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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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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 2 3

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


3/11


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


4/11


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


5/11


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


6/11


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


7/11


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,


8/11


9/11

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


10/11

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

Section Page Section Page


11/11

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

Section Page Section Page

Documents

netw oro guie.pdf