netw oro guie.pdf
TRANSCRIPT
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N e t w o r k P r o t e c t i o n & A u t o m a t i o n G u i d e
Voltage drops are also positive when acting in thedirection of current flow. From Figure 3.4(a) it can beseen that (
Z1+
Z2+
Z3)
Iis the total voltage drop in the
loop in the direction of current flow, and must equate tothe total voltage rise
E1-
E2. In Figure 3.4(b), the voltage
drop between nodes a and b designatedVab indicates
that point b is at a lower potential than a, and is positivewhen current flows from a to b. Conversely
Vba is a
negative voltage drop.
Symbolically:Vab =
Van -
Vbn
Vba =
Vbn -
Van Equation 3.14
where n is a common reference point.
3.4.3 Power
The product of the potential difference across and the
current through a branch of a circuit is a measure of therate at which energy is exchanged between that branchand the remainder of the circuit. If the potentialdifference is a positive voltage drop, the branch ispassive and absorbs energy. Conversely, if the potentialdifference is a positive voltage rise, the branch is activeand supplies energy.
The rate at which energy is exchanged is known aspower, and by convention, the power is positive whenenergy is being absorbed and negative when beingsupplied. With a.c. circuits the power alternates, so, toobtain a rate at which energy is supplied or absorbed, itis necessary to take the average power over one wholecycle.If e=Emsin(wt+) and i=Imsin(wt+-), then the powerequation is:
p=ei=P[1-cos2(wt+)]+Qsin2(wt+)
Equation 3.15where:
P=|E||I|cos and
Q=|E||I|sin
From Equation 3.15 it can be seen that the quantity Pvaries from 0 to 2Pand quantity Q varies from -Q to +Qin one cycle, and that the waveform is of twice theperiodic frequency of the current voltage waveform.
The average value of the power exchanged in one cycleis a constant, equal to quantity P, and as this quantity isthe product of the voltage and the component of currentwhich is 'in phase' with the voltage it is known as the'real' or 'active' power.
The average value of quantity Q is zero when taken over
a cycle, suggesting that energy is stored in one half-cycleand returned to the circuit in the remaining half-cycle.Q is the product of voltage and the quadrature
component of current, and is known as 'reactive power'.
As P and Q are constants which specify the powerexchange in a given circuit, and are products of thecurrent and voltage vectors, then if
S is the vector
productE
Iit follows that with
Eas the reference vector
and as the angle betweenEand
I:
S =P +jQ Equation 3.16
The quantity Sis described as the 'apparent power', andis the term used in establishing the rating of a circuit.Shas units of VA.
3.4.4 Single-Phase and Polyphase Systems
A system is single or polyphase depending upon whetherthe sources feeding it are single or polyphase. A sourceis single or polyphase according to whether there are oneor several driving voltages associated with it. For
example, a three-phase source is a source containingthree alternating driving voltages that are assumed toreach a maximum in phase order, A, B, C. Each phasedriving voltage is associated with a phase branch of thesystem network as shown in Figure 3.5(a).
If a polyphase system has balanced voltages, that is,equal in magnitude and reaching a maximum at equallydisplaced time intervals, and the phase branchimpedances are identical, it is called a 'balanced' system.It will become 'unbalanced' if any of the aboveconditions are not satisfied. Calculations using a
balanced polyphase system are simplified, as it is onlynecessary to solve for a single phase, the solution for theremaining phases being obtained by symmetry.
The power system is normally operated as a three-phase,balanced, system. For this reason the phase voltages areequal in magnitude and can be represented by threevectors spaced 120 or 2/3 radians apart, as shown inFigure 3.5(b).
3
Fundamenta
lTheory
2 2
Figure 3.5: Three-phase systems
(a) Three-phase system
BC B'C'
N N'
Ean
Ecn Ebn
A'A
Phase branches
Directionof rotation
(b) Balanced system of vectors
120
120
120
Ea
Ec=aEa Eb=a2Ea
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Since the voltages are symmetrical, they may beexpressed in terms of one, that is:
Ea =
Ea
Eb = a2
Ea
Ec= a
Ea Equation 3.17
where a is the vector operator ej2/3. Further, if the phasebranch impedances are identical in a balanced system, itfollows that the resulting currents are also balanced.
3.5 IMPEDANCE NOTATION
It can be seen by inspection of any power systemdiagram that:
a. several voltage levels exist in a system
b. it is common practice to refer to plant MVA in
terms of per unit or percentage valuesc. transmission line and cable constants are given in
ohms/km
Before any system calculations can take place, thesystem parameters must be referred to 'base quantities'and represented as a unified system of impedances ineither ohmic, percentage, or per unit values.
The base quantities are power and voltage. Normally,they are given in terms of the three-phase power in MVAand the line voltage in kV. The base impedance resulting
from the above base quantities is:
ohms Equation 3.18
and, provided the system is balanced, the baseimpedance may be calculated using either single-phaseor three-phase quantities.
The per unit or percentage value of any impedance in thesystem is the ratio of actual to base impedance values.
Hence:
Equation 3.19
where MVAb = base MVA
kVb = base kV
Simple transposition of the above formulae will refer theohmic value of impedance to the per unit or percentage
values and base quantities.Having chosen base quantities of suitable magnitude all
Z p u Z ohms MVA
kV
Z Z p u
b
b
. .
% . .
( )= ( )( )
( )= ( )
2
100
ZkV
MVAb=
( )2
system impedances may be converted to those basequantities by using the equations given below:
Equation 3.20
where suffix b1 denotes the value to the original base
and b2 denotes the value to new base
The choice of impedance notation depends upon thecomplexity of the system, plant impedance notation andthe nature of the system calculations envisaged.
If the system is relatively simple and contains mainlytransmission line data, given in ohms, then the ohmicmethod can be adopted with advantage. However, theper unit method of impedance notation is the mostcommon for general system studies since:
1. impedances are the same referred to either side ofa transformer if the ratio of base voltages on thetwo sides of a transformer is equal to thetransformer turns ratio
2. confusion caused by the introduction of powers of100 in percentage calculations is avoided
3. by a suitable choice of bases, the magnitudes ofthe data and results are kept within a predictablerange, and hence errors in data and computationsare easier to spot
Most power system studies are carried out usingsoftware in per unit quantities. Irrespective of themethod of calculation, the choice of base voltage, andunifying system impedances to this base, should beapproached with caution, as shown in the followingexample.
Z Z MVA
MVA
Z Z kV
kV
b bb
b
b bb
b
2 1
2
1
2 1
1
2
2
=
=
3
Fundamenta
lTheory
Figure 3.6: Selection of base voltages
11.8kV 11.8/141kV
132kVOverhead line
132/11kV
Distribution11kV
Wrong selection of base voltage
11.8kV 132kV 11kV
Right selection
11.8kV 141kV x 11=11.7kV141132
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From Figure 3.6 it can be seen that the base voltages inthe three circuits are related by the turns ratios of theintervening transformers. Care is required as thenominal transformation ratios of the transformersquoted may be different from the turns ratios- e.g. a110/33kV (nominal) transformer may have a turns ratioof 110/34.5kV. Therefore, the rule for hand calculationsis: 'to refer an impedance in ohms from one circuit to
another multiply the given impedance by the square ofthe turns ratio (open circuit voltage ratio) of theintervening transformer'.
Where power system simulation software is used, thesoftware normally has calculation routines built in toadjust transformer parameters to take account ofdifferences between the nominal primary and secondaryvoltages and turns ratios. In this case, the choice of basevoltages may be more conveniently made as the nominalvoltages of each section of the power system. Thisapproach avoids confusion when per unit or percentvalues are used in calculations in translating the finalresults into volts, amps, etc.
For example, in Figure 3.7, generators G1 and G2 have asub-transient reactance of 26% on 66.6MVA rating at11kV, and transformers T1 and T2 a voltage ratio of11/145kV and an impedance of 12.5% on 75MVA.Choosing 100MVA as base MVA and 132kV as basevoltage, find the percentage impedances to new basequantities.
a. Generator reactances to new bases are:
b. Transformer reactances to new bases are:
NOTE: The base voltages of the generator and circuits
are 11kV and 145kV respectively, that is, the turns
ratio of the transformer. The corresponding per unit
values can be found by dividing by 100, and the ohmic
value can be found by using Equation 3.19.
Figure 3.7
12 5 100
75
145
132
20 1
2
2. . %
( )
( )=
26 100
66 6
11
132
0 27
2
2
( )
( )=
.. %
3.6 BASIC CIRCUIT LAWS,
THEOREMS AND NETWORK REDUCTION
Most practical power system problems are solved byusing steady state analytical methods. The assumptionsmade are that the circuit parameters are linear andbilateral and constant for constant frequency circuitvariables. In some problems, described as initial value
problems, it is necessary to study the behaviour of acircuit in the transient state. Such problems can besolved using operational methods. Again, in otherproblems, which fortunately are few in number, theassumption of linear, bilateral circuit parameters is nolonger valid. These problems are solved using advancedmathematical techniques that are beyond the scope ofthis book.
3.6.1 Circuit Laws
In linear, bilateral circuits, three basic network lawsapply, regardless of the state of the circuit, at anyparticular instant of time. These laws are the branch,
junction and mesh laws, due to Ohm and Kirchhoff, andare stated below, using steady state a.c. nomenclature.
3.6.1.1 Branch law
The currentI in a given branch of impedance
Z is
proportional to the potential differenceV appearing
across the branch, that is,V=
I
Z.
3.6.1.2 Junction law
The algebraic sum of all currents entering any junction(or node) in a network is zero, that is:
3.6.1.3 Mesh law
The algebraic sum of all the driving voltages in anyclosed path (or mesh) in a network is equal to thealgebraic sum of all the passive voltages (products of theimpedances and the currents) in the componentsbranches, that is:
Alternatively, the total change in potential around aclosed loop is zero.
3.6.2 Circuit Theorems
From the above network laws, many theorems have beenderived for the rationalisation of networks, either toreach a quick, simple, solution to a problem or to
represent a complicated circuit by an equivalent. Thesetheorems are divided into two classes: those concernedwith the general properties of networks and those
E Z I=
I= 0
3
Fundamenta
lTheory
2 4
Figure 3.7: Section of a power system
G1
T1
T2
G2
132kVoverheadlines
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concerned with network reduction.
Of the many theorems that exist, the three mostimportant are given. These are: the SuperpositionTheorem, Thvenin's Theorem and Kennelly's Star/DeltaTheorem.
3.6.2.1 Superposition Theorem(general network theorem)
The resultant current that flows in any branch of anetwork due to the simultaneous action of severaldriving voltages is equal to the algebraic sum of thecomponent currents due to each driving voltage actingalone with the remainder short-circuited.
3.6.2.2 Thvenin's Theorem(active network reduction theorem)
Any active network that may be viewed from twoterminals can be replaced by a single driving voltageacting in series with a single impedance. The driving
voltage is the open-circuit voltage between the twoterminals and the impedance is the impedance of thenetwork viewed from the terminals with all sourcesshort-circuited.
3.6.2.3 Kennelly's Star/Delta Theorem(passive network reduction theorem)
Any three-terminal network can be replaced by a delta orstar impedance equivalent without disturbing theexternal network. The formulae relating the replacementof a delta network by the equivalent star network is as
follows (Figure 3.8):Zco =
Z13
Z23 / (
Z12 +
Z13 +
Z23)
and so on.
Figure 3.8: Star/Delta network reduction
The impedance of a delta network corresponding to andreplacing any star network is:
Z12 =
Zao +
Zbo +
Zao
Zbo
Zco
and so on.
3.6.3 Network Reduction
The aim of network reduction is to reduce a system to asimple equivalent while retaining the identity of thatpart of the system to be studied.
For example, consider the system shown in Figure 3.9.The network has two sources E and E, a line AOBshunted by an impedance, which may be regarded as the
reduction of a further network connected betweenA andB, and a load connected between O andN. The object ofthe reduction is to study the effect of opening a breakeratA or B during normal system operations, or of a faultatA or B. Thus the identity of nodesA and B must beretained together with the sources, but the branch ONcan be eliminated, simplifying the study. Proceeding,A,B,N, forms a star branch and can therefore be convertedto an equivalent delta.
Figure 3.9
= 51 ohms
=30.6 ohms
= 1.2 ohms (since ZNO>>> ZAOZBO)
Figure 3.10
Z Z Z Z Z
ZAN AO BO
AO BO
NO
= + +
= + + 0 45 18 85 0 45 18 850 75
. . . .
.
Z Z Z Z Z
Z
BN BO NOBO NO
AO
= + +
= + + 0 75 18 85 0 75 18 850 45
. . . .
.
Z Z Z Z Z
ZAN AO NO
AO NO
BO
= + +
3
Fundamenta
lTheory
Figure 3.8: Star-Delta network transformation
c
Zao
Zbo
Z12
Z23
Z13
Oa b 1 2
3
(a) Star network (b) Delta network
Zco
Figure 3.9: Typical power system network
E' E''
N
0
A B1.6
0.75 0.45
18.85
2.55
0.4
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The network is now reduced as shown in Figure 3.10.
By applying Thvenin's theorem to the active loops, thesecan be replaced by a single driving voltage in series withan impedance as shown in Figure 3.11.
Figure 3.11
The network shown in Figure 3.9 is now reduced to thatshown in Figure 3.12 with the nodesA and B retainingtheir identity. Further, the load impedance has beencompletely eliminated.
The network shown in Figure 3.12 may now be used tostudy system disturbances, for example power swingswith and without faults.
Figure 3.12
Most reduction problems follow the same pattern as theexample above. The rules to apply in practical networkreduction are:
a. decide on the nature of the disturbance ordisturbances to be studied
b. decide on the information required, for examplethe branch currents in the network for a fault at a
particular location
c. reduce all passive sections of the network notdirectly involved with the section underexamination
d. reduce all active meshes to a simple equivalent,that is, to a simple source in series with a singleimpedance
With the widespread availability of computer-basedpower system simulation software, it is now usual to usesuch software on a routine basis for network calculations
without significant network reduction taking place.However, the network reduction techniques given aboveare still valid, as there will be occasions where suchsoftware is not immediately available and a handcalculation must be carried out.
In certain circuits, for example parallel lines on the sametowers, there is mutual coupling between branches.Correct circuit reduction must take account of thiscoupling.
Figure 3.13
Three cases are of interest. These are:
a. two branches connected together at their nodes
b. two branches connected together at one node only
c. two branches that remain unconnected
3
Fundamenta
lTheory
2 6
Figure 3.10: Reduction usingstar/delta transform
E'
A
51 30.6
0.4
2.5
1.21.6
N
B
E''
Figure 3.12: Reduction of typicalpower system network
N
A B
1.2
2.5
1.55
0.97E'
0.39
0.99E''
Figure 3.11: Reduction of active meshes:Thvenin's Theorem
E'
A
N
(a) Reduction of left active mesh
N
A
(b) Reduction of right active mesh
E''
N
B B
N
E''
31
30.630.6
31
0.4 x30.6
52.6
1.6 x51
E'52.6
5151
1.6
0.4
Figure 3.13: Reduction of two brancheswith mutual coupling
(a) Actual circuit
IP Q
P Q
(b) Equivalent whenZaaZbb
(c) Equivalent whenZaa=Zbb
P Q
21Z= (Zaa+Zbb)
Zaa
Zbb
Z=ZaaZbb-Z
2ab
Zaa+Zbb-2Zab
Zab
Ia
Ib
I
I
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Considering each case in turn:
a. consider the circuit shown in Figure 3.13(a). Theapplication of a voltage Vbetween the terminals Pand Q gives:
V = IaZaa + IbZab
V = IaZab + IbZbb
where Ia and Ib are the currents in branches a andb, respectively and I= Ia +Ib , the total currententering at terminal Pand leaving at terminal Q.
Solving for Ia and Ib :
from which
and
so that the equivalent impedance of the originalcircuit is:
Equation 3.21
(Figure 3.13(b)), and, if the branch impedances areequal, the usual case, then:
Equation 3.22
(Figure 3.13(c)).
b. consider the circuit in Figure 3.14(a).
Z Z Zaa ab= +( )1
2
Z V
I
Z Z Z
Z Z Z
aa bb ab
aa bb ab
= =
+
2
2
I I IV Z Z Z
Z Z Za b
aa bb ab
aa bb ab
= + = + ( )
2
2
IZ Z V
Z Z Z
b
aa ab
aa bb ab
= ( )
2
IZ Z V
Z Z Za
bb ab
aa bb ab
= ( )
2
The assumption is made that an equivalent starnetwork can replace the network shown. Frominspection with one terminal isolated in turn and avoltage Vimpressed across the remaining terminalsit can be seen that:
Za+Zc=Zaa
Zb+Zc=Zbb
Za+Zb=Zaa+Zbb-2Zab
Solving these equations gives:
Equation 3.23
-see Figure 3.14(b).
c. consider the four-terminal network given in Figure3.15(a), in which the branches 11' and 22' areelectrically separate except for a mutual link. Theequations defining the network are:
V1=Z11I1+Z12I2
V2=Z21I1+Z22I2
I1=Y11V1+Y12V2
I2=Y21V1+Y22V2
where Z12=Z21 and Y12=Y21 , if the network is
assumed to be reciprocal. Further, by solving theabove equations it can be shown that:
Equation 3.24
There are three independent coefficients, namelyZ12, Z11, Z22, so the original circuit may be
replaced by an equivalent mesh containing fourexternal terminals, each terminal being connectedto the other three by branch impedances as shownin Figure 3.15(b).
Y Z
Y Z
Y Z
Z Z Z
11 22
22 11
12 12
11 22 122
=
=
=
=
Z Z Z
Z Z Z
Z Z
a aa ab
b bb ab
c ab
=
=
=
3
Fundamenta
lTheory
Figure 3.14: Reduction of mutually-coupled brancheswith a common terminal
A
C
B
(b) Equivalent circuit
B
C
A
(a) Actual circuit
Zaa
Zbb
Zab
Za=Zaa-Zab
Zb=Zbb-Zab
Zc=Zab
Figure 3.15 : Equivalent circuits forfour terminal network with mutual coupling
(a) Actual circuit
2
1
2'
1'
2'
1'
(b) Equivalent circuit
2
1
Z11
Z22
Z11
Z22
Z12 Z12 Z12 Z12Z21
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defining the equivalent mesh in Figure 3.15(b), andinserting radial branches having impedances equalto Z11 and Z22 in terminals 1 and 2, results inFigure 3.15(d).
3.7 REFERENCES
3.1Power System Analysis.
J. R. Mortlock andM. W. Humphrey Davies. Chapman & Hall.
3.2 Equivalent Circuits I. Frank M. Starr, Proc. A.I.E.E.Vol. 51. 1932, pp. 287-298.
3
Fundamenta
lTheory
2 8
Figure 3.15: Equivalent circuits forfour terminal network with mutual coupling
2'
1'
(d) Equivalent circuit
11
C 2
(c) Equivalent with all
nodes commoned except 1
Z11
Z12
Z11
Z12
Z12
Z12
-Z12 -Z12Z12
In order to evaluate the branches of the equivalentmesh let all points of entry of the actual circuit becommoned except node 1 of circuit 1, as shown inFigure 3.15(c). Then all impressed voltages exceptV1 will be zero and:
I1 = Y11V1
I2 = Y12V1
If the same conditions are applied to the equivalentmesh, then:
I1 = V1Z11
I2 = -V1/Z12 = -V1/Z12
These relations follow from the fact that the branchconnecting nodes 1 and 1' carries current I1 andthe branches connecting nodes 1 and 2' and 1 and2 carry current I2. This must be true since branchesbetween pairs of commoned nodes can carry no
current.By considering each node in turn with theremainder commoned, the following relationshipsare found:
Z11 = 1/Y11
Z22 = 1/Y22
Z12 = -1/Y12
Z12 = Z1 2 = -Z21 = -Z12
Hence:
Z11 = Z11Z22-Z212_______________Z22
Z22 = Z11Z22-Z212_______________Z11
Z12 = Z11Z22-Z212_______________Z12 Equation 3.25
A similar but equally rigorous equivalent circuit isshown in Figure 3.15(d). This circuit [3.2] followsfrom the fact that the self-impedance of any circuitis independent of all other circuits. Therefore, it
need not appear in any of the mutual branches if itis lumped as a radial branch at the terminals. Soputting Z11 and Z22 equal to zero in Equation 3.25,
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Introduction 4.1
Three phase fault calculations 4.2
Symmetrical component analysis 4.3
of a three-phase network
Equations and network connections 4.4
for various types of faults
Current and voltage distribution 4.5
in a system due to a fault
Effect of system earthing 4.6on zero sequence quantities
References 4.7
4 F a u l t C a l c u l a t i o n s
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Types of busbar protection systems . . 15.4 . . . . . . . . 235
Typical examples of timeand current grading,overcurrent relays . . . . . . . . . . . . . 9.20 . . . . . . . . 143
U
Unbalanced loading (negative sequence protection):- of generators . . . . . . . . . . . . . . 17.12 . . . . . . . . 293- of motors . . . . . . . . . . . . . . . . . 19.7 . . . . . . . . 346
Underfrequency protectionof generators . . . . . . . . . . . . . . 17.14.2 . . . . . . . . 295
Under-power protectionof generators . . . . . . . . . . . . . . 17.11.1 . . . . . . . . 293
Under-reach of a distance relay . . 11.10.3 . . . . . . . . 187
Under-reach of distance relayon parallel lines . . . . . . . . . . . . 13.2.2.2 . . . . . . . . 204
Undervoltage (Power Quality) . . . . 23.3.9 . . . . . . . . 415
Unit protection: . . . . . . . . . . 10.1-10.13 . . . . 153-169- balanced voltage system . . . . . . . 10.5 . . . . . . . . 156- circulating current system . . . . . . 10.4 . . . . . . . . 154- digital protection systems . . . . . . 10.8 . . . . . . . . 158- electromechanical protection
systems . . . . . . . . . . . . . . . . . . 10.7 . . . . . . . . 156
- numerical protection systems . . . .
10.8 . . . . . . . .
158- static protection systems . . . . . . . 10.7 . . . . . . . . 156- summation arrangements . . . . . . 10.6 . . . . . . . . 156
Unit protection schemes:- current differential . . . . . . 10.4, 10.10 . . . . 154-160- examples of . . . . . . . . . . . . . . . 10.12 . . . . . . . . 167- multi-ended feeders . . . . . . . . . . 13.3 . . . . . . . . 207- parallel feeders . . . . . . . . . . . . 13.2.1 . . . . . . . . 204- phase comparison . . . . . . . . . . . 10.11 . . . . . . . . 162- signalling in . . . . . . . . . . . . . . . . 8.2 . . . . . . . . 113- Teed feeders . . . . . . . . . 13.3.2-13.3.4 . . . . 207-209
- Translay . . . . . . . . . . . . 10.7.1, 10.7.2 . . . . 156-157- using carrier techniques . . . . . . . . 10.9 . . . . . . . . 160
Unit transformer protection(for generator unittransformers) . . . . . . . . . . . . . . 17.6.2 . . . . . . . . 286
Urban secondary distributionsystem automation . . . . . . . . . . . . 25.4 . . . . . . . . 447
V
Vacuum circuit breakers (VCBs) . . 18.5.5 . . . . . . . . 322
Van Warrington formulafor arc resistance . . . . . . . . . . . . . 11.7.3 . . . . . . . . 177
Variation of residual quantities . . . . 4.6.3 . . . . . . . . 42
Vector algebra . . . . . . . . . . . . . . . . 3.2 . . . . . . . . 18
Very inverse overcurrent relay . . . . . . 9.6 . . . . . . . . 128
Vibration type test . . . . . . . . . . . . 21.5.5 . . . . . . . . 381
Voltage and phase reversalprotection . . . . . . . . . . . . . . . . . 18.10 . . . . . . . . 327
Voltage control using substationautomation equipment . . . . . . . . . . 24.5 . . . . . . . . 430
Voltage controlled overcurrentprotection . . . . . . . . . . . . . . . . 17.7.2.1 . . . . . . . . 287
Voltage dependent overcurrentprotection . . . . . . . . . . . . . . . . . 17.7.2 . . . . . . . . 287
Voltage dips (Power Quality) . . . . 23.3.1 . . . . . . . . 413
Voltage distribution due toa fault . . . . . . . . . . . . . . . . . . . . 4.5.2 . . . . . . . . 40
Voltage factors for voltagetransformers . . . . . . . . . . . . . . . . 6.2.2 . . . . . . . . . 81
Voltage fluctuations (Power Quality) . 23.3.6 . . . . . . . . 415
Voltage limit for accurate reachpoint measurement . . . . . . . . . . . . 11.5 . . . . . . . . 174
Voltage restrained overcurrentprotection . . . . . . . . . . . . . . . . 17.7.2.2 . . . . . . . . 287
Voltage spikes (Power Quality) . . . 23.3.2 . . . . . . . . 413Voltage surges (Power Quality) . . 23.3.2 . . . . . . . . 413
Voltage transformer: . . . . . . . . . 6.2-6.3 . . . . . . 80-84- capacitor . . . . . . . . . . . . . . . . . . 6.3 . . . . . . . . 83- cascade . . . . . . . . . . . . . . . . . . 6.2.8 . . . . . . . . 82- construction . . . . . . . . . . . . . . . 6.2.5 . . . . . . . . . 81- errors . . . . . . . . . . . . . . . . . . . 6.2.1 . . . . . . . . 80- phasing check . . . . . . . . . . . . 21.9.4.3 . . . . . . . . 389- polarity check . . . . . . . . . . . . 21.9.4.1 . . . . . . . . 388- ratio check . . . . . . . . . . . . . . 21.9.4.2 . . . . . . . . 389- residually-connected . . . . . . . . . 6.2.6 . . . . . . . . . 81- secondary leads . . . . . . . . . . . . . 6.2.3 . . . . . . . . . 81- supervision in distance relays . . 11.10.7 . . . . . . . . 188- supervision in numerical relays . . . 7.6.2 . . . . . . . . 108- transient performance . . . . . . . . 6.2.7 . . . . . . . . 82- voltage factors . . . . . . . . . . . . . 6.2.2 . . . . . . . . . 81
Voltage unbalance(Power Quality) . . . . . . . . . . . . . 23.3.7 . . . . . . . . 415
Voltage vector shift relay . . . . . . 17.21.3 . . . . . . . . 307
WWarrington, van, formulafor arc resistance . . . . . . . . . . . . . 11.7.3 . . . . . . . . 177
Index
N e t w o r k P r o t e c t i o n & A u t o m a t i o n G u i d e 4 9 6
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Wattmetric protection, sensitive . . 9.19.2 . . . . . . . . 142
Wound primary currenttransformer . . . . . . . . . . . . . . . . 6.4.5.1 . . . . . . . . 87
ZZero sequence equivalent circuits:- auto-transformer . . . . . . . . . . . 5.16.2 . . . . . . . . 60- synchronous generator . . . . . . . . 5.10 . . . . . . . . 55- transformer . . . . . . . . . . . . . . . . 5.15 . . . . . . . . 57
Zero sequence network . . . . . . . . . 4.3.3 . . . . . . . . 35
Zero sequence quantities,effect of system earthing on . . . . . . . 4.6 . . . . . . . . . 41
Zero sequence reactance:- of cables . . . . . . . . . . . . . . . . . . 5.24 . . . . . . . . 69
- of generator . . . . . . . . . . . . . . . 5.10 . . . . . . . . 55- of overhead lines . . . . . . . . 5.21, 5.24 . . . . . . 66-69- of transformer . . . . . . . . . . 5.15, 5.17 . . . . . . 57-60
Zone 1 extension scheme(distance protection) . . . . . . . . . . . 12.2 . . . . . . . . 194
Zone 1 extension scheme inauto-reclose applications . . . . . . . 14.8.2 . . . . . . . . 226
Zones of protection . . . . . . . . . . . . . 2.3 . . . . . . . . . 8
Zones of protection,
distance relay . . . . . . . . . . . . . . . .
11.6 . . . . . . . .
174
Index
N e t w o r k P r o t e c t i o n & A u t o m a t i o n G u i d e 4 9 7
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