush-effect is by detecting fifth harmonics becausethey are typically descending from power transformers (as we learn from literature). Thislast possibility has not been examined because the research had to be stopped. Nevertheless an algorithme can be designed with the help from the flowchart diagram on page 37.

Conclusion:

The realised protection algorithme (see appendex page 92-94) functions if the inrusheffect is left out of consideration.

Further the Restricted Earth Fault protection algorithme can not detect a Three-phase toground fault because the zero sequence current 10 is equal to zero.

CONTENTS

page

INTRODUCTION

I SIMULATION OF THE S.E.P.A.M.2000

1.1 What is SEPAM 20001

1.2 Treatment of the input signal

1.2.1 The Rogowski coil

1.2.1.1 Model of the Rogowski coil

1.3 Treatments of the signal with a digital filter

1.3.1 The FIR filter

II SIMULATION OF AN ELECTRICAL NETWORKS

2.1 What is EMTP ?

2.2 Model of an electrical network

1

2

2

2

3

3

6

6

8

8

9

III CALCULATION OF A FAULT CURRENT IN STEADY STATE CONDITION 10

3.1 Symmetrical components method 10

3.1.1 First case: (Phase-to ground fault) 10

3.1.2 Second case: (Twophase-to ground fault) 13

3.2 Method with the value of the reactance 15

3.2.1 Third case:(Threephase-to ground fault) 15

IV THE RESTRICTED EARTH FAULT DIFFERENTIAL PROTECTION 16

4.1 The differential earth fault system or restricted earth fault protection 16

4.1.1 Principal of the REF 16

Pierre BERMEJO

restricted earth fault protectionUniversity of Technology in Eindhoven (The Netherlands)

15/04/94

1

4.1.2 The differential current

4.1.3 The through current

17

17

4.2 Differential current and through current in-and outside the protected zone 18

v THE SATURATION EFFECT 22

5.1 Output signals produced by EMTP for a phase-to ground fault inside theprotected zone 22

5.2 Output signals produced by EMTP for a phase-to ground fault outside theprotected zone 24

5.3.1 Saturation of the CT in consequence of very large fault current 26

5.3.2 The proportional current 28

5.3.3 Saturation in consequence of inrush current 30

5.3.3.1 Inrush phenomena 30

5.4 Choice of the harmonic 31

5.4.1 The second harmonic 31

5.4.2 The third harmonic 31

5.4.3 Higher harmonics 31

5.5 Detection of the second harmonic 31

5.5.1 Second harmonic from CT saturation in consequenceof large fault current 32

5.5.1.1 Analyse of the second harmonic when a fault appear insidethe protected zone in case of a phase-to earth faults. 32

5.5.1.2 Analyse of the second harmonic when a fault appear outsidethe protected zone in case of a phase-to earth faults. 33

5.5.2 Second harmonic from inrush current 34

5.5.2.1 Analyse of the second harmonic when a transformer is energized 34

Pierre BERMEJO


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5.5.2.1 Analyse of the second harmonic when a transformer is energized 34

VI RESULT OF THE PROTECTION ALGORITHME 35

6.1 Result of the protection algorithme for a fault inside the protected zone 35

6.2 Result of the protection algorithme for a fault outside the protected zone 35

VII CONCLUSION 37

VIII RECOMMENDATION FOR FURTHER WORKS 39

BIBLIOGRAPHY 40

Pierre BERMEJO


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INTRODUCTION

Nowadays there is an increasing tendancy in protecting electrical networks, by usingcomputers. Microprocessor technology is ideal for implementing and integrating protective functions to provide a lower cost per function. Such implementations improve theprecision and quality of classical protective functions and at the same time provideadvanced features including self diagnostics, metering and event recording at no additional cost. Another important gain of the application of computers is reliability. The accentlies on the safety-aspect for people and apparatus.

For this reason the division "Protection Control and Command (PCC) ", of Merlin Gerin(France) wants to develop in the near future a protection algorithme for transformerscalled "Restricted earth fault (REF)differential protection", to satisfy the customers need.

The REF is a zone protection that has to be able to continuously detect current to ground.For faults outside its zone it is necessary that the REF undertakes no action, for faultsinside its zone action has to be took upon.

Purpose of the experiment:Acquise insight in the application of the REF (advantages and disadvantages of theseprotection) .

Pierre-Raphael BERMEJO

Restricted Earth Fault differential protectionUniversity of Technology in Eindhoven (The Netherlands)

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I SIMULATION OF THE S.E.P.A.M.2000

1.1 What is SEPAM 20oo?

SEPAM is a digital protection unit. It is used for protecting electrical installations.Mastering electrical power calls for the use of units with the capacity to continuouslymonitor electrical networks and equipment, and to trigger the appropriate action forprotecting and controlling them.

It ensures all the protections, measurements and automation functions required for themost diversified applications. It is enhanced by a serial communication interface options.It is especially well-adapted for centralized control of electrical networks.

SEPAM 2000

Figl: Treatment of a input signal (lin) inside the SEPAM 2000

1.2 Treatments of the input signal

The treatments of the input signal, see Fig1, is as following. A current transformermeasures a signal. After this operation the signal must be clear from any noise and gothrough two Low Pass Filters. After filtering the analog signal is converted into a digitalform with the use of an analog - into digital convertor. After convolution of the signalwith a Finit Impuls Response (FIR) filter and the technics of the Discret Fourier Transform (DFT) the signal is ready to be analysed by the Central Processing Unit (CPU).



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Merlin Gerin used two different method to measure the input signal (lin)' The first one iswith the uses of a current transformer the other one is with the uses of a Rogowski coil.

Merlin Gerin used the Rogowski coil for measuring current waveforms containing fasttransients. For the simulation of this component we need a model.

1.2.1 The Rogowski coil

1.2.1.1 Model of the Rogowski coil

A Rogowski coil is an air cored solenoidal winding of small cross section wich can bereadily looped around a conductor[1]. If formed into a closed loop then the voltage E(t)induce in the coil is directly proportional to the rate of change of current i(t) passingthrough the loop according to the equation. It is relatively inexpensive to make, providesisolated measurement and being air cored it does not suffer from saturation.

There are obvious advantages in a measuring coil wich does not have a ferromagneticcore. The core may also be made flexible so that it can be strapped around a conductorwithout having to disconnect the primary circuit.

The principal of the Rogowski coil is the application of the induction law of Faraday[2].

with

~ = L. i

we get

E(t) = -L:ti(t)

further we know that

For the Rogowski coil

N NffBndA: =E BiA = AE B i = A (Bl +B2 + ..... +BN- l +BN )~=l ~=l

(1)

(2)

(3)

(4)

(5)

where B, = B2 = = BN B, is the magnetic field from a winding of the Rogowskicoil. For N windings



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(6)

(7)

(8)

with

B1 (t)

and

(9)

(area of a winding) (10)

(11)

In this case the frequency and the capacitors of the Rogowski coil are very low f < 1 kHzthus Do is constant thus d/dt(constant) =0the magnetic flux Ht(t)is equal to:

2TtR

fill'idl = H( R) f dl = H(R) 2nR = Il~H(R) =1=0

(12)

(13)

E( t)

where

= _ N r 2d I (t)

2R Jlo dt 1(14)

N r 2= --Jlo

2 R(15)

andJ.to=4?r.1O-7 [Him]



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Further the Rogowski coil has a proper Rogowski coil resistance from the windings R1

and finaly a capacitance C2 of the windings_ The Rogowski coil is connected to theSEPAM 2000 We have to take into consideration the presence of the input resistance (R2)

of the SEPAM-

The result scheme is as follows:

E{t) u{t)

Fig2: Model of the Rogowski coil

With the help of fig2 we can develop the following equations

1 ) E ( t) = i 1 ( t) R1 + L 1 ddt i 1 ( t) + u ( t) (16)

d= C2 dt U (t)

= u (t)R2

(17)

(18)

The differential equation of this scheme is:

E ( t) =[i R (t) + i c (t) ] R1 + L 1 dd [i R (t) + i c (t)] + u ( t)2 2 t 2 2



(19)

(20)

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E( t) ::: (R +L~)[U(t) +C2d

dt

U(t)] +U(t)1 1 dt R

2(21)

d 2 eRR +L d R +R 1--u(t)+( 212 l)_U(t)+( 1 2 )u(t)=--E(t)d t 2 £1R2 C2 d t £1R2 C2 £1 C2

(22)

To simulate this second order differential equation with a computer we have to transformthis equation into an equation of difference .This equation of difference enables us to simulate the conduct of the Rogowski coilduring short-current situation in the electrical network.

u(nTs ) -2u(nTs -Ts ) +u(nTs -2Ts ) (u(nTs)) -u(nTs-Ts)) )--......;;;...---......;;;...----:;'-----....:;;....-~ +A +Bu (nTs =Ce

T/ Ts

(23)

The software implementation of the Rogowski coil and the filters inside the SEPAM 2000is shown on the annexe on pages 83-86.

The protection algorithme has to take into account the phenomenons of saturation of theCT so in the first instance the simulation of the Rogowski coil won't be used.

1.3 Treatments of the signal with a digital filter

After treatment of the signal with a finit impuls response (FIR) filter and the technics ofthe Discret Fourier Transform (DFT), we are capable to detect multiple of the groundfrequency of 50 Hz component from the saturation effect[3].

1.3.1 The F.I.R filter

The SEPAM 2000 uses two digital filters DFT(n.50Hz) for the treatment of the signalsfrom the analog to digital convertor. Because the signal f(nTs) is respectively convolutewith a cosinus function (Fi_c) and a sinus function (Fi_s) of (n.50 Hz) frequency. Withthese filters we are capable to detect multiples of the 50Hz ground harmonic from thefault current. We need this information eventually for preventing false trips duringenergization of a power transformer[4]. These filters are known as FIR (Finit ImpulsResponse) filters.



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FIR

f(nTS)~C(nTS)FI_c

f(t) ADC

f(nTS~Wr~1 Js(nTs)

Fig3: Digltal treatment of the slgnal f(nTs) wlth Fl_C and Fl_S fllters

f(t) is the input signal sampled at 12 points per sequence.fc(nTs), fs(nTs) are the ouputs of the filters(Fi_c and Fi_s).

FILTER Fi s

m

fsm(nTs) = L an'f-nn=O

FILTER Fi c

m

fcm(nTs) = L an'f-nn=O

(23)

where Ts = lIfs (fs sample frequency) and where hk is the digital impuls response of thefilters



(25)

(26)

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II SIMULATION OF AN ELECTRICAL NETWORKS

For the testing of the algorithme we need to modelise an electrical power network. This ispossible by using EMTP.

2.1 What is EMTP?

With EMTP it is possible to modelise electrical power networks as functions of time,typically following some disturbance such as the switching of a circuit breaker, or a fault.It also is used by those who specialize in power electronics.

For testing the protection algorithme we need the simulation of an electrical network.Inside this network it is possible to create situations where earthfaults occur, for example:

-Phase-to ground fault-Twophase-to ground fault-Threephase-to ground fault

In faults without ground contact we are not interested because the algorithme of therestricted earth fault works with the current wich flows through the ground.The network to be simulated with EMTP is shown in Fig4 here under.



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2.2 Model of an electrical network

Z

YyO; 62,5/21 kV36MVA; 16,45%

SW2

Zn2

L. ~ REF1 ~---------~=j~~~):=:::L •••_••••J -

Dy1 ;62,5/36,08 kV500MVA;1,64%

SW1G "v+----------i

Fig4: Model of an electrical network

In this figure above the Dy! power transformer is dimentioned in a way such that he cannot get satureted because we have not used the saturable element 96 from EMTP.The other power transformer used this element because we want to know wat can happenin situations of energizing it, to study the protection algorithme.

The Dyl power transformer has on the secondary side an impedance (Znl) between thestar point of the transformer and the earth. For the other power transformer the primaryside have a impedance to ground (zn2). With Zn2 we can simulate different forms ofgrounding.

The electrical network is dimensionned in a way such that if a earth fault occurs, half thefault current will flow respectively through Znl and Zn2. With the use of the twomeasuring switches (SWI and SW2) we can distinguish a fault inside and a fault outsidethe protected zone. About this subject we will talk later.



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With the method of the symmetrical components, it is possible to verify the calcules ofEMTP.

III CALCULATION OF FAULT CURRENT IN STEADY STATE CONDITION

3.1 Symmetrical components method

With the methode of the symmetrical components it is possible to calculate the currentsand voltages on the faultplace.

Further we are interested in the current which flows through the ground because we needit for the working of the restricted earth fault differential protection.

3.1.1 First case: (Phase-to ground fault)

From the symmetrical components[5] we know that for a phase-to ground faultcounts:

10=11 =12

In addition

10 the zero sequence overcurrent11 the direct sequence overcurrent12 the inverse sequence overcurrent

further

UO+U1+U2=O

In addition

UO the zero sequence overvoltageU1 the direct sequence overvoltageU2 the inverse sequence overvoltage

For each component of the electrical network we give the complex value. For somecomponents these value are only reactif. There is no contribution of the resistif partbecause this one can be neglected. Its value is too low in comparaison to the reactif part.



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further we know that for the voltage of each phase equal to:

UA = a2U 1 + aU2 + UoUB = aU 1 + a2U2 + UoUe = Ui + U2 + Uo

further we know that for the current of each phase equal to:

IA = a2II + aI2 + 10IB = all + a2I 2 + 10Ie = Ii + 12 + 10

remarque: a2 = -112 -j (1I2).v3; a = -112 + j (1I2).V3

The result scheme is as follows:

Xs Xt1 XLI F XLr Xt2

IU1 ZL

t 12Xs Xt1 XLI F XLr Xt2

U2 ZL 11-12-10

Xt10 XUO lOt XLrO Xt20

X01 t UO X02 X03 OL

~- -

Fig5: Phase-to ground fault

The value of each component is as following:

S = 36 kVXs = j6,5 ohm (reactance of the source s)Xtl = < < j I ohmXLI = j4 ohm (reactance of the area line at the leftside of the fault)



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XLr = j4 ohm (reactance of the area line at the rightside of the fault)Xt2 = j17,85 ohmZL = infiniteX01 = 3*j40 = j 120 ohmXtlO = < < j 1 ohmXLlO = j4 ohmXLrO = j4 ohmXt20 = j125,8 ohmX02 = 1 E-4 ohmX03 = infiniteZOL = infinite

After any calculation the value of successively

Zd = j 10,5 ohm (total value of the direct network)Zi = j 10,5 ohm (total value of the inverse network)Zh = j63,61 omh (total value of the homopolare network)

With the help of the values we found it is possible to give a simplification of fig 5.Using this new scheme makes it easy to calculate the values of currents and voltages.The definitive scheme is like:

zd L-sr- i1 t IU1

zi 12 tl-[ -

t U2 11-12-10

zh loll _-I~

-t UO

I--

Fig6: Phase-to ground fault



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further

UO = -Zh.1O = -j63,63.-j426,67 103 = -27,14kVU2 = -Zi.I2 = -Zi.IO = -jlO,5.-j426,67 103 = -4,48kVUl = - U2 - VO = 31,62kV

thus

UA = -40,7 1<Y -j31,26 1<Y VUB = -40,7 1<Y +j31,26 103 VUe = 0 V

IA = aZI) + alz + 10 = (aZ + a + 1)10 = 0IB = al) + aZlz + 10 = (a + aZ + 1)10 = 0Ie = 11 + Iz + 10 = 310

IF = 3.10 where IF = fault current

IIFI = l,28kA .. f = y'2'l,28kA = l,8kA

EMTP (file P3A. dat) shows these results en thus are in accordance with the calculationof the method of the symmetrical components.

3.1.2 Second case: (Twophase-to ground fault)

From the symmetrical components we know that for a twophase-to ground faultcounts:

10+11 +12=0

further

UO=Ul=U2



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The equivalent scheme is like:

i1-zd- I

s~ I U1i2

zi -- I-I U2

iOZh -- I-

I UO

Fig7: Twophase-to ground fault

v, = S.Zp/(Zp+Zd) with Zp=(ZLZh)/(Zi+Zh)= j9 ohm= 36·103 * 0,46 = 16,65kV

VA = a2V, + aV, + V, = (a2 + a + 1 )V, = 0VB = aV, + a2V, + V, = (a + a2 + 1 )V, = 0Vc = V, + V, + V, = 3VI

thus

Vc = 3*16,65kv = 50kV ;

I, = (S-V,)/Zd = -j 1,85kA12 = -V/Zi = -V/Zi = jl,58kA10 = -Vo/Zh = -V,/Zh = j 261,75A

IA = a2I1 + al2 + 10 = -2,97kA + j 396,75AIB = all + a2I2 + 10 = 2,97kA + j 396,75AIe = I, + 12 + 10 = 0 A

EMTP (file P3B. dat) shows these results en thus are in accordance with the calculationof the method of the symmetrical components.



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3.2 Method with the value of the reactance

3.2.1 Third case:(Threephase-to ground fault)

For this case we do not need the technique of the symmetrical components methodebecause we have a symmetrical short circuit and it is not necessary to find the equivalentscheme of each phase. Only one phase is enough because the current through the differentphases is the same. Of course the network is symmetrical for all phases.

The equivalent scheme is shown below.

Dy1 ;62,5/36,08 kVSOOMVA;1,64%

Xt XI

Xg

Fig8: Threephase- to ground fault

~ S 36,08kV

~



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= (38,08)2. 65 =2,41062,5 '

(38,08)2Xtrafo = 1,64%· 500 = 0,0470

x = (36,08)2'4=1,330L 62,S

The total value of the reactance is:

Xtotal = j2,41 + jO.047 + jl.33 = j3,780

I = SF

13 XTotal

= 36,08 = 5, 5kA/phase13· 3,78

EMTP (file P3C. dat) shows these results en thus are in accordance with the calculationwith the method of the reactance value.

IV THE RESTRICTED EARTH FAULT DIFFERENTIAL PROTECTION

4.1 The differential earth fault system or Restricted Earth Fault protection

4.1.1 Principal of the REF

The principal of the REF is based on the detection of zero-sequence current. Thisdetection is only possible in case of fault(s) to ground. The system is operative for faultswithin the region between current transformers[6]. The system will remain stable for allfaults outside this zone.



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CTZn2~---------~-r-III

PT

CT

iaibic

iO\--.....----+ REF

Fig9: Detection of the zero sequence current 10

For the algorithme we need in the first instance two values called:

-the differential current(id)-the through current(it)

4.1.2 The differential current:

The differential current (id) is defined as the difference between the zerosequence current(ia + ib + ic) and the ground-current (in).

id = (ia + ib + ic) -in (27)

4.1.3 The through current:

The through current (it) is defined as the addition of the zerosequence current and theground-current.

it =(ia + ib + ic) + in

2(28)



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where

i.(t) = i.1i cos(wt + ~.)

<a> = 2rcf; f = 50Hz

.In

Fig 10: The differential current (id) and the through current (it)

For the correct working of the restricted earth fault we must distinguish a fault inside theprotected zone from a fault outside the zone.

4.2 Differential current and throu~h current in-and outside the protected zone

The principal of the Restricted Earth Fault is based upon the distinction between a faultcurrent inside the protected zone and a fault current outside the protected zone. This thereason that the three line currents inside the protected zone are called: ial, ib 1, icl andthe three line currents outside the protected zone are called: ia2, ib2, ic2.

For a phase-to ground fault we give this following scheme



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in tZn2

ib2

ia2

SW2

-

-ic2

-

ia1-

SW1

ib1-

-ic1

Zn1TRANSF01

Fig!!: Current in-and outside the protected zone

where at t=t1 the amplitude of the current inside respectively outside the protected zoneis equal to:

ia1=1,5kAib1 =292Aic1=292A

ia2=292Aib2=292Aic2=876A

For a fault inside the protected zone it is necessary that id ¢ 0 and it=O

After the moment of appearance of a fault inside the protected zone to ground thecurrents (id) and (it) can take the following values at any time.



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idl = [l500cos(wt + cpj + 292cos(wt + /Ph) + 292cos(wt + CPJ] - 876cos(wt) =1,79kA ;cO

itl = [l500cos(wt + cpj + 292cos(wt + /Ph) + 292cos(wt + CPJ] + 876cos(wt) =0

After the moment of appearance of a fault outside the protected zone to ground thecurrents (id) and (it) can take the following values at any time.

For a fault outside the protected zone it is necessary that id=O and it;cO

id2=[292cos(wt + CPJ + 292cos(wt + 'Ph) + 292cos(wt + CPJ] - 876cos(wt) =0

it2=[292cos(wt + CPJ + 292cos(wt + /Ph)+ 292cos(wt + CPJ] + 876cos(wt) = -1,75kA;cO

These results are in accordance with the plot of idl and id2 from file p3A.dat. see Figl2

calcul P3A2000,------,-------.---.:...:.----r------........------.,

oI---...L'---I-lr---'--f--\---f-+--H--\--+--+--+--+-'-+_t_-/--\---H-----___;

-2000 \-----\--~__t+_-+--_t_-I--t-+-'---+-f---'r+---I'r-t---_'d_--4d·-;..-----___;

0.250.20.150.10.05

-4000 L..- ---I.... .....I.- -JI....- -.l... ---J

oidl

x10--41,------,---,~-_rr_-"1Tr-__m_-----.T""'""""r--~-_mr-___,_----____,

0.250.20.150.10.05

-1 '-----_---'----"~ -...._ __WL_ __U...IL.-"------'Lll..__....Lll.._--lL- ----l

o

-0.5

-< 0\---__

id2,

Figl2: Differential current (id), inside respectively outside the protected zone



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conclusion:

We can already conclude by now that concerning the algoritme we only have to look atthe value of (id) and (it) to make a distinction between a fault inside te protected zone anda fault outside the protected zone.

Sometimes- under extreme conditions- the current-transformers can get satisfied inconsequence of an inrush-current or very large fault current. We will return to thissubject later on.

Let us suppose that the primary current is measured bij a Rogowski-coil. Because itsphysical property (the coil doesn't contain iron) it is not possible to get satisfied. So it islinear.

With this simple criteria we can imagine a flowchart diagram for the protection algorithme like:

yTRIPPING)

Fig13: flowchart diagram of the protection algoritme for a case without saturation

Of course we have not finished the determination of the protection algorithme because weneed more knowledge about the comportments of the signals (id), (it) in case of saturationand also we need to know how we can recognise a signal inside the protected zone withsaturation from a signal outside the protected zone with saturation?

If the primary current is measured by a current transformer the possibility to saturation isrealistic, for example when a fault occurs where the line current is very large or in caseof energizing of a power transformer where magnetizing inrush current appears[7].



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V THE SATURATION EFFECT

5.1 Output si~nals produced by EMTP for a phase-to ~round fault inside the protectedzone.

Between time t1 and t2 a fault to ground has been simulated. At the point of time t1, asinglephase-to ground sets in inside the protected zone (see fig14).

The output signals of the three line currents and the ground current produced by EMTPand measured by the CT are shown under. see Fig14.

2000

a

<

-2000

-40000

~~t

1000

500

<

a

-5000

0.05

0.05

0.1

0.1

calcul P3A

0.15

ial

0.15

ibl

0.2C2,..~

0.2

0.25

b+

0.25

/:;....



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1000 ,------.,...-------,..-------,-------,-----------,

......__ _j_._ _ _ _..__ _ __ _ --1 _ __ _.

<

0

-5000 0.05 0.1 0.15 0.2 0.25

icl t. .......

2000

1000

<

0

-10000

C"0.05 0.1 0.15 0.2 0.25

bJ.. /;;...:rt in1\

Figl4: phase currents and ground current for a fault inside the protected zone

These signals are worked up by the SEPAM 2000 to idl and it!. see Fig 15.

Sf ""'--../~~

I r id1I I . I! I Jt1 Ja~Ir+ltl+ttl+tll1+111+<1tli+1'f~!~.j;f!:±±!:III~II~II~11 ttlIIttjtli±!I'±±1I!:tIl!::I:II11±f1l±!lItlll±±II1±J11I!±llll±fll±fIi±±l:l±l:l:w±f::l::i±jIlI±fIl±t11±±1I1±11I!±l1l1±f1l±t1l±±III±JLllitHillL:H±±1±±lll±IllIl±lll±!II:l±II!:l:IIl±lIll±1l1l±1l1±l±J±JII±.1 .

a eL 0.05 0.1 0.15 0.2 0.25

l' te en [sec] t -7'

Fig15: differential current and through current inside the protected zone in case of nosaturation of the current transformers.



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Like we expected- for a fault inside the protected zone- the value at all times of idl largerthan zero and itl stay equal to zero. The value of idl and it! are shown here in aquadrature comings from the FIR filter. This image is dependent of its amplitude seen bythe computer as a "l" (amplitude of idl- it! larger then a equal to a maximum prescribedvalue) or as a "0" (amplitude of idl- itl lower then the maximum prescribed value).Depending from what value (id) and (it) will take, the computer will use these "l" and"0" values to give yes or no the switch-off command to the relay.

5.2 Output siinalS produced by EMTP for a phase-to ground fault outside the protectedzone.

The output signals of the three lines currents and the ground current produced by EMTPand measured by the CT are shown under. see Figl6.

calcul P3A500 ,---------.:-------,--------.---------r--------.----------,

of----.f-

0.25

'=4

0.25

t-'l'0.2

tt.1"

0.2

I:t.1"

0.15

0.15

ia2

ib2

0.1

0.1

-····--j ·······------..···----·1'·---·----·--..-.-. ·-···._- !-.__.__.._-_ - .._._ _.

0.05

0.05

-5000 .~

i'

1000

500

-<

0

-5000 t: l

l'



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3,I

I ~+~ I~ 2~

+

+ ~c I !QJ

I it.2J i.....1 ~

+:9-

I

I II

+

i+ id.1Jo1",",","11"'+ I

o !:t 0.05 0.1 0.15 0.2 0.25~ te en [sec] -C-,.

2000

1000

-<

a

-1000a t,

'l"in

0.15 0.2 0.25

t~

Fig16: phase currents and ground current for a fault outside the protected zone

These signals are worked up by the SEPAM 2000 to id2 and it2. see Fig 17.

1000

500

-<

a

-5000 t:;, 0.05

4'0.1

calcul P3A

ic2

0.15 0.2 0.25

t-4Fig17: differential current and through current outside the protected zone in case of nosaturation of the current transformers.

Like we expected- for a fault outside the protected zone- the value at all times of it2larger than zero and id2 stay equal to zero.



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This is a situation where the current transformers have not reached the point ofsaturation but sometimes the CT can get saturated. So we have to consider this possibility.

For a fault inside and a fault outside the protected zone we have now the situation wherethe current transformers have reached the point of saturation.

We can distinguish two cases where saturation of the current transformer can appear

-Saturation of current transformers in consequence of very large fault current-Saturation of current transformer in consequence of magnetizing inrush due tononlinearities of transformer core

5.3.1 Saturation of the CT in consequence of very high fault current

Analyse of id and it in case of saturation outside the protected zone for a phase- to earthfaults

Fig18: differential current and through current outside the protected zone 10 case ofsaturation of the current transformers.

For t<t1

We have a normal situation where (id) and (it) are iqual to zero.

For t1~t<t2

At t1 we have a fault to earth thus (it) grow up to a maximal value and (id) stay zero. Idis not immediately equal to (it)mu: because the delay time is the result of the impulseresponse of the FIR(Finite Impulse Response)filter.



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For t2<t<t3

At t2 as a result of an overshoot, the signal (it) will oscillate with a ground frequenceiqual to 50 Hz around its maximum value and finally extinguish to (it) = i1:max.

For t3<t<t4

At t3 the saturation effect of the current transformer begin because there is a DCcomponent in the filtered signal. Inside this signal there is a higher frequency value thanthe ground frequency of 50 Hz therefore the filter is a lowpass filter. Therefore is thereason that the magnitude of (it) became lower. A other reason to explain the saturationof a CT is that an asymmetrical current applied to a current transformer will induce a fluxwhich is greater than the peak flux corresponding to the steady state alternating component of the current. The ratio of the transient flux to the steady state flux is proportionalto the ratio of reactance to resistance in the primary system.

The very considerable build up of flux with an asymmetrical fault current may take theCT into saturation, With the result that the dynamic exciting impedance is reduced andthe exciting current greatly increased.

For t4~t~ 00

At t4 (it) begin to grow because little by little the DC-component is dieing as a result ofthe resistance inside the electrical network and thus the saturation of CT disappear.

In all other cases of ground fault (biphase - triphase- to ground) inside the protected zone,the signals of the differential current (id), and the through current (it), in case ofsaturation in the same way, of course independent of the kind of error will be the currentsvalue higher or lower but the principal stays the same.

For a fault outside the protected zone we have the same explanation but in this case thethrough current (it) is not equal to zero and of course (id) must be zero.

conclusion:

In case of saturation for a fault inside the protected zone the value of (it) will not be equalto zero but will reach a value higher than zero.

In case of saturation for a fault outside the protected zone the value of (id) will not beequal to zero but will reach a value higher than zero.



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This situation confuses the protection because we can longer distinguish a fault outside theprotected zone from a fault inside the protected zone only by looking at the value of (id)and (it).

To avoid this problem we introduce 'the proportional current (ip)'.

5.3.2 The proportional current:

The proportional current (ip) is the ratio between the differential current and the throughcurrent in percent.

idip = -.100%it

(30)

In case of a fault inside the protected zone, (it) will reach a lower value compared to (id)so (ip) will take a high value.

In case of a fault outside the protected zone, (it) will reach a higher value compared to(id) and therefore (ip) will take a low value.

So if (ip) is high we are dealing with a fault inside the protected zone and if (ip) is smallthen we are dealing with a fault outside the protected zone.

The proportional value of (ip) shows the sensitivity of the detection of a fault current.These values are adjusted to make the differential relay insensitive to inaccuracy ofrespectively CT and relay[9].

Ip is also a value for the sensitivity of the protection.

For a phase-to ground fault outside the protected zone we can see that in case ofsaturation of the CT, (ip) is not longer equal to zero but can reach a maximum valueequal to 59 %. see fig. 19.

80

60 ---~

/~'-'... 40- r \.III

a. -20 1---

)0a 0.05 0.1 0.15 0.2

te en [sec)

Fig19: phase-to ground fault with saturation of the CT outside the protected zone

0.25

t.-7



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To avoid these problem we can do as follows:

We want the protection to be sensitive to a fault current within the protected zone. Withsensitive is meant that the protection has to react as soon as possible (Switch-off).

From measured results we know that for values of (it) < Win there is a great possibilitythat a fault occured inside the protected zone.

Further the protection has to be insensitive for faults outside the protected zone for wewant to avoid a non-desired switch-off command. In this case (it) can take values that aresmaller than 60 (id). So we only need to take care that (ip) ~ 6O(id).

For all the cases (two- threephase to ground) for faults outside the protected zone thevalue of (ip) is lower than 60%.

With the help of the explanation above we can imagine the possible path of (ip) to preventfalse trips of the protection. see fig.20 here under.

id

t ip%

5% t____._~ _ it10ln

Fig20: graphics of (ip) to prevent fals trips of the protection

conclusion:

-

Against the saturation effect in consequence of a large fault current we can use theproportional current (ip) for preventing false trips of the protection. We can imagine (seefig21) a flowchart diagram for the protection algorithme like:



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1----

in~ n

y

n

yTRIPPING)

Fig21: Flowchart diagram of the protection algorithme in case of saturation

5.3.3 Saturation in consequence of an inrush current

An other problem is the energizing of a power transformer. In this case line current canreach values equal to 20 times the nominal line current and can be provoque the saturation of the CT or may cause the percent differential relay to trip during transformerenergization.

By far the most common technique used for preventing false trips during energization isthe use of a 'harmonic restraint' relay[lO). The fact that an inrush current is richer inharmonics than a fault current is key to the design of a harmonic restraint function. Theharmonic restraint function should be so designed that is restraints during the magnetizinginrush condition, while during an fault the harmonics generated by a saturated CT shouldnot restrain the differential relay.

5.3.3.1 Inrush phenomena

The phenomenon of magnetizing inrush is a transient condition that occurs primarily whena transformer is energized. It is not a fault condition, and therefore does not necessitatethe operation of protection, wich, on the contrary, must remain stable during the inrushtransient, a requirement which is a major limitation to the design of protective systems fortransformers.



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The question is now "how can we detect an inrush current from a fault current?".

The waveform of a transformer magnetizing current contains a proportion of harmonicswich increases as the peak flux density is raised to the saturating condition. As long asthe waveform is symmetrical about the horizontal axis, only odd harmonics will bepresent. The magnetizing current of a transformer contains a lot of third harmonics. If thedegree of saturation is progressively increased, not only will the harmonic contentincrease as a whole but the relative proportion of the fifth harmonic will increase andeventually overtake and exceed the third harmonic.

In case of transient conditions which result in an offset, the inrush current produces awaveform wich is not symmetrical to the horizontal. Such a wave typically contains botheven and odd harmonics. Typical inrush currents contain substantial amounts of secondand third harmonics and diminishing amounts of higher orders. Thus the proportion ofharmonics varies with the degree of saturation.

The question is now" what choice of harmonics we can make for the protection algorithme?"

5.4 Choice of the harmonic

5.4.1 The second harmonic

The second harmonic is present in all inrush waveforms. It is typical of waveforms inwhich successive half period portions do not repeat with reversal of polarity but in whichmirror-image symmetry can be found about certain ordinates. Normal fault currents donot contain second or other even harmonics.The second harmonic is therefore an attractive solution to avoid inrush effects.

5.4.2 The third harmonic

The third harmonic is also present in the inrush current, in roughly comparable proportion to the second harmonic. The separate phase inrush currents are still related in phase tothe primary applied electromotive forces and the harmonics have a similar time spacing,which brings the third harmonic waves in the three windings into phase.

If the windings are connected in delta, the line currents are each the difference of twophase currents. As the inrush components vary during the progress of the transientcondition it is possible for this difference to pass through zero, so that the third harmoniccomponent in the line current vanishes; this component cannot, therefore, be regarded asa reliable source of detection.



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To this must be added the further consideration that a substained third harmonic component is quite likely to be produced by CT saturation under heavy inzone fault conditions[lO]. All this means that the third harmonic is not a desirable means of stabilizing aprotective system against inrush effects.

5.4.3 Higher harmonics

Higher harmonics than the third harmonic are theoretically present in inrush current butthe relative magnitude diminishes rapidly as the order of harmonic increases; there maybe 5% of fourth harmonic in a given inrush current. This component would be similar inresponse to the second harmonic but the small magnitude hardly justifies the provision ofan extra filter circuit.

Conclusion:It will be seen from the foregoing examination that the second harmonic IS the mostdesirable component to use to provide inrush currents.

5.5 Detection of the second harmonic

With the use of the FIR(lOOHz) filter it is possible to detect the second harmonics.

There are two situations where second harmonics can appear:

-CT saturation in consequence of large fault current-CT saturation in consequence of inrush current

5.5.1 Second harmonic from CT saturation in consequence of large fault current

5.5.1.1 Analysis of the second harmonic when a fault appears inside the protected zonein case of a phase-to ground fault.

courant H2 dans Ies phases et Ie neutre2I,---------------r------."--------,--------,--------------,

0.25

~-.0.2

1.5t, 1\Ii I \/ \ I \,---

'

I \ I ",-,,' \ / ....../~ ...-..---, -,---..__./'>..

I ~ ~~~

1,".,1 I '-~_: i!\ I ..... ....0.5 It I/ '~~-~,~--~-----L--- , _-- ~~_~~_-_~~ . 1

o:----~I-"'-"~-'----=--:::-'-::'~'y.~-"",,---,--"::2.-'.-:'-'~--.:.-::..:--c.:.. .::::-~::=-::~-':_'-=::;.;-=-==-.::::--~--:.:..--..::..-::..c~---:_----------'---------.J

o c. 0.05 ~ 0.1 0.15

t l' te en [sec]

Fig22: Detection of second harmonic for a fault inside the protected zone



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At t1 we have a phase-to ground fault. Immediately after t1 the protection detects a lot ofsecond harmonics because we have a asymmetrical component from the transient.After16ms from t1 the value of H2 disappears because normal fault currents don't containsecond or other even harmonics. At t2 in consequence of the asymmetrical componentinside the fault current the CT reaches the point of saturation.

5.5.1.2 Analysis of the second harmonic when a fault aDpears outside the protected zonein case of a phase-to ground fault.

", '

1.5,:

:<c: 1,~

~::J

0.5 ~-0a I8 I

0 1

a 0.05 0.1

....--_ ...... ----

0.15

te en [sec]

0.2 0.25

Fig23: Detection of second harmonic for a fault outside the protected zone

At tl we have a phase-to ground fault. Immediately after tl the protection detects a lot ofsecond harmonics because we have a asymmetrical component from the transient.After16ms from tl the value of H2 disappears because normal fault currents don't containsecond or other even harmonics.

conclusion:

In case of a phase-to ground fault we have the possibility to detect when the transientphenomena has gone- after a certain time lap (20ms)- second harmonics if this faultappears inside the protected zone from a fault outside the zone. So here from we canconclude that we can distinguish a fault inside the protected zone from a fault outside theprotected zone only bij proving the existence of the second harmonics.

In all other cases of ground faults (twophase- threephase- to ground) inside the protectedzone we have the possibility to detect, after a certain time lap, second harmonics.



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0.8:

~ 0.6~c:: iQ.)

0.4 ~~::l i

"0

ooztaE

00

5.5.2 Second harmonic from inrush current

5.5.2.1 Analysis of the second harmonic when a transformer is energized

Like we expected we have a lot of second harmonics, see fig24.

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

te en [secJ

Fig24: detection of second harmonics from inrush current

Because in both cases- when a fault appears inside the protected zone and when there isan energizing of a power transformer- we may find many second harmonics. Thedetection of these harmonics doesn't give us enough information about this sources. Thiscan be a high fault current but also they can carne from an inrush current.

From the fig24 we see also that the amplitude of the second harmonic does not reach thevalue 0,8. From other measurements for faults inside the protected zone we know that theamplitude of the second harmonic is far higher than 0,8 in all other cases (two- threephase- to ground). Herefrom we can conclude that it is impossible to distinguish a secondharmonic that carnes from an inrush current of one that carnes from a large fault current.



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VI RESULT OF THE PROTECTION ALGORITHME

6.1 Result of the protection al~orithme for a fault inside the protected zone

For a fault inside the protected zone in cases with or without saturation the detection isgood because immediately after a fault follows a tripping of the protection.See annexe on page 16 for a 'phase-to ground fault', page 34 for a 'twophase-to ground.

The protection algorithme can not detect a Three-phase to ground fault. The vectorial sumof the three phase current is equal to zero because each phase current has the samemagnitude and is 1200 phase shift in respect of the other phases. Therefore the zerosequence current 10 is equal to zero.

6.2 Result of the protection algorithme for a fault outside the protected zone

In a situation without saturation it is easy to detect a fault outside the protected zonebecause we only need to look after the value of (ip).

In a situation with saturation it is necessary to detect second and fifth harmonics[ll].From the results we learn that we are not capable to distinguish a second harmonic causedby a high fault current from a second harmonic caused by an inrush current. But if wepreclude the possibility of an inrush-eurrent then will the detection of the secondharmonic be sufficient to distinguish a fault inside the protected zone (inside the zone thefault current is high enough to cause a CT saturation)from a fault outside the protectedzone (outside the zone the fault current cannot reaches values that cause a CT saturation).

To avoid this problem we can eventually detect a potential fifth harmonics because in themajority of cases the fifth harmonics are caused by power-transformers[12].



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We will give here under two possible cases in wich fifth harmonics are caused by powertransformers.

-as a result of an inrush current-in case of over excitation due to a dynamic over-voltage condition

To realise a detection of the fifth harmonics we need an extra filter[13].

In literature it does not show up that in case of a large fault current fifth harmonics arefound[14]. To get more information with regard to this more measurements will benecessary.

The detection of the 5th harmonics was not possible because the research must be stoptfrom Merlin Gerin.

The protection algorithme write in "matlab" is shown on the annexe page 92-94.

A possible Flow-chart of the Restricted Earth Fault Differential Protection is shown onfig.25



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1=

,----+-----l Y

WAIT 20 ms)I

n

Fig25: A possible flow chart diagram for the REF differential protection

VII CONCLUSION

The protection algorithme use a detection of zero sequence current.

The algorithme uses three values called:

-the differential current (id)-the through current (it)-the proportional current (ip)



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In a situation without saturation it is easy to detect a fault inside from a fault outsidebecause we only need to look after the value of (id). This is the case when for example aRogowski coil is used.

If the current transformer is not a Rogowsky coil the possibility to saturation is realistic,for example when a fault occurs where the line current is very large or in the case ofenergizing of a power transformer where magnetizing inrush current appears.

We have introduced the value (ip) to eliminate the problem of CT saturation when there isno inrush current.

Typical inrush currents contain substantial amounts of second and third harmonics anddiminishing amounts of higher orders. Thus the proportion of harmonics varies with thedegree of saturation.

It will be seen from the foregoing examination that the second harmonic is the mostdesirable component to use to provide inrush currents.

From the results we learn that we are not capable to distinguish second harmonics causedby a high fault current from second harmonics caused by an inrush current.

If we preclude the possibility of an inrush current then will the detection of the secondharmonic be sufficient to distinguish a fault inside the protected zone from a fault outsidethe protected zone.

If we have open the possibility of a present inrush current the protection may give aswitch-off command where as this is not desired. In this case the detection has seen anamount of second harmonics that is big enough to give a false trip command. Howeverthese harmonics do not came from a fault current but they come from the inrush currentthat brings the CT in state of saturation.

To avoid this problem we can eventually detect a potential fifth harmonics because in themajority of cases they are caused by power-transformers.

3The Restricted Earth Fault protection algorithme can not detect a Three-phase to groundfault because the zero sequence current 10 is equal to zero.



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VIII RECOMMENDAnON FOR FURTHER WORKS

Because this simulation only approaches reality we recommand the use of a real CT toeliminate possible imperfections.

Further we advise to use a Rogowski coil to prevoid saturation effect.

To test the working of the protection algorithme it is necessary to develop a filter todetect fifth harmonics.



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BIBLIOGRAPHY

[1] Oates, C.THE DESIGN AND USE OF ROGOWSKI COILS.In: lEE colloquium on:"Measurement techniques for Power Electronics".(Digest ~ 179),At the Lucas House Conference Centre,Birmingham, 22 October 1992.The institution of Electrical Enginers,Savoy Place London WC2R OBL, P. 3/1-5.

[2] Wollersheim, A.H.M.L.THE ROGOWSKI COIL.High Current Technology Groep.Report: CSIRO Division of Manufacturing Technology.Locked Bag N°9, Preston, Victoria 3072 Australia,Augustus 1990.

[3] Sykes, J.A. and Morrison, I.F.A PROPOSED METHOD FOR HARMONIC-RESTRAINT DIFFERENTIAL PROTECTION FOR POWER TRANSFORMERS.IEEE Trans. on PAS, Vo1.3(l972), P.1260-1272.

[4] Houston, J.M.and G.J. Carlson, F.A. Fisher, L.B. Major,M.P. Perry, P.H. Peters, H.R. Summerhayes, H.L. WittingNEW TECHNIQUES FOR CURRENT AN VOLTAGE MEASUREMENTON POWER TRANSMISSION LINES.In: Proc. World Electrotechnical Congress, Moscow,12 June 1977, P. 21-25.

[5] Overbeek, H.HELEKTRICITEITSOPWEKKING EN TRANSMISSIE II.Department of Electrical Engineering, Division EGUniversity of Technology in Eindhoven(The Netherlands)1993.



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[6] Wiszniewski, A.DIGITAL DIFFERENTIAL PROTECTION OF POWER TRANSFORMER.Proceedings of the 9. Power System calculation conference,VoI.8(1987), P.801-806.

[7] Korpanay, N.TRANSIENT RESPONSE OF CURRENT TRANSFORMERS.Brown Boveri Review, VoI.1l/12(l969), P.597-608.

[8] Hlawatsch, F., Boudreaux-Bartels, G.F.LINEAR AND QUADRATIC TIME-FREQUENCY SIGNAL REPRESENTATIONS.IEEE Signal Processing Magazine, april 1992, P. 21-67.

[9] Mathews, C.A.AN IMPROVED TRANSFORMER DIFFERENTIAL RELAY.AIEEE Transaction, Vo1.73(1954), P. 645-650.

[10] Gec MeasurementsPROTECTIVE RELAYS APPLICATION GUIDE.St.Leonard's Works, Shafford (england), 1975.

[11] Kennedy, L.F. and Hayward, C.D.HARMONIC-CURRENT-RESTRAINED RELAYS FOR DIFFERENTIALPROTECTION.AlEE Transaction, VoI.57(l938), P.262-266.

[12] Rioul, 0., Vetterli, M.WAVELETS AND SIGNAL PROCESSING.IEEE Signal Processing Magazine, oktober 1991, P. 14-38.

[13] Malik, O.P., Dash, P.K. and Hope. G.S.DIGITAL PROTECTION OF POWER TRANSFORMER.IEEE PES Winter Power Meeting, paper No. A76(1976), P. 191-197.New York.



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[14] Phadke, A.G.RECENT DEVELOPMENT IN DIGITAL COMPUTER BASEDPROTECTION AND CONTROL IN ELECTRIC POWER SYSTEM.Presented at Conference on Power System Protection,The Institution of Engineers, Madras India, April, 1980.

[15] Ray, W.F. and K.D. MurrayTHE USE OF ROGOWSKI COILS FOR CURRENT WAVEFORMMEASUREMENT IN POWER ELECTRONIC CIRCUITS.In: EPE: FIRENZE 4th European Conference on Powerelectronics and applications. P.379-83 Vo1.3,1991.



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EG/94/710a

FACULTV OF ELECTRICAL ENGINEERING

Group Electrical Energy Systems

APPENDIX TO

RESTRICTED EARTH FAULT

DIFFERENTIAL PROTECnON

Master Thesis of

Pierre Raphael Bermejo

The Faculty of Electrical Engineering of theEindhoven University of Technology does notaccept any responsibility for the contents oftraining or terminal reports.

M. Sc. graduation report coached by:Prof.dr.-ing. H. Rijanto (EUT)Ir. P. Bertrand (Group SCHNEIDER)Eindhoven, April 1994.

EINDHOVEN UNIVERSITY OF TECHNOLOGY

THE NETHERLANDS

199417 janvier

Cx

6.56.56.5

R

COPT EPSILN TOLMAT TSTART

- NEUTRE j40 SUR TFO AMONT- NEUTRE DIRECT Rn=1.E-4 ohm SUR TRANSFO AVAL- DEFAUT FRANC PHASE/TERRE

P. BermejoGROUPE SCHNEIDERP.C.C.

BEGIN NEV DATA CASEC +----------------------------------------------------------------------+C P3A.DATC ----------------------------------C ETUDE D'UNE PROTECTION DE TERRE RESTREINTEC ----------------------------------CCCCCCCCCCCC +----------------------------------------------------------------------+CCC DECLARATION DU NOH DU FICHIER DE SORTIE; ICI P3A.PL4C$OPEN, UNIT=4 FILE=P3A.PL4 FORH=FORMATTEDCC pas de calcul : 0.0222 ms ; pas de sortie: 0.111 ms soit 9.009 kHzC CE SONT LES MISC. DATA CARDS II-B-1 ,II-B-2C 3456789-123456789-123456789-123456789-123456789-123456789-123456789-123456789POYER FREQUENCY, 50.C DELTAT THAI XOPT

.222E-4 2.0E-1 50.0ClOUT IPLOT IDOUBL KSSOUT MAXOUT IPUN MEMSAV ICAT NERERG IPRSUP

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C *********************************C MODELISATION DU DEPART EN DEFAUTC *******************************C cable 1C ----------C BRANCH CARDS TYPE 0 IV.A.2.1C --BUS1--BUS2--BUS3--BUS4-----R-----XC 3456789-123456789-123456789-123456789-123456789-123456789-123456789-123456789-

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C *************************C MODELISATION DE LA CHARGEC *************************C SEA2C SEB2C SEC2C *******************C IMPEDANCE DU DEFAUT

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.2884 11940.1781221430.0 6892.6134700553

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.02361 3978.96790399350.0 -5957.9167178570.0 -3439.3761506840.0 -5957.9167178570.0 -3439.376150684

.2884 11940.1781221430.0 -3439.3761506840.0 -1985.4830642670.0 -3439.3761506840.0 -1985.4830642670.0 6892.6134700553

.02361 3978.9679039935

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SEC2 SECN23

3 PRB2 PRN

USE RL$UNITS, 0.50E+02 , o.

1 PRA2 PRN2 SEA2 SECN2

C *************************************************C MODELISATION DE L'IMPEDANCE DE NEUTRE DU TRANSF01C *************************************************C BRANCH CARDS TYPE 0 IV.A.2.1C NODE NAMES NODE NAMES-----R-----X-----CC 3456789-123456789-123456789-123456789-123456789-123456789-123456789-123456789C BUS1 BUS2 BUS3 BUS4C SECN 40.0C ****;";************************* \··J):I

C MODELISATION DU TRANSFORMATEUR2C *******************************$VINTAGE, 1,

1 SEA2 SECN22 SEB2 SECN2

4 SEB2 SECN2

5 PRC2 PRN

6 SEC2 SECN2

.2884 59581.6575841890.0 -9985.698623990.0 -3354.397653070.0 20008.958586089

.02361 6721.41291750.0 -29727.206281320.0 -9985.698623990.0 -29727.206281320.0 -9985.69862399

.2884 59581.6575841890.0 -9985.698623990.0 -3354.397653070.0 -9985.698623990.0 -3354.397653070.0 20008.958586089

.02361 6721.4129175$VINTAGE, 0,$UNITS, -1.,-1.

USE RLC 3456789-123456789-123456789-123456789-123456789-123456789-96 SEA2 SECN2 8888.

-2.3400E+00 -6.2431E+01-8.7949E-01 -6.0787E+01-5.8633E-01 -6.0419E+01-2.6385E-01 -5.9139E+01-1.1727E-01 -5.7856E+01-4.3975E-02 -5.6759E+01

1.4658E-02 -5.4562E+015. 1304E-02 -5.1999E+018.5017E-02 -4.7604E+011.0261E-01 -4.0281E+011.1727E-01 -2.9295E+011.4658E-01 1.9591E+011.6124E-01 2.7097E+012.0522E-01 3.6619E+012.6385E-01 4.3941E+013.1954E-01 4.7604E+014.1776E-01 5.1267E+015.7168E-01 5.4562E+017.8422E-01 5.7124E+011.0261E+00 5.8957E+011.4658E+00 6.0787E+012.3453E+00 6.2252E+013.5181E+01 6.2617E+01

9999.96 SEB2 SECN2 SEA2 SECN2 8888.96 SEC2 SECN2 SEA2 SECN2 8888.C *************************************************C MODELISATION DE L'IMPEDANCE DE NEUTRE DU TRANSF02C *************************************************C BRANCH CARDS TYPE 0 IV.A.2.1C NODE NAMES NODE NAMES R X CC 3456789-123456789-123456789-123456789-123456789-123456789-123456789-123456789C BUS1 BUS2 BUS3 BUS4

SYN 1.E-4SECN2 1.E+6

BLANK CARD TERMINATING BRANCHESC ***********************C MODELISATION DU DEFAUTC ***********************C 3456789-123456789-123456789-123456789-123456789-123456789-123456789-123456789-o DEFA1 20.0E-3 1.0E1 3

C *******************C SWITCHES DE MESURE

C *******************C 3456789-123456789-123456789-123456789-123456789-123456789-123456789-123456789-

SECA SVA1 MEASURING 1SECB SVB1 MEASURING 1SECC SVC1 MEASURING 1SVA2 PRA2 MEASURING 1SVB2 PRB2 MEASURING 1SVC2 PRC2 MEASURING 1

PRN SVN MEASURING 1BLANK CARD TERMINATING SVITCHESC **************************C MODELISATION DE LA SOURCEC **************************C STATIC ELECTRIC NETVORK SOURCES VII.C.4 TYPE 14C 3456789-123456789-123456789-123456789-123456789-123456789-123456789-123456789-C NAMEST AMPLITUDE FREQUENCY PHASE Al TSTART TSTOP14 GENA 51.0E3 50.0 090.0 -1.0014 GENB 51.0E3 50.0 -030.0 -1.0014 GENC 51.0E3 50.0 +210.0 -1.00BLANK CARD TERMINATING SOURCESC NAM1 NAM2 NAM3 NAM4 NAM5 NAM6 NAM7 NAM8 NAM9C GENA GENB GENC PRIA PRIB PRIC SECA SECB SECCC PRA2 PRB2 PRC2 SEA2 SEB2 SEC2CABLA1CABLB1CABLC1C PRN SECN2BLANK CARD TERMINATING OUTPUTBLANK CARDBEGIN NEV DATA CASE

4

2000calcul P3A

0

-<-2000

-40000 0.05 0.1 0.15 0.2 0.25

ia1

1000

500 ....... ..........................·........··..··..........M._.

-<0

-5000 0.05 0.1 0.15 0.2 0.25

ib1

5

calcul P3A1000 r-------..-------..-------.--------.-------___,

0.250.20.150.10.05

Of---,··'

500 ... ····....HH.·••••••••••• •••••

-500 L-- .l.....- .l.....- -"-- -"-- ------'

oicl

2000 r-------..-------..-------.--------.-------___,

0.250.20.150.10.05

Ol----d

1000

-1000 '---- .1.....- .1.....- -"-- -"-- ------'

oin

6

calcul P3A500,--------;:--.,..-------...,--------,---------,----------,

ot-------,.

0.250.20.150.10.05

-500 L.-- .L- -'--- ...L- --'-- ---'

oia2

1000 r-------r-------...,---------r--------r--------,

0.250.20.150.10.05

01---......7

-500'---------'-------....L..--------'--------'----------'o

ib2

7

calcul P3A1000 ,--------~-----.___-----.__-----...__----____"l

0.250.20.150.10.05

o r----'CJ

500

-500 L----- '----- .l....- .l....- -'-- ----'

oic2

2000 r-------~-----.___-----.__-----...__----____"l

0.250.20.150.10.05

o r----,...J

1000 .

-1000 L----- '----- .l....- .l....- -'-- ----'

oin

8

1courant differentiel et traversant sature:defaut interne:p3a

5 :- c'v/ ""~/"

I / \ --r-

-1+1 H+H-t+t++c~~~±!:t±!:±±±±:!:±±±:!±_+++++__I_11~_I--LII_III_1~_'l- L-_~~~~ III'

I + ~+ it

I + HIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIlIIIIIa'IIIIIII:IIII--~IIIIIIIIIIIIIIIIIIIIII, ! !

a 0.05 0.1 0.15 0.2 0.25

te en [sec]

courant proportionnel sature:defaut interne:p3a10000 ,-,-------r------~--------,--------,---------,I

! II

I'I 'I "'~/ '~-----'\\

aLl_~JLIV_'"._.,. __---.l...-_~\=======:::::===:;:::::===-__---L- ~:a 0.05 0.1 0.15 0.2 0.25

~ il';' 5000,Q) ,

0.

te en [sec]

courant differentiel et traversant non sature:defaut interne:p3a

it

id

1I

I00-4ftttl+f+t++t#±±±:I::I:!~'±±±!±!±!:±±±±:I±l±I:!±I±I:i:l±l:l±lI±l±l±I±l±l±:!±±±±:I±!±l±l::I±:t:I±Jt:!±I:l±l±±:l±I:!:l±I±±±:I±l±I±±:I±±JI±L- -------.J

0.05 0.1 0.15 0.2 0.25

c:Q)

te en [sec]

i-------....L.-.__.~ ,_ ~ __.J

II

I!

0.250.2

----..--r---.-.----

0.15

courant proportionnel non sature:defaut interne:p3a10000 r---- -------------r----------,---------.----,.---

I~ I

i 5000, I . F-_I.. ....j .~••~_-._~-._.& I II_-j~·

I J V ~aL ~j .._..1..-..- -"-- _

a 0.05 0.1

te en [sec]

9

courant differentiel et traversant non sature:defaut externe:p3a

I

I

l

l0.250.2

id

0.150.1

it

0.05

+

+

o

1 ~I +I +o11111111111114"+

.-:::

te en [sec]

courant proportionnel non sature:defaut externe:p3axlO-3

41

~ 3t~..........

z!c::IlJ

.9- 1

10 1 /,v-~,

0 0.05 0.1 0.15 0.2

11

l0.25

te en [sec]

10

courant differentiel et traversant sature

-4 ---.-..--- _ ..- .-- ;- -'- ..----- ·--t·-..- -_.--- i --_......_ .._- - ...._+-_...-._--._.._..--....--

...__._ __._.l... __ _ _.._ __

4r------r------r------r------r----------,

• i~ ~ ~ ~ ~ + A i A 1\ i2 f---.------..----.--..-;--.---- -A--~ -. -+'- .- --1\ - -'ri\--- .- ..-......-+.- r--..-···_-··-....-·..-·..··-....-

f\' A + . .

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-6 ----..--- .....-- ----..--_.-- ··---------·-r---·--·---..·-....·-·-+---·-------........--

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't:lUl....

0.250.20.150.10.05

-10 '---- ...I...- ....I.- ---1... ---' ~

o

t en [sec]

11

courant differentiel et traversant sature5,-----------,.-----,.....-----------,,......-------,------

,.......,-<'--'

I Ii;4

3

=~_, =-.--~~ T--'''-''--'--! ~-T-------r-" .~ .•- .._._- .----...---.---..;.---.-......---.•.-

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- 2 r- _ - - - --_.-.._.- - -.--;-.._.-_ -_ -.!.-: _t. ,-.._-- - - -..

.-.•..__ _.._ _._ _.-

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1 1--.-'._-"- •.-:10--:/:.•--.;$..._.. ._.. ....... -- .-- - .-- p~l--%lI1

"0en....

0.250.20.150.10.05

-3 L- .L- .Li' .....L Li'-------

o

t en [sec]

12

courant H2 dans les phases et Ie neutre defaut interne, p3Adat

------ ....

lII~

i

0.250.20.15

---/-- ....

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0.1

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0.05

i \I

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0 1

0

te en [sec]

courant point neutre, fondamental

j!I

0.05 0.1 0.15 0.2

III

0.25

te en [sec]

13

courant H2 dans Ies phases et Ie neutre2 j

~ 1.5~c:: i1) !1) 1 i-

"3"0

0.50S

00 0.05 0.1 0.15 0.2

JIII

I0.25

te en [sec]


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I

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Ii

A' -l

a 0.05 0.1 0.15

II

I-l

te en [sec]

courant H2 dans Ies phases et Ie neutre defaut externe1.5,---------,---------,----------,--------,-------,

I

10.250.20.15

,,,,,

"1 " '., ,,

, ,, ', ,

0.5 ),(\\1/ \1I I \\ _

al n __ ~l~\<:~~..L::====~·~-~'.2/~.'_'-;;..;;--.-:..:J:.,,;;;;.;~-;.;:;/-::..-,_,'--:.:=.::...__-'- - -_-.~.._--__l--

o 0.05 0.1

te en [sec]

---'--------------"-----__...J..--_ J

0.250.20.150.1

courant point neutre, fondamental3 In ~._,__------____,_ r

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21 Il~ /

I I

ol ~/ _a 0.05

te en [sec]

14

courant H2 dans Ies phases et Ie neutre defaut interne, p3A.dat

----- ---------~- -., ::::.:;.;..;::;.:.:.;.:.;::::c==>=c::::::=:c==+

2,

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='""::l ic 0.5 f-a

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IJiI

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te en [sec]

courant point neutre, fondamental3 1

I~"~"i

~I

J2l-c i !,:lJ Ic 1I- Ic

ii III /

0 1 .-J I

0 0.05 0.1

te en [sec]

0.15 0.2

15

1J

0.25

condition de declencheIl1ent P3A,defaut interneBr----------r-------,------,..----------,-------,

inn7 + . ........................................ .........•..••..•~...............•.- .

6 , _ ~ .

···········································1·········· .

,-----------~---------------------~---------------------~---------------------~r! lid

5·····················r······················j··············..·····································r················································1··- --.-1

4 .....................................................:.... ················..·······,········r.. . , r- -- : .

f' •••••••••••••••••••••••••..•••••••••••: •••••••••••••• ...................................................i _ 1 ~

3 --r + ·····..····················f·················· ·····································f!P 1........................ . .

2 . . , ······················..······t··..····················· ····..····_·····T·························..········..·· ; _ .

!"'._._._._._._._._.~.-._._._._._._._._._._._._._._.-!--.- ._._._._._._,_._._._._._._._.'f._._._._.-._._._._._._.-._._._._.,

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0.250.20.150.10.05

0'---------1. ........... .L.- ----1 ---'

o

16

condition de declenchement P3A,defaut externeB.---------.--------,-------...,.-------..----------,

7 ~ ~.P.,J! 1... ··········································r···········........................ ..............•.........•...........................................................

I6 f- . ..............................................................................~ ··········i···· .

,---------------t---------------------15 ~ ; i...~ .L. 1 .1 .1. .

i ~! ! j_____________________~--------------------- .1 i !

4············· ..··················· . ~ ·· · ·c .

I3----------!'----------~p+-F~~~~~:::t=~===:::~:=:::l-------------

........................................................•.•...•..'!••.•••....•••........•....~•...•..•................••.••....••••,..•.........•.•:

! j2 ,........................................ h ,.•••••~•••••••••••••••••••••••••••••••••••••••••••••••••••••••••••, •••••!' h + .·············1..········· ....····..·············· : !i :...._._._._._._._._._._._.1._._._._._._._._._._._._._._. _._.~

I

i !1 , ,,, , : ·················t··············'!···· ·· ..···············ig..· H ••••••• ;! -; i._._._._._ ....._._._._._._._....._.-\_._._....._._._._._._._._._._._._..;......_._.; ,

0.250.20.150.10.05O'----------'---------'-------...L-------'----------'o

17

199419 janvier

Cx

6.56.56.5

R

COPT EPSILN TOLHAT TSTART

- NEUTRE j40 SUR TFO AMONT- NEUTRE DIRECT Rn=1.E-4 ohm SUR TRANSFO AVAL- DEFAUT BIPHASE/TERRE FRANC


+----------------------------------------------------------------------+

BEGIN NEV DATA CASEC +----------------------------------------------------------------------+C P3B.DATC ----------------------------------C ETUDE D'UNE PROTECTION DE TERRE RESTREINTEC ----------------------------------CCCCCCCCCCCCCCC DECLARATION DU NOM DU FICHIER DE SORTIE; ICI : P3B.PL4CSOPEN, UNIT=4 FILE=P3B.PL4 FORM=FORMATTEDCC pas de calcul : 0.0222 ms ; pas de sortie: 0.111 ms soit 9.009 kHzC CE SONT LES MISC. DATA CARDS II-B-1 ,II-B-2C 3456789-123456789-123456789-123456789-123456789-123456789-123456789-123456789POYER FREQUENCY, 50.C DELTAT !MAX XOPT

.222E-4 2.OE-1 50.0ClOUT IPLOT IDOUBL KSSOUT HAXOUT IPUN MEMSAV ICAT NERERG IPRSUP

10000 5 0 1 1 0 0 2 0 0C 3456789-123456789-123456789-123456789-123456789-123456789-123456789-123456789-C ***********************C MODELISATION DE LA PCCC ***********************C BRANCH CARDS TYPE 0 IV.A.2.1C NODE NAMES NODE NAMESC BUS1 BUS2 BUS3 BUS4o GENA PRIA .65o GENB PRIB .65o GENC PRIC .65


SVA1CABLA1 .20 4.0SVB1CABLB1 .20 4.0SVC1CABLC1 .20 4.0


1.E-31.E-31.E-3


18

C *******************CABLA1 DEFA1CABLB1 DEFB1

0.10.1

.2884 11940.1781221430.0 6892.6134700553

.02361 3978.96790399350.0 -5957.9167178570.0 -3439.376150684

.2884 11940.1781221430.0 -3439.3761506840.0 -1985.4830642670.0 6892.6134700553

.02361 3978.96790399350.0 -5957.9167178570.0 -3439.3761506840.0 -5957.9167178570.0 -3439.376150684

.2884 11940.1781221430.0 -3439.3761506840.0 -1985.4830642670.0 -3439.3761506840.0 -1985.4830642670.0 6892.6134700553

.02361 3978.9679039935

221421. 353382000.0221421.353382000.00.0221421. 35338200

SECC SECN3

6 SECC SECN

4 SECB SECN

5 PRIC PRIB

3 PRIB PRIA



C *******************************C HODELISATION DU TRANSFORHATEUR1C *******************************C 3456789-123456789-123456789-123456789-123456789-123456789-123456789-123456789-$VINTAGE, 1,


19

.2884 59581.6575841890.0 20008.958586089

.02361 6721.41291750.0 -29727.20628132

40.0

16692.100203564-8290.06214476716692.100203564-8290.062144767-8290.06214476716692.100203564

SEC2 SECN23

3 PRB2 PRN

USE RL$UNITS, 0.50E+02 , o.


$VINTAGE, 0,$UNITS, -1. ,-1.

USE RLC *************************************************C HODELISATION DE L'IHPEDANCE DE NEUTRE DU TRANSF01C *************************************************C BRANCH CARDS TYPE 0 IV.A.2.1C NODE NAMES NODE NAMES-----R-----X-----CC 3456789-123456789-123456789-123456789-123456789-123456789-123456789-123456789C BUS1 BUS2 BUS3 BUS4

SECNC *******************************C HODELISATION DU TRANSFORHATEUR2C *******************************$VINTAGE, 1,


4 SEB2 SECN2

5 PRC2 PRN

6 SEC2 SECN2

0.0 -9985.69862399.2884 59581.657584189

0.0 -9985.698623990.0 -3354.397653070.0 20008.958586089

.02361 6721.41291750.0 -29727.206281320.0 -9985.698623990.0 -29727.206281320.0 -9985.69862399

.2884 59581.6575841890.0 -9985.698623990.0 -3354.397653070.0 -9985.698623990.0 -3354.397653070.0 20008.958586089

.02361 6721.4129175$VINTAGE, 0,$UNITS, -1.,-1.

USE RLC 3456789-123456789-123456789-123456789-123456789-123456789-96 SEA2 SECN2 8888.

-2.3400E+00 -6.2431E+01-8.7949E-01 -6.0787E+01-5.8633E-01 -6.0419E+01-2.6385E-01 -5.9139E+01-1.1727E-01 -5.7856E+01-4.3975E-02 -5.6759E+01

1.4658E-02 -5.4562E+015. 1304E-02 -5. 1999E+018.5017E-02 -4.7604E+011.0261E-01 -4.0281E+011.1727E-01 -2.9295E+011.4658E-01 1.9591E+011.6124E-01 2.7097E+012.0522E-01 3.6619E+012.6385E-01 4.3941E+013.1954E-01 4.7604E+014. 1776E-01 5. 1267E+015.7168E-01 5.4562E+017.8422E-01 5. 7124E+011.0261E+00 5.8957E+011.4658E+00 6.0787E+012.3453E+00 6.2252E+013.5181E+01 6.2617E+01


SVN 1.E-4SECN2 1.E+6

BLANK CARD TERMINATING BRANCHESC ***********************C HODELISATION DU DEFAUTC ***********************C 3456789-123456789-123456789-123456789-123456789-123456789-123456789-123456~-

o DEFA1 20.0E-3 1.0E1o DEFB1 20.0E-3 1.0E1

C *******************C SVITCHES DE ME SUREC *******************C 3456789-123456789-123456789-123456789-123456789-123456789-123456789-123456789-


PRN SVN MEASURING 1BLANK CARD TERMINATING SVITCHESC **************************C MODELISATION DE LA SOURCEC **************************C STATIC ELECTRIC NETVORK SOURCES VII.C.4 TYPE 14C 3456789-123456789-123456789-123456789-123456789-123456789-123456789-123456789-C NAMEST AMPLITUDE FREQUENCY PHASE Al TSTART TSTOP14 GENA 51.0E3 50.0 090.0 -1.0014 GENB 51.0E3 50.0 -030.0 -1.0014 GENC 51.0E3 50.0 +210.0 -1.00BLANK CARD TERMINATING SOURCESC NAM1 NAM2 NAM3 NAM4 NAM5 NAM6 NAM7 NAM8 NAM9C GENA GENB GENC PRIA PRIB PRIC SECA SECB SECCC PRA2 PRB2 PRC2 SEA2 SEB2 SEC2CABLA1CABLB1CABLC1C PRN SECN2BLANK CARD TERMINATING OUTPUTBLANK CARDBEGIN NEV DATA CASE

21

calcul P3B5000 r------,.---------r-------,--------.------------,

0.250.20.150.10.05

01----.

-5000

-10000 l-- ----l. ---'- ----'- --'-- ---'

o

ial

10000 r------,.---------r------,-------.------------,

0.250.20.150.1

................j. ·..···1···..·· .. ··· ..··..············..····..·····..···..·..·········r ···· ..········..··········· ····..·····..······! i

0.05

01--------'·

-5000 L-- ------' ----1. ----L.. ----'-- ---'

o

ibl

22

400calcul P3B

200

<: 0

-200

-4000 0.05 0.1 0.15 0.2 0.25

ic1

1000

500

<: 0 ............................................

-500

-10000 0.05 0.1 0.15 0.2 0.25

in

23

200calcul P3B

100

-< 0 ..................-..............

-100

-2000 0.05 0.1 0.15 0.2 0.25

ia2

200

100

-< 0

-100

-200 --

0 0.05 0.1 0.15 0.2 0.25

ib2

24

400calcul P3B

200

-< 0

-200

-4000 0.05 0.1 0.15 0.2 0.25

ic2

1000

500

-< 0 ......................... _..,.......

-500

-10000 0.05 0.1 0.15 0.2 0.25

in

25

courant differentiel et traversant sature2,--------,--------r---------,----------,,--------,

1.5 ,--....-...- ....-._.....-.-.. ""-'- '-"'-- .-....-----, '-_...- r ..---~-----:-:a_

1 1-....... ,............. . -. ,........... -. . - -.-. .~ _..~

0.,.-.....-f--4:---3~f-4_+_+-44~f-_f__++-4-4~t--¥_t- ....·....--·..- ..·..·....·........··......·......-

'-H'-~-'+"-"- _. --' - ~.- ,-- "-~~--$ _ -.. _ _..;._ _ - .._ _ - -

o.5 ..- - _ ~- -.. : - - - ...---.; '- :..__.._. - - ..- ---- .t-. .- -. ..-

- 1 1- _.......... . - .._ ~~---'3~-::.._- ._._._; _ __._ _ __._-

........-. ..- :-.~ _._-_.-.._._ _ _••......_ .

.;.-_...

+

~o...~

C;l....::l~C;ltil

tilQ)

Z. -0.5as~til...

"t:ltil...

- 1.5 ~ -... .. -;11l''';-'''''-''-'iI! ..~_.......•..- ..._ _-., - .._ _ _ - - - ..!

0.250.20.150.10.05-2 '-------.........-------'----------'-------'----------'

o

t en [sec]

26

courant differentiel et traversant sature5,.........---------,.--------.-------,....---------,--------,

'<......

-5

-10

----_ - ._--:-._ _._._._._-_.__..+.._._---_._---~--+------~----_.--~~ ..__-_ __ __.._--

l:lo...

.,)

IIII-<

3IIItil

til~I-<p.,III

.,)

til..."0.2l -15

-'---'- -.-.- ~--_._- _._- ·-f-

_·_--It--l--;---I

--- ---1-_.._..... M. •••·_ ••-~._••_ ......._.-.-....... - ••--_••---

i

-!----_.__._-....

0.250.20.150.10.05-20 '------'--------''--------'--------'--------'

o

t en [sec]

27

courant differentiel et traversant non sature:defaut externe:p3b1.5 I!----------:+-f'ci=�~IIIFRIIFRIIFRII+fII+iII+iIIHIIl+IIR=IIIFRIIFRIIFRII=R11+f11+iIIHII+iIl++llfFllf+IIIFRIIFRII+fII+lII'HIIHII++IIf+IIf+IIIFRIIFRII+t11+i11f+1 IHIIR=IIffI I f+IIIFRIIFRIIFRII'fili+fIl+fIIi=""1------1.

1r ++ 10.51 .:' it II

+ idoj 111111111111+ I

o 0.05 0.1 0.15 0.2 0.25

I

~

~

~I

0.250.2I

0.150.10.05

te en [sec)

X 10-3 courant proportionnel non sature:defaut exteme:p3b4 'I-----------r-----------,------------,~-------.----------

I

3r2~

:IA=te en [sec)

28

+

courant differentiel et traversant sature:defaut externe:p3b+i 1'1 ill 1111 " 11111111111111111111111111 II " III 1111 111111 1111111111111 II III 11111111111111111111111

0.250.2id

0.150.1

it

0.05

+

++-f<

+

ote en [sec]

courant proportionnel sature:defaut externe:p3bx10-34,

I

~

CII,)

.S<

00 "0.05 0.1 0.15 0.2

-j,

te en [sec]

29

0.25

I

H- ,Iii / ita111111111111101111111111 11111111111111111111111111111111I11111111111111111111111111111111111111111111111111111111111111111

courant differentiel et traversant non sature:defaut interne:p3b3 11------::==:::::::::========~==========~========~----I

I If2~ ~

I id ii

~

Ia 0.05 0.1 0.15 0.2

te en [sec]

courant proportionnel non sature:defaut interne:p3b8000 ,----------.-----------,--------~----------,--------------;

~~---'-

~ 6000l~~=4000

.~ 2000IioLa

o!J

0.05 0.1 0.15 0.2

--1Ij

IJII

0.25

te en [sec]

30

liI

I0.25

courant differentiel et traversant sature:defaut inteme:p3b

31 ( ~~ ~

2

1

1) ~r~

1 I, / +#-l::t+i-H+

j ~ ./ ~ ++H-~IIIIIH:: Ito 111111111111411111 ! *J 1111111111 111 1I1II1 ur!:t-t 11111111 &11111111/11/1111

o 0.05 0.1 0.15 0.2

te en [sec]

courant proportionnel sature:defaut inteme:p3b

'"0.......

8000,------I I

.--, 6000 ~ N -"~ 4000 ~ / ~ AA1\ JIlJ I I I" \J \J' ~/\ I' "

'&2000~ )1 l~~~- jv-J v~~ ~oI!'----L.-_~_~--'--!~r--.-----J______L_~__-------1__~__L__,__~o 0.05 0.1 0.15 0.2 0.25

te en [sec]

31

iI

I0.250.05 0.1 0.15 0.2

te en [sec]


courant H2 dans les phases et Ie neutre defaut interne, p3B.dat

------"'__-----L.- ------'--I L-I ------'-, J0.1 0.15 0.2 0.25

5

=<r::~

~::l

"d0

,

S i

i0 1

0

1.51

I

I=< 1 ~r:: I

I

~ I .,-1r:: 0.5 ~ /r::

i I

I /oL0 0.05

te en [sec]

32

courant H2 dans les phases et Ie neutre defaut externe:p3B.dat0.5,

<' Il:: I0 I

0

I"3"00 IS I

0 1

a

II

i\ " \I \ I '

/ I,

,!

,,,,,

0.05 0.1 0.15-" d

0.2

lII

i

I0.25

te en [sec]

1.5,courant point neutre, fondamental

=

/

l<' 1 r !l::0

0.5 ~l::.S I

I

I

I/OL ) I I

a 0.05 0.1 0.15 0.2 0.25

te en [sec]

33

condition de declenchement P3B,defaut interneB,----------.,.---------r----------,--------,--------,

!inn7 - , . . + , --!-..•.••....................•.••.

6 ,... . . ·····,,·········t···· _ _ ~ .

ro J -L --L .lI: . : .,

5 r·····················!.·····························;·... !4. 1... ' , .: iI________1

4 r························ ············1·..·..············ ·························..·..·t ························ ..t················· ·········· .

c····································!················ \ !3 r ...! !............................... ~P .l. [ ·····························1·..······················ .

2 r······················· ····································1············,,···················································f······ + ., ..{-.-.-.-.-.-.-.-.-.~.-.-.-.-.-._.-.-.-.-.-.-.-.-.-._t-._.-.-._._.-.-.-._.-.-._.-.-.-+-.-._.-.-.-._._.-.-.-.-.-'-'-'-'1;' ! ig ;1 '- ·······t ·················t-········ ······················I···........ ···························..·t················· .i

._._._._._._!

0.250.20.150.10.050'-----------'--------'--------'---------'--------'o

34

condition de declenchement P3B,defaut externeB.---------,--------,--------.---------,--------,

7 ,.................... ..!P.:!l......................................_; 1.-. 1 .

6 f- , . . ! ..j ~

. , !- ··········································<0··········1 -_ ~ _ .

5 ,... ., ..1. J4 , L : .---------------------r---------------------.---------------------~---------------------~

4 ················1····················..················ ""1"........ ·····················.. ·····r······················ , .

3 .,............................ 1 ~ ~p. _ L. ). .i! I • •

•••••• •••••••••, ••••••••••••••••••••••• ••••• n 1" , /'" ~ ·························..·········1

2 j ; ! ····.·.· i ······.·· ··.···· ··

1 f- .1

······1..···· ,. .........Jg l .·_·_·_·_·_·_·_·_·_·_·_·_·_·_·--1-·_·--_·_·_·_~·_·_·_·-._._._._.~._._._._._._._._._._._._._._._._.~._._._._.-._._._._._._._._._._.-l

0.250.20.150.10.05

OL.-- ...l- -L.. ---L ----l ----'

o

35

199419 janvier

Cx

6.56.56.5

R

COPT EPSILN TOLMAT TSTART

- NEUTRE j40 SUR TFO AMONT- NEUTRE DIRECT Rn=1.E-4 ohm SUR TRANSFO AVAL- DEFAUT TRIPHASE/TERRE FRANC


BEGIN NEV DATA CASEC +----------------------------------------------------------------------+C P3C.DATC ----------------------------------C ETUDE D'UNE PROTECTION DE TERRE RESTREINTEC ----------------------------------CCCCCCCCCCCC +----------------------------------------------------------------------+CCC DECLARATION DU NOM DU FICHIER DE SORTIE; ICI P3C.PL4C$OPEN, UNIT=4 FILE=P3C.PL4 FORM=FORMATTEDCC pas de calcul : 0.0222 ms ; pas de sortie: 0.111 ms soit 9.009 kHzC CE SONT LES MISC. DATA CARDS II-B-1 ,II-B-2C 3456789-123456789-123456789-123456789-123456789-123456789-123456789-123456789POYER FREQUENCY, 50.C DELTAT TMAX XOPT

.222E-4 2.0E-1 50.0ClOUT IPLOT IDOUBL KSSOUT MAXOUT IPUN MEHSAV ICAT NERERG IPRSUP

10000 5 0 1 1 0 0 2 0 0C 3456789-123456789-123456789-123456789-123456789-123456789-123456789-123456789-C ***********************C MODELISATION DE LA, PCCC ***********************C BRANCH CARDS TYPE 0 IV.A.2.1C NODE NAMES NODE NAMESC BUS1 BUS2 BUS3 BUS4o GENA PRIA .65o GENB PRIB .65o GENC PRIC .65


SVA1CABLA1 .20 4.0SVB1CABLB1 .20 4.0SVC1CABLC1 .20 4.0


1.E-31.E-31.E-3


36

C *******************CABLA1 DEFA1CABLB1 DEFB1CABLC1 DEFC1

0.10.10.1

.2884 11940.1781221430.0 6892.6134700553

.02361 3978.96790399350.0 -5957.9167178570.0 -3439.376150684

.2884 11940.1781221430.0 -3439.3761506840.0 -1985.4830642670.0 6892.6134700553

.02361 3978.96790399350.0 -5957.9167178570.0 -3439.3761506840.0 -5957.9167178570.0 -3439.376150684

.2884 11940.1781221430.0 -3439.3761506840.0 -1985.4830642670.0 -3439.3761506840.0 -1985.4830642670.0 6892.6134700553

.02361 3978.9679039935

221421. 353382000.0221421. 353382000.00.0221421.35338200

5 PRIC PRIB

6 SECC SECN

3 PRIB PRIA

4 SECB SECN

3 SECC SECN

C *******************************C MODELISATION DU TRANSFORHATEUR1C *******************************C 3456789-123456789-123456789-123456789-123456789-123456789-123456789-123456789-$VINTAGE, 1,




37.2884 59581.6575841890.0 20008.958586089

.02361 6721.4129175

40.0

16692.100203564-8290.06214476716692.100203564-8290.062144767-8290.06214476716692.100203564

3 SEC2 SECN2




USE RLC *************************************************C MODELISATION DE L'IHPEDANCE DE NEUTRE DU TRANSF01C *************************************************C BRANCH CARDS TYPE 0 IV.A.2.1C NODE NAMES NODE NAHES-----R-----X-----CC 3456789-123456789-123456789-123456789-123456789-123456789-123456789-123456789C BUS1 BUS2 BUS3 BUS4



3 PRB2 PRN

4 SEB2 SECN2

5 PRC2 PRN

6 SEC2 SECN2

0.0 -29727.206281320.0 -9985.69862399

.2884 59581.6575841890.0 -9985.698623990.0 -3354.397653070.0 20008.958586089

.02361 6721.41291750.0 -29727.206281320.0 -9985.698623990.0 -29727.206281320.0 -9985.69862399

.2884 59581.6575841890.0 -9985.698623990.0 -3354.397653070.0 -9985.698623990.0 -3354.397653070.0 20008.958586089

.02361 6721.4129175$VINTAGE, 0,$UNITS, -1.,-1.

USE RLC 3456789-123456789-123456789-123456789-123456789-123456789-96 SEA2 SECN2 8888.

-2.3400E+OO -6.2431E+01-8.7949E-01 -6.0787E+01-5.8633E-01 -6.0419E+01-2.6385E-01 -5.9139E+01-1.1727E-01 -5.7856E+01-4.3975E-02 -5.6759E+01

1.4658E-02 -5.4562E+015.1304E-02 -5.1999E+018.5017E-02 -4.7604E+011.0261E-01 -4.0281E+011.1727E-01 -2.9295E+011.4658E-01 1.9591E+011.6124E-01 2.7097E+012.0522E-01 3.6619E+012.6385E-01 4.3941E+013.1954E-01 4.7604E+014.1776E-01 5.1267E+015.7168E-01 5.4562E+017.8422E-01 5.7124E+011.0261E+OO 5.8957E+011.4658E+00 6.0787E+012.3453E+OO 6.2252E+013.5181E+01 6.2617E+01



BLANK CARD TERMINATING BRANCHESC ***********************C MODELISATION DU DEFAUTC *********************** 38C 3456789-123456789-123456789-123456789-123456789-123456789-123456789-1234567ff9-o DEFA1 20.0E-3 1.0E1

o DEFB1 20.0E-3 1.0E1o DEFC1 20.0E-3 1.0E1

C *******************C SVITCHES DE MESUREC *******************C 3456789-123456789-123456789-123456789-123456789-123456789-123456789-123456789-


PRN SVN MEASURING 1BLANK CARD TERMINATING SVITCHESC **************************C MODELISATION DE LA SOURCEC **************************C STATIC ELECTRIC NETVORK SOURCES VII.C.4 TYPE 14C 3456789-123456789-123456789-123456789-123456789-123456789-123456789-123456789-C NAMEST AMPLITUDE FREQUENCY PHASE Al TSTART TSTOP14 GENA 51.0E3 50.0 090.0 -1.0014 GENB 51.0E3 50.0 -030.0 -1.0014 GENC 51.0E3 50.0 +210.0 -1.00BLANK CARD TERMINATING SOURCESC NAH1 NAH2 NAH3 NAH4 NAM5 NAH6 NAM7 NAH8 NAH9C GENA GENB GENC PRIA PRIB PRIC SECA SECB SECCC PRA2 PRB2 PRC2 SEA2 SEB2 SEC2CABLA1CABLB1CABLC1C PRN SECN2BLANK CARD TERMINATING OUTPUTBLANK CARDBEGIN NEV DATA CASE

39

calcul P3C5000 ,------------,---------.--------:----r----c".----=-------,--------,

0.250.20.150.10.05

01------'

<-5000

-10000 L-- ------' -.L ---'- ---'- --l

oial

10000,------------r---------.--------,---------,--------,

0.250.20.150.10.05

o1-------'.

- 5000 L-- ----L ----'- -"-----'----"-_---''--_-=- ------'

o

ibl

40

10000calcuI P3C

5000

<0

-50000 0.05 0.1 0.15 0.2 0.25

ic1

0.1

0.05

< 0

-0.05

-0.10 0.05 0.1 0.15 0.2 0.25

in

41

~--I....... - - - ~

:"J

1

0.5

-< 0

-0.5

-1o 0.05 0.1

calcul P3C

0.15 0.2 0.25

ia2

1,------------,--------.---------.-------.------~

-0.5 I

0.250.20.150.10.05

-1 L-- ----' ---'- ---'- ----'- ~

oib2

42

calcul P3C1.----------r----------,---------r------r----------.

0.: ~--~\\;::::::=-;;;:.=-=:::±~= ::::_-'"""".-.:-=;:;;-..~~!i=-..--.;:;;_.._-.::.:-=-..:;:;---.-::_::;:;i:;:>---.;:;;;

0.250.20.150.10.05

- a.5 1\-1V··J····························..··-··-·················i···················································· - ~ ! ; - .

-1 L..- --'-- ---'-- ---' -'---- ---'

aic2

0.250.20.150.10.05

\.... + _ , + +- .

0.1

0.05

< a

-0.05

-0.1a

in

43

!

l

0.250.20.it50.10.05

X10-5 courant differentiel et traversant non sature:defaut interne:p3c8 '-1-----------,-------------,----------,,.------------.------------,

I6

1++-/y\

++ \+ \4 ,\

[ + J+/ +\++\ --, ~--2 r+++ * ++ \ / ~, -~-------------------------- .

1++++ + / +++Y-d-+~~IIIIIIIIII'IIIIIIIIII,IIIIIIIIIIIIIIII'IIIIIIIIIIIIII Lf0' -if(1

o

~i

I0.250.20.150.10.05

te en (sec]

courant proportionnel non sature:defaut interne:p3c300

1

II

........,200 ~*..........C I

n.l

100~0-

I

oL0

te en (sec]

44

courant differentiel et traversant sature:defaut interne:p3c

0.05 0.1 0.15it

0.2 0.25

,,~ 2001~ I.& 100 t

ii

te en [sec]

courant proportionnel sature:defaut interne:p3c300.-,----------------.,------------------.,--------,

J ~o,-I__.1-1 ---'-- -------'- --'----- ------'--,--------'1o 0.05 0.1 0.15 0.2 0.25

te en [sec]

45

0.250.20.150.10.05a

xl0-4 courant differentiel et traversant non sature:defaut externe:p3c1 'I-------,-------------,-----------r-------~------l

I + I

L

· -F+ +

~~ :0.5 1 +\ id 1

I + + ++

I ++ ++~+. ~~-++t~ 1111111111111111 \11111111\1111111111\ 11\11\ 111111111++++++l--q.+ +*+-tt-'

ai+ + + it

r::Q)

---J

JI

i0.250.2

=~

0.150.10.05

te en [sec]

xlO-3 courant proportionnel non sature:defaut externe:p3c41,---------r--------,-------~----------,-------_

:~1 ~o1\ /~"-a

c:Q)

0..

te en [sec]

46

xl0-4 courant differentiel et traversant sature:defaut exteme:p3c1 '--1--+-,-----------,-------------,.---------,-----------,1

1

-P-+ +++ -l+

it+

a 0.05 0.1 0.15 0.2 0.25

0.05 0.1

te en [sec]

0.15 0.2

47

courant H2 dans Ies phases et Ie neutre defaut interne:p3c5,-------.----------,----------,-------------,-------,

0.25

i

~0.25

1

0.21

0.15

0.5

!r\"" ..(\ :-" (,~, ,-r~~ / \.' I J \ ... X-/ \-\Q.) I' 1\ \ \

I ,. I \1 II II i! \ \./,,\\~: ::' '-~

L__L.:)~__~l ----' .J....'_--~_-=:-==:==':=:::-~:2._ ~o r, , ! =o 0.05 0.1 0.15 0.2

te en [sec]

xlO-4 courant point neutre, fondamental1 ~,--------,----------,-------,---------,---------,

j!

te en [sec]

48

xl0-4 courant H2 dans Ies phases et Ie neutre defaut externe:p3c8

1

I I I I

6rJ\. !ML , '\;: ! \\

41~{! C'\' f \\2 / ./ \--..

, ' \I ' \I I,J \a~~_/----'-,'/_--~

a 0.05 0.1 0.15 0.2

te en [sec]

1

i--j

~0.25

0.20.150.1

X 10-4 courant point neutre, fondamental1~--------------------'---------'---------'i

IJ

0.25

te en [sec]

49

courant differentiel et traversant sature15 r--------r------......,....--------,-------,....-----------,

10 1- -- _.- - ..-.-+ id------.~ ----.-.. ·~-------·~--~_·-¥-·-·---···-····-·--··--4--·-----····-.--- -~ ---

5 1--,,--,,-,--- ... •__•••....J _+_ _ ,_,_,_ . ._ _..___._ _._..___ _.

o.,..-_~+~:......~... '-- .f....:t_ ..

- 5 r--....---.---. -_. ··#··-----111'-

- 1 0 --..--- --- - -.- i--'''-'''''-- .. - - -. .._.__~---.-.------ ..-~.- -- -.-.---..----l._-.---.._-..--.._.-.---

- 15 _._..- .._- _ _ -.-- ..- ,.-_._.._ _-- - -.- , - -.·_..·..·..·-·-..-·-··..···-·····f·..·-..·.._.. ···..········-···· ~ - -- -

0.250.20.150.10.05

-20 '-- '-- '-- .1....- .1....- ----'

o

t en [sec]

50

0.250.20.150.1

id

courant differentiel et traversant sature

0.05

-_···~_·__·_--------t-_·_·_--·_··~·_·_-------_····_-_·---+._ _---- -.- -..----.

1±'''T'i' ---'r-----------!---------------;.· _ _ - _-.

I-:--::~rlr-ii·-··-~·-------------_···-··_----..j.·------_·-------,--.---.---- ..---.-..- .....

x10-4

2

1.5

,.......,<..........

1l::Q)

l::0.50.........,

ellr-.;:l a....,elltil

tilQ)

'"' -0.5p..ell

....,D'l..... -1

"Ctil....

-1.5

-2a

t en [sec]

51

condition de declenchement P3C.defaut interne7 ,-----~----_._-----___,,_-----____r-----___,------_,

inn6 - j .•.••........••...............•....................i································.. ··············.. ·····..y ; .

5

;--------l---------------------+---------------------i---------------------1

.....................: ~..d. ·······.·.···········1······.···················· ··········•·.·· ·············.il···········........... .I .II____________J

4 !,i .•...•................................................. ..... :...... . ~ ~..................................... ....................................................•.......1

......................................................····f'··.•....................................................+ .

3 .. .j.. j ip . !......................................................·······t ··· .

2 ....................................................+ ~ _ 1 ~ .

! I

1

iig...................., ~ ·..····..·t·..······ ·..······ .................f- .. . ; '"~ -

;

'-'-'-'-'-'-'-'-'-'-'-'-'-'-'-'i-'-'-'-'-'-'-'-'-'-'-'_._._._._.+._._._._._._._._._._._._._._._._.~._._._._._._._._._._._._._._._.-:

0.250.20.150.10.050'----------'-------'--------'------------'--------'o

52

condition de declenchement P3C,defaut externe7.--------..-----------.--------,---------,r-----------,

6 },..~.~ i . ......................................, ! .1

id!5 ~......................................................................................................... ·····f······················_··········..·············· + .---------------------,---------------------t---------------------i---------------------l

4------------.----------------'----~-:-------+-------- -r---- ----3 _......... . ; ~ ~.............................................. . ) .II!

.......................................................·····r······················································t········..························ ············ "1" ..J

2 +...................................... ................•,: ······f·····························..································i······································ .

!1 ~ _ ! L.. .

!ig ,

···,,·,,············r··············· ., .1 .

!'-'-'-'-'-'-'-'-'-'-'-'-'-'-'-'-i-'-'---'---'-'-'-'-'-'_·-·_·_·_·-:-·_·_·_·_·_·_·_·_·_·_·_·_·_·_·_·_·t·_·_·_·_·_._._._._._._._._._._.-;

0.250.20.150.10.050'---------'--------'----------'----------'----------'o

53

199420 janvier

Cx

6.56.56.5

R

.65

.65

.65


- NEUTRE j40 SUR TFO AMONT- NEUTRE DIRECT Rn=1.E-4 ohm SUR TRANSFO AVAL- ENCLENCHEMENT TRANSFO

BEGIN NEY DATA CASEC +----------------------------------------------------------------------+C P3D.DATC ----------------------------------C ETUDE D'UNE PROTECTION DE TERRE RESTREINTEC ----------------------------------CCCCCCCCC P. BermejoC GROUPE SCHNEIDERC P.C.C.C +----------------------------------------------------------------------+CCC DECLARATION DU NOM DU FICHIER DE SORTIE; ICI : P3D.PL4C$OPEN, UNIT=4 FILE=P3D.PL4 FORH=FORHATTEDCC pas de calcul : 0.0222 IDS ; pas de sortie: 0.111 IDS soit 9.009 kHzC CE SONT LES MISC. DATA CARDS II-B-1 ,II-B-2C 3456789-123456789-123456789-123456789-123456789-123456789-123456789-123456789POYER FREQUENCY, 50.C DELTAT TMAI XOPT

.222E-4 2.0E-1 50.0ClOUT IPLOT IDOUBL KSSOUT HAXOUT IPUN MEMSAV ICAT NERERG IPRSUP

10000 5 0 1 1 0 0 2 0 0C 3456789-123456789-123456789-123456789-123456789-123456789-123456789-123456789-C ***********************C MODELISATION DE LA PCCC ***********************C BRANCH CARDS TYPE 0 IV.A.2.1C NODE NAMES NODE NAMESC BUS1 BUS2 BUS3 BUS4o GENA PRIAo GENB PRIBo GENC PRIC

54


SVA1CABLA1 .20 4.0SVB1CABLB1 .20 4.0SYC1CABLC1 .20 4.0

CABLA1 SYA2 .20 4.0CABLB1 SVB2 .20 4.0CABLC1 SYC2 .20 4.0

C *************************C MODELISATION DE LA CHARGEC *************************C SEA2 1.E-3C SEB2 1.E-3C SEC2 1.E-3C *******************************C MODELISATION DU TRANSFORMATEUR1

.2884 11940.1781221430.0 6892.6134700553

.02361 3978.96790399350.0 -5957.9167178570.0 -3439.376150684

.2884 11940.1781221430.0 -3439.3761506840.0 -1985.4830642670.0 6892.6134700553

.02361 3978.96790399350.0 -5957.9167178570.0 -3439.3761506840.0 -5957.9167178570.0 -3439.376150684

.2884 11940.1781221430.0 -3439.3761506840.0 -1985.4830642670.0 -3439.3761506840.0 -1985.4830642670.0 6892.6134700553

.02361 3978.9679039935

221421.353382000.0221421. 353382000.00.0221421. 35338200

SECNSECC3

5 PRIC PRIB

6 SECC SECN

4 SECB SECN

3 PRIB PRIA

C *******************************C 3456789-123456789-123456789-123456789-123456789-123456789-123456789-123456789-$VINTAGE, 1,




55

.2884 59581.6575841890.0 20008.958586089

.02361 6721.41291750.0 -29727.206281320.0 -9985.69862399

.2884 59581.6575841890.0 -9985.698623990.0 -3354.397653070.0 20008.958586089

40.0

16692.100203564-8290.06214476716692.100203564-8290.062144767-8290.06214476716692.100203564

SEC2 SECN23

3 PRB2 PRN

4 SEB2 SECN2


USE RLC *************************************************C MODELISATION DE L'IMPEDANCE DE NEUTRE DU TRANSFOIC *************************************************C BRANCH CARDS TYPE 0 IV.A.2.1C NODE NAMES NODE NAMES-----R-----X-----CC 3456789-123456789-123456789-123456789-123456789-123456789-123456789-123456789C BUSI BUS2 BUS3 BUS4





5 PRC2 PRN

6 SEC2 SECN2

.02361 6721.41291750.0 -29727.206281320.0 -9985.698623990.0 -29727.206281320.0 -9985.69862399

.2884 59581.6575841890.0 -9985.698623990.0 -3354.397653070.0 -9985.698623990.0 -3354.397653070.0 20008.958586089

.02361 6721.4129175$VINTAGE, 0,$UNITS, -1.,-1.

USE RLC 3456789-123456789-123456789-123456789-123456789-123456789-96 SEA2 SECN2 8888. -54.0

-2.3400E+00 -6.2431E+01-8.7949E-01 -6.0787E+01-5.8633E-01 -6.0419E+01-2.6385E-01 -5.9139E+01-1.1727E-01 -5.7856E+01-4.3975E-02 -5.6759E+01

1.4658E-02 -5.4562E+015.1304E-02 -5.1999E+018.5017E-02 -4.7604E+011.0261E-01 -4.0281E+011.1727E-01 -2.9295E+011.4658E-01 1.9591E+011.6124E-01 2.7097E+012.0522E-01 3.6619E+012.6385E-01 4.3941E+013.1954E-01 4.7604E+014.1776E-01 5.1267E+015.7168E-01 5.4562E+017.8422E-01 5.7124E+011.0261E+00 5.8957E+011.4658E+00 6.0787E+012.3453E+00 6.2252E+013.5181E+01 6.2617E+01

9999.96 SEB2 SECN2 SEA2 SECN2 8888. 27.096 SEC2 SECN2 SEA2 SECN2 8888. 27.0C *************************************************C MODELISATION DE L'IMPEDANCE DE NEUTRE DU TRANSF02C *************************************************C BRANCH CARDS TYPE 0 IV.A.2.1C NODE NAMES NODE NAMES R X CC 3456789-123456789-123456789-123456789-123456789-123456789-123456789-123456789C BUS1 BUS2 BUS3 BUS4


BLANK CARD TERMINATING BRANCHESC **************************************************C DISJONCTEURC **************************************************00 SECA SVA1 0.02 5.000 SECB SVB1 0.02 5.000 SECC SVC1 0.02 5.0C *******************C SVITCHES DE MESUREC *******************C 3456789-123456789-123456789-123456789-123456789-123456789-123456789-123456jY9-

SVA2 PRA2 MEASURING 1

111

MEASURINGMEASURINGMEASURING

NAM6 NAM7 NAMa NAH9PRIC SECA SECB SECCSEC2CABLA1CABLB1CABLC1

SVB2 PRB2SVC2 PRC2

PRN SVNBLANK CARD TERMINATING SVITCHESC **************************C MODELISATION DE LA SOURCEC **************************C STATIC ELECTRIC NETVORK SOURCES VII.C.4 TYPE 14C 3456789-123456789-123456789-123456789-123456789-123456789-123456789-123456789-C NAMEST AMPLITUDE FREQUENCY PHASE A1 TSTART TSTOP14 GENA 51.0E3 50.0 120.0 -1.0014 GENB 51.0E3 50.0 -000.0 -1.0014 GENC 51.0E3 50.0 +240.0 -1.00BLANK CARD TERMINATING SOURCESC NAM1 NAM2 NAM3 NAM4 NAMSC GENA GENB GENC PRIA PRIBC PRA2 PRB2 PRC2 SEA2 SEB2C PRN SECN2BLANK CARD TERMINATING OUTPUTBLANK CARDBEGIN NEV DATA CASE

•

57

0.20.12 0.14 0.16 0.180.1

ial

0.02 0.04 0.06 0.08

calcul P3D500,-----------,---,----,-------r------,-----.----,------,----...,---------,

O~-~

<11 - 5 00 1- ; -\- -/- ; ······\···· ..··..······f ·..!· ..··+

-1 000 1- ; \, / , ..

-1500 l..--_---'__----1__---l.__-L__---L...__---'-__---'-__--'-__....l.-_----'

o

1000.-------,-----,-----,-------r------,-----.----,------,----...,-------,

0.20.12 0.14 0.16 0.180.1

ibl

0.02 0.04 0.06 0.08

500

- 500 l..--_---'__----1__---l.__-L__---L...__---'-__---'-__--'-__....l.-_----'

o

O~----;-<

58

1000calcul P3D

500

<0

-5000 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

icl

100

0 ... .••••••••••~ ••••••••"l' ••••••• ......._...

< -100 ........\

-200 .................~.~..

-3000 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

in

59

id

courant differentiel et traversant sature:defaut interne:p3d

I

r~/----- -~---, 1

/ j

0.5 ~ +111 11111 II , I~~ I \\1 II III 11\1\ II , I , I I II I I I III II I ./ jI

+++ Ii 11111: III lit ++++++++++#1111 1111111+11111111111111111

0-111111111111111+ !!! - I+! _ . Io 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

1.5 IIiI

1 ~

cQ)

I

,-, 1500 f-~ i

'ij 1000 ~0.. ,.- 500f--

te en [sec]

courant proportionnel sature:defaut interne:p3d2000 r--r---~-----,-----,------~-------r-------r------.------'---_!

!

i

~I

______1

oL -----'- L.-__....JI ...I...--__---L..__---..l_--'-_..L-__---l.-__---..l_~

o 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

te en [sec]

60

courant H2 dans les phases et Ie neutre:p3dI0.8,

~ 0.6 ~c:: i3,) i

.E 0.4 r;:] I

"':l,

'"' 0.2f--'"'6 I,

0:0 0.02

.\. \

0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

te en [sec]


,I

I ~

I ---I! !

/ i

) ~___"-,"""-__--'-, '-,__---'--,__-----', "-,__---'-'__----JI'----__-'-I I

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

te en [sec]

0.4,

~0.3

c:: 0.21J

c:: Ic:: ,.- 0.1 ~

0 1

0

61

courant differentiel et traversant sature2.5 ,---------,-----,------r-----;-----r-----r----r---r--~--___,

........-<'--'

r::Cll

ill i I ; ~2 _.---.--.--i-·--·-·-..--·-..i·..·-····-..·-·_-..L...- ...._._.--r--·....-_..-+-"""id-;.-;-i·,-·-t..·.._--/'1I,\.....-.......t-......-.-...-.-..+.-.....- .......----i

f\1.5 --..----..---..-..-..--·-..- ..·--..-·-t..-·-·-..l--...- ..i---+~f--.;---+

't:lUl....

0.20.12 0.14 0.16 0.180.10.02 0.04 0.06 0.08

-1 L..--_-----'__----'-__----'-__---'-__....I......__-'--__..L...-__L--_---l__..........l

o

t en [sec]

62

condition de declenchement P3D, enclanchement transformateur8

1

I I71 I inn

II

6~I

IidI

iSf-

I:

~:-----------------------------------------. I/ I

~-----------------------------------------------------------------------------~I

4Llp

3~

19J

i

0.18oL-i__---'-I__--"-__---l...__----'- -----l' '--__.L--__-'--

o 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

te en [sec]

_--'--__I0.2

63

199417 janvier

CxR


I- NEUTRE DIRECT Rn=1.E-4 ohm SUR TRANSFO AVAL- DEFAUT FRANC BIPHASE/TERRE

BEGIN NEY DATA CASEC +----------------------------------------------------------------------+C P3E.DATC ----------------------------------C ETUDE D'UNE PROTECTION DE TERRE RESTREINTEC ----------------------------------CCCCCCCCC P. BermejoC GROUPE SCHNEIDERC P.C.C.C +----------------------------------------------------------------------+CCC DECLARATION DU NOM DU FICHIER DE SORTIE; ICI : P3E.PL4C$OPEN, UNIT=4 FILE=P3E.PL4 FORH=FORHATTEDCC pas de calcul : 0.0222 ms ; pas de sortie: 0.111 ms soit 9.009 kHzC CE SONT LES HISC. DATA CARDS II-B-1 ,II-B-2C 3456789-123456789-123456789-123456789-123456789-123456789-123456789-123456789POYER FREQUENCY, 50.C DELTAT THAX XOPT

.222E-4 5.0E-1 50.0ClOUT IPLOT IDOUBL KSSOUT MAXOUT IPUN MEMSAV ICAT NERERG IPRSUP

10000 5 0 1 1 0 0 2 0 0C 3456789-123456789-123456789-123456789-123456789-123456789-123456789-123456789-C ***********************C MODELISATION DE LA PCCC ***********************C BRANCH CARDS TYPE 0 IV.A.2.1C NODE NAMES NODE NAMESC BUS1 BUS2 BUS3 BUS4o GENA PRA2 .65 6.5o GENB PRB2 .65 6.5o GENC PRC2 .65 6.5

C *********************************C MODELISATION DU DEPART EN DEFAUTC *******************************C cableC ----------C BRANCH CARDS TYPE 0 IV.A.2.1C --BUS1--BUS2--BUS3--BUS4-----R-----XC 3456789-123456789-123456789-123456789-123456789-123456789-123456789-123456789-

SYA2 CABLA .01 .01SYB2 CABLB .01 .01SYC2 CABLC .01 .01

C *************************C MODELISATION DE LA CHARGEC *************************C CABLA 1.E+3C CABLB 1.E+3C CABLC 1.E+3C *******************C IMPEDANCE DU DEFAUTC *******************

DEFA 0.1C *******************************

64

.2884 59581.6575841890.0 20008.958586089

.02361 6721.41291750.0 -29727.206281320.0 -9985.69862399

.2884 59581.6575841890.0 -9985.698623990.0 -3354.397653070.0 20008.958586089

.02361 6721.41291750.0 -29727.206281320.0 -9985.698623990.0 -29727.206281320.0 -9985.69862399

.2884 59581.6575841890.0 -9985.698623990.0 -3354.397653070.0 -9985.698623990.0 -3354.397653070.0 20008.958586089

.02361 6721.4129175

16692.100203564-8290.06214476716692.100203564-8290.062144767-8290.06214476716692.100203564

6 SEC2 SECN2

5 PRC2 PRN

3 SEC2 SECN2

3 PRB2 PRN

4 SEB2 SECN2

C HODELISATION DU TRANSFORHATEUR2C *******************************$VINTAGE, 1,





USE RLC 3456789-123456789-123456789-123456789-123456789-123456789-96 SEA2 SECN2 8888.

-2.3400E+00 -6.2431E+01-8.7949E-01 -6.0787E+01-5.8633E-01 -6.0419E+01-2.6385E-01 -5.9139E+01-1.1727E-01 -5.7856E+01-4.3975E-02 -5.6759E+01

1.4658E-02 -5.4562E+015.1304E-02 -5. 1999E+018.5017E-02 -4.7604E+011.0261E-01 -4.0281E+011.1727E-01 -2.9295E+011.4658E-01 1.9591E+011.6124E-01 2.7097E+012.0522E-01 3.6619E+012.6385E-01 4.3941E+013.1954E-01 4.7604E+014.1776E-01 5.1267E+015.7168E-01 5.4562E+017.8422E-01 5.7124E+011.0261E+00 5.8957E+011.4658E+00 6.0787E+012.3453E+00 6.2252E+013.5181E+01 6.2617E+01

9999.96 SEB2 SECN2 SEA2 SECN2 8888.96 SEC2 SECN2 SEA2 SECN2 8888.C *************************************************

65

C MODELISATION DE L'IMPEDANCE DE NEUTRE DU TRANSF02C *************************************************C BRANCH CARDS TYPE 0 IV.A.2.1C NODE NAMES NODE NAMES R X CC 3456789-123456789-123456789-123456789-123456789-123456789-123456789-123456789C BUS1 BUS2 BUS3 BUS4

SVN 1.E+6SVN2 1.E-4

BLANK CARD TERMINATING BRANCHESC ***********************C MODELISATION DU DEFAUTC ***********************C 3456789-123456789-123456789-123456789-123456789-123456789-123456789-123456789-o CABLA DEFA 20.0E-3 1.0E1o CABLA CABLB 20.0E-3 1.0E1

C *******************C SYITCHES DE MESUREC *******************C 3456789-123456789-123456789-123456789-123456789-123456789-123456789-123456789-

SYA2 SEA2 MEASURING 1SYB2 SEB2 MEASURING 1SYC2 SEC2 MEASURING 1

SECN2 SVN2 MEASURING 1BLANK CARD TERMINATING SYITCHESC **************************C MODELISATION DE LA SOURCEC **************************C STATIC ELECTRIC NETWORK SOURCES VII.C.4 TYPE 14C 3456789-123456789-123456789-123456789-123456789-123456789-123456789-123456789-C NAMEST AMPLITUDE FREQUENCY PHASE Al TSTART TSTOP14 GENA 51.0E3 50.0 090.0 -1.0014 GENB 51.0E3 50.0 -030.0 -1.0014 GENC 51.0E3 50.0 +210.0 -1.00BLANK CARD TERMINATING SOURCESC NAM1 NAM2 NAM3 NAM4 NAM5 NAM6 NAM7 NAM8 NAM9BLANK CARD TERMINATING OUTPUTBLANK CARDBEGIN NEW DATA CASE

66

X104 ca1cul P3e

-0.5 1 ,~ v '1-1 L-L---'-'_------'-,--,~--,---,---,-,------',---'---,-~------,,-_I

o 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

ia2

\.f\J1V-\/\/\/\/\/C\/l\ ~ I

_. I! ! ) ! I I I ! ! ~

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

ib2

xl041c--------r------------r----,---~---_-__,

i0.5 1-

I

67

0.05calcul P3e

I

II

i II

\< o!I

I iI

I IIII

-005 I ! I I ! I I I

. 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

ic2

/\ (\ l

J\/10.16 0.18 0.2

4000 ~I-----,---------,---,--------,---~----,----------,----------,--,-------

i

/OOO~ (\ t \ /~ / (\-2000L_ I I I ! I I I

o 0.02 0.04 0.06 0.08 0.1 0.12 0.14

III

68

courant diffliuentiel et traversant sature3,----,-----,------,------;.='------,-----r---,---.,....----.------,

0.20.180.160.140.120.10.080.060.04

i +

l/* IO++-Hi+t+l+tt-t+"'----'--L..----''-----.L.-----'-----'------''-----.L.-----'-----'o 0.02

1 f- .

(I2 f- .........................•.......................~+.:I±J:-'i" L .i 1·········_····it·········L ..1 1 .

+ ! i ' I I +i-tl#1" ILI 1++++1 II ,It I 1++I II " d"11-#

..........T~" " ~~Jrt.~~~t.~ ;., ".=III i ~""I..I"I"I,'..I..~I ","", ,',.:" ,', ,."., :",.."" ..,..,."., ", ,."" " , .'d....

te en [sec]

courant proportionnel sature300 .---r----r---r---..--"'--~.__--.__--.__--..----.---___,

0.20.180.160.140.120.10.080.04 0.060.02

g 200 1- 1' : (.",:M,+ + " ,j ! ·1..· · · ; · · ·,

c::CI.l

.8' 100 I- ~ t , +·..·' ·..I..., ..'.. ! · ,.. ,\'--,..,·..•..+r--_..·~--.. ·_..··T+_.. _·~..·~·"'·_..1.. '--.. ·--,·_,.._..,~..·,_..·_·.. _,·..--·.. -·····_··Li··_·_·..~_··.._..·li_.. _~.__.._,

OI..-====:::~L--_---l_.L-----I.__----L__---L__--L__--l..-__...L-__....L-_--.--J

ote en [sec]

69

courant H2 dans les phases et Ie neutre sature:defaut externe:p3E

3

1

' I

2 1 (~ I~~/\ '- -,I~~~ J1,1 ~' ! \~ V/-~~~--\ j

i i\ I I ~-- -------- ',,--- ~il "-'1" I ,/ '---,-------, I

Iif'" J,"" --"

;1 - ~ ... _--/ __ ::_ Io,'--_ ___JJ"'-,__-.L-__-.L--=----=---:....IJ --,-':...=..0....--....:..-,,-,,--c..=..l-,-~~~~~___J'~ _ ____l,___',~-_~---.11

o 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

3,

<' 2~I::::II)

c 1~I::::

iI

0 1

0 0.02

te en [sec]

courant point neutre, fondamental:p3E

0.2

te en [sec]

70

courant differentiel et traversant sature8 r__---,-------r"---r__----r-~l--,-----r----r------r-------r----r----,

6 I-_ _ _.'- _ __-..;_.._.._...••...__~..-+..- -+.__j__ i__ ..__ _ _._.._~__.__._ _._.__._._L _

.• ..l. ._.---.;....__ - --~-...---.-_.~.-.--_.-:- ..---_-.--:...-..-._.._-~_..-..--..------1-·-~-._--_·~._--

N •••--+_. ._.+.__ _

01--~_#_-~,,·

4 !--·-..-- -----·····..-;··-·..··--·..-··..··c····-t-·-·-·..·--';...-···1·----'- -.-.-~ - ..__._.L ..- ~-..- ..-. -- ;-.-..-.---

2 t---..---.."---......-;.-

it

- 6 .._ _L_ _ _ ,. . .- --+.-._.--._.-,-_.-- --.-- + -- - _.-t·--··-···-·····- ---·-..·t-···--

-4

-2

- 8 -.-- -.;---..- -- ;..---- -- -...;.....- - -; --..-.-.-....\ ----; - ----.-; -.-..-....;-.-.- -- .;. ---.-

0.20.180.160.140.120.10.080.060.040.02-10 '-__-'--__--'--__--'-__----1. '-__-'--__--'-__---'-__----1.__-----'

o

t en [sec]

71

condition de dec1enchement P3E, defaut externe biphase/terre

8/ -l7~ I mD J

6~ ~I ,------------------------------------------------------------------------------------------~

5 ~--------------i id II I

4i JI

3~Ip

~I------------------------------------------------------ -------------- I

1

1~I1- - - -

oL-I__..L'__-----',__-----...L'__---'---_--------'-

o 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18

!I

0.2

te en [sec]

72

courant differentiel et traversant satureB.-----.,-----.----....,....---....,....-----,------,-----,-------r-----,.---,

6 ._.._------.__..._----_..._-_.~.- ---~-- ._-_..~_.

i 1 ! ;__.__1.._...._...__.1._... 1 .. 1__..... _

- 4 ...._.__~._._._...._..__L_._ ... __~_.__._l......._. ._..L ._..__..~__. ! ._._...l __... ..;...._..--

--~--._---:-- ._--..~---- --~-----! \

--·-·----it-L-.---;..-t--~.----l

2

4

01--~-I--_\_...i

- 2 - ..._._.--......;.-_.....---+_.

"0Ul.... - 6 ·-···-·--·..-.·_.._··..····__..·····-i··--- .. ---i--··---;··------i-....----.·--·-·-·-~··-- ..--i·-·---···-..._...L_...__._

-8 ....., _-_..__..~ _.__ _-_.~ ..__._.- id:----···+---------··f·..·..··-·-·--··-i--··-·---·--t-·---·-··--·-·t-..······--·--·--i·--·----·!'--·····..··..·..··-

0.20.160.160.140.120.10.060.060.040.02

-10 L.-__.L.-__.L.-__L.-_---J'--_---J'--_---J__---'__---'__---'__---'

o

t en [sec]

73

BEGIN NEW DATA CASE~ +----------------------------------------------------------------------+

P3F.DAT

ETUDE D'UNE PROTECTION DE TERRE RESTREINTE

NEUTRE DIRECT Rn=1.E-4 ohmDEFAUT FRANC TRlHASE/TERRE

ISUR TRANSFO AVAL


17 fevier 1994

~ +----------------------------------------------------------------------+

~ DECLARATION DU NOM DU FICHIER DE SORTIE; ICI P3F.PL4

$OPEN, UNIT=4 FILE=P3F.PL4 FORM=FORMATTED

TSTARTTOLMATEPSILNCOPT

: pas de calcul : 0.0222 ms ; pas de sortie: 0.111 ms soit 9.009 kHz: CE SONT LES MISC. DATA CARDS II-B-1 ,II-B-2: 3456789-123456789-123456789-123456789-123456789-123456789-123456789-1234~

~OWER FREQUENCY, 50.: DELTAT TMAX XOPT

.222E-4 5.0E-1 50.0lOUT IPLOT IDOUBL KSSOUT MAXOUT IPUN MEMSAV ICAT NERERG

10000 5 0 1 1 0 0 2 0~ 3456789-123456789-123456789-123456789-123456789-123456789-123456789-1234~

~ ***********************~ MODELISATION DE LA PCC~ ***********************

~ *********************************

~ BRANCH CARDSNODE NAMESBUS1 BUS2

o GENA PRA2o GENB PRB2o GENC PRC2

TYPE 0 IV.A.2.1NODE NAMES RBUS3 BUS4

.65

.65

.65

x

6.56.56.5

C

~ MODELISATION DU DEPART EN DEFAUT~ *******************************

cable

~ BRANCH CARDS TYPE 0 IV.A.2.1~ --BUS1--BUS2--BUS3--BUS4-----R-----X~ 3456789-123456789-123456789-123456789-123456789-123456789-123456789-1234!

SWA2 CABLA .01 .01SWB2 CABLB .01 .01SWC2 CABLC .01 .01

~ *************************~ MODELISATION DE LA CHARGE~ *************************

CABLACABLBCABLC

~ *******************

1.E+31.E+31.E+3

~ IMPEDANCE DU DEFAUT~ *******************

74

DEFA 0.1~ *******************************

MODELISATION DU TRANSFORMATEUR2*******************************INTAGE, 1,

SEA2 SECN2SEB2 SECN2

SEC2 SECN2

USE RLNITS, 0.50E+02

PRA2 PRNSEA2 SECN2

PRB2 PRN

SEB2 SECN2

PRC2 PRN

SEC2 SECN2

, O.

16692.100203564-8290.06214476716692.100203564-8290.062144767-8290.06214476716692.100203564

.28840.0

.023610.00.0

.28840.00.00.0

.023610.00.00.00.0

.28840.00.00.00.00.0

.02361

59581.65758418920008.958586089

6721.4129175-29727.20628132

-9985.6986239959581.657584189

-9985.69862399-3354.39765307

20008.9585860896721.4129175

-29727.20628132-9985.69862399

-29727.20628132-9985.69862399

59581.657584189-9985.69862399-3354.39765307-9985.69862399-3354.39765307

20008.9585860896721.4129175

CNTAGE, 0,HTS I -1. I -1 .JSE RL\456789-123456789-123456789-123456789-123456789-123456789-

SEA2 SECN2 8888.-2.3400E+00 -6.2431E+Ol-8.7949E-Ol -6.0787E+Ol-5.8633E-Ol -6.0419E+Ol-2.6385E-Ol -5.9139E+Ol-1.1727E-Ol -5.7856E+Ol-4.3975E-02 -5.6759E+Ol1.4658E-02 -5.4562E+Ol5.1304E-02 -5.1999E+Ol8.5017E-02 -4.7604E+Ol1.0261E-Ol -4.0281E+Ol1.1727E-Ol -2.9295E+Ol1.4658E-Ol 1.9591E+Ol1.6124E-Ol 2.7097E+Ol2.0522E-Ol 3.6619E+Ol2.6385E-Ol 4.3941E+Ol3.1954E-Ol 4.7604E+Ol4.1776E-Ol 5.1267E+Ol5.7168E-Ol 5.4562E+Ol7.8422E-Ol 5.7124E+Ol1.0261E+00 5.8957E+Ol1.4658E+00 6.0787E+Ol2.3453E+00 6.2252E+Ol3.5181E+Ol 6.2617E+Ol

9999.SEB2 SECN2 SEA2 SECN2 8888.SEC2 SECN2 SEA2 SECN2 8888.~***********************************************

75

C MODELISATION DE L'IMPEDANCE DE NEUTRE DU TRANSF02C *************************************************C BRANCH CARDS TYPE 0 IV.A.2.1C NODE NAMES NODE NAMES R X CC 3456789-123456789-123456789-123456789-123456789-123456789-123456789-12345C BUS1 BUS2 BUS3 BUS4

SWN 1.E+6SWN2 1.E-4

BLANK CARD TERMINATING BRANCHESC ***********************C MODELISATION DU DEFAUTC ***********************C 3456789-123456789-123456789-123456789-123456789-123456789-123456789-12345o CABLA DEFA 20.0E-3 1.0E1o CABLA CABLB 20.0E-3 1.0E1o CABLA CABLC 20.0E-3 1.0E1

C *******************C SWITCHES DE MESUREC *******************C 3456789-123456789-123456789-123456789-123456789-123456789-123456789-1234=

SWA2 SEA2 MEASURINGSWB2 SEB2 MEASURINGSWC2 SEC2 MEASURING

SECN2 SWN2 MEASURINGBLANK CARD TERMINATING SWITCHESC **************************C MODELISATION DE LA SOURCEC **************************C STATIC ELECTRIC NETWORK SOURCES VII.C.4 TYPE 14C 3456789-123456789-123456789-123456789-123456789-123456789-123456789-1234~

C NAMEST AMPLITUDE FREQUENCY PHASE Al TSTART14 GENA 51.0E3 50.0 090.0 -1.0014 GENB 51.0E3 50.0 -030.0 -1.0014 GENC 51.0E3 50.0 +210.0 -1.00BLANK CARD TERMINATING SOURCESC NAM1 NAM2 NAM3 NAM4 NAM5 NAM6 NAM7 NAM8 NAM9BLANK CARD TERMINATING OUTPUTBLANK CARDBEGIN NEW DATA CASE

76

X104 calcul P3fi2 i

-<

I Ii Ii i

0.6-1 L i

0.4 0.50.1 0.2 0.30

ia2

ib2

77

11x104

0.5 1 1

~ _O~~\ I~ i~j\ n\~~0.5 r j \ \ \

-11 ~ Vo - 'I

0.11

0.2

calcul P3f

!

0.3

ic2

1

0.4!

0.5

JJ!JI

0.6

In

78

-i

iJ

i0.6

xl0-4 courant differentiel et traversant non sature:defaut externe:p3f4 '---,------,------,----,---------r--------.------,-----r-----,-----.--------,j

:l !: it ]+ +

o 0.05 0.1 0.15 0.2 0.25

te en [sec]

0.3 0.35 0.4 0.45 0.5

I

I~ 100

c::u

.8--

courant proportionnel non sature:defaut externe:p3f150,---,-------.--------.--------.--------.--------,--------.--------,----------,,----------,---

I

!

~ l50 I -

l/yJ\)JV~:v~~~~~f'd0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

te en [sec]

79

0.50.45I

0.40.350.30.25

te en [sec]

I

0.20.150.10.05

courant differentiel et traversant sature:defaut exteme:p3f

15[ ~ --------.----r--i101 (\ id i

. i \r-~ :5r r·~V\~~ ~

0-1","""""" ...........~--S''''''' .."III'..... III"""'" "''''''''''""""""",:,:"""""""'."",,,,'""".""""""""""'""""""''''''''''''''''"'"''''''''''o 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

te en [sec]

courant proportionnel sature:defaut exteme:p3f2001

150 ~ II

~

It:: 100It)

50 II.S-

L~00

80

courant H2 dans Ies phases et Ie neutre sature:defaut exteme:p3fI I I i

0.4!

0.45

1~

0.5

te en [sec]

courant point neutre, fondamentaI:p3f

1

l(\ 1\fV\j-\./-'V~\'-/'\~"f'vF'j~!j~j-'--~'--~-----------------------------------1

~,\ -I

'-----'---------'- l.I__----'--__---'-__--'-1__-'1 --.1.1__----'--1 ----'--__..1

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

te en [sec]

X 10-4

3, i\! \i i

" "

« 21 (t::11)

1 ~t::,S I

iII

0 1 ;0 0.05

81

condition de declenchement P3F, defaut externe triphase franc

,

3~lp

2~ ~

I I

1 ~ ig 1~-------------------------------------------------------------------------------------------1

0 1 ! ! ~

o 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

te en [sec]

82

% ceci est une valeur quelconque% ceci est une valeur quelconque

.ete chainel.met;

.d off;lar;

[;...,limulation de la chaine de mesure avec bobine de Rogowski~ur une voie courant phase.lans saturation par voie magnetique ou par ecretage'1: freqence du signal'2:frequence du bruit

imulation de la bobine de Rogowski Ep=K*[di(t)/dt]Iremiere partie:1/9000:0.1;SO;350;2*pi*f1;2*pi*f2;.001; %ceci est une valeur quelconque/9000;4;0.1;

ignale d'entree sans bruit-A1*sin(w1*t) ;:It (t, Is1)

ignale d'entree avec bruit1=A1*sin(w1*t)+ A2*sin(w2*t);

[K/T -K/T];1;Ei1ter(b1,a1,Is1); , signale a la sortie de la bobine de Rogowski

?lot (221) ,plot (t, Ep, 'b' ,t, Is1, 'w' )Le('signale capte par bobine de Rogowski'))el ('Ep in [V], Is1 in [A]'))el('t in [sec]')I:t( 'Ep'):t ( , Is1' )

mulation de la bobine de Rogowskiuxieme partie (equation differentielle)cours d'etude

0.8;30; %ceci est une valeur quelconque.014e-6;7e-9;C2*R1)+(L1/R2»/(L1*C2);~1/R2)+1)/(L1*C2);

(L1*C2) ;(A*T)+(B*T"'2);(C*T"'2) /01 ;L -(2+(A*T)/D) 1/0];:ilter(bO,aO,Ep);: ( t , Ep, t , Up)

mlation locale du filtre d'ordre 1

~]=butter(1,5.6/(9000/2»;

'*8.05;'ilter(b2,a2,Ep); % signale a la sortie du filtre d'ordre1

83

.., simulation 'locale' de l'ecretage a la sortie du filtre d'ordre 1

Is3=ecrete(Is2.',26*O.4*sqrt(2»i

% multiplication du signale par le gain (g2)

g2=2.4223; , calibrateur en position 1 (ceci est un choix quelconque)Is4=g2*Is3; , signale a la sortie du gain g2

subplot(222),plot(t,Is2,'b',t,Is3,'w',t,Is4, 'r')title('signale filtre, ecrete, calibre')ylabel('Is2,Is3,Is4 in [A)')xlabel('t in [sec)')gridgtext('Is2=Is3')'gtext ( , Is3' )gtext ( , Is4' )

clear Epclear lsIclear Is2clear Is3

% simulation 'locale'du filtre d'ordre 2

[b3,a3)=butter(2,180/(9000/2»;Is5=filter(b3,a3,Is4); , Signale a la sortie du filtre d'ordre 2

subplot(223),plot(t,Is4,'r',t,IsS,'w')title('signale calibre est filtre')ylabel('Is4,IsS in [A)')xlabel('t in [sec)')gridgtext ( , I s4 ' )gtext ( , IsS' )

clear Is4

, Simulation 'locale' de l'ecretage a la sortie du filtre d'ordre 2

Is6= ecrete(IsS,3);

subplot(224),plot(t,Is5,'w',t,Is6,'b')title('signale filtre est ecrete')ylabel('Is4,Is5 in [A)')xlabel('t in [sec)')grid%gtext ( , IsS' )%gtext ( , Is6' )gtext('Is5=Is6')

, decimation d'un signal en prenant un point sur N=lS

Is7=decibrut(Is6,15);

% interpolation du signal Is6

Is8=inter(Is6,15);

% traitement du signal Is8 par filtre numerique (sincos)

Is9=sico(Is8);

'meta chaine1

84

\ ceci est une valeur quelconque\ ceci est une valeur quelcon~e

Lete chaine2.met;ld off;!ar;

'I;

limulation de la chaine de mesure avec bobine de Rogowski)Our la voie courant HOMOPOLAlRE.lans saturation par voie magnetique ou par ecretage;l:freqence du signal;2:frequence du bruit

)remiere partie

1:1/9000:0.1;'50;'350;'2*pi*fl;'2*pi*f2;1.001; \ceci est une valeur quelconque/9000;:4;:0.1;

ignale d'entree sans bruit-Al*sin(wl*t);

igna1e d'entree avec bruitl-Al*sin(wl*t)+ A2*sin(w2*t);

imulation de la bobine de Rogowski Ep-K*(di(t)/dt}

(K/T -K/T];1;filter(bl,al,Isl); , Signale a la sortie de la bobine de Rogowski

plot(22l),plot(t,Ep, 'b',t,Isl,'w')le('signale capte par bobine de Rogowski')oel ('Ep in (V), Isl in (A)')oe1('t in (sec}')ict('Ep')et('Isl')

~ulation de la bobine de Rogowski!uxieme partie (equation differentielle)l cours d' etude

0.8;30; \ceci est une valeur quelconque.014e-6;7e-9;C2*Rl)+(Ll/R2»/(Ll*C2);Rl/R2)+1)/(Ll*C2);(Ll*C2);(A*T)+(B*T A 2);(C*T A 2)/Oj ;1 -(2+(A*T)/0) 1/0);filter(bO,aO,Ep);

nulation locale du filtre d'ordre 1

l2)=butter(1,S.6/(9000/2»;2*9.06;;ilter(b2,a2,Ep); , signale a 1a sortie du filtre d'ordrel

85

clear Epclear Isl

% simulation 'locale' de l'ecretage a la sortie du filtre d'ordre 1

IaJ=ecrete(Is2.',2J.S*O.4*sqrt(2»;

clear Is2

% multiplication du signale par le gain (g2h)

g2h=1.696; % calibrateur gl en position 1 (ceci est un choix quelconque)Is4=g2h*IsJ; % signale a la sortie du gain g2h

clear IsJ

sUbplot(222),plot(t,Is2, 'b',t,IsJ,'w',t,Is4,'r')title('signale filtre, ecrete, calibre')ylabel('Is2,IsJ,Is4 in [A]')xlabel('t in [sec]')gridgtext('Is2=IsJ')%gtext ( , IsJ ' )gtext ( , I s4 ' )

% simulation 'locale'du filtre d'ordre 2

[bJ,aJ]=butter(2,180/(9000/2»;Is5=filter(bJ,a3,Is4); % Signale a la sortie du filtre d'ordre 2

subplot(223),plot(t,Is4,'r',t,IsS,'w')title('signale calibre est filtre')ylabel('Is4,IsS in [A]')xlabel('t in [sec]')gridgtext ( , Is4' )gtext ( , IsS' )

clear Is4

% Simulation 'locale' de l'ecretage a la sortie du filtre d'ordre 2

Ia6= ecrete(IsS,3);

subplot(224),plot(t,IsS,'w',t,Is6, 'b')title('signale filtre est ecrete')ylabel('Is4,IsS in [A]')xlabel('t in [sec]')grid%gtext ( , IsS' )%gtext ( , Is6' )gtext('IsS=Is6')

clear IsS

Is7=decibrut(Is6,lS);

Is8=inter(Is6,lS);

Ia9=sico(Is8) ;

%meta chaine2

86

,lete chaine3. met;ld off;ear;g;c;simulation de la chaine de mesure avec tore magnetiquepour une voie courant phase.fl:freqence du signalf2:frequence du bruit

0:1/9000:0.1;-50;-350;-2*pi*fl;-2*pi*f2 ;0.001; %ceci est une valeur quelconque1/9000;-1; %ceci est une valeur quelconque-0.1; 'ceci est une valeur quelconque

lignale d'entree sans bruitL-U*sin(wl*t) ;

lignale d' entree avec bruit11-Al*ain(wl*t)+ A2*sin(w2*t);

.imulation locale de la saturation a la sortie d'un tore magnetique

!-sature(Isl,3,1/9000);

~plot(221),plot(t,Isl,'b',t,Is2,'w')

.tle('signale capte par tore magnetique')

.abel ( , Isl in (A), Is2 in (A)')

.abel('t in (sec)')'id,ext ( , Is1-Is2' )lar Isl

imulation 'locale' du premier ecretage

-ecrete(Is2,153*O.04*sqrt(2»;\Is2.'

imulation 'locale'du filtre d'ordre 2

,a3J~butter(2,180/(9000/2»;

-filter(b3,a3,Is3); \ Signale a 1a sortie du filtre d'ordre 2

Jplot(222),plot(t,Is3, 'w',t,Is4, 'r'):le('signale ecrete,filtre')lbel('Is3,Is4 in [AJ')lbel ( , t in [sec)').dtxt ( 'Is3')txt ( 'Is4')Lr Is2Lr Is3

iltiplication du signale par le gain (g)

2;g*Is4; \ signale a 1a sortie du gain g

plot(223),plot(t,Is4, 'r',t,IsS,'w')le('signale filtre est amplifie')

87

- ..%ylabel('Is4,IsS in [A)')%xlabel('t in [sec)')%grid%gtext ( , Is4' )%gtext ( , IsS' )clear Is4

% Simulation 'locale' de l'ecretage apres traitement par gain g

Is6= ecrete(ISS,3);

%Is7= decibrut(Is6,lS);%save temp Is6

IsS= inter(Is6,lS);%pack IsS

%subplot(224),%plot(t,Is6,'w',t,Is8,'b')%title('signale filtre ')%ylabel('Is6,IsS in [A]')%xlabel('t in [sec]')%grid%gtext ( , Is6' )%gtext ( , IsS ' )

% traitement du signal par sico

Is9=sico(IsS);

%meta chaine3a

lete chaine4.met;Id off;ear;g;c;s~ulation de la chaine de mesure avec tore magnetiquepour une voie courant HOKOPOLAIRE.f1:freqence du signalf2:frequence du bruit0:1/9000:0.1;-SO;=350;=2*pi*fl;=2*pi*f2;).001; 'ceci est une valeur quelconqueL/9000;=1; %ceci est une valeur quelconque=0.1; %ceci est une valeur quelconque

lignale d'entree sans bruitL=Al*sin (wl*t) ;

Jignale d'entree avec bruit,1-A1*sin(wl*t)+ A2*sin(w2*t);

limulation locale de la saturation a la sortie d'un tore magnetique

:-sature(Isl,3,1/9000);

,plot (221) ,plot (t, Isl, 'b' ,t, Is2, 'w' ),le('signale capte par tore magnetique')hel('Is1 in [A],Is2 in [A]')hel('t in [sec]')dxt ( , IsI-Is2' )

imulation 'locale' du premier ecretage

-ecrete(Is2,153*0.04*sqrt(2»;

~ltiplication du signale par le gain (gh)

Z. 2;=gh*Is3; , signale a la sortie du gain (gh)

)lot(222),plot(t,Is3, 'w',t,Is4,'r')Le('signale ecrete est amplifie'))el('Is3,Is4 in [A]')Ie1 ( , t in [sec]')I:t ( , 183' ):t ( , Is4' )

mulation 'locale'du filtre d'ordre 2

a3]-butter(2,1BO/(9000/2»;filter(b3,a3,Is4); % Signale a la sortie du filtre d'ordre 2

lot (223 ) , plot (t, 184, , r' , t , Is5 , , w' )e('8ignale filtre ')el( '184,185 in [A]')el('t in [sec]')

C( 'Is4')

88

!xt ( , Is5 ' )

;imulation 'locale' de l'ecretage apres traitement par gain 9

;= ecrete(Is5,3);

)plot(224),plot(t,IsS,'w',t,Is6,'b');le ( , signale ecrete ')~el('Is4,Is5 in [AJ')~el('t in [sec]').dtxt ( , Is5=ls6' )

'=decibrut (ls6, 15);

,=inter (ls6, 15) ;

=sico (IsB) ;

ta chaine4

89

% fichier diff1.rn% P. BERMEJO 01/94% PROTECTION DIFFERENTIELLE A POURCENTAGE% MESURE DES 4 COURANTS PAR DES CHAINES DE MESURE AVEC TORE MAGNETIQUE

%function [id,it,ip]=diff1(i1,i2,i3,in);

% calibre des TC reseaukp 400/1;kn = 400

% TC phase% TC neutre

% niveau de saturation de la chaine de rnesure, en A secondaireisat =400;

% niveau d'ecretage de la chaine de mesure, en A secondaireimax = 24*sqrt(2)j

% calcul des courants au secondaire des TC11 !k2/kp;12 = ib21kp;13 = JC?/kpjIn = in/knj

% simulation locale de la saturation a la sortie d'un tore magnetiqueIs1 sature(I1,isat,1/9000)jIs2 sature(I2,isat,1/9000)jIs3 sature(I3,isat,1/9000)jIsn sature(In,isat,1/9000)j

% simulation du filtre d'ordre 2

(b3,a3]=butter(2,180/(9000/2))jIf1 = filter(b3,a3,Is1)j % Signale a la sortie du filtre d'ordre 2If2 filter(b3,a3,Is2);If3 = filter(b3,a3,Is3)jIfn = filter(b3,a3,Isn);

% Simulation de l'ecretageIm1 ecrete(If1,imax)j1m2 ecrete(If2,imax)j1m3 ecrete(If3,imax)jImn ecrete(Ifn,imax)j

% echantilonnage 600HzIe1 decibrut(Im1,15)jIe2 decibrut(Im2,15)jIe3 decibrut(Im3,15)jlen decibrut(Imn,15);

% traitement du signal par sico(Ix1,Iy1] sico(Ie1)j(Ix2,Iy2] sico(Ie2)j(Ix3,Iy3] sico(Ie3)j[Ixn,Iyn] = sico(Ien)j

% calcul de l'algorithme

% courant differentielixd = Ix1+Ix2+Ix3-Ixnjiyd = Iy1+Iy2+Iy3-Iynjid = sqrt(ixd."2+iyd."2)j

% courant traversant

90

ixt = (Ixl+Ix2+Ix3+Ixn)/2;iyt = (Iyl+Iy2+Iy3+Iyn)/2;it = sqrt(ixt. '2+iyt.'2)i

% courant differentiel a pourcentageip = id./(it+eps)*100;

te=decibrut(t,lS);

subplot(211),plot(te,id,te.it, '+')title('courant differentiel et traversant non sature')ylabel('id,it en [A)')xlabel('te en [sec]')grid

subplot(212),plot(te,ip)title('courant proportionnel dDn sature')ylabel('ip en [A}')xlabel('te en [sec}')gridgtext('id')gtext('it')

91

% fichier diff2.m% P. BERMEJO 01/94% PROTECTION DIFFERENTIELLE A POURCENTAGE% MESURE DES 4 COURANTS PAR DES CHAINES DE MESURE AVEC TORE MAGNETIQUE% avec filtrage H2

% calibre des TC reseaukp 400/1;kn = 400/1;

% TC phase% TC neutre

% niveau de saturation de la chaine de mesure, en A secondaireisat =40;

% niveau d'ecretage de la chaine de mesure, en A secondaireimax = 24*sqrt(2);

% calcul des courants au secondaire des TCII = ia1/kp;12 = ib1/kp;13 ic1/kp;In in/kn;

% simulation locale de la saturation a la sortie d'un tore magnetiquelsI = sature(I1,isat,1/9000);Is2 = sature(I2,isat,1/9000);Is3 = sature(I3,isat,1/9000);Isn = sature(In,isat,1/9000);

% trace des courants satures

isdist =

Is1+Is2+Is3-Isn;(Is1+Is2+Is3+Isn)/2;

clg%plot(t,isd,t,ist,'+')%title('courant differentiel et traversant sature')%ylabel('isd,ist apres saturation, en [A]')%xlabel('t en [sec]')%grid

%gtext('id')%gtext('it')%print

% simulation du filtre d'ordre 2

[b3,a3]=butter(2,180/(9000/2»;If1 filter(b3,a3,Is1); % Signale a la sortie du filtre d'ordre 2If2 filter(b3,a3,Is2);If3 = filter(b3,a3,Is3);Ifn = filter(b3,a3,Isn);

% Simulation de l'ecretageIm1 ecrete(If1,imax);1m2 ecrete(If2,imax);1m3 = ecrete(If3,imax);Imn = ecrete(Ifn,imax);

% echantilonnage 600HzleI = decibrut(Im1,lS);Ie2 decibrut(Im2,lS);Ie3 decibrut(Im3,lS);len decibrut(Imn,lS); 92

% traitement du signal par sico[Ix1,Iy1] sico(Ie1);[Ix2,Iy2] sico(Ie2);[Ix3,Iy3] sico(Ie3);[Ixn,Iyn] = sico(Ien);

% traitement du signal par sico2 (FILTRAGE H2)[I2x1,I2y1] = sico2(Ie1);[I2x2,I2y2] = sico2(Ie2);[I2x3,I2y3] = sico2(Ie3);[I2xn,I2yn] = sico2(Ien);

% calcul de l'algorithme

% module courant point neutreinn = sqrt(Ixn."2+Iyn."2);

% courant differentielixd = Ix1+Ix2+Ix3-Ixn;iyd = Iy1+Iy2+Iy3-Iyn;id = sqrt(ixd."2+iyd."2);

% courant traversantixt = (Ix1+Ix2+Ix3+Ixn)/2;iyt = (Iy1+Iy2+Iy3+Iyn)/2;it = sqrt(ixt."2+iyt."2);

% courant differentiel a pourcentageip = id./(it+eps)*100;

% module des courants 100Hzi21 = sqrt(I2x1."2+12y1."2);i22 sqrt(I2x2."2+12y2."2);i23 sqrt(I2x3."2+12y3."2);i2n sqrt(I2xn."2+12yn."2);

te=decibrut(t,lS);

%subplot(211),plot(te,id,te,it,'+')%title('courant differentiel et traversant sature')%ylabel('id,it en [A]')%xlabel('te en [sec]')%grid

%subplot(212),plot(te,ip)%title('courant proportionnel sature')%ylabel('ip en [Xl')%xlabel('te en [sec]')%grid%gtext('id')%gtext('it')%print;

%clg;%subplot(211),plot(te,i21,te,i22,te,i23,te,i2n)%title('courant H2 dans les phases et Ie neutre')%ylabel('module en [A]')%xlabel('te en [sec]')%grid

%subplot(212),plot(te,inn)%title('courant point neutre, fondamental')%ylabel('inn en [A]')%xlabel('te en [sec]')

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%grid%print

% conditions de declenchement

% sur le module de i neutrecl=inn> (ones(inn)*O.05/sqrt(2));

% sur le courant diffc2=id> (ones(id)*O.05/sqrt(2));

% sur le courant prop.c3=ip> (ones(ip)*5);

% globalc4 = cl.*c2.*c3;

%traceclgplot(te,cl+6.5,te,c2+4.5,te,c3+2.5,te,c4+0.5);gridtitle('condition de declenchement P3D,defaut interne ');gridgtext ( , inn' )gtext ( , id ' )gtext ( , i P , )gtext ( , i g , )print

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Restricted Earth Fault Relay Project