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On travelling-wave-based protection of high-voltage networks
Citation for published version (APA):Bollen, M. H. J. (1989). On travelling-wave-based protection of high-voltage networks. Eindhoven: TechnischeUniversiteit Eindhoven. https://doi.org/10.6100/IR316599
DOI:10.6100/IR316599
Document status and date:Published: 01/01/1989
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ON TRAVELLING-WAVE-BASED PROTECTION OF
HIGH-VOLTAGE NETWORKS
MATH BOLLEN
ON TRAVELLING-WAVE-BASED PROTECTION OF HIGH-VOLTAGE NETWORKS
CIP-GEGEVENS KONINKLIJKE BIBLIOTHEEK, DEN HAAG
Bollen, Mathias Henricus Johannes
On travelling-wave-based protection of high-voltage networks I Mathias Henricus Johannes Bollen. -[S.l. : s.n.]. Fig., tab. Proefschrift Eindhoven. Met lit.opg., reg. ISBN 90-9002955-9 SISO 661.55 UDC 621.316.925(043.3) NUGI 832 Trefw.: hoogspanningsnetten; beveiliging I transmissielijnen; elektrische overgangsverschijnselen.
ON TRAVELLING-WAVE-BASED PROTECTION OF
HIGH-VOLTAGE NETWORKS
PROEFSCHRIFf
ter verkrijging van de graad van doctor aan de Technische Universiteit Eindhoven, op gezag van de Rector Magnificus prof. ir. M. Tels, voor een commissie aangewezen door het College van Dekanen in het openbaar te verdedigen
op vrijdag 15 september 1989 om 16.00 uur
door
Mathias Henricus Johannes Bollen
geboren te Stein (L)
&'uk wibr-o dicsertatie<:fr\.lkkerlj, holrnood
Dit proefschrift is goedgekeurd door de promotoren:
Prof. Dr. Ir. W.M. C. van den Heuvel
en
Prof. Dr.-Ing. HJ. Butterweck.
We can walk our road together
If our goals are all the same
We can run alone and free
If we persue a different aim
Let the truth of love be lighted
Let the love of truth shine clear
Sensibility
Armed with sense and liberty
With the heart and mind united
In a single perfect sphere
Neil Peart, 1978.
TABLE OF CONTENTS:
1. Introduction ................................................ .
2. Travelling waves and high-voltage lines ...................... 7
3. Network modelling ............................................. 26
4. Testing of algorithms for travelling-wave-based protection ... 41
5. Directional detection ........................................ 58
6. Differential protection ...................................... 73
7. Other algorithms for travelling-wave-based protection ........ SO
8. A protective scheme for a double-circuit line ............... 102
9. Summary and conclusions ..................................... 114
10. References .................................................. 118
Samenvatting .................................................... 127
cxxx ............................................................ 130
Levens loop ...................................................... 131
-1-
1. Introduction
1.1. The protection of public supply systems
A public supply system is set up to transport and distribute electrical
energy from the generators to the users. Due to the interconnection of a
large number of generators (power plants) a high reliability is achieved. An
important role in maintaining this high reliability is played by the
power-system protection. The function of the protection is the disconnection
of defective lines and apparatus from the system. This thesis concerns the
detection and disconnection of faults1 on high-voltage lines.
Before the turn of the century, this was mainly achieved by using
fuses. This century showed the introduction of protective relays in
combination with circuit-breakers. The first to detect the fault, the latter
to disconnect it. The protective relay uses voltages or currents to detect a
fault. Upon detecting, a tripping signal is sent to the circuit breaker that
disconnects the fault. At first. simple relays were used, like time
overcurrent relays, directional-power relays and differential relays . By
using these relays it was difficult to maintain the selectivity (only
disconnecting the faulted line or apparatus), especially in the growing
high-voltage networks in Europe in the twenties. This led to the proposal of
a number of new protection principles drawing much attention from the
professional world. But all of them were overruled by the principle of
distance protection. The first distance relays were used in 1925 for the
100 kV double-circuit 1 ine betw:een the power plant of Seestadl and Prague
[Walter, 1967]. Nowadays the protection of high-voltage lines is largely
achieved by means of distance relays. From power frequency voltages and
currents measured at one line terminal an input impedance is determined for
the line. If this value is below a certain preset value, a tripping signal
is sent to the circuit breaker and the line is disconnected.
The main advantage of di,t}tcmce (Yl,otecUoo is the fact that no
communication link is needed. Each relay can determine the position of the
fault from voltages and currents measured at the relay position. Due to all
kinds of errors, the reach of a distance relay cannot be determined exactly.
It is therefore impossible to distinguish between a fault a 1 i ttle before
the next substation and a fault a little beyond that substation. But by
introducing different distance zones a highly reliable network protection
A fault (or short-circuit) is an inadvertent accidental connection between two or more phase conductors or between one or more phase conductors and ground [Blackburn, 1987].
-2-
has been achieved.
Zone 1 of each distance relay reaches up to about 90% into the
line-to-be-protected. zone 2 up to 50% into the next adjacent line and zone
3 approximately 25% into the adjacent line beyond [Blackburn, 1987]. If a
relay detects a fault in its zone 1 an instantaneous tripping signal will be
generated (no delay introduced on purpose). In case of a fault in zone 2 or
3 a tripping signal will be generated if the fault remains during a certain
time. This verification time is longer for more distant zones. A fault
somewhere on a line, not too close to one of the line terminals, (position 1
in Figure 1.1) will lead to an instantaneous tripping signal of both A and
B. In case of a fault at position 2 (i.e. close to one of the line
terminals) only B will generate an instantaneous tripping signal. Relay A
will generate a tripping signal if the fault lasts for longer than a certain
time. This time is longer than the time needed to disconnect a fault at
position 3 by relay C and its circuit breaker. In that way zone 2 of relay A
serves as a primary protection for faults close to the other line terminal
and as a remote backup for relay C in case of faults on the first half of
the next adjacent line. Zone 3 serves as a remote backup for faults on the
second half of the next adjacent line (e.g. position 4).
--- --· ZONE 3
ZONE2
Figure 1.1. Protection of a high-vottage tine by means of distance retays
When reliable communication links are available it is possible to use
information from both 1 ine terminals. In that case each fault on the 1 ine
wi 11 lead to an instantaneous trip. Two principles can be distinguished:
differential protection and directional detection. A attte~entiai ~tection
relay uses currents from both line terminals. If the difference between
corresponding currents exceeds a certain threshold a tripping signal is
generated. This principle is mainly used for short lines and for the
protection of busbars, as the current values must be transmitted from one
line terminal to the other. A simple communication link can be used
-3-
for dL'tecti.Oitai detecti.Oit. On each line terminal a "directional detector"
determines the direction to the fault (generally from the direction of the
power flow). By exchanging this result each relay decides whether a tripping
signal should be generated or not.
Protection needing communication links is
connections in the United States [I.andoll et al.,
used for important
1981] and is already
common practice in Japan [CIGRE, 1980]. In most cases distance protection is
used as a remote backup. In Europe, 50-Hz based distance protection is used
almost throughout the high-voltage network. In some protection schemes a
signal is transmitted to the relay on the other line terminal when a zone
fault is detected {a t'tan~fe't-t'ti.p ~cheme). Immediately upon receiving the
signal the relay on the other line terminal is prepared to generate a
tripping signal. An interruption of the communication link will not endanger
the reliability of these schemes.
In most protection schemes the final backup consists of a
tLme-o~e'tCU't'tent 'tel.~. In case the current exceeds a certain value during a
certain time, a tripping signal will be generated.
1.2. Why fast protection?
The first public supply network was built in 1882 on the initiative of
Thomas Alva Edison. An electrical power system supplied energy for a small
quarter of New York by means of a relatively low D.C. voltage. Within a few
years such networks arose all over the world. The protection took place by
means of a large fuse at the outlet of the generator.
Developments in A.C. technology like the invention of the transformer,
made it possible to connect power stations with each other. This led to an
enormous growth of the electric supply networks in the twenties. With the
larger transmitted power and the larger generators the need arose for faster
fault clearing. Where a disconnection (or clearing) time of 10 seconds was
still acceptable in 1910 a time below 2 seconds was asked for in 1925. In
later years a continued growth of the supply networks is observed. This does
not primarily concern the aerial extent but the generated and transmitted
power as well as the network complexity.
Fault clearing times have decreased ever more. In the present state of
the art fault detection times of 20 to 40 milliseconds are general practice,
leading to fault clearing times of 40 to 100 milliseconds depending on the
circuit breaker used [Blackburn, 1987]. In the past ten years there has been
a call for even shorter fault clearing times {and detection times). Three
causes for this can be given:
-4-
In case of a fault close to a generator, the disconnection of resistive
load will speed up the generator. The larger the pre-fault transmitted
power is, the larger the acceleration. If such a fault lasts too long,
this will lead to transient instability. The increasing power exchange
between networks thus calls for a decreasing fault clearing time or
additional high-voltage lines. The first solution is preferable from an
economic and environmental point of view. A fault clearing time of one
or two cycles is needed in some situations to prevent transient
instability [Hicks and Butt, 1980]. Utilizing 3/4-cycle breakers, this
leaves about 5 milliseconds for fault detection. This is the main cause
for research after faster fault detection in the late seventies and
eighties.
The large currents during a short circuit constitute a heavy mechanical
stress on the power systems apparatus. Since the electrodynamical
forces are proportional to the square of the current, reducing the
maximum current is an effective way of reducing the mechanical stress.
Because the first current maximum will be the highest {due to
exponential current terms) current limiting devices will only be
effective when action is taken before the first current maximum. This
calls for a fault detection within one or two milliseconds [Thuries and
Pham Van Doan, 1979].
The availability of fast and cheap microprocessors made microprocessor
based protection relays possible. A few of these relays are already
available, all of them using distance protection [-,1988]. But the
microprocessor also enables the use of other {better, faster)
protection principles. This triggers the call for fast protection. In
this context Chamia [1988] speaks about "technology-driven"
applications.
The development of one-cycle 500 kV air blast circuit-breakers prompted
Bonneville Power Administration, Portland, Oregon to launch a special
program in 1974 aiming at Ultra-High-Speed Relaying systems. The scope of
this program was to dev~lop a relaying system with an operating time of 4
milliseconds or less for multi-phase faults close to the relay position.
This resulted in a relay with an operating time of 4 milliseconds based on
travelling wave principles [Esztergalyos, Yee, Chamia and Liberman, 1978].
It will be discussed as Chamia's algorithm in Section 5.1.
At about the same time a japanese group developed a prototype of a
travelling-wave-based differential relay to solve some relaying problems
encountered in EHV and UHV networks [Takagi, Baba. Uemura, Sakaguchi, 1977].
-5-
Despite promising testing results presented in a number of papers, the relay
has not been applied in existing power systems. It will be discussed as
Takagi's algorithm in Section 6.1.
Since 1978 more algorithms for travelling-wave-based protection of
high-voltage lines have been proposed. But, except for Chamia's algorithm,
none of them has reached the state of commercial availability.
Also some non travelling-wave-based algorithms for fast protection have
been proposed. Most of them determine the stationary quantities from a time
window of less than one cycle of the power frequency. None of them is able
to determine the fault position with an acceptable accuracy within half a
cycle [Glavitsch, Btirki, Ungrad, 1987].
1.3. The aim of this study
2 As already noted several algorithms for travelling-wave-based protection of
high-voltage lines have been proposed. In the author's opinion none of them
has been sufficiently tested to answer the question ":J!J. /]a':J.t fJ'totectioo,
ba!J.ed oo, t'ta1!>eUing.-fl9(t1!>e fJ'tincipte':J. f;o!J.!J.i/..te?" On the other hand some of the
proposed algorithms are based on very simple principles making it (almost)
impossible to find even simpler algorithms. In view of this situation it is
not appropriate to search for a completely new algorithm.
First the existing algorithms must be subject to a thorough and
critical review. It must be investigated whether the algorithm will react
3 properly to all possible fault situations in the zone-to-be-protected .
Further it must be studied how the algorithm reacts on disturbances not
caused by faults in the zone-to-be-protected.
It is not possible to perform a large number of field experiments in
high-voltage networks. Therefore we have to resort to network models for the
testing of protection algorithms. ~he de1!>etopment ot netmo'tk modeL!J. j]o't the
!J.tudy- ot t'ta1!>eLUng,-wa1!>e-ba!J.ed pwtecti..oo, forms the first part of this
study. The models are described in Chapters 2 and 3. An existing model as
well as a newly developed model have been used.
2 A protection algorithm has been defined here as: "The way in which measured voltages and currents are used to calculate certain functions and the way how these functions are used to take decisions concerning protection".
3 For line protection, discussed here, the zone-to-be-protected consists in general of three phase-conductors (one circuit) between two substations. But for some relays the zone-to-be-protected consists of just one conductor, for others of two parallel circuits.
-6-
The second part of the study concerns the tell.Ung. ot the P"tePoll.ed
aLg.o'ti.thnlll., the introduction of simplications, changes and/or extensions
followed by a new round of testing. Also some new proposals have been
studied. Chapter 4 gives a list of situations that might lead to an
incorrect decision by the relay. It also describes how the network models
and the list of situations have been used for extensive testing of
protection algorithms. Chapters 5 through 7 give an overview of existing
algorithms as well as the results of the testing.
The third part of the study concerns the c'teatton ot a Li.nk ~eteeen the
P'toPoll.ed aig.o'ti.thnlll. ana a tata'te 'teL~ that is capable of protecting a high
voltage line. The results of this part can be found in Chapter 8.
The conclusions of this study may form a next ll.tep. on the ~ to a
P.'tDtectton ll.cheme ~ll.ed on t~etti.ng.-~e P.'ti.nci.P.Lell..
-1-
2. Travelling waves and high-voltage lines
2.1. The line model
A high-voltage 4 line5 is a structure consisting of parallel conducting
wires, of towers to support the wires and of isolating chains to prevent
electrical contact between the wires and the towers. An example is depicted
in Figure 2.1.
Figure 2.1. A high-voltage line, consisting of 20 conductors. Six bundles of
3 conductors (6 phase conductors} are used to transport electrical energy .
Tile tlllO other conductors (shielding wires} are used to prevent a direct
lightning stroke to one of the phase conductors. Tile left set of phase
conductors can operate independently of the right set. Such a set of three
is called a circuit. The line shoun here is a "double-circuit line".
4
5
There are no internationally accepted standards to define the terms high voltage, extra high voltage and ultra high voltage. According to the IEEE standards board the term high voltage refers to voltage levels between 115 kV and 230 kV [Blackburn, 1987]. As the principles discussed in this thesis can be applied to any voltage level, the term "high voltage" is used here in a broader sense.
The term line is used here from the modelling point-of-view. All sets of electromagnetically coupled parallel conductors will be described as one transmission line . Such a line may consist, from the protection point-of-view, of several zones-to-be-protected.
-s-
A detailed electronagnetic analysis of an actual high-voltage line is
impossible and undesirable. As in any theoretical treatment of technical
systems we need an appropriate model which is
a. simple enough to yield basic insight and to allow fast calculations;
b. accurate enough to yield sufficient agreement with measured results.
Some remarks concerning the last item can be found in Section 3.6.
~~~~ ~ez ! . X .
• ~,'i';w-&/1
Figure 2.2. A si.x-}ilase transmission line:
Six paralleL conductors above a conducting
grCJl.llld.
The line model used in this thesis is characterized by the following
assumptions:
1. The high-voltage line is viewed as a homogeneous multi -phase
transmission line with constant parameters along the line, cf. Figure
2.2. Effects of towers and due to the sag of the conductors are
neglected. (Calculations concerning the electrical properties of towers
are given by Okumura and Kijima [1985], while Menemenlis and Zhu Tong
Chun [1982] propose a model that includes the sag of the conductors);
2. Only TEM waves propagate along the line. This requires that the
characteristic transverse dimensions are much smaller than the wave
length used. The TEM character implies that the total field can be
represented in terms of currents through the conductors and voltages
between them. The last assertion is due to the fact that the line
integral of the electric field vector evaluated between two points in a
transverse plane is the same for all paths in that plane;
3. Ground is considered as an additional conductor. With n aetaUtc
conductors we then haven independent currents iu, u=l .. n (the current
through the ground _being determined by Kirchhoff's current law) and n
independent voltages Vu, u=l. .n. between the metallic conductors and
ground (all other voltages can be expressed in terms of these voltages
with the aid of Kirchhoff's voltage law);
4. In due course suitable assumptions are introduced concerning the ohmic
losses of the conductors. Such assumptions are required to guarantee
the TEM character of the wave propagation at least in an approximate
way.
-9-
Sections 2.2 and 2.3. will discuss this model for the single-phase and
multi-phase line, respectively.
Assumption 2 applies if the condition
b < h/4. {2.1}
is satisfied [Lorenz, 1971]. Here i\ is the wavelength pertaining to the
frequency of interest and b is the maximum distance between the conductors
of the transmission line. Condition {2.1} results in an upper limit for the
frequency for which our model is valid. To estimate this upper limit we
consider the typical example b 50 m {maximum distance between metallic
conductor and ground} leading to a frequency limit of 1.5 MHz.
In the presence of losses the rEM-character of the wave propagation is
more or less disturbed. Lorenz [1971] has shown that this effect increases
with growing frequency. However it can be neglected for frequencies below
the limit given by (2.1).
Summarizing it can be stated that the model applies to the transmission
lines under study up to some hundreds of kHz.
2.2. The single-phase line
The telegraphist's equations for a lossless single-phase transmission line
have been derived from electromagnetic theory by Heaviside [1893]. They read
as
a i z
a v z
{2.2}
(2.3}
The constant parameters C and L denote the parallel {shunt) capacitance and
the series inductance per unit length, respectively.
If {weak) ohmic and dielectric losses have to be taken into account
(2.2) and (2.3} cannot be generalized in the time domain. Instead, we have
to confine ourselves to time-harmonic signals for which the phasors V and I
of voltage and current satisfy the pair of equations
d I -YV z
d v -ZI z
where G and R
conductance and
y G+jc.£
z R+jwL
denote the
series {ohmic}
{2.4}
(2.5)
frequency-dependent parallel {dielectric}
resistance per unit length, respectively6
6 A time-domain equivalent of (2.4} and (2.5) does not exist due to the frequency dependence of R and G, which represent integral operators in the time domain. It should be noted that in general also L and C can exhibit some form of frequency dependence.
-10-
Elimination of V or I leads to wave equations for current and voltage only
d2 V 2 w="Y v {2.6}
d 2 I 2 w="Y I (2. 7)
where "Y = J(R + jwL) (G + jc.>C) "propagation coefficient" . {2.8}
Equations {2.4} and (2.5) have travelling waves as solutions [e.g. King,
1955]
V(z) = y{+)exp(-"YZ) + v<-)exp{+"YZ)
I(z) = I(+}exp(-"Yz) + I(-)exp{+"Yz)
where y(+) = Z0
I{+) ,
y(-) = - Z0
I(-)
Z0 = ~ I G + jc.>C "wave impedance"
(2.9)
{2. 10}
{2.11}
(2.12}
(2. 13)
For a qualitative description of travelling-wave phenomena the losses
can be neglected, so that {2.2) and (2.3} apply. These equations have the
solutions
v(z,t) = v+(t - z/c) + v-{t + z/c) (2. 14)
i(z, t} = i+{t - z/c) + i-{t + z/c) (2. 15)
where v+(t) = Z0 i+{t} (2. 16)
v-{t} = - Z0 i ( t} (2.17}
c {LC}~ "velocity of propagation" (2.18}
Zo = (UC)~ "wave impedance" (2. 19}
Here v+(.} and v-(.) represent "travelling waves" in positive and negative
z-direction. From {2.14} through (2.17} it is possible to derive so-called
Bergeron s equations [Bergeron, 1950] for the terminal behaviour of a line
with length~ {cf. Figure 2.3):
v(~.t) + Z0 i{~.t) = v{O,t- ~/c)+ Z0 i(O,t- ~/c)
v(~.t) - Z0 i{~.t) = v{O,t +~/c) - Z0 i(O,t +~/c)
i(O,t}
+
v{O,t}
i{~. t)
+ v(~.t)
(2.20)
(2. 21)
Figure 2.3. A line of
finite length~-
-11-
For the study of protection algorithms we henceforth use the symmetrical
notation of Figure 2.4. Bergeron's equations then transform into the form
v 1 (t} + Zo i 1 (t} = v2(t + ~) - Z0 i 2(t + ~}
v1 (t} - Z0 i 1 (t) = v2(t - ~) + Z0 i 2(t- ~)
(2.22)
(2.23)
The quantities vv(t) + Zo iv(t) and vv(t) - Z0 iv(t) (v=l.2) will be
referred to as incoming and outgoing waves at port v, respectively.
Fi.gure 2.4. A finite
i,(t) ~ Une with traveLling
time ~. ... + v 1 ( t) v2(t)
2.3. The multi-phase line
In general a high-voltage line consists of n metallic conductors plus
ground. Such a system of (n+l} conductors can be described as an n-phase
transmission line through generalizing (2.4) and (2.5) [e.g. Bewley, 1933:
Wedepohl, 1963; Djordjevic et al., 1987]. The result reads as
{2.24)
(2.25)
The n-dimensional vectors y(P) and I(p) are formed by the phase voltages
(voltages between the metallic conductors and ground) and the phase currents
(currents through the metallic conductors), respectively. The nxn matrices
z(P) and y(P) are formed by the series (self or mutual) impedances and
parallel (self or mutual) admittances per unit length, respectively. Both
matrices z(P) and y(P) are symmetrical. Elimination of the current vector
from {2.24) and (2.25) gives rise to a second-order wave equation for the
voltage vector:
d2V{p) (p) (p) (p) ~=Z Y V {2.26)
Similarly the current vector satisfies
(2.27}
In the limit of a Lo~~Le~~ line we obtain a pure TEM wave for which a close
relation exists between z(P) and y{P), for the product of z(P) and y{P)
-12-
(which are both imaginary) equals the unit matrix times a scalar constant:
z(P) y(P) y(P) z(P) = 72 U
7 jw/c ,
(2.28)
where c denotes the velocity of light and U denotes the unit matrix. The
matrix equation (2.26} then represents a set of n ancoaPtea wave equations,
leading to n different waves having equal propagation coefficients (i.e.
equal velocities of propagation). the same holds for (2.27) describing the
phase currents. Olrrent and voltage for each phase satisfy {2.14) through
(2. 19).
For a to!l!lff line the matrix products z(P )y(P) and y(P )z(P) are no
longer diagonal so that (2.26) and (2.27) each represent n coaPtea wave
equations. To uncouple Equation {2.27) "component currents" I(c) are
introduced according to
(2.29)
where the. transformation matrix Q has to be chosen such that I(c) again
satisfies a set of uncoupled equations. Insertion of (2.29) into (2.27),
then leads to
d21(c) -1 y(P)z(P) Q 1(c) . w- = Q (2.30}
To achieve the above aim the transformation matrix Q has to be composed of
the (suitably normalized) eigenvectors of the matrix product y(P)z(P).
Equation {2.30) then transforms into
d 2 I(c) 2 {c) w- = 7 I {2.31)
where 72 = Q-1y(P)z{P)Q (2.32)
is a diagonal matrix. The general solution of (2.31) is
I(c){z) = exp(-7z} I{c+) + exp(72) I(c-) . (2.33}
From (2.33) together with (2.29) and (2.24) the general solution of the set
of equations (2.24) and {2.25) is found. It reads as
I(p)(z) = Q exp{-72) I(c+) + Q exp(72) I(c-). (2.34)
y(P){z) = [y(P)]-1
Q7 exp(-72) I(c+)_[y(P)]-1
Q7 exp(72) I(c-) (2.35}
The constant vectors I{c+) and I(c-) are determined by the boundary
conditions. The expression exp (7z) denotes a diagonal matrix whose elements
are formed by taking the exponent of the corresponding element of the
diagonal matrix 7Z·
In case all elements. except one, of I(c) equal zero, the resulting
current and voltage distribution travels along the multi-phase line without
-13-
changing its structure. Such a combination of voltages between and currents
through the conductors is called a mode or modal wave. So the elements of
the component current vector indicate which modes are present in the phase
currents. The current vector belonging to such a modal wave is an
eigenvector of the matrix product y(P)z(P), containing the coefficients of
the right-hand members of the coupled wave equations (2.27) for the currents
through the conductors. As expected the corresponding voltage vector is an
eigenvector of z(P)y(P), containing the coefficients of the wave equations
(2.26) for the voltages between the conductors.
Although {2.34) and (2.35) fully describe the wave behaviour of the
n-phase transmission line, some authors [e.g. Wedepohl. 1963] make use of
two transformation matrices instead of one. Apart from component currents
I(c), "component voltages" V(c) are introduced according to
y(P) = sv{c) . (2.36)
Such an introduction is only attractive if it is possible to derive
single-phase {frequency domain) equivalents of Bergeron's equations for the
component quantities. In that case each component can be described
independent of the others. From (2.34) and (2.35), together with {2.29} and
(2.36) the following equation is derived for the terminal behaviour of a
line of length~ (cf. Figure 2.3 and Equation 2.20):
y(c)(~) + z~c)I(c}(~) = exp(-~) {v(c)(O} + ~c)I(c)(O)} ,
where z1c} = s-t [y(P)r1
Q 7 "wave impedance matrix".
(2.37)
(2.38}
To obtain a set of single-phase equations, the voltage transformation matrix
S must be so chosen that the matrix ~c) becomes diagonal. It can be proved
that each matrix S leading to a diagonal matrix z~c), is a matrix of
eigenvectors of the matrix product z(P)y{P). Then {2.36) will uncouple the
wave equation for the voltage vector {2.26). Within the computer program EMTP {cf. Chapter 3) a voltage trans
formation matrix S is derived from Q through the equation
{2.39)
where st denotes the transposed of s. Such a choice will lead to a diagonal
matrix z1c) if y{P) and z{P) are symmetrical and all eigenvalues of z{P)y(P)
are different. For an actual line the first condition will always be met,
the second one might not be fulfilled in a very limited number of
situations.
-14-
As the wave impedance matrix Z~c) depends on the choice of the
transformation matrices, their normalization deserves special attention.
Within EMTP, the matrix Q is normalized such that for each column (i.e. for
each eigenvector) the sum of the squares of the real parts equals unity and
the sum of the squares of the imaginary parts is minimal.
Recently it has been shown [Brandao Faria, 1988] that some transmission
line configurations have a non-diagonizable matrix product y(P)z(P)_ In that
case the above theory fails and the resulting travelling waves are no longer
of the form given in (2.34) and (2.35). A more general solution of the
multi-phase transmission line equations, covering this nondiagonalizable
case is given by Brandao Faria and Borges da Silva [1986]. Such a
degeneration is always 11mi ted to an isolated frequency for a lossy line.
Whether the degeneration also appears on a physical line or is just a
consequence of the approximations of the model is not yet clear [Luis
Naredo, 1986; Olsen, 1986].
2.3.1. The balanced single-circuit line
The balanced single-circuit 1 ine is a hypothetical line where all three
metallic conductors are considered to behave equally. Since in that case the
conductors need to have equal distances to each other and to the ground
plane, the balanced single-circuit line is physically impossible7 In
reality the differences in distance are relatively small so that the
balanced single-circuit line is useful as a first-order description. Due to
the symmetrical nature of the {hypothetical) structure the resulting
equations are of a simple form. These equations will be used as a basis for
most of the protection algorithms discussed in forthcoming chapters. For a
balanced single-circuit line the z{P) and y{P) matrices are of the following
structure (s stands for "self", m for "mutual"):
z zz l [y yy
z{P)= s m m
y{P) s m m
z z z • y y y {2.40) m s m m s m z z z y y y m m s m m s
The matrix products z{P)y(P) and y{P)z{P) are of the same symmetrical
structure. The eigenvalues 712 (1=1,2,3) are found as
2 71 (Zs + 2Zm){Ys + 2Ym)
732 = (Zs - Zm){Ys- Ym)
7 Such a symmetry is, however, possible for a three-phase cable.
(2.41)
{2.42)
-15-
while a general expression for the matrix of eigenvectors reads as
(2.43)
In this case there is a "homopolar" or "zero sequence" wave with equal
currents through all three phase-conductors. closing through ground and two
"aerial" waves restricted to the phase conductors. An often used
transformation matrix satisfying {2.43) is
1 "] 1
:.] -l 1 Q 1 a2 a2 Q =3 a2 (2.44)
1 a a a
with a=exp (j2Jr/3); Voltages and currents under this transformation are
known as "symmetrical components".
Another modal transformation, used in algorithms for travelling
wave-based protection is the following one:
[
1 1 2
Q = t 1 -2 -1
1 1 -1
(2.45)
By using this transformation, component quantities are derived from
(measured) phase quantities through simple calculations. Figure 2.5 shows
the current distributions for this transformation.
0 ® 0
0 0 0 0 0 ®
X X X
2.3.2 The balanced double-circuit line
Figure 2.5. Current distribu
tions corresponding
homopotar unue (left)
aerial unues on a
stngte-circutt line.
to the
and the
balaru:ed
A balanced double-circuit line consists of six (metallic) phase conductors
and one reference conductor (ground). The phase conductors are divided into
two groups of three. called circuits. Each phase conductor is considered to
have the same distance to ground. The distances between each pair of
conductors within one circuit are equal. so are the distances between a
conductor in one circuit and a conductor in the other circuit. Again this
situation is physically impossible but it provides us with a simple line
-16-
model. For the balanced double-circuit line z<P) and y{P) are of the
following structure {d stands for "double circuit")
z z z zd zd zd s m m
z z z zd zd zd m s m
z z z zd zd zd m m s z{P)
zd zd zd z z z {2.46) s m m
zd zd zd z z z m s m
zd zd zd z z z m m s
y y y yd yd yd s m m
y y y yd yd yd m s m y y y yd yd yd m m s
y{P) yd yd yd y y y {2.47) s m m
yd yd yd y y y m s m
yd yd yd y y y m m s
Three different eigenvalues are found:
2 {Z + 2 z + 3 Zd) {Y + 2 y + 3 Yd) {2.48) "'t s m s m 2 {Z + 2 Zm - 3 Zd) {Y + 2 y - 3 Yd) {2.49) "12 s s m 2 2 2 = 'Ys2 = {Z - z ) {Y - Ym) {2.50) "!3 "14 "'s s m s
with the following general expression for the matrix of eigenvectors:
Q, Qt2 Qt3 Qt4 Qts Qt6
Q, Qt2 Q23 Q24 Q25 Q26
Q, Qt2 Q33 Q34 Q35 Q36
Q Q, -Qt2 Q43 Q44 Q45 Q46 {2.51)
Q, -Qt2 Q53 Q54 Q55 Q56
Q, -Qt2 Q63 Q64 Q65 Qss
where Q1j + ~j +Q3j = 0 and Q4 j + ~j + ~j = 0, j = 3,4,5,6.
"ft is the propagation coefficient of the "homopolar wave", "{2 of the
"double-circuit wave" going "up" in one circuit and "down" in the other. "{3
through "'s correspond to the "single-circuit waves" closing inside each
circuit. An example of such a transformation is found as {cf. Figure 2.6)
-17-
1 2 4 0 0 1
1 -4 -2 0 0 1 1 -1 -1 -1
Q=1/6 1 2 -2 0 0 Q-1_ . - 0 -1 1 0 0 0 (2.52)
1 -1 0 0 2 4 0 -1 0 0 0
1 -1 0 0 -4 -2 0 0 0 0 -1
1 -1 0 0 2 -2 0 0 0 1 0 -1
0 0 0 ®
0 0 0 0 0 0 e @
""" >< X :.
@ 0 0 0
0 0 0 0 @ 0 0 0
0 @ 0 0
0 0 0 0 0 0 @ 0
Figure 2.6. Current distributions corresponding to the homopoLar wave (top
Left), the doubLe-circuit wave (top right) and the singLe-circuit waves on a
balanced double-circuit line.
2.4. Travelling waves in high-voltage networks
2.4.1. A subdivision of transients, according to their origin
The transients occurring in a high-voltage network can be divided into three
groups, according to their origin.
1. ~~~~eat~ caa~ed ~ ~~LtchLn~ oPe~tLon~ Ln the netwo~
These can be called on-purpose operations, because there is always
someone or something giving a conunand to open or close the switch.
Typical examples are:
energizing an unloaded line:
deenergizing a short-circuited line:
connecting two separated high-voltage networks.
-IS-
2. ~~an~Lent~ ha~Ln~ theL~ caa~e out~Lde the net~k
High-voltage lines consist of very long wires (tens of kilometers or
more). These are very good antennas, so radio signals are easily picked
up. Other examples are very low frequency (0.01 Hz} currents induced by
ionospheric currents [e.g. Pirjola and Viljanen, 1989] and injected
signals with a frequency of some kHz used for communication purposes. A
more spectacular case is a lightning stroke to a high-voltage line or
somewhere in the vicinity of a high voltage line.
3. ~~~Lent~ caa~ed log. taait LnLUatLoo
Faults are inadvertent, accidental connections between phase wires or
between one or more phase wires and ground [Blackburn, 1987]. Causes
for faults (short circuits} are lightning (induced voltage or direct
strike}, switching overvoltages, wind, ice, earthquake, fire, falling
trees, flying objects, physical contact by animals or human beings,
digging into underground cables and so on.
These three groups will be further discussed in Section 2.4.3 through 2.4.5.
A number of studies have been performed during the last years to
determine the number of transient phenomena that occur in a high-voltage
network. All studies make use of a transient recorder that is· triggered by a
sudden change in voltage or current. The number of recorded phenomena
depends largely on the kind of measurement and on the position in the
network. Further the seasons turn out to have influence on the frequency of
recorded phenomena.
During a three-year monitoring period in a 500 kV substation and in a
138 kV substation a total of 341 phenomena has been recorded [EPRI, 1986];
190 of them were caused by switching operations, 114 by lightning strokes
and 37 by faults. A study by EdF (Electricite de France) in the 400 kV
network [Barnard et al., 1984] showed 93 transients caused by faults and 19
caused by switching operations in a period of about 2 years. Malewski,
Douville and Lavallee (1987] found a total of 300 transient phenomena during
a two year monitoring period in a 735 kV substation. A four-month
(july-october) monitoring period in the Dutch 220 kV network yielded 39
lightning-caused transients (27 occurring within one week), 1 due to a fault
and 3 due to switching operations [Koreman, 1988]. Johns and Walker [1988]
found 93 transient phenomena within 39 days (December '83 till February
'84), 29 of which occurred within 3 hours.
2.4.2 Superimposed quantities
A high-voltage network is fed by 50 or 60 Hz sources (in the remainder only
50 Hz will be used). During an undisturbed situation all voltages and
currents in the network are sinusoidal in time. The sinusoidal voltages and
-19-
currents as existing before a certain disturbance will be called
"un.di,(l.tu'tl.ect ~titLe().". After the disturbance this term denotes their
continuation, i.e. the fictitious voltages and currents that would have
occurred without disturbance.
After a transient due to some disturbance a new sinusoidal state will
be reached which may or may not differ from the undisturbed state. To study
the transient phenomenon it is sometimes attractive not to use the actual
voltages and currents but "(l.U/>e'tLIII(Jo(l.ed ~titLe().". Their values are
defined as the difference between the actual and the undisturbed values.
The disturbance can be any of those described in the previous section.
We illustrate the concept of superimposed quantities by means of a fault on
a single-phase line. The undisturbed network is shown in Figure 2.7.
Figure 2.7. Undisturbed values.
Undisturbed voltages at line terminal A. at the future fault position F
and at line terminal Bare given as
VA (t) =VA sin (~Uot + <PA) , (2.53}
VF (t) = VF sin {~Uot + <PF) • (2.54)
VB ( t) =VB sin (~Uot + <PB) (2.55)
respectively.
Figure 2.8 shows the network situation after the occurrence of the
fault at time-zero. Actual voltages at A, F. and Bare denoted by vA(t),
vF(t), and vB(t), respectively.
t:(tl F
Figure 2.8. Actual values: uF (t) = 0, t)O.
-20-
The superimposed quantities, being the difference between the actual
values of Figure 2.8 and the undisturbed values of Figure 2.7 are given in
Figure 2.9.
A . F
Figure 2.9. Superimposed vatues: vF (t) = 0, t<O.
Superimposed voltages at line terminal A, at the fault position F, and
at line terminal B are given as
VA (t) =VA (t) - ~A (t) (2.56)
{ -~F (t)
t < 0 VF (t) = VF (t) - ~F (t) t ) 0 (2.57)
VB (t) = VB (t) - \IB (t) {2.58}
respectively.
2.4.3. Transients caused by switching Olli!rations
Figure 2.10. Travetting waves initiated during tine energizing.
As an example Figure 2.10 shows the configuration for energizing one of the
circuits of a double-circuit line. Closing the circuit breaker (1) leads to
voltage jumps on both sides of it. This sets up travelling waves into the
line to be energized (2) as well as into the feeding network (3). At the
remote line-terminal (4) the circuit breaker in the line-to-be-energized is
open. At this discontinuity a part of the wave is reflected (5) and through
the coupling with the second circuit a part travels into the network behind
the remote line-terminal (6). The reflected wave (5) is again reflected at
the circuit breaker (1} and so gives rise to multiple reflections.
Figure 2.11 shows the voltages during 1 ina-energizing as measured on
the line side of the open circuit-breaker (4).
-21-
f 1.2
vr (pu)
0
0,8
f 1,
~r\1 Vs ~pu) -
1ms 0,4
lo,4 vto
(pu)
1,2
2.4.4. Transients caused by lightning
Figure 2.11. Voltages at the open
line terminal measured during
line energizing. Adopted from
[Kersten and Jacobs, 1988]
There are three different mechanisms for a lightning stroke to interfere
with a high-voltage line; dependent on the distance between the position of
the stroke and the phase conductors.
1. ~ LLghtnLng ~t~oke ~oaemhe~e Ln the ~LcLnLtv ot the LLne
This can be a stroke between a cloud and earth as well as a stroke between
two clouds. In most cases the waveform of the induced voltages is bipolar
with substantial amplitude being attained in the first few microseconds.
Theoretically amplitudes higher than 1 MV are possible for a 100 kA stroke
at a distance of a few hundreds of meters from the line [Eriks~on, 1976].
Lightning strokes to earth of high current amplitude in the vicinity of a
high-voltage line are rare due to the attractive effect of the line. But
high objects (e.g. trees) close to the line can increase this possibility.
Measurements show induced voltages up to 200 kV [Cornfield and Stringfellow,
1974].
-22-
De la Rosa et al. [1988] have installed a single-phase line in Mexico,
in a region with a high ground-flash density. Their measurements show that
lightning strokes tens of kilometers away from the line can induce voltages
of some kV. An overvoltage of 244 kV has been measured for a stroke at a
distance of 4.5 km. It appears that a stroke next to a line will create the
highest overvol tage some distance further down, which can be explained
electromagnetically [Cooray and De la Rosa, 1986].
l v
(kV)
-40
-SOL---------------------------------------------------~
Figure 2.12. TypicaL voLtage shape due to a Lightning stroke dose to a
high-vottage tine, adopted from [Koreman, 1988}.
A typical shape of the voltage pulse due to a nearby stroke is shown in
Figure 2.12. The superimposed voltages for the three phases are shown, with
the vertical axes shifted with respect to each other.
2. d LLghtnLng ~t~oke to a ~hLeLdLng ~L~e o~ to a t~e~
To prevent dangerous lightning strokes to phase conductors, shielding wires
are used. The so-called electro-geometric theory describes how a lightning
stroke develops [e.g. Eriksson, 1976]. According to this theory only
lightning strokes below a certain current amplitude can reach the phase
conductors. So all high-current strokes will reach the shielding wire or a
-23-
tower. This causes intense electromagnetic fields, leading in a few cases to
flashovers between phase conductors and ground.
When the lightning stroke does not lead to such a flashover the three
phases are influenced in about the same manner. i.e. the induced voltages
(and currents) in the three phases are of about equal shape and magnitude.
Mainly a homopolar wave is initiated. The voltage amplitudes are tens of
kilovolts.
3. Ell Ughtni.ng o.t'!.oke to a Pkao.e condu.ctO'l-
When the lightning strikes directly to a phase conductor. this will cause a
large voltage between that conductor and the other conductors {including
ground). If this voltage exceeds the breakdown voltage of the insulation a
flashover wi 11 occur leading to a fault. According to electro-geometric
theory such a flashover will never occur if the shielding wires are
correctly positioned. A direct stroke is often called a shielding failure,
although the word is sometimes reserved for direct strokes leading to a
flashover.
Figure 2.13 shows voltages due to a direct stroke leading to a fault.
They have been measured in a substation about 10 km from the fault. In phase
1 a negative spike is visible followed by a transient due to the
single-phase fault. At the fault position the spike must have been much
higher. The amplitude reduction takes place on the 10 km line between the
position of the stroke and the substation and in the substation between the
line being hit and the line being monitored. The negative slope of the spike
corresponds to the lightning current, the positive slope corresponds to the
flashover between the phase being hit and ground.
A stroke not leading to a fault causes a high voltage spike in the
phase that has been hit . The other phases show a 1 ower vo 1 tage spike.
Whether the spikes in the other phases are of the same polarity or of
opposite polarity is still a matter of debate. The coupling between the
phases would lead to a spike of equal polarity [e.g. Anderson, 1985] but the
release of the induced charge would lead to spikes of opposite polarity.
Figure 2.13 shows spikes of opposite polarity.
Kinoshita et al. [1987] present measurements of the simultaneous
occurrence of a positive spike in one phase and a negative in another. This
is caused by a negative stroke followed, almost immediately, by a positive
stroke somewhere else in the same cloud. If both strokes hit a phase
conductor the above phenomenon can be observed.
-24-
Q5 -1,0 t(ms}
t1 fase2
Q5 -1,0 Hms)
~~--------------------------------------------------~
Figure 2.13. Transient voltages caused by a. lightning stroke to a. JJw.se
conductor leading to a. Flashover. adopted from [Koreman. 1988].
2.4.5. Fault transients
A fault (short circuit) on a high-voltage line, normally implies a voltage
jump at the fault position. This voltage jump leads to travelling waves that
can be detected in a large part of the network. All protection principles in
this study use these travelling waves to retrieve information from the
fault.
In most studies of fault transients the resistance of the conducting
path at the fault post tion is neglected. Although there is always some
resistance present, the approximation is certainly acceptable for solid
faults or those with only a small arc distance. An analysis for longer arc
distances is given by Cornick. Ko and Pek [1981]. These authors also show
that the fault initiation (due to the spark) takes place within one
microsecond. After that it takes a few microseconds for the arc to develop.
During this time the arc voltage drops from 100 V/cm down to about 10 V/cm.
For arcs across wooden structures (wood-pole-lines, flashover to a tree) the
arc voltage-gradient drops from 800 to SO V/cm.
-25-
As long as the pre-fault voltage is large compared to the post-fault
(arc) voltage, the latter can be neglected. For an arc length of 10 meter
and an arc-voltage gradient of 10 V/cm, the pre-fault voltage must be much
higher than 10 kV. As the systems studied have voltage amplitudes of
hundreds of kilovolts, the arc voltage will not be of great influence on the
fault transients. Of course this is no longer true in case of a pre-fault
voltage close to zero. But then a high resistive fault (= long arc distance)
will (generally) not occur.
Faults on high-voltage lines can have many causes. The main cause for
faults on the high-voltage lines is lightning. According to a study of a
number of networks all over the world, about 40% of all faults are
lightning-caused [Anderson. 1985]. This value shows a large deviation for
different utilities. A large part of the lightning-caused faults are
multi-phase or double-circuit. According to Sargent and Darveniza [1970],
40% of the lightning-caused faults on double-circuit lines are double
circuit faults. Figure 2.14 shows some double-circuit faults caused by
lightning. Other important fault causes are storm (10-30%} and galopping
conductors [Mackay, Barber and Rowbottom, 1976; Leppers, 1985].
R w X 0 0 0 X 0 0 X
s v 0 0 X X 0 0 0 0 X X
T u X X X 0 X 0 X 0 0
Figure 2.14. Examptes of doubte-circuit fautts caused by tightning [adopted
from Sargent and Dnrventza, 1970]. x:fautted phase, o=non-fautted phase, the
phase order is shown on the teft.
From a number of studies the following distribution of faults among
different types can be concluded [Anders, Dandeno and Neudorf, 1984, Light,
1979; Recker, Reisner and Waste, 1986; Liew and Darveniza, 1982].
Single-phase-to-ground 7o-90%
Phase-to-phase 10-20%
Two-phase-to-ground and three phase: 5-15%
single-circuit faults
Double-circuit faults
75-98%
2-25%
-26-
3. Network modelling
Chapter 2 dealt with the transition from a high-voltage line (an actual
physical inhomogeneous structure) to the simplified model "transmission
line". In this chapter we further elaborate the concept "multi-phase
transmission line" and present a number of pertinent data which are in
current use in modern computer programs. Two of these programs (cf. Section
3.2 and 3.3) have been used in this thesis to determine transient voltages
and currents in a high-voltage network. Such simulations are required to
test protection algorithms, as described in forthcoming chapters.
3.1. Impedance and admittance matrices
Extensive analysis is available concerning the determination of the z(P) and
y(P) matrices for configurations consisting of a set of thin metallic
conductors (cf. Figure 3.1). The basic situation studied in this context is
that of a single circular conductor above a homogeneously conducting
half-space (cf. Figure 3.2). Parameters for two or more metallic conductors
are approximately evaluated under the assumption that the electromagnetic
field can be viewed as a linear combination of the individual fields of the
single-conductor configurations. Minor possible refinements reckoning with
the vertical dependence of the conductivity of the ground (as discussed by
Wedepohl and Wasley [1966] and by Nakagawa, Ametani and Iwamoto [1973]) will
be left out of consideration.
'-0 0
transmtsston ltne consisting of three 0 Figure 3.1. The cross-section of a
conductors and a conducting half-space.
l///////J/l/77
Carson [1926] was one of the first who evaluated transmission line
parameters. He found expressions for the elements of the impedance matrix
z(P) that nowadays serve as a reference under the name "Carson's
equations". These are used in most modern computer programs for the analysis
of transients in high-voltage networks, including the programs used in our
study. The elements of the matrix y(P) are determined from .the electrostatic
fields.
Similar expressions for the transmission line parameters have been
found at about the same time by Rlidenberg [1925], Mayr [1925] and Pollaczek
[1926]. Whereas these authors only give integral expressions, Carson [1926]
-27-
rewrites his integral solution in the form of fast converging infinite
series. This series solution has certainly contributed much to the
widespread use of Carson's equations.
_yz
/
X
~-------------~--------~/
h
Figure 3.2. Configuration studied by
Carson [1926].
The configuration under study is depicted in Figure 3.2. Following
Carson [1926] {and in conformity with Chapter 2) we consider a time-space
dependence of the form exp(jwt-?£), where~ is the propagation coefficient
to be determined. While y(P) is assumed to have its {lossless, i.e.
imaginary) electrostatic value, expressions for the {complex) elements of
z(P) are evaluated under several low-frequency approximations.
In later years other authors have found expressions for the line
parameters under less simplifying approximations. Wise [1948] finds that the
elements of the admittance matrix y(P) have to be corrected as a consequence
of the finite conductivity of the ground. However his correction terms are
small for normal configurations and frequencies below 1 MHz [Hedmann, 1965].
Wedepohl and Efthymiadis [1978] evaluate the electromagnetic field due to a
current with an exponential time-space dependence and find a "modal
equation" which is solved numerically [Efthymiadis and Wedepohl, 1978]. For
practical high-voltage lines and frequencies up to a few hundreds of kHz,
their value of the propagation coefficient ~ again does not considerably
differ from that found from Carson s equations. Wait [1972] derives an even
more general modal equation that is solved by Olsen and Chang [Olsen, 1974;
Olsen and Chang, 1974; Chang and Olsen, 1975]. Contrary to Wedepohl and
Efthymiadis [1978] they find more than one solution. It appears that a
single wire above ground can support two discrete modes (apart from a
continuous mode spectrum). One of the discrete modes {the "transmission line
mode") corresponds to Carson's solution, the other (the "fast mode") is
associated with a high phase velocity and a low damping. According to Olsen
and Pankaskie [1983] it is safe to assume that only the transmission line
mode is present when
h ( i\/20 .
-28-
(3. 1)
where h is the height of the conductor and A is the wavelength pertaining to
the frequency under consideration. For a height of 50 meters a limit of 300
kHz is found. This admits the final conclusion that for a high-voltage line
Carson's equations are valid up to a few hundreds of kHz.
3.2. The computer program EMTP.
3.2.1. The solution method used in EMTP
The "Electromagnetic transients program" (EMTP) is a universal computer
program for the calculation of electromagnetic transients in high-voltage
networks. It has been developed in the late sixties by Bonneville Power
Administration, Portland, Oregon and the University of British Columbia,
Vancouver, Canada. After a few years it was in widespread use through
computers all over the world, where many people provided the program with
extensions. This rapid growth in use as well as in size can be described to
the compatibility (it only uses standard FORTRAN) and the availability (it
was public domain software). Although the term EMTP is already used as a
standard, there still exist many program versions. In order to create one
real standard version, Leuven EMTP Center8 has started to co-ordinate all
improvement efforts. As long as this standard does not exist, it is
necessary to tell what version has been used. All EMTP calculations
described in this thesis are performed with the M39 version on an
APOLLO-domain computer.
EMTP is able to calculate voltages and currents in networks consisting
of resistances, inductances, capacitances, single and multi-phase
~-circuits, transmission lines9 and other elements. Each network element is
represented by means of an equation that relates a node voltage at time t to
node voltages and branch currents at times t-kAt, k=l,2, ... By combining
all element equations and the pertinent Kirchhoff's equations a matrix
equation is derived for a network of n nodes:
G.v(t) = j(t) hist(t) - Ge e(t)
8 Leuven EMTP Center Kard. Mercierlaan 94 3030 Heverlee Belgium.
(3.2)
9 In the EMTP-related literature the name "distributed-parameter lines" is used instead of transmission lines.
-29-
where v( t} vector of unknown voltages,
j(t} vector of current sources,
e(t} vector of voltage sources,
hist(t} vector of "history terms" taking into account voltages
from the past,
G, Ge nxn matrices determined by the network topology and the
values of the elements.
Starting from a (given} situation voltages are calculated for equidistant
points in time. Finally, the currents can be determined with the aid of the
element equations. More details on EMTP are given by Dommel [1986].
3.2.2. The LINEa:>NSTANTS routine
32.4 31.4
0 24.4 0
• • s 17.4 w
• • • • R ~T v u
/}\0.~ \tf..--~ , __ .7
('I) ~~ ,...: ...
Figure 3.3. Cross-section of
a specific
tine. The
transmission
open circLes
correspond to the shielding
wires, with an outer
diameter of 2.2 em and an
inner df.am.eter10 of 0.8 em.
The cLosed circLes corres
pond to a bundLe of three
conductors as sholm. in the
insert. Each conductor has
outer and inner diameters of
2.8 and 0.8 em, respectiveLy. ALL dimensions are given in meters.
From Carson's equations it is possible to determine impedance and admittance
matrices for a multi-phase transmission line. This is done by EMT~ s
LINECONSTANTS routine. We illustrate the routine by means of the 20-phase
transmission line depicted in Figure 3.3. It is a model of the high-voltage
line of Figure 2.1. The average height of the sagging conductors in the
transmission line model is determined as:
h = t ht + ~ hm ' (3.3}
10 Within EMT~ s LINEmNSTANTS routine wires are considered to be tubular conductors with certain inner and outer diameters. In reality the wires consist of a good conducting mantle and a core with a lower conductivity. Due to eddy-current effects the current will concentrate in the mantle.
-30-
where ht is the height at the tower position and hm is the height midway
between two towers. The resistivity of the ground is taken to be 100 Qm,
which is an acceptable value for over 50% of the world land area. Higher
values might be needed for mountainous terrain and permafrost areas
[OCIR.19SS]. The 20 x 20 matrices y(P) and z(P) are reduced to 6 x 6
matrices by assuming:
the voltage between a shielding wire and ground is zero;
- the voltage between two conductors in one bundle is zero.
From the resulting 6x6-matrices a current transformation matrix Q, a
(diagonal) wave-impedance vector zic) and propagation coefficients 7 are
determined, according to the theory of Section 2.3.
Each column of Q is normalized such that the sum of the squares of the
real parts equals one and the sum of the squares of the imaginary parts is
minimum. In a next step the imaginary parts are neglected. leading to the
following current transformation matrix for the transmission line depicted
in Figure 3.3:
0.46 -0.30 0.53 0.25 0.58 0.16
0.24 -0.20 -0.38 0.54 -Q.35 0.47
Q 0.48 -0.61 -0.27 -0.38 -0.20 -o.51 (3.4)
0.48 0.61 -Q.27 0.38 0.20 -0.51
0.46 0.30 0.53 -0.25 -Q.58 0.16
0.24 0.20 -0.38 -Q.54 0.35 0.47
This matrix considerably differs from that for a balanced double-circuit
line (2.51). Obviously the transformation matrices for a balanced line
cannot be applied to nonbalanced lines. Nevertheless the transformation
matrix for a balanced 1 ine turns out to be sui table for the protection
algorithms to be discussed in forthcoming chapters.
3.2.3. The .!MARTI SETUP routine
A number of numerical transmission-line models are available within EMTP.
The model applied in this study is the ".}MARTI SETUP" proposed by Marti
[1982]. It is the most detailed model available. Whether its results are
close enough to reality is still a matter of debate [e.g. Empereur and
Somatilake, 1986; Lima, 1987; Marti, et al., 1987; Ametani, 1988]. This
question can only be answered by performing field tests (cf. Section 3.6).
The JMARTI SETUP incorporates the frequency dependence of modal wave
impedances and propagation coefficients. The transformation matrix Q is
considered to be frequency independent. (The debate concentrates on this
approximation that might not be valid for low frequencies.)
-31-
In Section 2.3 Bergeron's equations are given for a 1ossless frequency
independent line (2.22 and 2.23). The JMARTI SETUP uses a more general form
[Meyer and Dommel, 1974]. For the single-phase line of Figure 3.4. the
following equations hold:
B1 (w} = H(w).F2{w}
B2(w} = H{w).F1 (w}
where F1 (w} = V1 {w)
F2(w} = V2(w}
+ Z0 {w}
+ Zo(w}
B1 (w} = V1 (w} - Z0 (w}
B2(w) = V2(w} - Zo(w)
H(w} = exp (-'#}
11 {w)
12{w}
11 {w} ,
12(w}
;!! , -y(w) , Z0 (w}
"incoming waves"
"outgoing waves"
"weighting function".
(3.5}
(3.6}
Figure 3.~. SingLe-phase
line of Length ;!!; vot t
age and current defini
tions for EKTP' s JlfAKfi
SErUP.
As EMTP uses a time-domain description to calculate voltages and currents,
some simple 1 ink is required between the frequency-domain description of
(3.5) and (3.6} and its time-domain description. To this end the wave
impedance Z0 (w) is approximated by a rational function of jw with real
poles. K
+-njw+pn . {3.7)
Satisfactory approximations can be obtained with orders n between 5 and 15.
Figure 3.5. Repre
sentation of uuve
impedance in JlfAKf I
SETUP. This impedance Z0 {<.J) can be realized by means of a series connection of
resistance-capacitance blocks. as shown in Figure 3.5, where
Ro = Ko .
Ri = K/pi
ci = 1/Kt
i
i
1. .n
1. .n
-32-
The time-domain equivalent of Z0 (w)I(w) is obtained by injecting a current
i(t} in the network of Figure 3.5.
The weighting function H{w} is approximated through
. [ H, H2 H ] H(w) = e-Jc.YT jw+q
1 + jw+q
2 + .. + j;~ .
where T is the travelling time of the highest frequency.
following weighting function in time domain {the "impulse
h(t} = [ H1exp{-q1 {t-r}) + .. + Hmexp(-~{t-r})] U(t-r) ,
(3.S)
This leads to the
response"):
(3.9}
where the step function U{t) is zero for t(O and unity for t>O. According to
Semlyen and Dabuleanu [1975] the time-domain equivalent of {3.5) can be
written, by using (3.9) as
b 1 (t) =a b 1 (t-At} +X f 2 (t-r) + ~ f 2 (t-r-At) , (3. 10)
where b 1 (t) and f 2 (t} are the transform of B1 (w) and F2 (w), respectively.
The parameters a, X and~ depend on the values of Hi' qi and the time step
At. This "recursive convolution technique" accounts for a considerable
reduction in computation time . The above procedure is used for every mode
to determine modal voltages and currents. The node (phase) voltages and
branch (phase) currents are found by using the transformation matrices Q and
S. In our example the value of the transformation matrix Q for a frequency
of 5000 Hz has been used.
The parameters describing a high-voltage line are, for each mode:
the wave impedance for very high frequencies (K0
in (3. 7}); a number of
residues (K1 .. Kn) and poles (p1 .. pn) for the wave impedance; the travelling
time for the highes frequency (T in (3.S)); a number of residues and poles
for the weighting function; and the current transformation matrix Q. Table
3.1 gives those parameters for the line of Figures 2.1 and 3.3. To describe
this line (100 km length) a total of 306 parameters is used.
3.3. The computer program TWONFIL
The simulation capabilities of EMTP are almost unlimited. On the one hand
this makes it very suitable to analyze transient phenomena in detail. On the
other hand it becomes less suitable for a quick overview of a large number
of situations. To overcome the latter limitation we developed the computer
program TWONFIL (Iravelling !aves Qn Honbalanced frequency Independent
transmission Lines). It consists of a number of PASCAL procedures for calcu
lating travelling waves due to all kinds of faults and switching operations.
The reflection and transmission of waves at various discontinuities as well
as voltages and currents at the relay position can be analyzed.
-33-
-1 II 5'14.8 -. 75E3 . 11£5 '32£5 '70£6 . 53£7 . 15ES . 2JE6 .14£6 '23£6 '36£6 '69£6
.JOEl .29£2 .52E3 .18£5 .99£5 .61E6 .19E7 .47£7 .90£7 .12£8 .24£6 II .1901E-QJ
.28 .12E2 .20£2 .55£2 .55E3 -.13£4 .OOE4 .18£5 .27£7 .29£9 -.29E9
.5iE2 .18£4 .19£4 .28£4 .95£1 .21£5 .21£5 .41£5 .14£6 .13£6 .13£6 -2 12 379.2 .17£4 .20£3 .43E3 .20£3 .61E2 .19£3 .44£1 .12£6 .64£6 '17£7 .45£7 .26£6 .43EI .7JEI .11E2 .19£2 .32E2 .88E2 .18£4 .18£5 .28£6 .72£6 .19£7 .11£6
6 .1721E-()3 .JJ£5 .41£5 .35£6 .39E1 .63EI 10£2 '13£6 .21E6 . 48E6 . 11£7 .11E7 .11£7 -3 ll 259.3 . 19£4 . 26E3 . 83E3 .10E3 . 26E3 . 28£3 . 69£3 . 56E4 . 11£5 . 45£6 .JOEl .45£1 .95EI .17E2 .41£2 .5iE2 .60£3 .47£4 .12£5 .39E6
12 . 1701E-()3 .47E2 .78EI .15£3 .55£3 .17£4 .67£4-.53£6 .70£6 .21£6 .43£6 .liE! -.liE! .91£4 .16£4 .29£5 .11£6 .83£5 .17£6 .20£7 .17£7 .21E7 .33£9 .22£8 .22£8 -1 ll 264.1 .15E4 .72E2 .66E3 .JOE3 .19E3 .17£3 .ISE3 .83£2 .17£3 .35E1 .50£5 .33£1 .45£1 .SSE! .11E2 .20£2 .30£2 .50£2 .81E2 .16E3 .JOE4 .41£5
9 .1719E-oJ .23£2 .JOE3 .31E3 .17£4 .63£4 .13£7 -.10£7 -.51£7 .27£6 .37£4 .46£5 .52£6 .31£6 .28£6 .18£7 .18£7 .51£9 .33£6 -5 II 247.8 .11£4 .51E3 .72E3 .24£3 .10E3 .18£3 .16E3 .78£2 .14£3 .27£4 .42£5 .29EI .48£1 .OOEI .11E2 .18£2 .31£2 .48£2 .78£2 .14£3 .21£4 .37£5
10 .1681£-()3 .10£2 .91£2 .48E3 .76£3 .28£4 .41£5 .44£6 .53£6 .28£7 .ISES .22£4 19£5 .99£5 .18£6 .15E6 .10£7 .62£7 .33£7 .12£8 .39E8 -6 13 273.5 .12£4 .25E3 .77£3 .73E3 .41E3 .45E3 .14£3 .19£3 .26£4 .47£4 .11£5 .52£6 .79Z6 .31El .45El .95£1 .21£2 .32E2 .58£2 .78£2 .17£3 .21£4 .39E4 .ll£5 .43£5 .66E6
12 .1743£-()3 .78E1 .57E2 .61£2 .44£3 .19£4 .39£4 .99£5 .ll£6 .19£7 .20£7 .53-.53 .11£4 .11£5 .10£5 .61£5 .10£6.82£5 .13£7 .62£6 .35£7 .77£7 .31E8 .34£6
.460!5799 -.29982807 .52965392 .24901443 .58179180 .15831060
.21073739 19463382 -.39216777 .51208824 -.34661831 .46861377
.47999595 -.61009901 -.27095114 -.390J0143 -.20335198 -.50531068
.47999596 .61009901 -.27095114 .390J0143 .20335198 -.50531068
.46015799 .29982907 .52965392 -.24901443 -.58179190 .15831060
.21073739 .19463392 -.38216777 -.5420S824 .34661831 .46861377
Table 3.1. Parameters
used within E1ffP to
describe the high
voltage tine of Fig
ure 2 .1. Given are
successively (for
each IIIOde): the IIIOde
number, the number of
poles to represent
the wave impedance,
the wave impedance
for very high fre-
quenctes, residues
and poles for the
wave impedance, the
number of poles for
the weighting func
tion, the trave t t in.g
ttme for 'the highest
frequency, residues and poles for the weighting function. The last six tines
give the current transformation matrix.
3.3.1. A general description of TWONFIL
Within TWONFIL. a line is described in time domain by means of the modal
wave impedance matrix Z~ c) and the transformation matrices Q and S=Qt - 1 •
These matrices are evaluated by using EMTYs LINEOONSTANTS routine and are
approximated by omitting their imaginary parts. Further the propagation of
each modal waves is considered to be undamped and without dispersion. The
modes only differ with respect to their propagation velocities and their
wave impedances. This way the existing nonbalance of the multi-phase line is
incorporated. The propagation of each modal wave can now be described by
means of the simple form of Bergeron's equations (2.22 and 2.23).
The TWONFIL model is a modern version of Bewley's lattice diagram
[Bewley, 1963]. TWONFIL provides a number of PASCAL procedures to determine
waves generated during fault initiation and due to switching operations, as
well as reflected and transmitted waves at various discontinuities, and
superimposed voltages and currents {voltage and current jumps) at the relay
post tion. These voltages and currents can be used for the testing of
protection algorithms. After a certain reflection pattern has been chosen
-34-
some procedures can be taken from a 1 ibrary to write a PASCAL program to
calculate detection functions for all possible fault types and
fault-initiation-angles.
There are several arguments to use our new program for the study of
algorithms for travelling-wave-based protection:
The simplicity of the model makes the program fast and easy to implement
under different situations (line type, phase-initiation-angle, faulted
phase). so that the behaviour of protection algorithms in thousands of
fault and non-fault situations can be studied;
- Since travelling-wave-based protection detects a fault from information
obtained from the first travel! ing waves generated by the fault, the
(neglected) attenuation and dispersion do not yet play an important role;
-A comparison with EMTP (cf. Section 3.3.3) shows the approximations to be
acceptable;
-The results of the TWONFIL study can be a starting point for a more
complex study (e.g. EMTP): only the worst cases need to be studied which
leads to an enormous time saving.
3.3.2 An example of TWONFIL-calculations
i IF
j-,
I I I
I I r?r- 1
z~~ (C) I 0 F I
I z• I - - I! L/ ! I I
! I 1 i
Figure 3.6. FauLt initiation on a doubLe-circuit tine.
We demonstrate the TWONFIL program by calculating the superimposed voltages
and currents at the relay position, due to a fault somewhere on a line.
Consider the situation shown in Figure 3.6. A fault is initiated at the
fault position F. This will generate waves travelling from F to the relay
position R. At R the double-circuit line is terminated by a three-phase
busbar. The latter is connected to a network with homopolar mode impedance M M
Z0 and aerial mode impedance Z1 .The (superimposed} travelling waves that
-35-
originate from the fault position during a fault with earth connection11
satisfy the boundary conditions
= 0
= e m
for j non-faulted phase
form= faulted phase ,
and em = voltage jump caused by the fault.
(3.11)
{3.12}
During a fault without earth connection the waves satisfy the boundary
conditions
i~p) = 0 J
for j =non-faulted phase (3.13)
~ ik(p) = 0 fork= faulted phases , (3.14}
V(p}_v(p)_ e i j - ij for i,j = faulted phases , {3.15}
and eij =voltage jump caused by fault.
Because the fault initiation is supposed to be the only source of travelling
waves. there are, during a certain time, only waves travelling away from the
fault into the line section between F and R. At F this reads as
(3.16)
By using i(p}=Q i(c). v(p}=S v(c) and (3.16) together with (3.11} and (3.12)
or (3.13) through {3.15} voltages and currents at the fault position are
calculated. The incoming waves at F generated by the fault initiation are
given by
(3.17)
From Bergeron's equations it follows that these waves arrive at Rat a later
time and there play the role of outgoing waves G( c} with each individual
mode k having a characteristic delay:
~c)(t} = F~c)(t--rk) . (3.18)
The terminal impedance z(P) at R is a combination of the three-phase busbar
and a connected network (Z0 *, Z1 *>. At the relay position R (with inverted
reference direction of i} the following equations hold: v(c)- z(c)i(c) = G(c}, (3.19}
v(p} + z(P)i(p) = o . (3.20}
11 In case of a fault with earth connection one or more phase conductors come into (electrical) contact with ground. Therefore their voltage jumps to zero. In case of a fault without earth connection two or more conductors come into contact with each other.
-36-
By using the above equations in combination with i(p}=Q i(c}and v(p}=S v(c}
a TWONFIL-procedure determines voltages and currents at the relay position.
3.3.3. TWONFIL versus EMTP
Figure 3.7: FauLt position
and reLay position used in a
certain TWONFIL-study.
No direct comparison has been made between TWONFIL and reality. Instead
TWONFIL has been compared with EMTP whose reliablity is discussed in Section
3.6.
Figure 3.8. shows the stylized "forward detection functions" 12 (i.e. a
linear combination of certain voltages and currents) during a fault on the
parallel circuit. The configuration under study is shown in Figure 3.7. The
spike (value 1) is caused by the difference in travelling time between the 13 different modal waves The height of the spike cannot be reproduced
exactly by TWONFIL due to the neglection of the damping. But a relay for
travelling-wave-based protection contains a low-pass filter. This smears out
the fine details of the measured signals so that the fi I tered versions of
EMTP and TWONFIL become almost identical. Value 2 is reached when all modal
waves have arrived at the relay position. This value can be reproduced
almost exactly by TWONFIL. After a number of reflections between the fault
and the busbar value 3 is reached. This value turns out to correspond to the
TWONFIL value for a "close fault", where it is assumed that the voltage at
the relay position equals that at the fault position.
Figure
TWONFIL resuLts.
3.8. ReLation
resuLts and
betllleen
EKfP
12 Forward detection functions are used for directional detection as discussed in detail in Chapter 5.
13 More about these spikes and the differences in travelling time can be found in Section 4.3, subsection ~pLke~ Ln the detectLon tanctLon~.
3.3.4. Line types studied
17.4 24A
0 0 0
To
type A
17.4
0 0
0 0
0 ;J 0
type B
-37-
t~-00 w··
type C
Figure 3.9. Line types
used for TWONFIL-study.
The basic line type is that depicted in Figure 3.3. Because the phase
conductors are in a triangular configuration, the impedance and admittance
matrices will be fairly symmetrical. This line type will be denoted as line
type A. The two other (less symmetrical} line types used in our study are
also shown in Figure 3.9. Insulation distances and bundle conductors are the
same as for line type A. Differences are in the position of the phase
conductors. Line type B is a vertical configuration, line type C a
horizontal one.
3.4. Other network elements
So far only the modelling of high-voltage lines has been discussed. But a
high-voltage network contains other elements, too. These are situated in or
near a high-voltage substation, which makes the representation rather easy.
The spatial extent of such a substation is a few hundreds of meters. As the
validity of the line model used is only guaranteed for frequencies below a
few hundreds of kHz it is not needed to take this spatial extent into
account. Therefore the substation is described by a few lumped elements
representing the trafo between the high-voltage (380 kV} node and the
low-voltage {220 kV or 150 kV) node, as depicted in the inserts A and B of
Figure 3.10. {The inductance is mainly the short-circuit inductance of the
power transformer. which is different for the homopolar mode and the aerial
mode}. Measurements on large power transformers [Bollen and Vaessen, 1987]
confirm that a transformer can be represented by such a circuit with an
acceptable accuracy, up to at least 100 kHz. Measurements on 380/150 kV
transformers as used in the Dutch 380 kV-network yielded a capacitance of
about 10 nF, as seen from 380 kV-side. This value has been chosen as a
typical value per phase per transformer, for the 380/150 kV substations
{insert B). For the 380/220 kV substation Ens {insert A} values according to
Kersten and Jacobs [1988] have been used.
Within TWONFIL the substation is viewed as a single {three-phase} node,
with all other apparatus, except high-voltage lines, neglected.
3.5. The basic network
Oude Haske
71.4 km
150 kV 81.2 km
150 kV
-38-
LK(mH) 22
- 1.4 33.9
!iK (ohm) 0. 1 0.62 0.5
!Bl
Voltage(I<Vll 360 ' 220
65
3~ ~ 10 nF R
:Lo•388 mH Ro•lOO ohm ILl-185 mH Rl•lOO ohm
G'berg Eindhoven
Maaebracht
62.4 l<m
150 kV 150 l<V
Ftgure 3.10.
Baste network
used for ElffP
study.
The program EMTP has been used to analyse the behaviour of protective
relays in the network depicted in Figure 3.10, where the squares denote the
relay positions. The simulated network is based on the Dutch 380 kV grid.
The lines Ens-Diemen, Diemen-Krimpen, Krimpen-Maasvlakte, Krimpen
Geertruidenberg and Geertruidenberg-Eindhoven are represented in detail by
using JMARTI SETUP. The other network elements have been respresented
through lumped elements. More details on the simulations can be found in
[Bollen and Jacobs, 1988] and in [Kersten and Jacobs, 1988].
3.6. Model versus reality.
Representing the high-voltage 1 ine depicted in Figure 2.1 by our model and
the associated list of numbers in Table 3.1, implies various approximations.
Since voltages and currents resulting from this model are used for testing
protection algorithms by simulations, we have to check by field measurements
to what degree these quanti ties are in agreement with the actual physical
voltages and currents.
-39-
Figure 3.11. Comparison between mea.surements (left) and EMTP results
(right); adopted from [Von Heesch, et at.,1989].
some comparisons between field measurements and model results have been
made in our group by Kersten and Jacobs [1988] and by Van Heesch et al.
[1989]. Figure 3.11 is adopted from the latter publication. It shows
voltages and currents at the receiving end of a circuit being energized. The
circuit was part of a double-circuit line with the other circuit in
operation (cf. Figure 3.12). During the simulation most of the problems
occurred in obtaining information about the feeding networks. They affect
not only the new stationary situation but also the transient and even the
initial waves created by closing the breakers. This may largely account for
the deviation between model and reality.
Figure 3.12. Field mea.surements during tine energizing. At position 1 the
circuit breakers are being dosed, voltages are measured at position 2. A
and B are feeding networks affecting the transient phenomena.
To get a better insight into the limitations of the line model special
field experiments can be performed, e.g. as proposed in Figure 3.13. To
ensure that all deviations between model and reality are due to
-40-
imperfections of the line model, the feeding source has to be almost
perfectly modelled. Therefore a simple feeding source is recommended, e.g. a
low-impedance D.C. source or a large capacitor.
Figure 3.13. Proposal for field experiments to test transmission line model.
Nakanishi and Ametani [1986] have compared a number of modelling
techniques with field measurements. Figure 3.14 presents their results for
the energizing of a single phase of a three-phase line (voltages measured on
the receiving end are depicted). Two models are compared:
- EMTP' s .]MARTI SETUP with frequency dependent modal parameters but
frequency independent transformation matrix (dashed line):
-a model with both frequency dependences incorporated (dotted line):
The solid lines represent the measurements. It follows from the figure that
the results of the second model slightly differ from the EMTP results. But
the second model does not significantly reduce the deviation between model
and reality.
Figure 3.11f. Compl.ri-
--·(1) son between measure-
ments (solid lines)
and model results; (i)
refers to the phase
being energized, (iii)
to one of the other
phases; adopted from
[Nakanishi and
Ametani, 1986].
20 100 time(lls)
-41-
4. Testing of algorithms for travelling-wave-based protection
4.1. Potentially dangerous events
A protective relay must be able to take a correct decision in all cases. A
tripping signal must be generated for each fault in the zone-to-be
protected. No tripping signal shall be generated in all other cases. In this
study special emphasis is laid on these "no-fault situations". An incorrect
decision can be due to technical failure of the relay or due to limitations
of the protection algorithm used. This study only concerns the latter case.
Many disturbances can take place in a high-voltage network. some are
listed in Section 2.4. Fach automobile crossing a high-voltage line will
cause some change in charge distribution and thus travel! ing waves. The
amplitude however will be very small, so not of any importance for this
study. The greatest possible disturbances in high-voltage networks are line
energizing, fault initiation and lightning. Therefore these have been
studied in detail.
~auLt~ L~ the ~one-to~e~tected
These are the situations where the relay should generate a tripping signal.
The following situations have been studied:
1. faults somewhere on the line;
2. faults close to one of the line terminals;
3. evolving faults;
4. faults due to lightning;
5. faults during line energizing.
Single-circuit faults: Single phase to ground Phase-to-phase Two-phase-to-ground Three-phase Three-phase-to-ground
Double-circuit faults: Phase-to-phase Two-phase-to-ground Three-phase Three-phase-to-ground Four-phase Four-phase-to-ground
Five-phase Five-phase-to-ground Six-phase Six-phase-to-ground
RNSNTN RSRTST RSN RTN STN RST RSTN
RV RW SW RUN RVN RWN SVN SWN Tt!N RSU RSV RSW RTU RTV RTW RVW STY STW RSUN RSVN RSWN RTUN RTVN RTWN RVWN STVN STWN RSTU RSTV RSTW RSUV RSUW RSVW RTUW RTVW STVW RSTUN RSTVN RSTWN RSUVN RSIJWN RSVWN RTUWN RTVWN STVWN RSTUV RSTVW RSUVW RSTUVN RSTVWN RSUVWN RSTUVW RSTUVWN
Table 4.1. Fault types studied by using TWONFIL. R S T denote }ilase
conductors of the first circuit, U V I of the second one. RS stands for a
faul.t between }ilase R and }ilase S, RJN for a faul.t between }ilase R and
}ilase I (T of the second circuit) with earth connection.
-42-
Ad. 1. Single-circuit as well as double-circuit faults have been studied. In
case of synunetry between both circuits (SU=RV. TII=RW. etc.) 64 different
combinations of faulted phases are possible. They are given in Table 4.1.
These faults have been studied by using TWONFIL for 12 fault-initiation
angles, 15° apart.
Ad. 2. Only single-circuit faults have been studied (11 combinations of
faulted phases for 12 fault-initiation-angles each}.
Ad. 3. A fault can evolve to a more complex fault (more faulted phases) in
two ways: a rapidly changing elektromagnetic field may cause multiple
flashover (e.g. due to lightning): an arcing fault may spread to other
phases. In the first case the speed of expansion will be a substantial part
of the speed of light being 300 ml~s. As the distance between neighbouring
phases is around 10 meter. the evolution of the fault takes place on a
submicrosecond scale. So this multi-phase fault can be considered as
simultaneously. In the second case the speed of expansion will be at maximum
of the order of the speed of sound (360 m/s), leading to an evolution taking
place on a 10 to 100 millisecond scale. The situation studied is an evolving
fault after the new steady state has been reached. About 700 evolving faults
have been studied for 12 fault-initiation-angles each.
Ad. 4 and 5. To be duscussed further on.
~auLt~ out~Lde ot the ~ane-to-be-p~otected
For these situations the relay shall not generate a tripping signal. The
following faults have been studied (cf. Figure 4.1}:
6. faults somewhere on the parallel circuit;
7. faults close to one of the line terminals:
8. faults somewhere on another line;
9. evolving faults on the parallel circuit;
10. evolving faults somewhere on another line:
11. faults during energizing of the parallel circuit.
2
Figure 4.1. Fault postitions studied.
-43-
Ad. 6. Only single-circuit faults are of interest here: 11 combinations of
faulted phases for 12 fault-initiation-angles each.
Ad. 7. Compare Ad. 2.
Ad. 8. Compare Ad. 1.
Ad. 9. Only single-circuit faults evolving to other single-circuit faults
have been studied: 19 combinations of faulted phases for 12
fault-initiation-angles each.
Ad. 10. Compare Ad. 3.
Ad. 11. To be discussed further on.
Othe~ di~tu~bance~
These are situations where none of the relays shall generate a tripping
signal. The following situations have been studied:
12. energizing of a non-loaded line:
13. de-energizing of a short-circuited line;
14. lightning.
7 ')
Figure 4.2. Circuit breaker positions
studied for line energizing.
Ad. 12. The energizing situations studied are summarised in Figure 4.2. Each
switch in this figure denotes three circuit breakers studied for 19
combinations and 12 fault-initiation-angles each. The combinations of closed
phases and closing phases are given in Table 4.2.
Closed
none R s T SandT Rand T RandS
Closing
R. S, T. R and S, S. T. SandT R. T. R and T R, S. RandS R s T
Rand T. SandT. RandS and T
Table 4.2. Combinations
of dosed and cLosing
phases for energizing
as studied by using
TWONFIL.
Ad. 13. Like during line energizing, line de-energizing will cause
travelling waves. The most intense phenomena will occur between the circuit
breaker and the fault, i.e. on the line to be de-energized. This is not of
concern for protection anymore. Travelling waves will also appear on healthy
lines, where they may endanger the reliability of a relay. As de-energizing
-44-
will only take place at current zero, the number of situations is limited.
Line de-energizing has been studied by using EMTP.
Ad. 14. To be discussed further on.
4.2. General discription of a protection algorithm
An algorithm for travelling-wave-based protection uses travelling-wave
principles to detect a fault on a high-voltage line; it determines incoming
and outgoing waves from measured voltages and currents. As only the waves
caused by the fault initiation must be detected, "superimposed quanti ties"
must be used. Some algorithms derive them by subtracting the values one
power frequency cycle back in time. Other algorithms (e.g. differential
protection} take the difference between two values a small period in time
apart. In that case superimposed as well as momentary values can be used.
As shown in Section 2.2 for a single-phase line, the expressions v+Z0 i
and v-Z0 i denote incoming and outgoing waves, respectively, where Z0 is the
wave impedance. This also holds for the modal waves on a multi-phase line,
as shown in Section 2.3. A hypothetic algorithm to detect the outgoing waves
should use the following set of detection functions:
( 4.1}
where y(P} and I(p} are vectors of (superimposed} val tages and currents,
respectively; S, Q and zic} are val tage transformation matrix, current
transformation matrix and (diagonal} wave impedance matrix, respectively.
It is not practical trying to use the exact transformation matrices in
a protection algorithm, because:
the transformation matrices are not exactly known (i.e. the difference
between the exact values and the calculated values are very difficult
to determine};
problems occur for lines showing transposition points as well as for
double-circuit lines where parameters from both circuits are needed;
relatively complicated expressions show up.
To avoid all these problems the transformation matrices are considered to be
those for a balanced three-phase line. The errors introduced by this
approximation will be discussed further on. Using the transformation of
(2.45) leads to the following detection functions:
(vr+V8 +Vt} - Ro(ir+1 8 +1t)
(vt-V8 } - R1 (it-i 8 }
(4.2}
(4.3)
(4.4}
where R0 and R1 represent the homopolar and aerial mode wave impedance,
respectively. The homopolar detection function D0 will not be used because:
-45-
it shows large pulses of short duration ("spikes") during a fault on
the parallel circuit. They cannot be removed sufficiently by a low pass
filter. These spikes may cause false tripping of a circuit parallel to
the faulted circuit [Bollen and Jacobs 1988]:
homopolar mode quanti ties are strongly dependent on frequency as well
as on the composition of the ground. They are also dependent on the
state of the parallel circuit. It is therefore difficult to choose a
wave impedance setting for the relay;
a lightning stroke to a tower, to a shielding wire or somewhere in the
vicinity of the line will affect all conductors in about the same
extend, leading to a large homopolar wave, but almost none aerial
waves:
fault detection without the homopolar quantities does not introduce any
additional problems, but it will reduce the number of calculations to
perform with about 50%.
In this hypothetic case the following detection criteria are used to
distinguish between a "fault situation" and a "non-fault situation":
ID1 l<b and ID2I<b IDtl>b or ID2I>b
non fault
fault .
(4.5)
(4.6)
The setting of the threshold b as well as of the impedance value R1 will be
discussed in the next section.
4.3. Setting of,the different parameters.
~Lt~ and de~ee~
The protection algorithms to be discussed in this and forthcoming chapters
hold for every value of the nominal voltage. To get a reference, the
amplitude of the nominal phase voltage is considered to be equal to 1000
units. This makes it possible to express all detection functions (having the
dimension of a voltage) and all thresholds in these arbitrary units. The
second reference to be made conderns the fault-initiation-angle: zero
degrees corresponds to voltage maximum in phase R.
$hne~hold and Lapet:loll,ce ~etUng,
The detection functions (4.3 and 4.4) are equal to zero for a non-fault
situation on a balanced line. On a nonbalanced line the detection functions
possess a small but nonzero value during a non-fault situation. That is one
of the reasons to introduce a threshold value b. Criterion (4.5) must be
valid for all non-fault situations. Thus both detection functions must, in
absolute value, be below the threshold. Putting it the other way around: the
-46-
threshold b must be higher than the highest possible value of the detection
functions during a non-fault situation. This minimum threshold value is a
function of the impedance setting R1 • The shape of this function is shown in
Figure 4.3. The knee in the curve denotes optimum impedance setting.
R,-
Figure 4.3. Minimum threshoLd vatue b as a
function of impedance setting.
In reality it is not possible to set the impedance exactly to its
optimum value {e.g. due to uncertainties in the line parameters). As a
consequence of this the threshold must be higher than the optimum value.
Other settings can also deviate from their optimum values leading to even
higher thresholds, as will be seen further on.
The impedance uncertainty will greatly differ from situation to
situation. For this study an uncertainty of 5% has been choosen. In the
Dutch 380 kV network measurements give 50 Hz values for inductance and
capacitance of 0.882 mHIKm and 13.22 nF/Km respectively for the aerial
modes. This leads to a wave impedance value of 258.3 Q, being within 3% of
the optimum setting of 266 Q. So 5% seems to be an acceptable value.
:/!OU;-pa,o.o, tLLtc'I-
All kinds of disturbances cause high-frequency noise in the detection
functions. This can be due to characteristics of the lines {e.g. different
travelling times for the different modes) or due to external phenomena
(lightning strokes, radio transmissions). If such a high frequency
disturbance occurs during a non-fault situation it might lead to an
incorrect trip. To prevent this a low pass filter will be introduced.
For one of the algorithms14 a non-fault situation must be detected
within one travelling time of the line T. Therefore a block function with a
duration T shall not be distorted too much. From this a criterion as shown
in Figure 4.4 is introduced. Following an input step the output must be
within 10% of the final value after 1/2 T.
14 Directional detection {cf. Section 5.2).
rnfiltered
«10%1-------,...,.---, I
/ I ~ I
/ I I '
I I I
-47-
\ \ \--filtered
' ', ...... ..... _ ... _
-t
Figure. 4.4. Criterion to determine the cut-off frequency.
A first order filter will be used. with a transfer function of the form
H(f) 1 + jf/fc •
where fc is the cut-off frequency.
The step response a(t) or this filter is
a(t) = 1 exp (-2n£ct) • t > 0 .
From the criterion of Figure 4.4. follows
f > 0.73 . C T
(4.7)
(4.8)
(4.9)
An acceptable value for the cut-of£ frequency is rc = 1/-r, where T is the
travelling time of the line-to-be-protected. For a 100 km line this will be
3000Hz. This cut-of£ frequency will be used for other algorithms too. also
when theoretically no lower limit for the cut-of£ frequency is required. For
some combinations of algorithm and line type a lower cut-of£ frequency is
required and will thus be used.
The cut-off frequencies used (a few kHz) are of the same order of
magnitude as those used by other authors. Chamia and Liberman [1978] use the
low-pass behaviour of the voltage and current transformers. According to
them that cut-of£ frequency is a few kHz. The same is done by Mansour and
Swift [1986] using a sample frequency of 2kHz in accordance with a cut-of£
frequency of 1 kHz. Johns et al. [1986] use a cut-off frequency of 2kHz and
Ermolenko et al. [1988] one of 1 kHz.
-48-
'J''tal9-eULn,g. Use
Two of the algori thms15• determine the difference between a wave at a
certain moment and the same wave, some travelling time later. The algorithms
check whether Bergeron's equations (2.22 and 2.23) are valid or not. As
shown in Chapter 2, a multi-phase line can support more than one wave, each
having a different travelling time. The travelling time setting must be
somewhere in this interval. For line type A of Section 3.3.4 the travelling
time for a 100 km line is 364 JLS for the homopolar wave and 337 JLS for the
fastest wave. The slowest aerial wave possesses a travelling time of 349 JLS.
Consider the detection function to have the following form
D(t) = A(t) - B(t+T) : (4.10)
where A and B are expressions like (4.3) and (4.4) and T is the travelling
time setting. During a no-fault situation A(t) and B(t+T) are almost equal,
so ID(t)l is below the threshold b. The travelling time setting T must be
such that ID(t)l is as low as possible during a no-fault situation. Suppose
that A shows a sudden jump, e.g. due to a fault just outside of the
zone-to-be-protected. After a certain time. B will show a jump too. Due to
differences in travelling time the wave front will be less steep, as shown
in Figure 4.5.a and b.
Is A
® @ @ t s
I f s
B I D I I I I
0 t- l.j4t t- t-®
t t-D D D
t-
Figure. 4.5. InfLuence of traveLling ttme setting T on shape of detection
functions. a: initial wave; b: wave after travelling ttme; c: setting
according to fastest wave (T=t0 ); d: setting according to slowest wave
(T=t0 +At); e: optimum setting; f: extremely erronous setting.
15 Differential protection (cf. Section 6.2) and switch-on-to-fault detection (cf. Section 7.4).
-49-
In case the travelling time is set according to the fastest wave a
positive spike results in the detection function as shown in Figure 4.5.c. A
setting according to the slowest wave results in a negative spike of the
same dimensions (cf. Figure 4.5.d}. Figure 4.5.e shows the detection
function for a travelling time setting in the middle of these two extremes.
This is considered to be the optimum setting as it leads to the lowest
amplitude for the spikes. Because the detection functions do not use the
homopolar mode, only the aerial mode travelling times need to be considered.
It is assumed here that the properties of the different modes are such
that the front of B possesses a constant slope. This is certainly not true
for all situations. In case only the fastest waves are present or only the
slowest waves, the optimum setting will not decrease the amplitude of the
spike in the detection function. But it will decrease the duration by a
factor of two, leading to a reduction of the amplitude by a factor of two
after passing a low pass filter.
In case the travelling time setting deviates from its optimum value,
the duration and amplitude of the spikes in the detection function will
increase. Figure 4.5.f shows the detection function in case the travelling
time shows a setting error T, i.e. it is set to t 0 + At/2 + T. In the worst
case of only the fastest mode present a block with a heigth Sand a duration
T+At/2, results. After low pass filtering, the maximum value of ID(t) I
equals:
s[ 1 - exp {- 2x fc(At/2 + T)}] ~ 2x fc S(At/2 + T) ( 4.11)
The time above a threshold b is given by:
1 [ 2xf CS(At/2+T) ] T + At/2 + 2xf ln b .
c ( 4. 12}
As S can be high, it is clear that already a small error in travelling time
setting can introduce large spikes in the detection functions during
non-fault situations.
Othe~ ~PLke~ Ln the detectLon tunctLon~
The preceeding subsection discussed spikes due to differences in travelling
time for algorithms using a travelling time setting. But spikes also occur
for algorithms without such a setting16
16 The problem occurs with directional detection (cf. Section 5.2) for fau1 ts on a paralle 1 circuit and in a more intense way with a special double-circuit algorithm called DOOCP (cf. Section 7.2) for faults in the remote substation.
-50-
Consider the situation shown in Figure 4. 6, where the double-circuit
line consists of just two conductors. Two modes are possible: one with
currents having the same sign in both conductors. one with currents having
opposite sign. If the second one has the highest speed. the shape of the
detection functions for both relays during a fault in one of the circuits is
as shown in the right part of Figure 4.6. The detection function of Relay B
shows a spike. These spikes must be removed by the low pass filter
introduced above.
~etectLon •Lndoe
I Ftgure. 4 .6. Different modes on a
doubte-circuit tine (teft) and
resuLting detection functions
(right).
Due to multiple reflections two of the algorithms cannot be used anymore
from a certain (short) time after the occurrence of an external fault,
onward17 . As a consequence of this the relay must be blocked after the
detection of an external fault. This calls for additional detection
functions to detect the external disturbance within a "detection window".
After the relay has been blocked, it must remain blocked during a "blocking
time". Different authors propose different blocking times. Johns (1980]
proposes a blocking time of 60 milliseconds. Mansour and Swift [1986] one of
100 milliseconds, Ermolenko et al. [1988] use a blocking time between 500
and 2000 milliseconds. Such a fixed length will be too long for most
situations, as the relay cannot detect any fault when it is blocked. But the
blocking time may also be too short for some extreme situations. leading to
incorrect tripping. It is considered a better solution to deblock the relay
immediately after the end-of-transient, i.e. when all relevant detection
functions are below their threshold again.
~etectLon tL•e, 5e~LtLcatLon tL•e. t~LPPL~ tL•e
When a fault occurs somewhere in the zone-to-be-protected of a relay. waves
start to travel from the fault position to the relay position (actually the
position of the measurement transformers). After a certain travelling time
the fastest waves arrive at the relay position. At this moment the detection
function starts to deviate from zero. Due to the low pass filter introduced
it will take some time before the detection function exceeds the threshold
b. The "detection time" (DT in Figure 4. 7) will be defined as the time
17 Directional detection (cf. Section 5.2) and DOOCP (cf. Section 7.2).
-51-
between the arrival of the fastest waves at the relay position and the
moment the detection function exceeds the threshold.
D 8
0 0 t
Ftgure 4.7. Definition of detection time (DT).
uertftcat ton time (VT) and tripping time (TT).
oof = occurence of fault; gts = generation of
tripping signal.
To prevent false tripping, a tripping signal wi 11 not be generated
before the detection function has · been above the threshold during a
"verification time" (VI' in Figure 4.7). The "tripping time" is the sum of
detection time and verification time. A short verification time wil give a
short fault clearing time, but will also increase the chance of incorrect
tripping. In reality the choice of the length of the verification time will
be a compramise between speed and reliability. This trade-off is outside the
scope of this study.
'£tg.lr.tntng.
The most troublesome situation to occur during lightning is a direct stroke
to a phase conductor. not leading to a flashover. As this is a source of
travelling waves a travelling-wave-based algorithm may generate an incor
rect trip. The risk of such an incorrect trip is reduced by introducing:
a threshold;
a low pass filter;
a verification time.
Consider the folowing shape for a (nonfiltered) detection function after a
lightning stroke:
D(t) = A exp(-t/T) U(t) , ( 4.13)
where the step function U(t) is zero for t < 0 and unity for t > 0; a
standard value for the time constant T is 70 ~s. The detection function has
the following shape (for 2xfcT ~1. where fc is the cut-off frequency):
2xf T [ ] D(t) =A 2xfcT-l exp(-t/T) - exp(-2xfct)
c ( 4. 14)
Figure 4.8 shows a few of these detection functions.
-52-
140 f'S-
Figure. 4.8. InfLuence of Low-puss filtering on Lightning-caused detection
functions ..
The highest possible value of A is determined by the flashover voltage
of the insulator chain. According to Kersten and van der Meijden [1984) the
flashover voltage for the Dutch 380 kV network is about 2.2 MV (for a
1.2/~s pulse). Reckoning the agreement at the start of this section the
flashover voltage will be 7000 units. This is considered to be the highest
possible voltage jump not leading to a flashover. For directional detection
and differential protection a voltage jump of 1000 units in one phase will
lead to a jump in the detection function of 1400 units. So the highest
possible direct stroke not leading to a fault causes a detection function of
the form (4.14) with A=10,000.
The time above threshold of such a lightning-caused detection function
must be shorter than the verification time. Figure 4.9 gives this time above
threshold (i.e. the minimum verification time) as a function of the cut-off
frequency for a few threshold values (notice the change in horizontal scale
at 1kHz). For low cut-off frequencies the verification time can be
considerably shortened when the threshold level is increased. This may
decrease the tripping time in a few cases. But for frequencies above 1 kHz
an higher threshold will not significantly shorten the verification time.
-53-
t
6
Figure. 4.9. Time above threshold for lightning-caused detection functions
as a function of cut ·off frequency, for different threshold values. The
maxtllltlllt value of the nonfHtered detection function is 10,000 units, its
time constant 70 ~s.
~e~L~tLon of the ~upe~L•PD~ed ~tLtLe~
Two of the algoritlnns18 use superimposed quantities (cf. Section 2.4.2).
They can be derived as the difference between the actual values and the
values one power frequency cycle back in time (the undisturbed values). As
the power frequency shows small changes on a minute scale, the delay time of
one power frequency cycle needs to be adjusted. A method for this is
proposed by Johns and El-din Mahmoud [1986]. Nevertheless the time delay
will not fit the power frequency exactly.
Consider a detection function D(t) being the difference of an actual
value M(t) and an undisturbed value Dcos (~0 t):
D(t) = M(t) - Dcos (~0 t-~oT) , (4.15)
where T is the time delay used, showing an error AT,
T = 2ltl~0 + AT (4.16)
If AT<<T the maximum error in the detection function is given by
18 Directional detection (cf. Section 5.2) and DOOCP (cf. Section 7.2).
-54-
( 4. 17)
Figure 4.10 shows the frequency drop measured during a 5500 MW power
shortage in the West European grid [Maas. 1987]. The maximum frequency
deviation was 0.4 Hz. This is the biggest frequency deviation ever observed
in the West European grid.
so.sl (~zll 504--------~------~~. ---------
49.51 ~. 50s t (sl-
Figure. 4 .10. Frequency deviation due to a. large power shortage, adopted
from [Raas, 1987].
From this it can be concluded that the frequency deviation in the relay
will almost certainly not exceed a value of 100 mHz. To cope with the worst
frequency deviation and to incorporate other errors too, 1% error will be
considered in this study (corresponding to 0.2 ms or 0.5 Hz on a 50 Hz
base).
4.4. Fault detection time
Each algorithm is based on superimposed voltages and currents, even though
not all of them actually derive these quantities. During a fault superimpos
ed voltages and currents are caused by a virtual sinusoidal source switched
on at the instant of fault initiation. Before multiple reflections disturb
it the nonfiltered detection function will be of a sinusoidal shape too:
D(t) = Dcos(w0t~). t>O , ( 4.18)
where ~ is related to the fault-initiation angle. After passing a low-pass
filter with cut-off frequency fc (fc>>50 Hz) the detection function has the
following form:
D(t) = n[cos(w0 t~) ( 4. 19)
The detection time is the lowest positive t being a solution of
ID( t) I = 0 . (4.20)
The detection time is given in Figure 4.11 as a function of the
fault-initiation angle ~. for D/6 = 3.5 (a single-phase-to-ground fault in
combination with differential protection or directional detection) and
fc =5000Hz (60 km line).
-55-
Figure. 4.11. Detection time as a
function of fault-initiation-angle.
For Dcos(~)>b ( ~<73° in Figure 4.11 ) the curve can be approximated by
1 b t = 211:f ln (1 - Dcos~ ) (4.21)
c
This function has a very steep asymptote at~= arccos(b/D), the angle where
the jump in the nonfiltered detection function equals the threshold.
Slightly to the left of this asymptote the detection time is of the order of
tens of microseconds (10. 7 JlS for ~0 : 14.9 JlS for ~0°: 57.5 JlS for
~ = 70°). This is small as compared to the verification time (cf. Figure
4.9). So for a wide range of fault-initiation-angles (including those with
the highest chance of occurence) the length of the tripping time is
determined by the length of the verification time.
j) _] -----------
Figure 4.12. Detection function for a
fault somewhat before voltage zero. The
dot ted ltne denotes the threshold
level.
In case Dcos(~) < b (the jump in the nonftltered detection function is
less than the threshold value), the detection time will be much larger. The
worst case is shown in Figure 4. 12. The fault occurs before the zero
crossing of the detection function and the jump in the detection function is
just below the threshold. The chance of occurence of such a fault is not
known but it is clear that faults around voltage zero are seldom.
The basic assumption for (4.18) is the absence of multiple reflections.
This will hold for a detection time of 10.7 JlS but not for one of 1800 JlS.
It has been shown that multiple reflections speed up the fault detection
-56-
except for situations with a very weak infeed (low short-circuit power).
The above discussion holds for single-phase-to-ground and for phase-to
phase faults. For these faults all detection functions show a zero crossing
at the same angle as the pre-fault voltage. For two-phase-to-ground and
three-phase faults the detection functions show their zero crossings at
different angles, so that always at least one of the detection functions
will exceed the threshold within a short time. For a three-phase fault on
line type A, and a cut-off frequency of 5000Hz, the detection time ranges
from 4 to 10 Jl.S.
4.5. Phase selection
After a fault had been detected the fault type can be selected. Depending on
the fault type a single-phase trip or a three-phase trip can be given. Phase
selection combined with travelling-wave-based protection is possible by
calculating six selection functions from the detection functions D1 and D2 •
8t=Dt
82=D2
83 =D1 +D2 ,
8 4 =Dt-D2 ,
8s=Dt+2D2 ,
86 =-2Dt-D2 •
(4.22) (4.23)
(4.24) (4.25)
(4.26)
(4.27)
Inserting (4.3) and (4.4) results in the following expressions (only the
voltage terms are given):
81=vt-Vs (4.28)
82=vr-Vt (4.29) 83 =vr-v., (4.30)
84=2vt-Vr-Vs (4.31)
8s=2vr-vs-vt (4.32)
86 =2v5 -vr-Vt (4.33)
During an R-N fault the superimposed voltage in phase S wi 11 be almost equal
to the one in phase T. The same applies to the current. Because of this the
selection function S 1 will be near to zero. The same is valid for 82 during
an 8-N fault and 83 during a T-N fault. This leads to the following
selection criteria for single-phase-to-ground faults.
IS1 I <cr l82l <cr IS:~I<cr
R-N
S-N T-N
(4.34)
(4.35)
(4.36)
-57-
During an R-S fault the superimposed current in phase R is about opposite to
the one in phase S. The current in phase T is almost equal to zero. The same
applies to the voltages. The selection function S4 is therefore near to
zero. In the same way S5 corresponds to an S-T fault and S6 to an R-T fault.
This leads to the following selection criteria for phase-to-phase faults:
ls .. l<a lssl<a ISsl<a
:R-S • :S-T , :R-T
(4.37)
(4.38)
{4.39)
When a single-phase-to-ground fault is detected the faulted phase will be
tripped. After a phase-to-phase fault only one of the faulted phases will be
tripped. More details on this can be found in [Bollen and Jacobs, 1988,
1989: Bollen. 1989]. The principal results are:
For most fault situations the additional time needed for phase
selection is just a few tens of microseconds. A few situations (e.g.
R-S-N around a zero crossing of the phase R voltage) show an initial
single-phase trip followed by the necessary three-phase trip after
about 1 ms):
Due to spikes in the selection functions additional filtering is needed
to prevent an incorrect three-phase trip during phase-to-phase faults:
During some double-circuit faults the algoritlun for phase selection
fails. Then two three-phase trips are generated in stead of two
single-phase trips.
-58-
5. Directional detection
The basic assumption for travelling-wave-based directional detection is: "a
source of travelling waves within the zone-to-be-protected is a fault" {cf.
figure 5.1). As the closing of the circuit breaker can also be a source of
travelling waves the circuit breakers must be located outside of the
zone-to-be-protected. So voltage and current must be measured on the line
side of the circuit breaker.
)(ll~--- --~------::_f8 )( Figure 5.1. Principle of travelling-wave-bused directional detection.
A directional detector at each line terminal determines the direction of
origin of the travelling waves (i.e. the direction to the fault). If both
detectors find a fault in their forward direction (the direction into the
line) tripping signals must be generated. To exchange this information a
communication link between both line terminals is necessary. Each detector
only needs to determine the direction of origin of the waves. The algorithms
proposed to determine this are discussed below.
Multiple reflections after a backward fault will lead to waves from the
forward direction; this might cause incorrect tripping of the line. To
prevent this, the relay will be blocked after the detection of a backward
fault. The blocking time has to continue ti 11 the amplitude of the waves
from the forward direction is low again. During this blocking time a fault
will not be detected. This is a fundamental disadvantage of travelling
wave-based directional detection.
5.1. History
~La·~ at~Lthm
The algorithm proposed by Chamia and Liberman [1978] compares the polarity
of superimposed voltages and currents to yield the direction of origin of
the first travelling waves arriving at the relay position.
Figure 5.2. Travelling wuves due to a
forwurd and a backward fault
The different travelling waves after a fault initiation are shown in
-59-
Figure 5.2. Due to the fault a wave (1) travels from the fault position to
the substation, where a part is transmitted (2) and another part reflected
(3). Relay A measures a wave from the forward direction (an outgoing wave)
as well as one from the backward direction (an incoming wave). For the
superimposed voltages and currents measured by relay A, the two following
equations hold:
VA- Z.iA ¢ 0 •
vA + Z. tA = r(vA-z. tA)
(5.1)
(5.2)
where r is the reflection-coefficient, lr I<I. From this it follows that v A
and iA are of different polarity.
Relay B only measures an incoming wave leading to the following relations:
v8 - Z iB = 0 (5.3)
VB + z iB ~ 0 (5.4)
So vB and i 8 are of equal polarity.
This leads to the following detection criteria:
(v > 0 and i < 0) or (v < 0 and i > 0): forward fault
(v > 0 and i > 0) or (v < 0 and i < 0): backward fault .
(5.5) (5.6)
Olamia' s algorithm is used on a segregated phase basis in ASEA' s RALDA and
RALZA relays [Yee and Esztergalyos, 1978: Giulante et al., 1983].
I~ Zi !L{ 1 /
/ / 1
----------~---------v
Figure 5.3. The v, i-diagram., with pos
itions obtained immediately after a for
unrd fault (shaded area) and immediately
after a lxu:kunrd fault (dotted lines).
Vitins [1981] relates (5.1) through (5.4) to positions in a v,i-diagram, as
shown in Figure 5.3. He shows that {5.5) and {5.6) also hold during a few
milliseconds after the fault in case the new stationary situation should be
reached without any transient. This leads to the following detection
criteria:
{v.i) reaches region 1 or 3 first
{v,i) reaches region 2 or 4 first
-60-
backward fault ;
forward fault .
{5.7)
{5.8)
The principle has been extended further by Engler et al. [1985]. They use a
"replica impedance" Zr to derive an auxiliary voltage v 1
from the
superimposed current at the relay position ir:
{5.9)
They show that the fault-trajectory of the post-fault stationary quantities
in the v-vi-plane is a straight line in case Zr=a.Zs' a>o. where Zs is the
{stationary) short-circuit impedance of the feeding network. From the
superimposed voltage at the relay post tion v and the replica voltage vi a
correlation function F{t) is determined:
t
F(t) I v(T).vi{T)dT {5.10)
0
A forward fault is concluded if F{t) exceeds a negative threshold, a
backward if F{t) exceeds a positive threshold. This principle is used in
BBC s LR-91 relay.
Figure 5.4. The first travelLing wave arriving
at the relay positian.
If a fault occurs with a small voltage jump, it will in general take some
time before the directional detectors detect the fault (cf. Section 4.4).
Dommel and Michels [1978] propose a method to detect each fault as soon as
the first travelling waves arrive. Figure 5.4 shows the single-phase
situation. The superimposed voltage at the fault position is: A
vF(t) = - V cos(w0
t + ~).U(t) , {5.11)
where V is the voltage amplitude and ~ the fault-initiation-angle, U(t) is
the unit step function (U{t)=O,t<O; U(t)=l,t>O). At the relay position a
wave from the forward direction (i.e. an outgoing wave) can be measured: A
v(t)-Z.i{t)=-2 V cos(w0t-w0T~).U(t) , (5.12)
The <1>-dependence is eliminated by using Pythagoras' law, leading to the
following detection function:
2
DFw(t) = [ v(t)-Z.i(t)] 1 + ;;;!.)
0
By using (5.12} it follows:
DFw(t) = 4(V)2 .t>O.
[ dv dt
-61-
z di] dt
2
The following detection criteria have been proposed
DFw( t)>O
DFw(t)=O
forward fault ,
backward fault .
(5.13}
(5. 14)
(5.15)
(5. 16}
Mansour and Swift [1986] use a second detection function beside (5.14) to
prevent false detection of a forward fault due to successive reflections: 2
ItJw(t) = [ v(t)+Z. i{t)]
2
+ 1 [ dv + z di] 7 dt dt 0
They propose the following detection criteria:
ItJw(t) > b and DFw(t) < b
DFW(t) > b
backward fault
forward fault .
(5.17)
(5.18)
{5.19)
The algorithm is very well capable of detecting a forward fault as shown by
Dommel and Michel [1978] as well as by Mansour and Swift [1986]. But non of
them mentions the problems during a backward fault. The time derivative
introduces large spikes in the forward detection functions, this necessi
tates the use of low pass filters with a low cut-off frequency. It will be
shown in Section 5.2 that the gain in speed will be undone by these filters.
lolms' a.tg.ottttlu&
Johns [1980] proposes a relatively simple algorithm, based on (5.1} through
(5.4). From the superimposed voltages and currents six detection functions
are calculated:
DoFw Vr + V8 + vtl - Ro( ir + i 5 + it) , (5.20) D Fw _ 1 - (3/2 Vr - 3/2 Vt) - R1 (3/2 ir - 3/2 itl (5.21) D2Fw = ( 1/2 Vr - v,. + 1/2 vtJ - R1 C/2 ir - is + 1/2 itJ (5.22)
DoBw (vr + V5 + vt) +Ro (ir + i,. + it} (5.23) D1Bw (3/2 Vr - 3/2 vtJ + Rt (3/2 ir - 3/2 it) (5.24) D2Bw (1/2 Vr - Vs + 1/2 vtJ + R1 e/2 ir - is + 1/2 it} (5.25)
where Vr• v5 and Vt are phase voltages; ir• i 5 and it are phase currents,
the positive reference direction is from the substation into the line; Ro
and R1 are real approximations of the wave impedances for the ground wave Fw
and the aerial waves respectively. The forward detection functions Do •
D1 Fw and D2Fw are a measure for the outcoming waves i.e. from the forward
-62-
direction. The backward detection functions 00 Bw, D, Bw and D2 Bw are a
measure for the incoming waves, i.e. from the backward direction. A backward
fault is concluded if only incoming waves are present:
{ lo/wl < band IDo8wl > b }
or { ID,Fwl < band ID,Bwl ) b }
or { lo/wl < band ID2Bwl > b } (5.26)
If the relay is not in the blocking mode, a forward fault will be concluded
the soon an outgoing wave is present:
{ IDoFwl > b or IDo8wl < b }
and { ID,Fwl ) b or ID,Bwl < b }
and { io/wl ) o or ID2Bwl < 0 }
and { IDoFwl ) o or ID,Fwl ) o or lo/wl > o} . (5.27)
In a later version of the algorithm, the homopolar quantities have been
omitted and simpler combinations of voltages and currents are used [Johns et
al., 1986]. The homopolar quantities are also omitted in a recent proposal
by a Russian group [Ermelenko et al., 1988].
Johns and Walker [1988] give a very detailed description of the
development and testing of a prototype relay based on Johns' algorithm.
5.2. Results of the testing of Dommel' s algorithm
The following forward detection functions have been used in agreement with
the standard form of (4.3) and (4.4):
D, -['' + _1_ r:·fr - 1 (,)2
0
(5.28)
[ x' [ :2(
'/2
02 = 2 + _1_ (,)2
0
(5.29)
where x 1 (vt-vs) - R1 (it-is)'
x2 (vr-vt) - R1 (ir-it).
During a forward fault x 1 and x2 jump to a high value. During a backward
fault x 1 and x2 also show a jump (due to the unbalance of the line), but to
a lower value (cf. Figure 5.5). Due to the time derivative used in equations
(5.28) and (5.29) the detection functions 0 1 and 02 show very large values
the moment the waves arrive at the relay position. The spike due to a
backward fault might be much higher than the final value (i.e. after the
spike) during a forward fault. This will make a reliable detection very
-63-
difficult. A low-pass filter will be needed to reduce the amplitude of the
spikes. The filtering wi 11 be performed here on x 1 and x2 before the
determination of the derivative.
X
(j,---1-----
1--------2
t-
D
Figure 5.5. "Forunrd unues" during
backunrd fault (1) an.d during forunrd
• faul.t (2).
Figure 5.6. Detection. functions
durtn.g back.unrd fault (a) an.d durtn.g
forunrd fault (b). The dotted l.in.e
indicates the threshol.d needed to
distinguish between. the two
st tuation.s.
t-
The shape of D1 and D2 when using a low-pass filter is shown in Figure 5.6,
where the dotted line is a threshold value bused in the detection criterion
D1 >6 or D2 >6
D1 <6 and D2 <6
forward fault ,
backward fault .
(5.30)
(5.31)
For a reliable directional detection the threshold must be such that it is
above the highest value of D1 and D2 during a backward fault. But during
each possible forward fault at least one of the detection functions must be
above the threshold.
TWONFIL calculations have been performed to determine the values of the
nonfiltered detection functions after the initial spike. The detection
functions have been determined for all possible backward as well as forward
faults {cf. Section 4.1). It appeared for line type A that the threshold
should be below 1222 units ( 1000 units is the amplitude of the phase-to
ground voltage). It has also been found that the highest value of x 1 and x2
during a backward fault is 215 units (an impedance value of 250 Q has been
used).
-64-
To suppress the spikes during a backward fault, x 1 and x2 are send
through a low-pass filter with a cut-off frequency fc. The worst backward
fault situation occurs when x{t) shows a jump: A
x{t) = x.U(t) .
After the low-pass filter this read as
x{t) = ~ { 1- exp(-2ttfct)}.U(t) •
leading to the following detection function: 4x2f 2 ~
D{t) = ~ [1-2 exp{-2ttf t) + (1 + __ c_)exp{-4xf t)] c 2 c
w 0
For fc~w0/2tt the highest value (reached for t=O) is equal to
A 2ttfc Dmax = x -w-- .
0
This value must be below the threshold 6, so
A
(5.32)
(5.33)
(5.34)
(5.35)
(5.36)
For 6=1222, x=215, this gives fc=284 Hz. For a forward fault during voltage
maximum this low cut-off frequency introduces no problems. The fault will be
detected illlllediately due to the high spike in the detection function.
Problems will arise however for faults around voltage zero, when x{t) is a
ramp function A
x{t)= w0
x t . (5.37)
After the low pass filter the shape is as follows:
A W X { } x(t) = w
0 x.t- ~f 1- exp{-2ttfct) ,
c (5.38)
leading to the following detection function:
D{t) = ~ wo [ [ t 1-e~~~fct) ]2
+ [ 1-exp::2ttfct) ]2
]~ . (5.39}
During an RN fault x=1400 units, together with fc=284 Hz. the threshold of
1222 units will be exceeded after 1030 JiS. This is not much faster than
obtained with the considerably more simple Johns' algorithm.
Multiple reflections will result in multiple spikes in the detection
functions leading to a constant noise level of considerable magnitude. This
calls for even lower cut-off frequencies and thus even longer detection
-65-
times. So despite of the more complicated calculations Dommel's algorithm is
not faster than others.
5.3. Results of the testing of Johns' algorithm
~he atg.<Ytt,tha
The algorithm by Johns [ 1980] has been used as a starting point for the
extensive testing. It has been chosen due to it's simplicity. During the
testing some modifications have been introduced leading to the algorithm
described in this section.
After the superimposed quantities have passed a low-pass filter with a
cut-off frequency 1/T ( T being the travelling time of the line ), four
detection functions are calculated:
D Fw _ 1 - ( Vt - Vs - R, ( it - is
D2Fw ( v,. - Vt - R, ( i,. it
01Bw
( Vt - Vs + R, ( it is D Bw _
2 - ( v,. - Vt + Rt ( i,. - it
(5.40)
(5.41)
(5.42)
(5.43)
As compared to the original algorithm other combinations of phases have been
used to reduce the number of calculations needed (compare (5.40) through
(5.43) with (5.20) through (5.25) ).
The following detection criterion will be applied:
[IDtFwl<o and ID2Fwl<o]and[IDtBwl>o or ID2Bwl>o]: Backward fault. (5.44)
IDtFwl>o or ID2Fwl>o : Forward fault , (5.45)
[IDtFwl<o and ID2Fwl<o]and[IDtBwl<o and ID2Bwl<o]: No fault . (5.46)
A backward fault is concluded if one of the backward detection functions
becomes high while both forward detection functions are still low {5.44). In
the original algorithm a backward fault was concluded if the above was valid
for at least one of the modes. During some forward double-circuit faults the
following situation arises : ID1 Fwl<o. ID/wi>o. ID1Bwl>o. ID2Bwl>o. This
leads to an incorrect blocking with the original algorithm. but to a correct
tripping with the new one.
After the detection of a backward fault the relay sends a blocking
signal to the other line terminal and waits for the end-of-transient to
continue its protection task:
ID1Fwl>o or ID2Fwl>o or IDtBw!>o or ID2Bwl>o :
end-of-transient not yet reached , (5.47)
-66-
ID2Fwl<b and ID2Fwl<b and IDtBwl<b and ID2Bwl<b
end-of-transient reached {5.48}
After the end-of-transient a clearing signal is send to the remote line
terminal. The end-of-transient will be reached after a few periods of the
power frequency.
If the relay is not in the blocking mode a forward fault is concluded
if one of the forward detection functions becomes non-zero. After a forward
fault has been detected the relay sends a clearing signal to the other line
terminal and waits for the reception of a clearing or blocking signal. After
receiving a clearing signal a tripping signal is generated by the relay if
the forward fault remains. If a blocking signal is received no tripping
signal will be generated and the relay waits for the end-of-transient.
WaGe-imPedance ~ettin~
The optimum setting of the wave impedance (the one leading to the lowest
threshold. cf. Section 4.3) is given in Table 5.1 together with the
corresponding threshold value for the three different line types.
line A line B line C Table 5.1. OptiiiiUlll impecUm.ce
(Q} 266 276 254 setting R1 and miniii!UlR threshold
b (units) 145 200 235 setting b for different line
b' {units) 239 270 304 types. The last row gives the
m.intii!UlR threshold when the
tmpecUm.ce setting shows an
uncertainty of 5%.
0 @ 1~ @ tg It)
jN Ill Ill
~ -1: ·c: :I :I :I
16 0 0 ... N
250 260 n2~ 240 .n-2-m._
Figure 5.7. Influence of im.pecUm.ce setting on m.ifUJliU.Uil threshold value for
three different tine types.
Figure 5.7 gives the influence of the impedance setting on the
threshold value. It gives an impression of the additional threshold needed
when the impedance setting deviates from the optimum value. Table 5.1 gives
-67-
the minimum threshold value in case the impedance setting deviates 5% from
its optimum value.
~h~e~hotd ~ettin~
The forward detection functions must remain below the threshold for some
time, after a disturbance in the backward direction. To put it the other way
around: the threshold value must be higher than the highest possible value
for the forward detection functions during backward disturbances. Four
mechanisms can be distinguished to create an undesirable non-zero value for
the forward detection functions:
1. the incorrect modal transformation used; the influence of this is given
in Table 5.1 row 2;
2. an incorrect frequency value during the derivation of the superimposed
quantities; this leads to a maximum error of about 100 units: (cf.
(4.15) with 0=1800 units);
3. an incorrect value of the wave-impedance setting (cf. Figure 5.7);
4. all kinds of noise picked up from the outside world, or created inside
of the protection system (e.g extragalactic noise. radio stations,
measurement errors and quantisation errors): a substantial part of the
external noise will be suppressed by the low pass filter and false
trips due to short duration spikes like lightning are. in general. not
possible because of the verification time introduced.
Settings for the three line types discussed here are given in Table 5.2. The
last column gives a setting that can be used for all three line types. The
threshold value is higher for this setting {making fault detection slower)
and it is not clear whether this setting holds for all possible line types.
line A Line B line C Universal R, (Q) 266 276 254 260
b (units) 400 430 470 550
Table 5.2. Relay settings for the three different line types
and universal settings usefuU for "all" U.ne types.
The following error sources have been incorporated in the thresholds of
table 5.2.:
the nonbalance of the line;
5% error in wave impedance setting;
0.5 Hz error in stationary frequency;
50 units additional noise.
-68-
figure 5.8. fault on a paraLLeL circuit; T 1
1; T 2 =traveLLing time fault to relay 2.
travelling time fault to relay
After the detection of a backward fault the relay must be blocked to prevent
false detection of a forward fault due to reflected waves. The shortest time
window between the arrival of the backward waves and the arrival of the for
ward waves occurs during faults on the parallel circuit (c£. Figure 5.12).
As soon as the waves following path A arrive at relay 1 (T1 after raul t
initiation) the backward detection functions will become non-zero. The
forward detection functions become non-zero as soon as the waves following
path B arrive (T1 +2T2 after fault initiation). I£ the fault is close to
relay 2 the time difference (2T2 ) is very short and relay 1 will probably
{incorrectly) detect the fault as a forward fault. Fortunately relay 2 will
have almost twice the travelling time of the line (2T1 ) to detect the fault
as a backward fault. The communication between the relays will prevent the
disconnection of the non-faulted circuit.
The worst situation is a fault midway on the parallel circuit. In that
case both relays have only one travelling time (T1 +T2 ) available. So after a
backward fault the relay must go into the blocking mode within one
travelling time of the line-to-be-protected.
~ication and ~e~ification time
With directional detection there are two ways of communication between the
line terminals: a "directional blocking scheme" and a "directional clearing
scheme". In the t:LL~e.cUonai ~ioekLng. !!.eke-me a tripping signal will be
generated in case of a" forward raul t not followed by the receipt of a
blocking signal within a certain time. This verification time must at least
be equal to the difference in travelling time between the communication link
and the high-voltage line. It must also be longer than the minimum
verification time as introduced in Section 4.3.
In the t:LL~ectLonai cie~L~~ !!.eke-me. a tripping signal will be generated
in case of a forward fault followed by the receipt of a clearing signal. The
time between detection and tripping depends on the fault position. For a
fault close to the relay it is equal to the sum of the travelling times of
-69-
the communication link and the high-voltage line. For a fault close to the
remote line terminal it is equal to the difference in travelling time.
In both schemes a tripping signal must only be generated if the forward
detection function remains above the threshold during the verification time.
Figure 5.9 gives the verification and communication time as a function of
the line length. The travelling time of the communication link is considered
to be 530 J.ts/100 km (a fiber optic link) versus 330 J.ts/100 km for the
high-voltage line. The upper dotted line denotes the sum of the travelling
times, the lower one the difference between them. The solid curve gives the
minimum verification time needed to cope with lightning. for a threshold
setting of 400 units.
In case of a blocking scheme the communication time (equal to the
difference in travelling time) is too short to cope with lightning. An
additional verification time will be needed. Only for lines longer than 200
km this is not necessary. In case of a clearing scheme the verification time
due to communication is in between the two dotted lines. To cope with the
worst case (a stroke close to the remote line terminal) the same additional
verification time as with the blocking scheme is needed.
It can also be concluded from figure 5.9 that a blocking scheme is not
faster than a clearing scheme for short lines (i.e. shorter than 35 km).
t t s
I / I 1 / / 1 I I I
o I / g I 1
I / I I I I I I I I I
50 100
I I
I
I I
I I
I
/ I
I
I I
/
200 d(km)--
Figure 5.9. Duration of "light
ning stroke" in foriiXlrd detection
function for different line
lengths. The dotted Lines give
communi cat ion time.
I
-7o-
~aatt detection time
As shown in Section 4.4 the detection time is very small for most faults,
typically 10-100 ~s. Only for faults around voltage zero the detection time
can be much longer. The maximum detection time depends on the feeding
network as well as on the distance to the fault. Table 5.3 gives this
maximum for the network of Section 3.5. The fault was situated at a distance
of 12 km from Diemen and 45.7 km from Krimpen. All detection times appeared
to be below 1.5 milliseconds. The tripping time will be about 500 ~s for
most faults but increase to somewhat below 2000 ~s for faults around voltage
zero. It follows from Section 4.4 that only a small region around voltage
zero possesses long detection times. For a single-phase-to-ground fault the
width of this region is about 30°. In case of a verification time of 500 ~s.
24% of the power frequency cycle will show a tripping time above 1
millisecond. But this will be much less than 24% of the number of faults.
Fault
Diernen
R-N 1120 ~s
S-N 1050
detection
Krimpen
1460,.Js
1400
Table 5.3. Detection time for single
I~tase-to-grOlllld and I~tase-to-phase
fa.u:tts.
lT-N 1010 1440
R-S Sr,O 1220
R-T 500 660
S-T 520 730
Nondetect~Le ~~~ fauLt~
After the detection of a backward disturbance the relay is blocked. This
blocking will last for a few cycles of the power frequency. If a fault
occurs on the line-to-be-protected during the blocking time the relay will
not react. Examples of these nondetectable faults are:
faults during line energizing;
faults evolving from the parallel circuit;
a fault in the zone-to-be-protected within a few cycles after a fault
on the parallel cicruit or on an adjacent line: this might occur due to
two lightning stokes shortly after each other or due to some strange
coincidence.
Figure 5.10. Waves during a non
detectable double-circuit fault.
-71-
Also some rare double-circuit faults showed to be nondetectable. With
these faults the zero crossings of the forward detection functions (i.e. of
the waves generated at fault initiation) do not coincide for both circuits.
Figure 5.10 shows the travelling waves for a double-circuit fault that
occurred close to a zero crossing in circuit 1. Trave ll i ng waves are
initiated in circuit 2. but not in circuit 1. At the busbar behind the relay
position both circuits are connected. A forward wave in one circuit will
cause a backward wave in both circuits. In circuit 2 forward and backward
detection functions exceed the thresholds leading to the detection of a
forward fault. In circuit 1 only the backward detection functions exceed the
threshold. This will cause the relay to make a wrong decision (backward
fault instead of forward fault).
8 I()
8 I()
I
········ ........... .
\.----'\ 0 sw
I, 1 ...... :~······· .......... .
• ...... '\ ..... .! \ i :
0Fw 2
-t (~S)
Figure 5.11. RVN-fault, .P=%0
, at 12 km.
frOIIl Diemen and 45.7
km. fr011t Krimpen (cf.
Figure 3.10). De tee-
tion functions are
given for the relay in
Dtemen in circuit 1.
Dotted Lines denote
the threshold.
Figure 5.11 shows an example of such a nondetectable situation. An RVN fault
at a fault-initiation-angle of 96° causes travelling waves in circuit 2 but
not in circuit 1. The figure shows the situation for the relay in Diemen.
The forward detection functions remain below the threshold for some hundreds
of microseconds, while D1 Bw exceeds the threshold soon after the waves ar
rive at the relay position. Therefore a backward fault is detected instead
of a forward fault. Even if the relay in Krimpen detects a forward fault,
both relays will be blocked and the (faulted) circuit will not be disconnect
ed. The other circuit shows no problems during this fault situation.
Although this is an extremely rare situation a back-up relay will be
necessary for this. According to Light [1979] about 130 faults occur each
year in the British CEGB network. Three percent of them are double-circuit
faults. There are 53 types of double-circuit faults, 15 of them show the
behaviour discussed above. Suppose all double-circuit faults and all
-72-
fault-initiation angles are of equal probability. Further suppose that those
15 fault-situations are nondetectable during 10 X of the power-frequency
cycle. In that case 1 nondetectable double-circuit fault is expected each 10
years on the CEGB network.
~ ~umaa~ of tke ~e~att~
It is shown in this section that the somewhat modified version of Johns'
algorithm is capable of generating a tripping signal within about 500 J.Ls.
This time holds for faults with a considerable voltage jump. Faults around
voltage zero show a longer detection time. The longest tripping time is
about 2000 J.LS.
A few situations showed to be nondetectable:
-a fault during (due to) line energizing;
-a single-circuit fault evolving to a double-circuit fault:
- a fault within a few cycles after a "backward disturbance";
a few rarely occuring double-circuit faults.
A false trip will only be generated in case of a direct lightning
stroke with an extreme shape (high maximum current, slow decay) but not
leading to a flashover.
-73-
6. Differential protection
The basic assumption for travelling-wave-based differential protection is
the same as for directional detection: " a source of travelling waves in the
zone-to-be-protected is a fault". The detection functions, determined from
incoming and outgoing waves at both line terminals, are proportional to the
fault current. This leads to a highly reliable algorithm but at the same
time it calls for a highly reliable communication link. Like with
directional detection, voltages and currents have to be measured at the line
side of the circuit breakers.
6.1. History
The algorithm for travelling-wave-based differential protection is proposed
by Takagi et al. [1977]. When a line is healthy, the incoming waves at one
terminal will be outgoing waves at the other terminal after one travelling
time.
i .L I Flgure 6.1. Line-to-be-protected and -0+ + definitions used for differential
v T z v' protection.
For a loss less single-phase line (cf. Figure 6.1} Bergeron's equations
(2.22) and (2.23) read as
v(t) + Z.i(t) = v' (t+T) - Zi' (t+T)
v(t} - Z. i(t) = v' (t-T) + Zi' (t-T)
(6.1}
(6.2)
where Z and T are wave impedance and travelling time, respectively. For a
multi-phase line these equations hold for each modal component. The soon a
fault occurs on the line Bergeron's equations do not hold anymore. This has
led to the following detection function for mode k:
fk(t)=ik(t)+ik' (t-Tk) ~{vk(t)-v.; (t-Tk)} . (6.3)
It can be proved that this detection fucntion is equal to the (modal}
current at the fault position. This led to the following detection
criterion, for a three-phase line:
ft::O and f2::0 and E3::0 Et~ or f2~ or E3~
, no internal fault ,
, internal fault .
(6.4)
(6.5)
Takagi at al. [197Sa, 1978b] use equation (6.3) for their "simply d' Alembert
relay". Instead of modal quanti ties they use phase quanti ties. They have
-74-
studied the influence of variations in the impedance setting Z and the
travelling time setting T. An incorrect travelling time setting appears
shown to introduce spikes in f(t) during an external fault. This may cause
misoperation of the relay. A low-pass filter is proposed to reduce this
risk. An error in impedance setting does not seem to have much influence on
the detection functions.
6.2. Results of the testing
Takagi's algorithm has been modified slightly to make it correspond to the
standard algorithm of Section 4.2.
~he aigc'tt.tha
From the actual values of filtered voltages and currents measured at both
line terminals, two detection functions are calculated:
£1 (t) = [ {vt(t)-vs(t)} - R1{tt(t)-is(t)} ]
- [ {vt' (t-T)-vs' (t-T)} + R1{it' (t-T)-is'(t-T)}] • (6.6)
[ {vr(t)-vt(t)}- R1{ir(t)-it(t)} ]
- [ {vr' (t-T)-vt' (t--r)} + R1{ir' (t--r)-it' {t--r)} ] (6.7)
where R1 and T are wave impedance setting and travelling time setting,
respectively. The following criteria are used for fault detection:
l£t{t)l > b or l£2{t)l > o internal fault •
l£t(t)l < o and l£ 2{t)l < o no internal fault
{6.8)
{6.9)
After the detection of an internal fault, the verification time is started
as introduced in Section 4.3.
~he OOARUnicatLon iink
A differential relay uses voltages and currents from both line-terminals. To
transmit these signals communication links are needed (cf. Figure 6.2).
Three voltages and three currents are transmitted from terminal 8 to termi
nal A. Three tripping signals are transmitted back to terminal B. Shorter
communication links are present between the relay and the circuit breaker
and between the relay and the measurement transformers at terminal A.
-75-
3x trip y 3V 3i
A l B
'-" '-"
Figure 6.2. Communication links used for differential protection.
The relay takes the difference between local quantities and remote
quantities one travelling time of the high-voltage line back in time. The
remote quantities are transmitted to the relay via a communication link. As
the travelling time of this communication link is always larger than that of
the high-voltage line. the remote quantities are delayed too much when they
arrive at the relay. To compensate this excess delay the local quantities
must be delayed too. This local delay must be equal to the difference in
travelling time between the communication link and the high voltage line. It
is interesting to note that this is equal to the minimum time needed for
communication when using directional detection. But with directional
detection this time could be used as a verification time to prevent false
tripping. This is not possible with differential protection as the detection
functions are calculated after the delay. So this difference in travelling
time will lead to a fundamental delay in fault clearing.
For a glass fiber link the tr~velling time will be about 500 ~-ts/100 km.
for the high-voltage line this is about 330 ~-ts/100 km. The additional delay
will be about 200 ~-ts/100 km plus the delay in transmitter and receiver. In
case a cable is used as a communication link, the delay will be longer. The
transmitter/receiver delay is not included in these figures.
1ettt~g of tapedaace ~a t~etttng ttae
As already stated in Section 4.1, all kinds of external disturbances have
been studied by using TWONFIL as well as EMTP. From this study it appeared
that "backward external faults" (c£. Figure 4.3) give rise to higher values
of the detection functions than "forward external faults". The highest
values are reached when the first waves arrive at substation A. The
detection functions remain at this value for twice the travelling time of
the line. As the (superimposed) remote quantities are zero during twice the
travelling time of the line, the detection functions of differential
protection (6.6-6.7) transfer to the forward detection functions of
directional detection (5.40-5.41). Because of this the impedance setting for
directional detection can also be applied to differential protection. So can
the corresponding value of the threshold. Both can be found in Table 6.1.
-76-
AI~ 61" I Figure 6.3. Backux:trd (1} and
72 ·fonoo.rd (2} external faults.
~ The travelling time setting will be midway between the travelling time
of the fastest mode and that of the slowest aerial mode (cf. Section 4.3).
~Pike~ i~ the detection tunction~
It was shown in Section 4.3 that the different modal velocities cause spikes
in the detection functions. The highest spikes occur for a forward external
fault, just outside of the zone-to-be-protected (i.e. a fault in the remote
substation}.
One of the most beautiful examples of spikes in detection functions is
shown in Figure 6.4. The simulated network was the basic network of Figure
3.10 with the line between Diemen and Krimpen replaced by a 50 km line of
type B. An RSTN-fault at a fault-initiation-angle of 60 degrees occurred in
the substation Diemen. The differential relay was situated in the substation
Krimpen and protecting circuit 1 of the line to Diemen. Wave impedance and
travelling time have been set according to their optimum values.
500
t{JJS) --500
-1000
Ftgure 6.4 Spike in detection function.
-77-
In case the travelling time is not set according to its optimum value
the spikes in the detection functions are of longer duration. Expressions
for the height of the spike, as well as the time-above-threshold are given
in Section 4.3. Of interest here is the time-above-threshold; it must be
shorter than the verification time. With f =1/T, (4.12) transfers into c
t = ~ ln { ~ S . O.~At+T} + T + 0.5At {6.10)
where At is the difference in travelling time between the fastest and
slowest aerial waves and T the error in travelling time setting. To prevent
accumulation of spikes due to multiple reflections the time-above-threshold
may only be a fraction of the travelling time of the line.
The height of the block S is at maximum about 4000 units. a threshold of 450
units and a maximum allowed time-above-threshold of 20% of the travelling
time of the line allows for 3% error in travelling time setting for line
type A and C; for line type B the allowable error is only 1%. This calls for
a highly accurate synchronisation between both line terminals. More details
on this will be given in Section 8.3.
~h~e~hota ~etttn~. ~e~Lttcatton tL•e
Multiple reflections will cause multiple spikes in the detection functions.
They are of much lower amplitude than the first spike, especially after
filtering. These filtered multiple spikes cause a kind of background noise
on the detection functions. This calls for an increase in threshold value.
An increase of about 150 units appeared to be more than sufficient to
prevent false tripping. This leads to the following threshold settings for
the three line types :
450 units for line type A;
475 units for line type B:
500 units for line type C.
The following error sources have been incorporated in this setting:
5X error in impedance setting:
3% error in travelling time setting (1% for line type B):
150 units noise due to multiple reflections:
50 units additional noise.
The minimum verification time needed to cope with lightning strokes is only
a 11 ttle shorter than the one for directional detection. All settings for
the differential relay are given in Table 6.1.
-78-
line A line B line C
Impedance 266 Q 276 Q 254Q
Threshold 450 units 475 units 500 units
Travelling time 346 J.I.S 364 j.I.S 342 j.I.S
Verification time 260 j.I.S 260 j.I.S 260 j.I.S
Cut-off frequency 3kHz 3kHz 3kHz
Table 6.1. Settings for differential protection of a 100 km line.
~i.,ne ene'l.g-L:fLttg
The algorithm for differential protection shows a "perfect" discrimination
between internal and external faults. However during line energizing (or
during fast reclosure) a nondetectable situation occurs. The relevant part
of the high-voltage network is shown in Figure 6.5. The circuit breaker on
the right remains open whereas the left one closes. The differential relay
will detect any fault on the line in between the measurement transformers.
Problems might occur for a fault in one of the two small regions A and B in
between the circuit breaker and the measurement transformer. A fault in
region A can be detected by the busbar protection or by a special zero
voltage detector (the voltage drops to a very small value almost immediately
due to such a close fault). A fault in region B will not be detected. As
this is the place where the highest overvoltages occur during line
energizing, it is the place with the highest chance of insulation failure.
Switch-on-to-fault situations in regions A and B also occur when the ground
connectors are not removed after a line has been out of operation. This is a
situation that seems to occur quite often. A special algorithm will be
needed for switch-on-to-fault detection. Some possible solutions are
proposed in Section 7.4.
Figure 6.5. Line energizing and differential protection.
-79-
~Peed ot taait detectLon
The time between fault initiation and the generation of a tripping signal
consists of the following contributions:
a. travelling time between the fault position and the relay position; this
contribution will not be considered here;
b. additional .delay to compensate the longer travelling time of the
communication link; it is about 200 ~s per 100 km, as discussed before;
c. the detection time as discussed in Section 4.4; the detection time for
faults around voltage zero is given in Table 6.2 for line type A for
the same situations as shown in Table 4.4; it is about equal to the one
for directional detection:
d. the verification time (to exclude false tripping); this is between 200
and 400 ~s depending on the line length.
For a 100 km line the tripping time (b+c+d} will be between 500 and 1600 ~s.
when using a glass fiber communication link.
Fault time (!-is) TabLe 6.2. Detection time for single-phase-to-ground
and phase-to-phase fauLts on Line type A. RN 1100
SN 1000
1N 1100
RS 900
Rf 550
ST 600
6.3. Differential or directional ?
In the preceeding chapters similarities as well as differences between
directional detection and differential protection have been found:
both are able to generate a tripping signal within a few milliseconds;
the hardware requirements will be about equal for both principles.
except for the derivation of the superimposed quantities with
directional detection and the synchronising between both terminals for
differential protection;
both might generate a false tripping signal due to extremely shaped
direct lightning strokes:
directional detection shows a few nondetectable situations but
differential protection shows none.
Although differential protection might show hardware problems due to the
synchronization needed, the author gives prefers this one because of its
high reliability. But others may have a different opinion in this.
-so-
7. Other algorithms for travelling-wave-based protection
7.1 History of distance protection
~he c~~eLatLon aethod
The time delay between incoming and outgoing waves at the relay position,
can be a measure for the travelling time between the relay and the fault and
hence of the distance to the fault. This method for distance protection has
been proposed by Vitins [1978] and was further developed at the University
of Manchester [Crossley and McLaren, 1983; McLaren et al., 1985].
__!_.
:· ~· 1_ : Figure 7.1. Incoming (F) and
outgoing (B) waves as used for • /\JV\f"'- F
correlation method.
Consider the single-phase situation shown in figure 7.1. From the actual or
superimposed voltages and currents two quantities are formed:
F(t) = R i{t) + v{t)
B{t) = R i{t) - v{t)
(7.1)
{7.2)
where R is the wave impedance setting. In case of a solid fault and a travel
ling timeT between the relay and the fault, the following expression holds:
B{t) = F{t-2T) . {7.3)
From B{t) and F{t) a correlation function can be formed: T
~(x) = T~x I B{t)F{t-x}dt , (7.4}
X
where T is the measurement window. The correlation function ~{x) will show a
maximum for x=2T.
Crossley and McLaren [1983] use superimposed modal quantities to
calculate correlation functions according to {7.4}. But {7.3) only holds for
modal quantities during a three-phase fault. In case of a single-phase fault
the maximum in the correlation function is not as pronounced as during a
three-phase fault. This causes difficulties in fault detection, especially
for faults close to one of the line terminals. Problems also appear for
faults around voltage zero. In most situations the algorithm cannot
discriminate between a fault at a distance x behind the remote terminal and
a fault at a distance x from the relay. Some problems can be solved by
combining the correlation method with Donmel' s method [Koglin and Biao
Zhang, 1987], by using two different measurement windows [Shebab-Eldin and
-Bl-
McLaren, 19BB] or by using the difference in travelling time between the
ground mode and the aerial modes [Christopoulos et al., l9B9]. But still no
satisfying solution has been found.
::ltoh.i..a(l.' aLgcnithm
Kohlas [1973] proposes a method to calculate the voltages and currents along
a single-phase line from the voltages and currents measured at one of the
line terminals. The line is considered to have frequency independent R, L
and C values and G = 0. He gives complicated expressions for voltages and
currents along the 1 ine and rewrites these to somewhat less complicated
discrete expressions.
When the voltages along the line are known, a fault will show up as a
place where the voltage remains zero. Ibe and Cory [19B6, l9B7] use the
discrete expressions of Kohlas to calculate voltages along the line and from
those the following detection function:
T-z/c
d2
[ 1 I 2 ] G(z) = d? T-2z/c v (z, t)dt ,
zlc
(7.5)
where c is the propagation velocity of the waves and T the measurement
window. The fault position will show up as a very sharp maximum in G(z).
....!.!i: tl
vlz,tJ AZ At
i(l!~)
V (Z+IIZ,t)
Figure 7.2. Part of a stngte-phase
tosstess tine.
Our experiments have shown that it is not necessary to use the
complicated expressions of Kohlas. Leaving out the terms caused by the
resistance R, will give expressions that can be derived from Bergeron's
equations, (2.22) and (2.23). These expressions read as (cf. Figure 7.2):
2v(z+Az,t) = v(z,t+At) + v(z.t-At)
- Zi(z,t+At) + Zi(z.t-At) ,
2Zi(z+Az,t) = v(z,t+At) - v(z,t-At)
+ Zi(z,t+At)+ Zi(z.t-At)
(7.6)
(7.7)
Bergeron's equations as weel as (7.6) and (7.7) hold for a single-phase line
and for the modal quantities on a multi-phase line. But only phase
quanti ties can be measured and in general, only the phase voltage at the
fault position is equal to zero. From (7.6) and (7.7) the following
expression can be derived for the phase currents:
-82-
I(p)(z+!z,t) = Q y(c) S-1
[ y(P)(z,t+!t)- y(P)(z,t-!t)
+ I(p)(z,t+!t) + I(p)(z,t-!t) • (7.8)
where y(c) is the inverse of the wave impedance matrix z(c). A similar
expression can be derived for the phase voltages. For the balanced
three-phase line of Section 2.3.1 these equations transfer to:
2vr(z+!z,t) = Vr(z,t+!t) + Vr(z,t-!t)
- Ztir(z,t+!t) + Z1 1r(z,t-!t)
- t (Zo-Z1 ) {to(z,t+!t)- i 0 (z,t-!t)}
2Z1 ir(z+!z,t) = Vr(z,t+!t) - Vr(z,t-!t)
+ Z1 ir(z,t+!t) + Z1 1r(z,t-!t)
-(Z0 -Z 1 )/3Zo {v0 (z,t+!t)- v0 (z.t-!t)}
where i 0 =ir+i 8 +it
and v0 =vr+v5 +Vt
(7.9)
(7 .10)
Similar equations are valid for the other phases. From the voltage profiles
six detection functions are determined:
T-z/c
F(z) = T-2!/c J v2(z,t)dt
z/c
(7 .11)
Three detection functions are calculated from the phase voltages Vr.v •• vt,
to detect single-phase-to-ground faults; three detection functions are
calculated from the line voltages vr-v8 , v,.-vt• vt-Vr to detect
phase-to-phase faults. If a fault is detected by only one detection function
a single-phase trip will be generated. A three-phase trip will be given as
soon as two or more detection functions detect a fault.
A fault is detected if all three conditions below are true:
the detection function F(z) shows a minimum not coinciding with one of
the line terminals;
if Fmax and Fmin are maximum and minimum value of F(z) respectively,
than Fmax/Fmin > !;
at the suspected fault position 50% of the voltage values must be, in
absolute value, below 100 units.
EMTP simulations have shown that a fairly good discrimination can be made
between internal faults and external faults [Van Dongen. 1988]. Still some
problems remain:
faults close to one of the line terminals are not detected;
most of the double-circuit faults are not detected;
-83-
the calculations to perform need a lot of computation time, making a
relay based on this principle slow.
Nimmersjo and Saba [1989] use equations somewhat more complicated than
(7.6) for the detection of a close fault. They include losses by introducing
an exponential factor in Bergeron's equations. A low-pass filter with a low
cut-off frequency is used. Their experiments yield a tripping time of about
10 mi 11 !seconds.
~ke atgo~LthM ot ~L~topouto~
Christopoulos et al. [1988, 1989] propose an algorithm that derives
information from successive reflections of travelling waves. From the
measured time delay between incoming and outgoing waves a fault distance is
estimated. This leads to a certain redundancy. In case of a contradiction a
new distance is estimated.
The principle shall be reproduced in a modified form. From the first
waves arriving at the relay position the direction to the fault is
determined by using the following detection functions:
DFw = v - Zi ,
r/'W = v + Zi
(7.12)
(7. 13)
In case of a forward fault more computations are performed. The reflected
wave travelling from the relay position back to the fault (with amplitude
r/'W) is reflected at the fault and travels back to the relay position again.
Upon arriving there it causes a jump in DFw and r/'W. From the jump ADFw in
DFw and the pre-jump value of r/'w. the fault impedance RF can be determined:
(7 .14)
From the elapsed time between the first and the second jump in DFw an
estimate for the fault distance is found. The pre-fault voltages and
currents at the relay position are used to calculate the pre-fault voltage
at this estimated fault position. If the pre-fault voltage is equal to VF
and the post-fault resistance equal to RF' the amplitude of the initiated
wave is equal to: Fw 2Zo
D = - Zo+~ VF (7 .15)
This wave is detected at the relay position as the first jump in ufw. From
this jump a second estimate for the fault resistance is found:
0Fw _ 2Zo (7. 16)
-84-
If this value agrees with the value of (7.14) the fault is considered to be
at the estimated distance. If the values do not agree the procedure is
repeated for another jump in DFw. This is continued untill the fault
position is found or untill the fault is shown to be outside of the
zone-to-be-protected.
The algorithm has been tested for a few situations. It has been shown
by Christopoulos et al. [1988, 1989] that it is possible, in those
situations, to distinguish between an internal and an external fault.
7.2. Double circuit current comparison protection (DOOCP}
The algorithm discussed in this chapter deviates from the algorithms
discussed before on two counts:
quantities from both circuits of a double-circuit line are used:
The algorithm makes use of a specific network configuration.
Special measures have to be taken to prevent the above differences from
becoming disadvantages of DOOCP.
~he P'Li-nci-pie
Figure 7.3. Double-
circuit tine with
ZJ3 I® ZJ, ~2 internal fCllllt (1)
and external fCllllts
(2,3). R denotes a
ZXXJ.:;P- relay .
Consider the double-circuit situation shown in Figure 7 .3. In case of an
internal single-circuit fault (position 1), the currents in the faulted
circuit will be different from the currents in the non-faulted circuit. In
case of an external fault (position 2 or 3), the currents in both circuits
are equal. This leads to a very simple relaying algorithm:
(ir=iu) and (i 5 =iv) and (it=iw)
(ir#iu) or (i 5 #iv) or (it#iw)
no fault
fault .
(7 .17)
(7 .18)
It holds for stationary quantities, as well as for travelling waves. The
travelling-wave-based algorithms is be named double-circuit current
comparison protection or in short DOOCP. The principle has been used in the
past, based on the balance of stationary currents [Clemens and Rothe, 1980].
It has never been in general use, because [Blackburn 1987]:
it is not applicable to single-circuit lines;
it must be disabled for single-circuit operation:
-85-
it requires interconnections between the controls for the two lines,
which is not desirable for reasons of reliability:
it can experience difficulties for a fault involving both circuits.
The first disadvantage is fundamental and applies also to the travelling
wave version. The second disadvantage is strongly related to the first one.
It calls for some kind of external blocking when only one cicrui t is in
operation. This used to be a problem in the past but integration of
protection and control will facilitate it to a large extend. Chapter Swill
provide an example of such an integrated scheme.
In case usually only one circuit is in operation, it is of course not
very practical using ~- But in the majority of cases usually both
circuits are in operation.
The third disadvantage is overruled by tripping at most one circuit (to
prevent incorrect double-circuit tripping) and by combining I:lCXl:P with a
backup working on a single-circuit basis. The fourth disadvantage is also
overruled by this backup.
DOOCP shows a few important advantages when compared to other
travelling-wave-based algorithms:
it does not use quantities from the remote line-terminal, therefore no
additional delay nor any unreliability due to the communication link,
is introduced:
the calculations to perform are much less complicated than for other
algorithms not needing a communication link.
This section will discuss the algorithm for ~ as if it operates
independently. Chapter S will discuss it as part of a protective scheme.
Also some hardware requirements will be given there.
~he aLg.o'tLtha
AI though the basic principle is the same, the detection functions are
somewhat different from (7.17) and (7.18). The new detection functions only
use aerial mode quantities (cf. Section 4.2).
From the superimposed currents at one line terminal the following
"disturbance-detection functions" are determined:
X1 = R (it-is) • (7 .19)
X2 = R (ir-it) (7.20}
x3 =R (iw-iv) • (7.21)
x .. = R (iu-iw} (7 .22)
The value of R is not of any importance for the performance of the
algorithm. It is only used to get values comparable to the values of the
detection functions for directional detection and differential protection.
-86-
This is done by making R equal to an approximation of the aerial mode wave
impedance. In this study the round value of 250 Q has been used. Two
"fault-detection functions" are determined:
Dt = X1-X3
D2 = X2 -x .. (7.23)
(7.24)
For circuit selection two "circuit-selection functions" are determined after
the detection of an internal fault:
c1 1x1 1-1x31 C2 = 1x21-1x .. 1 .
N
Figure 7.4. Decision process of DCOCP.
(7.25)
(7.26)
A flow chart of the detection criteria is shown in Figure 7 .4. After the
detection of a disturbance (at least one of the disturbance-detection
functions exceeds the threshold f) an internal fault is detected if a
-87-
raul t-detection function exceeds the threshold b. If the raul t-detection
functions all remain below the threshold ban external fault is detected and
the relay will be blocked till the end-of-transient. This is to prevent a
false trip due to the unbalance of the stationary short-circuit currents
during an external disturbance.
After detection of an internal fault the faulted circuit is selected.
Only one circuit is tripped, also during double-circuit faults. This is to
rule out incorrect double-circuit trips as much as possible. After detection
of an internal fault and selection of the faulted circuit a verification
time is started.
~ett~ng ot the cut-ott t~e~enc~
For a quantitive study. the three line types of Section 3.3. have been used
in combination with TWONFIL, as well as the EMTP networks shown in Figures
7.5 and 3. 10.
ENS MAAS~--~~~-----r------~~~--+-------~~--~VLAKT
66.2km 59.7km ~"""-- 52km
DIEM EN KRIMPEN
2R85km
G' BERG -"---
Figure 7.5. Network configuration used for EKTP testtng of rx::a:;p, The
presentations of the terminations at Ens, Diemen and .Haasulakte are the same
as discussed in Sectton 3.5. The line Geertruidenberg-Eindhouen has been
represented by its wave impedance. The stationary short-circuit current at
Kr!mpen due to a three-phase subs tat !on faut t has been increased to 50 kA on
a 380 kV basis, to get a high short-circuit current.
The external faults studied by using TWONFIL are shown in Figure 7.6.
The worst cases {highest values of the fault-detection functions) appeared
to occur for fault position 3, due to the differences in travelling time for
the different modes as discussed in Section 4.3.
-88-
Figure 7.6. External faults studied for DDOCP.
3
Figure 7. 7 Shape of the
filtered detectton func
tton for DDOCP during a.
faul.t a.t the remote line
term.inal.
Figure 7. 7 shows such a spike after having passed through a low-pass
filter. The shape can be approximated as:
(7.27)
where fc is the cut-off frequency of the low-pass filter used. The values of
x0 and x 1 have been calculated for faults at the remote line-terminal. The
travelling times of the different modes have been derived from EMTP
("travelling time for the highest frequency" as used by JMARTI SETUP;
Section 3.2.3). A comparison between filtered EMTP values and filtered
TWONFIL values showed the difference to be less than 6%.
The highest values of x0 and x1 found from TWONFIL have been used to
determine minimum threshold values for the three line types. If a cut-off
frequency equal to 1/T is used, the condition that the detection function
shall not be above the threshold for longer than 0.2T during an external
fault, leads to the following minimum threshold value:
b = xo + (x1 -x0 ) exp(-Q.4n) . (7.28)
-89-
The minimum threshold values found under this assumption are:
line type A 305 units;
line type B 815 units;
line type C 407 units.
Using a lower cut-off frequency decreases the value of x1 , but it also makes
the tail of the spike longer. Therefore the minimum threshold is only
slightly lower. A cut-off frequency equal to 0.5/~ gives values of 251, 778
and 382 units for line type A, Band C, respectively. For fc=0.3/T they are
207, 623 and 382 units.
On line type B the initial jump in the disturbance-detection functions
after a single-phase-to-ground fault is about 900 units. In case of a
threshold above this value none of the single-phase-to-ground faults could
be detected by its initial travelling wave (cf. Section 4.4). Therefore a
cut-off frequency of 0.3/T is used. For line types A and C a cut-off
frequency equal to 1/T appears to be sui table.
q2T
100 200 d(km)-
Figure 7. 8. Minimum verification
time for the three line types as
a fWlCtion of the ttne length.
Circles are for line type A
(fc=l/T;0=300), triangles are for
line type B (0.3/T;800}, squares
are for line type C (1/T;I!OO).
Tite dotted line corresponds to 20
% of the trave n tng time of the
Une : the "maximum t tme above
threshold" for the fault detec-
tion fW1Ctions during an external
fault.
Like with directional detection and differential protection a lightning
stroke direct to a phase conductor might lead to an incorrect trip. This can
-90-
be prevented by introducing a verification time. As shown in Section 4.3.
the length of this verification time depends on the threshold setting and on
the cut-off frequency used. For each line type the threshold setting is
constant and the cut-off frequency is inversely proportional to the line
length. It is therefore possible to give the minimum verification time
needed as a function of the line length, as shown in Figure 7.8.
On a double-circuit line. the loss of one circuit during a short time
(e.g. 1 second) will not disturb the electricity supply. In most cases the
loss of one circuit even for a long time will not disturb the supply. It may
therefore be more practical to use a shorter verification time. in
combination with fast reclosure. Then faults will be detected faster and the
relay will detect faults closer to the remote line-terminal, as shown in the
subsection "faults near the remote 1 ine terminal". The verification time
should never be less than 20% of the travelling time of the line as this
will lead to incorrect trips due to faults in or behind the remote station.
~upe~L•Po~ed quantLtLe~
During large power flow over a high-voltage line, the unbalance between the
circuits might cause ])(XX]l to give an incorrect trip ( in case actual
current values are used). An effective current of 2500 A (corresponding to
three times the natural power flow on the Dutch 380 kV line) would cause a
maximum value for the fault-detection functions of 750 units on line type A.
This would lead to a final threshold of 1100 units which is considered far
too high. This problem can be overruled by using superimposed quanti ties.
Only a small additional threshold is needed then due to variations in the
power frequency as shown in Section 4.3. Row four of Table 7.1 gives the
additional threshold needed for the three 1 ine types in case of 0.5 Hz
frequency deviation.
~k~e~hotd ~ettLng
The fifth row of Table 7.1 gives the final threshold for the three line
types. This threshold is made up of the following contributions:
the threshold needed to keep the "time-above-threshold" for external
faults below 20% of the travelling time of the line (row two of table
7.1);
the maximum error in the fault-detection functions due to 0.5 Hz
frequency deviation (row four);
50 units additional noise.
Contrary to differential protection and directional detection, the threshold
setting shows a large variety among the three line types. This implies that
-91-
the relay setting must be determined for each line type before installation.
All discussion on thresholds hitherto concerned the threshold for the
fault-detection functions (o in Figure 7.4). An internal fault is detected
if, immediately after the threshold crossing of one of the disturbance
detection functions. the raul t-detection function is above its threshold.
This implies that, during an internal fault, the fault-detection function
must exceed its threshold f before the disturbance-detection function ex
ceeds its threshold o. According to TWONFIL calculations the fault-detection
functions show a higher absolute value than the disturbance-detection func
tions for each internal fault. This means that taking f equal to o will pre
vent incorrect blocking. EMTP simulations support this conclusion. It is
assumed here that the fault is not too close to the remote line-terminal.
line A line B line C
cut-off frequency 1/-r 0.3/T 1/-r
minimal threshold 305 units 623 units 407 units
verification time ( lOOkm) 300 J-I.S 350 J-I.S 325 J-I.S
superimposed threshold 47 units 138 units 21 units
final threshold 400 units 800 units 500 units
speed ~n 288 J-I.S 807 j.I.S 2fi1 IJ.S
speed ~ 2S3 J-I.S 471 J-I.S 267 j.I.S
speed~ 281 J-I.S 465 J-I.S 262 !lS
relay reach 92% 71% 89%
Table 7.1. Optillllllli setttngs and performance for OCI::CP on three different
Hnes of 100 km.
1aaLt~ ne~ the ~e•ote LLne-te~LnaL
An internal fault close to the remote line-terminal cannot be distinghuised
from an external fault close to the remote line-terminal. The relay reach
will therefore be less than 100 %. If the distance between the fault and the
remote 1 ine-terminal corresponds to a travel! ing time liT. the non£ i l tered
fault-detection function wi 11 possess a high value during a time 2\T and
then decrease to a lower value. Consider the fault-detection function to be
a rectangular pulse with a height D and a duration 2/iT, and the disturbance
detection function to show a step X (X<D). The "time-above-threshold" is the
time between the threshold crossing of the disturbance-detection function
and the downward threshold-crossing of the fault-detection-function. For a
-92-
threshold o and a cut-off frequency fc it is given by:
td = 2~T - ~fc ln(XIX-6} + 2:fc ln[ ~ { 1-exp(-4:n:fc~T) } ] {7.29)
This "time-above-threshold" must be longer than the verification time.
Considering the verification time to be equal to 20% of the travelling time,
the relay reach for each of the three lines for a single-phase-to-ground
fault at voltage maximum is:
line A 92%;
line B 71%;
line C 89%.
For a three-phase fault the relay reach is a little more.
~Peed ot the GLgo~Lthm
The last three rows of Table 7.1 give the tripping time of the algorithm for
specific situations. The row "speed <1>-n" gives the tripping time for a
single-phase-to-ground fault at voltage maximum. The next row applies to
phase-to-phase faults. The last row gives the tripping time for a
three-phase fault. All values have been determined for a 100 km line. As a
comparison the tripping time of a phase-to-ground fault for differential
protection on a 100 km line (line type A) is about 600 ~s. The difference is
predominantly determined by the delay due to the communication link.
Fault type detection time TabLe 7.2. Detection
1 RN 0° Diemen 12 lon 16 j.J.S
2 Krimpen 46 lon 16 j.J.S ttm.e for zx::x::;cp • as
3 RN 90° Diemen 12 lon 797 j.J.S determined by using
4 Krimpen 46 lon relay blocked ElffP. Situations 1 5 RS 30° Diemen 12 lon 14 j.J.S through 10 heme been 6 Krimpen 46 lon '12 j.J.S studted tn the basic 7 RS 120° Die men 12 lon 612 j.J.S
network of Section 8 Krimpen 46 lon relay blocked
9 RSN 120° Diemen 12 lon 68 j.J.S 3.5; situations 11
10 Krimpen 46 lon 46 j.J.S through 11, f.n the
11 RSf 60° Diemen 58lon 16 IJ.S* network of Figure 12 Krimpen 2lon 8 IJ.S 7.5. 13 Diemen 29 lon 12 IJ.S
14 Krimpen 31 lon 12 j.J.S
"Blocked if verification time is longer than 120 IJ.S.
-93-
Table 7.2 summarizes a few results of EMTP-testing. The detection time
is given for a cut-off frequency of 5000Hz and a thresholds of 400 units.
Most fault situations are detected very fast, an exception are faults around
voltage zero. Faults too close to the remote line-terminal are not detected
at all. especially those around voltage zero. The latter can be overruled by
means of a transfer-trip mechanism or by using some backup algorithm.
~Le ct~cuit taaLt~
The algorithm is, fundamentally. not suitable for double-circuit faults. Two
kinds of wrong decisions occur:
during a symmetrical double-circuit fault (e.g. R-U-N) none of the
fault-detection functions will exceed the threshold and the relay will
be. blocked;
during a non-symmetrical double-circuit fault only one circuit will be
tripped.
This again calls for a backup protection.
~tage~ and di~ad~tage~
The algorithm shows the following advantages. as compared to differential
protection:
no communication link is needed;
the tripping time is smaller;
no precise setting of impedance or travelling time is needed.
DOOCP shows a few disadvantages, too:
the relay must be blocked as soon as the double-circuit line is no
longer operated as a double-circuit line;
double-circuit faults wil not be detected;
faults close to the remote line-terminal, especially those around
voltage zero, are not detected at all;
one relay is used for the protection of both circuits;
the relay setting must be determined for each line type to get optimal
results.
The next chapter will discuss a protective scheme in which DOOCP and
differential protection are used. In that case advantages of the two
algorithms are combined.
7.3. Distance protection. yes or no?
All algorithms discussed in this section have one great advantage in common:
the reliability of the protection does not depend on the availability of a
long communication link. A common disadvantage of all distance-protection
algorithms is the inability to distinguish between a short-circuit somewhat
-94-
before the remote line-terminal and a short-circuit in or somewhat behind
the remote substation. This problem might be overruled by using a transfer
trip scheme or by introducing a delayed tripping for faults close to the
remote line-terminal. The first solution introduces a communication link as
yet, whereas the second solution slows down the protection and is not
possible for all algorithms.
Almost all algorithms for travelling-wave-based distance protection
show a fairly high degree of complexity. This makes the implementation on a
microprocessor difficult and the relay relatively slow. It will also make a
prediction of the correct operation very difficult. These kinds of
algorithms are not very suitable for fast protection. Some of the proposed
algorithms may however be used as a "slow" remote back-up. A simple
principle for distance protection is DOOCP. Its disadvantages. can be
overruled by combining it with other algorithms, as will be shown in the
next chapter.
It can be concluded that none of the proposed algorithms for
travelling-wave-based distance protection is generally suitable for the
protection of high-voltage lines.
7.4. Switch-on-to-fault detection
7 .4.1. History
One fundamental disadvantage of travelling-wave-based directional detection
is the inability to detect a switch-on-to-fault situation. Also differential
protection shows a few non-detectable fault situations during line
energizing. To overrule this Yee and Esztergalyos [1978] use a switch-on-to
fault detector in combination with Chamia's algorithm (cf. section 5.1). If
the initial current is zero and the current change is of sufficient
magnitude, but the voltage does not rise within a preset time limit, a
switch-on-to-fault condition is recognized. The time limit is set to 5-12
milliseconds. A similar principle is used by Johns and Walker [1988] in a
prototype relay based on Johns' algorithm. Ermolenko et al. [1988] use an
additional distance relay, disabled during normal practice.
-95-
7.4.2. Travelling-wave-based switch-on-to-fault detection
_/\.....!- i' Figure 7.9. Ltne energi-- zing; single-phase sttua---o 0 + +
z T tion.
v V'
Consider the (single-phase) situation shown in Figure 7.9. At the instant of
breaker closure a wave is initiated travelling from left to right. After a
travelling time T, the wave arrives at the remote line-terminal where a
reflected wave is initiated travelling back to the circuit breaker. For a
non-fault situation both waves are of equal sign and magnitude. This is no
longer true if a fault occurs somewhere on the line-to-be-protected. So the
difference between incoming and outgoing waves can be used as a fault
detection criterium.
For the line of Figure 7.9 Bergeron's equations read as:
v(t-2T) + Z i(t-2T} : v' (t-T} + Z i' (t-T}
v(t) - Z i(t) v' (t-T) Z i' (t-T}
During line energizing the other line terminal is open, so
i' (t-T) = 0 .
(7.30}
(7. 31)
(7.32}
From the above three equations an expression for the quantities on the line
side of the circuit-breaker can be derived:
v(t-2r) + Z i(t-2r) = v(t) z i(t) . (7.33)
This holds in case the line is healthy (i.e. no internal reflection point)
and if the current at the remote line-terminal is zero. This leads to the
detection algorithm below:
D(t) = {v(t-2T) + Z i(t-2r)} {v(t) - Z i(t)} . (7.34)
ID(t)l < o no fault (7.35)
ID(t)l > o fault . (7.36)
'he muttL-pha~e P~LncLPte
In case all phases of a multi-phase line are open at the remote line
terminal, equation (7.33) holds for all modes. But in general not all phases
are open. During energizing of a parallel circuit only three phases are open
(three are closed). During single-phase reclosure only one phase is open.
Both situations will be discussed further on.
-96-
Equation (7.33) refers to the phase currents, but (7.30} and (7.31} to modal
waves. From the two latter equations it follows:
[ y(c)(t-2T) + z(c) I(c)(t-2T)] - [ y(c)(t)- z{c) I(c)(t)]
= 2Z(c) I' (c){t-T) ' (7.37}
where V(c) and I(c} are vectors of component voltages and currents.
respectively; z(c} is the diagonal wave impedance matrix. Using
transformation matrices Sand Q (cf. Section 2.3} and the admittance matrix -1
y(c) = [z(c)] (7.38)
gives the following expression for the phase currents at the remote
1 ine-terminal:
2 I' (p)(t-T) [Q y(c) S-1
y(P) (t-2T} + I(p)(t-2T)]
- [Q y(c) S-1
y(P} (t)- I(p) (t)] . (7.39}
It is considered here that all modal waves travel at the same velocity.
Using the transformation matrices for the balanced double-circuit line, {cf.
Section 2.3.2). gives (the elements of the wave-admittance matrix are
denoted Y0 , Yd. Y1 , Y1• Y1 • Y1 ):
21r' (t-T) = [Yi Vr{t-2T) + ir{t-2T)]- [Y1 Vr{t}- ir{t)]
+ (Y0 +Yd-2Y1)/6 [vr(t-2T)+vs(t-2T)+vt(t-2T)-vr{t)-vs(t)-vt{t)]
+ {Yo-Yd)/6 [vu(t-2T)+vv(t-2T)+vw(t-2T)-vu(t}-vv(t)-vw(t)] . (7.40)
Similar expressions can be derived for the current in the other phases.
Figure 7 . 10. Three-phase re
ctosure on a double-circuit
tine.
-fJl-
During the energizing of one circuit of a double-circuit line (cf. Figure
7.10) three currents at the remote line-terminal equal zero:
t .. • (t) 0
is' (t) 0
it'(t)=O
(7.41)
(7.42)
(7 .43)
So are the current differences it'-1 8 ' and ir'-it', leading to the detection
functions below:
D1 (t) = [ {vt(t-2T)-v5 (t-2T)} + R1 {it(t-2T)-i8 (t-2T)}
- [ {vt(t)-v5 (t)} R1 {it(t)-i 8 (t)} ] • (7 .44)
D2 (t) [ {v .. (t-2T)-vt(t-2T)} + R1 {i .. (t-2T)-it(t-2T)}
- [ {v .. (t}-vt(t)} - R, {i .. (t)-it(t)} ] , (7 .45)
where R1 is the wave-impedance setting.
Before energizing all voltages and currents are zero. Therefore it does
not make any difference whether the relay uses momentary values or
superimposed values. Also during the new stationary situation after line
energizing both can be used because Bergeron's equations hold for momentary
as well as for superimposed quantities. For the testing of the algorithm as
discussed in the next subsection, momentary values have been used.
To detect a switch-on-to-fault situation or a fault during line
energizing the following algorithm will be used:
ID1(t)l <band ID2 (t)l < b no fault (7.46)
ID1(t)l > b or ID2 (t)l > b fault. (7.47)
~he Pe~to~ance of th~ee-Pha~e ~~-detection
The setting of the threshold value b (7.46-47) is largely determined by the
differences in travelling time between the different modes, as discussed in
Section 4.3. The optimum travelling time setting is half-way between the
fastest and the slowest aerial waves. The threshold value and cut-off
frequency needed have been determined by using TWONFIL in the following way.
On a double-circuit line. six waves are initiated by the closing of a
circuit breaker. Each wave reflects at the open line-terminal creating six
reflected waves, leading to a total of 36 travelling times. These 36 "waves"
have been split in two: those arriving before the travelling time set and
those arriving after it. The first group leads to a negative spike, the
second one to a positive spike. The waves from the first group have been
considered to arrive all together at the arriving instant of the fastest
-98-
wave. The travelling time of the second group has been set equal to that of
the slowest aerial wave. After filtering this will lead to higher values for
the detection functions than in reality. The highest possible value of the
filtered detection functions has been determined for the three line types by
simulating all energizing situations.
The results of the study are reproduced in Table 7.3. The impedance setting
has been determined by neglecting the differences in travelling time. The
cut-off frequency has been chosen such that the maximum detection time is of
an acceptable value. Another value for the cut-off frequency will lead to
other values for the threshold and for the fault-detection time.
The maximum detection time is twice the time between the arrival of the
fasted reflected waves and the threshold crossing for the closing of the
R-phase at voltage zero. when there exists a short-circuit in the R-phase at
the remote line-terminal (cf. Figure 4.12).
line A line B line C
cut-off frequency 1/2T 1/5T 1/2T
trav. time (50 km} 343 I-tS 364 I-tS 342 I-tS
I impedance setting 260 Q 270 Q 250 Q 1
threshold setting 400 units 600 units 550 units
max. detection time 1120 I-tS 1620 J"S 1280 I!S
Table 7.3. setting and performance of three-phase SOTF.
~he atgo~~tha to~ ~~ngte-pka~e ~ecto~a~e
Single-phase reclosure is used after single-phase tripping. In that case
only one phase at the remote line-terminal is open. Figure 7.11 shows the
situation when phase R is rec1osed at one line terminal and remains open at
the other. In that case the detection function should. apart from a constant
factor. be equal to the right-hand member of equation (7.40), but this leads
to a complicated expression. Therefore some simplification will be made.
' R ! >.~SOTF f!LY I y s )...1
'-"I
T ,t_
u v w
·"---Figure 7.11. single
phase rectosure.
-99-
After the closing of the circuit breaker the voltages in both circuits are
equal. thus also
{7 .48)
This leads to the following detection algorithm during reclosure of phase R:
Dr = [vr(t-2-r) + R1ir(t-2T)] - [vr{t) R1ir{t)]
+a [v0 (t-2T)- v0 (t)] ,
R0 is an approximation of the homopolar-mode wave-impedance.
In I < 6: fault has extinguished . r
In I > 6: fault has not extinguished r
(7.49)
(7.50)
(7.51)
Similar detection functions are used during reclosure of the other phases.
~he pe~fo~ance of ~Ln~le-pha~e ~~~-detectLon
The values of the wave impedance R0 and R1, the time delay 2T and the
threshold o, as introduced in the preceeding subsection. have been
determined by using the network models discussed before. The optimal
impedance settings have been determined by using TWONFIL. To find the
optimum travelling time setting, EMTP has been used. Due to the limited
number of possible non-fault situations (only three) it was easy to study
them all in detail. The results are reproduced in Table 7.4. The travelling
time setting is valid for a 50 km line; the optimum time delay and the
threshold value have been determined for a cut-off frequency equal to 6 kHz.
The following error sources have been incorporated in the threshold setting:
- 1.5% deviation in travelling time setting;
- 5 % deviation in wave-impedance setting;
-50 units additional noise.
The last two rows give the detection time for single-phase-to-ground faults.
The fault is considered to be a solid connection between one phase and
ground close to the remote 1 ine-terminal. The last row but one gives the
fault detection time for the closing instant at voltage maximum. The last
row gives the longest possible detection time, i.e. for a closing instant
somewhat before voltage zero.
-100-
line A line B line C
homopolar impedance 650Q 670 Q 790 Q
aerial impedance 265Q 2S5Q 267 Q
trav. time (2T) 354 j.I.S 355 J.tS 347.5 J.tS
threshold 450 units 725 units 525 units
detect time fast 45 J.'S 70 J.tS 50 J.tS
detect time slow 1100 J.'S }90() J.'S 1300 J.tS
Table 7.4. setting and performace for single-phase SOTF.
'£i-glttn.i-ng.
Because the SOTF-detector is only in use during short periods. the chance of
an incorrect trip due to a lightning stroke is in general very small. There
are however situations when the chance is much higher. Single-phase
reclosure is used after single-phase tripping. A large number of these
single-phase trips are caused by lightning. Therefore the chance of a
lightning stroke during single-phase reclosure may be not so small. This
subsection wi 11 discuss some measures to prevent false tripping due to a
lightning stroke.
With three-phase SOTF, the only situation of concern is a 1 ightning
stroke to a phase conductor not leading to a fault. Considering the same
shape of the lightning stroke as in Section 4.3 gives the minimum
verification time for the three line types: 260 ~s for line type A; 225 ~s
for line type B and 250 ~s for line type C. all for a 50 km line length.
With single-phase SOTF the situation is somewhat more complicated
because the homopolar mode is used. Therefore also lightning strokes to a
tower or shielding wire will cause high values of the detection functions.
This will increase the chance of an incorrect trip and therefore the need
for a verification time. The verification time needed will be about 300 ~s
for the three line-types, for a line length of 50 km.
~ ~umma~ ot the ~e~uit~,
It has been shown that fast switch-on-to-fault protection is possible. By
using simple detection functions a fault during line energizing can be
detected within some hundreds of microseconds. Only situations around
voltage zero will take more time, up till two milliseconds. The proposed
algorithm will minimize the risk of transient instability during line
energizing and single-phase reclosure.
-101-
7.5. Which algorithm is the best one?
An algorithm for travel! ing-wave-based protection should be capable of
detecting a fault from the travelling waves caused by the voltage jump at
fault initiation. From quantities measured during a short period of time the
algorithm must decide whether the waves originated from a fault in the zone
to-be-protected or not. The ideal algorithm is able to do this without com
plicated ( =expensive, vulnerable and unreliable ? ) technical facilities.
From the chapters 4 through 7 is has become clear that such an ideal
algorithm does not (yet?) exist. Therefore a compromise has to be found. The
preference of differential protection over directional detection became
already evident in Section 6.3. Differential protection is capable to
distinguish between internal and external disturbances very fast (i.e.
within a few microseconds for most disturbances but up to one or two
milliseconds for faults arounds voltage zero}. But discrimination between an
internal fault and a direct lightning stroke is only possible through the
short duration of the latter. As a consequence of this a verification time
has to be introduced. An additional delay is introduced by the necessary
communication link. As a consequence of this the decision takes place some
hundreds of microseconds after the arrival of the travelling wave.
Algorithms for distance protection have much more difficulty in
distinguishing between an internal and an external fault. Besides, the
calculations needed are, in general, much more complicated. An exception to
the latter disadvantage is the IXXX:P-algorithm being, fundamentally. only
suitable for double-circuit lines. The DOOCP-algorithm is very fast for the
majority of short circuit situations. But a number of short circuit
situations will not be detected at all. A large advantage of DOOCP is the
simplicity. No long communication links are needed nor any precise setting
of impedance or travelling time.
Summarizing: differential protection is the most reliable algorithm and
already quite fast, DOOCP is even faster and more simple but less reliable.
-102-
8. A Protective scheme for a double-circuit line
Three of the algorithm discussed in the preceeding chapters will be used
here in a fast protective scheme for a double-circuit line. First the
protective scheme will be described roughly, then the different protective
relays and finally the local protection control forming the center of the
protective scheme. Some thoughts shall be given concerning the
implementation of the algorithms in a protective relay.
uoccp: Double-circuit Current Comparison Protection
SOTF
LPF
CB
LPC
MMI
Switch-On-To-fault
Low Pass Filter
Circuit Breaker
Local Protection Control
Man Machine Interface.
Travelling time of the line-to-be-protected
Table 8.1. Abbreviations used in chapter 8.
8.1. The protective scheme
I I
1 I
8------------- -----ffi
Figure 8.1 . A double
circuit line together
with protect ion aPJXlr
atus as discussed in
the text.
Figure 8.1. shows a double circuit line together with the position of
measurement transformers, communication links and protective relays. The
following protective devices are present:
1. a J:JCXXP-relay acting as primary protection; it generates a tripping
signal for single-circuit faults with a considerable voltage jump not
too close to the remote line-terminal; it has to be blocked as soon as
one circuit is out of operation;
2. differential protection acting as a local backup; it serves as a
primary protection for the non-detectable situations of DCOCP and when
the J:JCXXP-relay is blocked:
-103-
3. a switch-on-to-fault detector taking over the primary protection during
line energizing and during fast reclosure;
4. a "local protection control" for adaptive relay setting, for breaker
failure detection and to serve as a communication buffer;
5. a remote backup to disconnect the fault in case all other devices
should fai 1.
The DOOCP algorithm is discussed in Section 7.2, the algorithm for
differential protection in Section 6.2 and the SOTF algorithm in Section
7.4.2.
Fault type relay line A line B line C
cp-n max DOOCP I 110 IJ.S 700 IJ.S 120 IJ.S
Differential 530!J.s 510 IJ.S 530 IJ.S
SOTF 130 IJ.S 240 IJ.S 130 IJ.S
cp-n zero IXXCP 1090 IJ.S 2110 IJ.S 1340 IJ.S
Differential 1230 IJ.S 1320 IJ.S 1340 IJ.S
SOTF 740 IJ.S 1170 !-IS 910 IJ.S
cp-cp-cp IXXCP 100 IJ.S 270 IJ.S 90 !-IS
Differential 530 IJ.S 510 IJ.S 530 !-IS
Table 8.2. Performance of the algorithms for three different lines of length
100 km. Tripping time !s given for single-phase-to-ground faults at voltage
maxii!UlJ!t (cp-n max), at voltage zero (cp-n zero) and for three-phase faults
(cp-cp-cp).
Table 8.2 shows the tripping time of the relays for some fault situations.
The settings for DOOCP are according to Table 7.7, except for the verifica
tion time, which was set equal to 0.2 T; the settings for differential pro
tection are as in Table 6.5 and for SOTF as in Table 7.9; for the latter a
verification time of 0.2 T has been used. The travelling time of the commu
nication channel needed for differential protection is considered to be
600 IJ.S. For DOOCP and differential protection tripping times have been de
termined for a fault midway on a 100 km line. For SOTF tripping times have
been determined for the closing of the R-phase in case of a solid R-N fault
at the remote line-terminal. The network simulation has been performed on
the EMTP model of Section 3.5 where the line between Diemen and Krimpen is
replaced by a 100 km line. All relays are situated in Diemen. For the
interpretation of the table it must be kept in mind that faults close to the
remote line-terminal will not be detected by DOOCP. This holds especially
for faults around voltage zero.
-104-
For different fault situations different relays will generate the first
tripping signal. The discussion further on applies to line type A and C. For
line type B differential protection is not slower than DOX:P for single
phase-to-ground faults, making the protective scheme too complicated. Faults
with a considerable voltage jump not too close to the remote line-terminal
are detected by DOX:P with a tripping time of about 100 ~s. Faults close to
the remote 1 ine-terminal and double-circuit faults are detected by the
differential relay with a tripping time of about 600 ~s. Faults around
voltage zero are detected by the differential relay or by the DOX:P relay
with a tripping time of one or two milliseconds. Faults during line energi
zing are detected by the SOTF-relay with a tripping time between 100 ~s and
1.5 milliseconds. In case one circuit is out-of-operation (the DOX:P relay
is blocked) faults on the other circuit are detected by the differential
relay.
8.2. Implementation of the DOX:P-algorithm
input unit
status word
decision unit from
LPC
Figure 8.2. Hardware requirements for
DOCCP. CB = circuit breakers, LPC = local protection control, LPF = Low
pass fitter.
Figure 8.2 shows a possible global structure for a DOX:P-relay. The six
input currents pass through a filter and reach the input unit, where eight
logical signals are formed Clx,l>f •..• lx4 l>f.ID,I>o. ID2 I>o. C1 >0. C2> 0).
They form the status word that serves as an input for the decision unit,
consisting of a microprocessor that generates tripping signals when needed.
External blocking can take place by using a logical "and" in the link to the
circuit breaker or by means of an interrupt to the microprocessor.
Figure 8.3 provides more details on the input unit. From the six input
currents four differential signals are formed. From these the four
disturbance-detection functions (X 1 through X4 ) are formed by subtracting
the value one power frequency period ago. Its length is provided from some
external device. From the disturbance-detection functions two fault
detection functions and two circuit-selection functions are determined.
-105-
From the detection and selection functions an eight bit status word is
formed by comparing them with preset thresholds b and f. The status word
will be transfered to the decision unit at predefined points in time
(provided by an external clock).
Figure 8.3. The input unit.
···-~··-~·-~--····~~~~-~~----~~---'
Figure 8.4. shows the flow chart of the algorithm to be implemented on the
decision unit's microprocessor. On an MC6BOOO-processor [Harman and Lawson,
1985] the longest loop between two input-instructions takes 170 clock
cycles. In case of a 12 MHz processor clock a sampling frequency up to
94 kHz is possible (taking two inputs during the verification time of 0.2 T
this corresponds to line longer than 30 km). Synchronisation between A.D.
convertors and microprocessor is provided by means of a low-level interrupt.
External blocking is provided by means of a high-level interrupt. The
processor will turn into a wait state. External unblocking is provided by
means of a reset. After the generation of a tripping signal the processor
will turn into a wait state by itself.
8.3. Implementation of differential protection
To reduce the amount of data to be transmitted and to decrease the tripping
time. the relay is split in two identical parts, one at each line
terminal.The structure of one half-relay is shown in Figure 8.5. The input
unit forms four combinations of voltages and currents:
(vt-vs) + R(it-is)
(vr-vd + R(ir-id
(vt-vs) - R{it-is)
(vr-vd R(ir-id.
The first two signals are sent to the remote line-terminal, the other two
are provided to the local decision unit. The delay for the last two signals
-106-
I __ J
Figure 8.4. Flow chart for the decision processor of DCOCP. x1 stands for
IXt l)f, d1 for IDt 1)6, c 1 for C1 )0.
is equal to the difference in travelling time between the communication link
and the high-voltage line.
!l!fltclv!.OO.iA),at/-oo.
As shown in Section 6.2, only minor changes in travelling time setting are
allowed. This calls for a highly stable communication link and for some kind
of synchronisation between both units. Figure 8.5 shows a possible solution.
The clock pulses are generated at the remote terminal and recovered from the
transmitted signal. The recovered clock will trigger the local A.D.
convertor as well as the decision unit's microprocessor. As the delay
compensates the difference in travelling time between the communication link
and the line, both signals are synchronised at the input of the decision
unit. Even if the clock recovery misses a clock pulse. no error is
introduced. It is supposed here that changes in travelling time can be
neglected. In case the recovered sample frequency is stable on a timescale
-107-
corresponding to the travelling time of the line, delay and A.D. conversion
may be interchanged in Figure 8.5 ..
R
T
8
remote lineterminal
1------ce
.,_---•LPC
remote lineterminal
Figure 8.5. Hardware requirements for differentiaL protection.
~ampie e~eqae~cy
Differential protection works on every time scale. This is one of the main
advantages of this principle, for there is no need for a very high sample
frequency. A very low sample frequency wi 11 of course make the fault
detection too slow. To justify the term "travelling-wave-based" the sample
time must at least be of the order of the travelling time of the line. A
sample frequency of 10kHz will suite in most cases.
Hum.l..e~ ot t..i.t().
An A.D. convertor can be characterised by its dynamic range and the number
of bits used. If the analog input is higher than some upper limit, the
digital representation is equal to that of the upper limit. The same holds
for the lower limit. In case one of the A.D. convertor outputs of the
differential relay shows such an overflow the decision unit will calculate
an incorrect value for the detection function. But as long as no incorrect
decisions are taken this is not of any concern for the protection of the
line.
During an external fault the two corresponding input signals (v-Ri and
v+Ri) are of the same sign and of almost equal magnitude. In case one of
them shows an over£ low the detection function (the difference between the
input signals) will become less in absolute value. As it remains below the
threshold no incorrect decision will occur. In fact the detection function
will become zero soon after the overflow because the second function will
show an overflow, too.
During an internal fault an overflow will also cause the detection
functions to become less in absolute value. Therefore this overflow must not
-108-
occur before a tripping signal is generated. As the two corresponding inputs
are of opposite sign, the upper limit must be higher than the upper
threshold and the lower 1 imi t lower than the lower threshold. Values of +
2500 units and - 2500 units are more than sufficient. An 8-bit A.D.
convertor will then give a quantisation step of about 20 units (thus at
maximum 20 units quantisation noise).
~he eommantcatton channet
The communication channel must be able to transmit two 8-bi t signals at a
frequency of 10 kHz. This calls for a bit rate of at least 160.000 baud. In
case four extra bits are included for synchronisation and error detection a
bit rate of 240,000 baud is needed.
Two of these channels are needed for each circuit, i.e. four for a
double-circuit line. It is recommended to use one fiber for each circuit.
For a glass fibre the product of bandwidth and length is constant. Depending
on the type of cable this figure ranges from 10 MHz.km up to 50 GHz.km
[Lohage et al .• 1987]. In case of a bandwidth of 1 MHz (four channels in one
fibre) the maximum possible line length is between 10 km and 50,000 km. Thus
for a line length in the order of 100 km it is certainly possible to find an
appropriate glass fibre.
Figure 8.6. Flow chart of the decision unit's microprocessor.
Figure 8.6 gives a flow_chart for the decision proces as performed by the
decision unit's microprocessor. The synchronisation with the remote
line-terminal is created by means of a low level interrupt. The interrupt
can only interfere when the processor is in the "wait for interrupt" state.
On a MC68000 processor the longest loop will take about 200 clock cycles. So
even the lowest clock frequeney of the MC68000 (4 MHz) can support sample
frequencies up to 20 kHz.
-109-
8.4. Implementation of SOTF detection
fc
Figure 8.7. Hardware requirements for SOTF-detection.
to CB
Figure 8.7 shows a possible structure for the SOTF-detector. After filtering
of voltages and currents the two detection functions are formed by analog
circuitry. The decision process is performed by means of four comparators
(two for each detection function). a number of logical or-gates (+) and a
counter. If the counter's input is high during a number of consecutive clock
pulses, the output becomes high. A tripping signal is generated if the L~s
output is also high (i.e. if the relay is not blocked).
The settings are controled by the local protection control (LPC) or through
a man-machine interface (MMI).
The structure shown in figure 8. 7 does not make use of a
microprocessor. Microprocessor based implementations are possible.e.g. by
using the microprocessor of the differential relay.
8.5. Breaker-failure detection.
In case a tripping signal is generated by one of the local relays (DOOCP,
differential or SOTF) a number of circuit breakers need to open. If one of
the circuit breakers fails to open. the fault will not be disconnected. If
no other measures are taken, the remote backup will disconnect the fault.
Unfortunately also a number of healthy lines will be deenergized.
A less severe method is to detect the breaker failure and give tripping
signals to those circuit breakers disconnecting the fault plus a minimum
part of the high-voltage network. As most high-voltage stations are of the
double-bus type, only one busbar needs to be deenergized to disconnect the
fault.
In the proposed scheme each generated tripping signal is not only sent
to the circuit breaker but also to the local protection control. By
measuring voltage across and/or current through the breaker its opening can
easily be detected. If the breaker fails to open within a certain time,
tripping signals will be sent to the backup circuit breakers.
-llo-
To determine which circuit breakers should open in case of breaker
failure the substation configuration must be known. This information is
obtained from the system center computer.
8.6. The remote backup
In case all protections should fail to operate, the remote backup will
disconnect the fault. Together with the fault a number of healthy lines will
be disconnected. Therefore the remote backup must be extremely reliable.
As the most reliable relay available today is a simple time-curr.ent relay
[Heising and Patterson, 1989], it is the first candidates to serve as a
remote backup.
Despite of this the proposed scheme containes distance relays as a
remote backup. It will be considered that each relay's setting is adapted to
the momentary load flow situation [e.g. Phadke et al., 1987]. The
information needed for this adaptive protection will be obtained through the
local protection control and the system center computer.
After a fault in one of the zones a certain verification time starts.
This verificaton time is of a much longer duration than the verification
times introduced before (tens of milliseconds in stead of hundreds of
microseconds). The verification time can be set in two ways:
1. constant verification time, each zone has a fixed verification time,
increasing for more distant zones;
2. adaptive verification time: the duration of the verification time is
controlled by the LPC' s.
~~tant ~e~tttcatton ttae
For zone 1 (0-80%) no verification time will be needed. The relay will act
as an additional local backup. For zone 2 (SD-160%) the verification time
must be equal to the sum of the following contributions:
maximum clearing time of the circuit breakers;
maximum time needed for breaker-failure detection;
maximum clearing time of the backup breakers;
safety margin.
For zone 3 ( 160-240%) the verification time must be equal to the zone 2
verification time plus the last two contributions. Especially for zone 3 the
verification time may become very long. For complicated network configura
tions it will be difficult to define the borders of the different zones.
Both problems can be solved by using an adaptive verification time.
-111-
ddapti~e ~e~itication time
In the normal state the remote backups have no verification time in their
zones one and two. The verification time in zone 3 is equal to the maximum
clearing time for a fault on the adjacent line. If a fault occurs somewhere
in the network this will be detected by the travelling-wave-based relays
long before the remote backup reacts. Upon detecting a fault the local
protection control sends a signal to the remote backups to increase the
verification time of zone 2 and 3. The verification time will depend on the
location of the relay. An example will be discussed from Figure 8.8.
)(
A
Ftgure 8.8. Position of remote backup reLays.
Circuit breaker "A" should open in case of a f au 1 t at the posit ton
shown. When the tripping signal is generated by one of the relays. the local
protection control will inform this to the relays through 4. The
verification time of zone 2 and 3 of relay 2 will be increased with the
maximum clearing time of breaker "A". It will generate a tripping signal in
case breaker "A" should fail to open. The verification time of zone 2 and 3
of relay 1 and 3 will be increased with the maximum clearing time of breaker
"A" plus that of breaker "C". They will generate tripping signals in case
breakers "A" and "C" both fail to open (or breaker "A" and the
breaker-failure-detection both fail). The verification time of zone 3 of
relay 4 will be set equal to the sum of the maximum clearing times of the
breakers "A", "C" and "D". Zone 1 of all relays as well as zone 2 of relay 4
are not affected. As soon as the fault is cleared all remote backup relays
reset themselves to the normal state.
The main advantage of the adaptive verification time shows up in case
none of the local relays generates a tripping signal. The local protection
control will not send a message to the remote backups and relays 1,2 and 3
will generate a tripping signal without a long verification time.
-112-
8.7. The local protection control
The local protection control serves as a link between the protective relays
among themselves and between the relays and the system center computer. It
is part of the hierarchical system as described by Phadke [1988] (his
"substation host computer" corresponds to our "local protection control").
The structure of the hierarchical system is shown in Figure 8.9.
system center computer
---------------.
Figure 8.9. Hternrchicnl structure for protection and control (R=protectiue
relay)
Most of the communication is between different levels but some is on the
same level. Communication between LPC' s in neighbouring substations is e.g.
needed for adaptive verification time setting of remote backups (cf. Section
5.6). between relays in different substations for differential protection.
The local protection control will perform the following functions:
adaptive blocking and unblocking;
adaptive setting of the remote backup relays;
breaker-failure detection;
generation of sequence of events records:
monitoring and checking of the relays.
As an example Figure 8.10 sUI'IUIIarizes some of the LPC' s actions during a
reclosure session. In the double-circuit state all four sets of circuit
breakers are closed. In the double-circuit state the IXXCP relay is in
operation and the SOTF detector is blocked.
If one of the local relays generates a tripping signal the IXXCP relay
will be blocked and the breaker-failure detection starts. The LPC will also
generate messages for the neighbouring LPC' s and the system center. Also in
case of a manual trip the IXXCP relay will be blocked.
-113-
If the local breakers have opened within the available time and the
circuit breakers at the remote line-terminal are also open the SOTF-relay
will be declocked. After a certain time (needed for the fault to
extinghuish) the local breakers will be closed again. If no tripping signal
is generated the SOTF-detector will be blocked, the circuit breakers at the
remote line-terminal will be closed and the DOOCP-relay will be deblocked.
N
Figure 8.10. Actions of tocat protection control during a reclosure session.
-114-
9. Summary and conclusions
This thesis consists of three parts:
i) the development of network models for the study of travelling-wave
based protection;
ii) the testing of the proposed algorithms for travelling-wave-based
protection;
iii) a few proposals for the design and use of future relays.
This work tries to answer the question: "Is fast protection based on
travelling-wave principles possible?".
Travel! ing-wave-based protection detects a fault on a high-voltage 1 ine
through measuring incoming and outgoing waves at one or more line terminals.
Therefore the modelling effort is focussed on travelling waves along
high-voltage lines.
The high-voltage line is viewed as a number of parallel conductors
above a lossy ground. Up to a few hundreds of kHz such a system can be
mathematically described through a set of coupled differential equations
which the voltages and currents have to satisfy. Their solutions are weakly
damped travelling waves. A system of n metallic conductors plus ground can
support n different modal waves. For existing high-voltage lines the
expressions for the L and R-parameters found by Carson in 1926 can be used
to calculate the pertinent wave constants.
The line model is used in two computer programs for network
calculations: an existing one, called EMTP and a newly developed one, called
TWONFIL. Within EMTP the frequency dependence of the wave parameters is
reckoned with for each mode. Although the frequency dependence of the modal
transformation matrix is neglected, EMTP is considered to be very closes to
reality.
The detailed modelling as used in EMTP makes it very suitable for an
accurate simulation of voltages and currents. On the other hand the
associated complexity prevents its use for the study of a large number of
situations. To overcome this, TWONFIL has been developed. Within TWONFIL the
wave parameters are considered frequency independent. TWONFIL has been used
to calculate voltages and currents in thousands of fault and non-fault
situations. A limited number of typical situations and worst cases has been
studied in more detail by using EMTP.
-115-
9.2. The testing of algorithms
An algorithm for travelling-wave-based protection uses filtered values of
voltage and current to determine a set of detection functions and detect a
fault from them. A low pass filter with a cut-off frequency equal to one
divided by the travelling time of the line, showed to give good results. The
algorithms are based on expressions for the aerial waves on a balanced
three-phase line. The nonbalance of the line is not incorporated in the
protection algorithm (i) because the exact transformation matrices are not
known. (ii) to prevent problems when transposition points are used and (iii)
to keep the algorithm as simple as possible. Homopolar quanti ties are not
used (i) because of their strong frequency dependence, (ii) to prevent
problems on double-circuit lines and during lightning and (iii) because they
are not really needed.
The algorithms use the difference between voltages and currents at
different points of time (one power frequency cycle apart or one travelling
time apart) or at different positions in the network. General expressions
for the detection functions used are:
(vt-vs) + R, (it-is)
(vr-Vt) + R1 (ir-it)
(9.1)
(9.2)
where R1 is a wave-impedance setting, Vr,Vs,Vt and ir,is,it are voltage
{differences) and current (differences), respectively. General detection
criteria used are:
ID, I< 6 and ID2I < o: no fault
ID, I > o or ID2I > o : fault ,
where o is a threshold needed to prevent incorrect tripping.
(9.3)
(9.4)
After one or two detection functions exceed the threshold, a
verification time is started.
Methods have been developed to find the optimum settings for wave impedance
and travelling time, i.e. those leading to the lowest threshold value. The
threshold value must be higher than the highest value of the detection
functions during a non-fault situation. Therefore special emphasis is laid
on the study of these non-fault situations. The length of the verification
time is evaluated by considering the worst case, i.e. a lightning stroke to
a phase conductor not leading to a fault.
After the study of those non-fault situations needed for setting of
cut-off frequency, threshold, travelling time, wave impedance and
verification time, the speed of the algorithm can be evaluated from the
study of fault situations.
-116-
This way about a dozen algorithms have been considered, four of them
have been investigated in detai 1. From this vast study no other algorithm
has been found that can compete with the reliability of ditte~entiai
p~otection. This algorithm is able to detect any internal fault within one
or two milliseconds without the risk of an incorrect trip due to external
disturbances. The majority of internal faults can even be detected within
half a millisecond. A disadvantage of differential protection is the need
for a long high-speed communication link.
Many investigators have searched for a travelling-wave-based algorithm
for di~tance P~otectLon (i.e. one not needing a communication link). But
none of the existing algorithms is able to determine the distance to the
fault without complicated (time consuming) calculations.
Two new algorithms that do not need a communication link have been
developed in this study. The first one, DCCCP,
double-circuit lines. The second one (SOTF)
is especially sui ted for
is especially suited for
switch-on-to-fault detection. DCCCP is a very simple algorithm not needing a
long communication link, neither any precise setting of wave impedance or
travelling time. It gives a considerable reduction of tripping time as
compared to differential protection. It does, however, show a few
nondetectable situations.
Concluding: differential protection is the most reliable algorithm and DCCCP
is the fastest and most simple one.
9.3. A future relay
Three of the algorithms are used in a proposal for a protective scheme:
DCCCP, differential protection and SOTF. The blocking and unblocking of
DCCCP and SOTF is governed by a "local protection control". The
travelling-wave-based algorithms provide primary protection and local
backup. The remote backup is formed by (conventional) distance relays with
an adaptive verification-time setting. This setting is again governed by the
local protection control.
Suggestions for implementation in a relay are given for the three
travelling-wave-based algorithms used in the protective scheme. No great
technical problems are to be expected. But the communication link needed for
differential protection may become an economical problem.
-117-
9.4. Suggestions for future work
From the study presented in this thesis an answer in the affirmative is
concluded for the question whether fast protection. based on travelling-wave
principles is possible. Therefore future work can concentrate on building
travelling-wave relays. As very short tripping times are not yet wanted,
such a relay can be made extremely reliable by introducing a verification
time of one or two milliseconds.
In case very fast fault-clearing times are really needed much emphasis
must be laid on the setting of verification time, wave impedance, travelling
time and threshold. As the length of the verification time is determined by
the shape of lightning-caused waves, more research must be performed after
this shape.
The introduction of these very fast relays is only meaningful in
combination with fast circuit breakers. The use of active current-limiting
devices will justify the introduction of fast relays even more.
On the field of network modelling work must be performed to get a
better justification of the model. Nowadays ever more complicated structures
can be simulated by using numerical techniques like EMTP. But the foundation
of this must be provided from measurements.
-118-
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SAMENVATIING Het optreden van een kortsluiting in een elektriciteitsnet kan zeer grote
stromen tot gevolg hebben. Deze stromen zijn ongewenst aangezien ze de on
derdelen van het net zwaar kunnen beschadigen en tevens de elektriciteits
voorziening op andere wijze kunnen ontregelen. Om de gevolgen van zo'n kort
sluiting zoveel mogelijk te beperken wordt getracht zo snel mogelijk na het
optreden ervan een aantal schakelaars te openen, waardoor de kortsluitstroom
verdwijnt zonder dat de elektriciteitsvoorziening ontregeld wordt (men
spreekt in deze context van "kortsluitbeveiliging" of kortweg
"beveiliging").
Wanneer ergens op een hoogspanningslijn een kortsluiting optreedt
veranderen daar ter plaatse ogenblikkelijk de voorheen aanwezige spanningen
en stromen. Deze veranderingen planten zich vervolgens vanaf de kortsluiting
voort met een zeer hoge snelheid (nagenoeg de lichtsnelheid). Een derge
lijke, zich snel voortplantende spannings- en stroomverandering wordt een
lopende golf genoemd. Na een zekere, geringe, looptijd arriveren deze golven
in een hoogspanningsstation. waar ze de eerste melding vormen van een kort
sluiting verderop. Men zou deze golven daarom, in principe. kunnen gebruiken
als detektiesignaal voor een zeer snelle beveiliging. Een moeilijkheid daar
bij is, dat vele andere gebeurtenissen (schakelhandelingen, bliksemontla
dingen, fouten elders) ook lopende golven veroorzaken maar niet tot een
afschakeling mogen leiden.
Het onderzoek beschreven in dit proefschrift tracht een antwoord te geven op
de vraag of het mogelijk is een betrouwbare lopende-golfbeveiliging te
ontwerpen. Het onderzoek bestaat uit drie delen:
1 het ontwikkelen van modellen geschikt voor het bestuderen van lopende
golven in elektriciteitsnetten;
2 het testen van voorgestelde methoden voor lopende-golfbeveiliging;
3 het inpassen van deze methoden in toekomstige beveiligingsrelais.
1. De modelvorming is vooral gericht op lopende golven op hoogspannings
lijnen. De hoogspanningslijn wordt gezien als een aantal paralelle geleiders
hoven een geleidende aarde. Tot enkele honderden kHz blijkt het mogelijk bet
gedrag van een dergelijk systeem te beschrijven door middel van een stelsel
gekoppelde differentiaalvergelijkingen voor spanning en stroom. De oplos
singen hiervan zijn zwak-gedempte lopende golven waarvan de eigenschappen
kunnen worden bepaald met behulp van in 1926 door Carson gevonden uitdruk
kingen.
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Het op deze manter ontstane lijnmodel is gebruikt in twee computerpro
gr~s voor netwerkberekeningen: een bestaand, genaamd EMTP en een nieuw
ontwikkeld, genaamd TWONFIL. EMTP neemt het grootste deel van de frequentie
afhankelijkheden van de golfeigenschappen mee. EMTP' s rijkdom aan mogelijk
heden maakt het zeer geschikt voor het nauwkeurig berekenen van spanningen
en stromen. De hiermee samenhangende complexiteit maakt het echter minder
geschikt voor het in detail bestuderen van een groot aantal gevallen. Voor
dat laatste is TWONFIL ontwikkeld. Binnen TWONFIL worden de golfeigenschap
pen frequentie-onafhakelijk beschouwd. TWONFIL is gebruikt voor het bereke
nen van spanningen en stromen in duizenden gevallen. Een beperkt aantal
karakteristieke gevalen is in detail bestudeerd met behulp van EMTP.
2. Lopende-golfbeveil iging gebruikt gefil terde waarden van spanning en
stroom en berekent hieruit een aantal detectiefuncties waarmee een kort
sluiting op het te beveiligen traject kan worden gedetecteerd. Uitgaande van
spanningen en stromen gemeten op verschillende plaatsen en/of tijdstippen.
in combinatie met golfimpedantie- en looptijdinstellingen, worden twee
detectiefuncties berekend. Wanneer een of beide detectiefuncties een zekere
drempel overschrijden start een zogenaamde verificatietijd. Blijven de
detectiefuncties boven de drempel gedurende deze tijd. dan wordt er een af
schakelcommando naar de schakelaars gestuurd.
Er zijn technieken ontwikkeld ter bepaling van optimale golfimpedantie
en looptijdinstelling, d.w.z. die instelwaarde welke leidt tot de laagste
drempelwaarde, en dus tot de snelste afschakeling. De drempelwaarde moet
boger zijn dan de hoogstmogelijke waarde welke optreedt tijdens si tuaties
die niet tot een afschakel tng mogen leiden. Daarom is er extra aandacht
besteed aan dit soort situaties. Na het bestuderen hiervan en het instellen
van afsnijfrequentie, drempelwaarde, loopttjd, golfimpedantie en verifica
tietijd, is de snelheid van de beveiliging bepaald uit het bestuderen van
alle mogelijke kortsluitingen op de te beveiligen lijn._De minimale duur van
de verificatietijd is bepaald door de maximale duur van de drempelover
schrijding als gevolg van een blikseminslag. welke niet leidt tot een kort
sluiting.
Op deze wijze is een tiental methoden beschouwd, waarvan vier in
detail. Uit deze grondige studie blijkt dat geen van de andere bestudeerde
methoden de betrouwbaarheid van lopende-golfdifferentiaalbeveil iging kan
evenaren. Deze methode is in staat elke kortsluiting op de te beveiligen
lijn binnen een a twee milliseconden te detecteren zonder het risico van een
onterechte afschakeling als gevolg van een gebeurtenis buiten die lijn. De
meeste kortslui tingen kunnen zelfs binnen een halve milliseconde worden
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gedetecteerd. De andere methoden zijn veelal wel in staat kortslui tingen
snel te detecteren doch niet in alle gevallen of geven in somrnige gevallen
onterechte afschakelcomrnando' s. Het nadeel van lopende-golfdi fferentiaal
beveiliging is de vereiste aanwezigheid van lange, hoogwaardige comrnunica
tieverbindingen. Er zijn twee nieuwe methoden ontwikkeld, welke geen gebruik
maken van dit soort verbindingen. De eerste (DOOCP} is speciaal ontwikkeld
voor dubbelcircuitlijnen, de tweede (S<YfF} voor het inschakelen van onbe
laste lijnen. DOOCP is een eenvoudige methode die geen nauwkeurige instel
ling van looptijd of golfimpedantie vereist. Deze methode geeft een aan
zienlijke versnelling ten opzichte van lopende-golfdifferentiaalbeveiliging,
doch vertoont een aantal niet-detecteerbare gevallen.
Concluste: lopende-golfdifferentiaalbeveiliging is de meest betrouwbare
methode; DOOCP is daarentegen sneller en eenvoudiger.
3. Er is een volledig beveiligingsconcept voor een dubbelcircuitlijn voor
gesteld. Hierin zijn drie van de bestudeerde methoden gebruikt, nl. DOOCP.
lopende-golfdifferentiaalbeveiliging en sarF, die tezamen de primaire
beveiliging en de reserve ter plaatse vormen. De reserve op afstand wordt
gevormd door (conventionele) distantiebeveiliging.
Er zijn voorstellen gedaan voor de technische uitvoering van de lopende
golfbeveil igingen in het voorgestelde beveil igingsconcept. Er zijn geen
grote technische problemen te verwachten. De comrnunicatieverbinding vereist
voor lopende-golfdifferentiaalbeveiliging zou echter een economisch probleem
kunnen zijn.
Uit het onderzoek, beschreven in dit proefschrift, blijkt dat de vraag
of lopende-golfbeveiliging mogelijk is, met "ja" kan worden beantwoord.
-130-
Aan dit proefschrift werd medewerking verleend door:
Ir. W.F.J. Kersten, Prof.dr.ir. W.M.C. van den Heuvel en Prof.Dr.-Ing. H.J.
Butterweck (technische en tactische tips);
Marijke van de Wijdeven (typewerk en ondersteuning);
Gerard jacobs (figuren en diverse metingen);
vele anderen.
-131-
Levens loop:
Math Bollen werd op 21 juli 1960 geboren te Stein (L). Na enkele maanden
verhuisde hij naar bet nabijgelegen Ceulle, alwaar hij zowel de kleuter
school als de lagere school bezocht. Na bet eindexamen Atheneum B aan de
Scholengerneenschap St. Michie} te Celeen ging hij Elektrotechniek studeren
aan de Technische Hogeschool Eindhoven (tegenwoordig Technische Universiteit
geheten). Daar studeerde hij in februari 1985 (met lof) af in de groep
"Theoretische Elektrotechniek", onder leiding van Prof .dr. M.P.H. Ween ink.
Het afstudeerwerk betrof elektrornagnetische verschijnselen in de hogere
delen van de aardatmosfeer.
In september 1985 trad hij in dienst bij de groep "Elektrische Energie
systernen" van de Technische Hogeschool Eindhoven. Onder Ieiding van
Prof.dr.ir. W.M.C. van de Heuvel en Ir. W.F.j. Kersten verrichtte hij onder
zoek naar snelle beveiliging van hoogspanningsnetten en modelvorrning van
hoogspanningsl ijnen en verrnogenstransforrnatoren. Een deel van dat werk
resulteerde in dit proefschrift.
Stellingen beborende bij het proefschrift van Math Bollen.
-1-
Samenwerking en bet geven van onderlinge steun zijn veel belangrijker voor
bet voortbesta.an van de soort dan onderlinge "strijd om bet bestaan".
M.. de Geus, "Het onbegrepen a.narchisme", Intermediair, 3 feb. 1989.
-2-
Zowel de vergelijkingen van Carson als de telegraafvergelijkingen verliezen,
voor boogspanningslijnen, hun betekenis voor frequenties van 1 MHz en boger.
Di t maakt bet gebruik van hierop gebaseerde lijnmodellen zinloos voor
verschijnselen welke zich afspelen op een submicroseconde-tijdschaal.
].R. Carson, Belt System Technical ]ournat. §. 539, 1926;
dit proefschrift, hoofdstuk 2.
-3-
Een wijziging van de winkelslui tingswet zou voor een groot deel overbodig
worden door de wekelijkse koopavond naar dinsdag of woensdag te verplaatsen.
-4-
Bij bet bestuderen van foutdetectie-algoritmen gebaseerd op lopende golven
dient de nadruk te liggen op bet gedrag van het algoritme in die gevallen
waarbij er geen fout gedetecteerd dient te worden.
Dit proefschrift, hoofdstuk 4.
-5-
Het door Dommel en Michels voorgestelde beveiligingsalgoritme zal, voor een
betrouwbare werking, moeten worden gecombineerd met een laagdoorlaatfilter
met een lage afsnijfrequentie. Hierdoor zal de foutdetectie ui teindelijk
niet of nauwelijks sneller zijn dan bij bet gebruik van andere, aanzienlijk
eenvoudigere, algoritmen.
H.W Dommel en ].H. Hichets, IEEE/PES Winter Meeting 1978, paper 214-9;
dit proefschrift, hoofdstuk 5.
-6-
Lopende-golfdifferentiaalbeveiliging in combinatie met een verificatietijd
van een a twee milliseconden maakt een zeer betrouwbaar beveiligingsrelais
mogelijk dat in staat is een afschakelcommando te genereren twee tot vijf
milliseconden na bet optreden van een kortsluiting op bet te beveiligen
traject.
Dit proefschrift, hoofdstuk 6.
-7-
Hoewel de basisgedachte achter de kritische theorie van Horkheimer en
Adorno, "elk individu stelt zijn eigenbelang hoven het algemeen belang", bij
haar aanhangers steeds tot een pessimistische visie heeft geleid met
betrekking tot de grootschalige problemen welke zich in onze maatschappij
voordoen, volgt uit dezelfde basisgedachte dat een naderende catastrofe kan
worden afgewend wanneer elk individu ervan doordrongen raakt dat onsociaal
gedrag uiteindelijk tot zijn of haar eigen ondergang leidt; elk individu zal
dan uit eigenbelang het algemeen belang nastreven.
H.Hoefnagets, "Kritische sociotogie', in: Auta 588, 1971, p.2~5-271.
-8-
In tegenstelling tot recente berichten1 bestaat er geen discrepantie tussen
de waa.rgenomen relatieve heliumconcentratie en de massadichtheid van het
heelal 2• Di t maakt het postuleren van exotische elementaire deel tjes ter
oplossing van het probleem van de "missing mass", overbodig.
1: Sky and Telescope, feb.'89, p.131; Zenit, mrt.'89, p.lOl.
2: Steuen Weinberg, "The first three mtTU.Ites", p.112.
-9-
De frequentie-afhankelijke wervelstroomeffecten zowel als de niet-lineaire
magnetisatie-effecten in de ijzerkern van een transformator kunnen samen
worden gerepresenteerd door middel van de parallelschakeling van een
frequentie-onafhankelijke niet-1ineaire zelfinductie en een frequentie
onafhankelijke lineaire weerstand.
M.H.]. Botten, 16th European EMTP Meeting, Dubrounik, 1989.
-10-
Het wantrouwen als gevolg van de criminaliteit is een veel grater
maatschappelijk probleem dan de economische gevolgen van de criminaliteit.
-11-
Zolang niet aangetoond is dat er andere bewoonde J>Janeten bestaan heeft de
mensheid een extra reden om zuinig te zijn op de enige bewoonde planeet in
het heelal.
-12-
Wanneer de vereiste sterke daling van het elektriciteitsverbruik inderdaad
wordt gerealiseerd is onderzoek naar snelle beveiliginsalgori tmen. zoals
uitgevoerd door Bollen, overbodig.
M.H.]. Botten, proefschrift Eindhoven, 1989.
