ee - aac) PeeCRC
`
`GE 2016
`Vestas v. GE
`IPR2018-01015
`
`i
`
`

`

`Copyright 1964
`by Westinghouse Electric Corporation, Hast Pittsburgh, Pennsylvania
`Fourth Edition: Fourth Printing
`Printed in the United States of America
`
`ii
`
`

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`PECENTAGE
`DIFFERENTIAL
`RELAY
`
`RESTRAINING
`WINDINGS
`
`:
`tagedill
`
`EI cos (0-+20 degrees) is used to re-
`7? operating against
`ea to assist other relays in differenti-
`strict the tripping ar
`A reactance element,
`ating heavy load swings from faults.
`shift devices ar-
`(x), 18 obtained similarly with the phase-
`s along the #
`ranged so that the maximum-torque line i
`(reactance) axis.
`Inductor-Loop Element—The inductor loop, (h), pro-
`vides a very high speed and very reliable directional ele-
`ment which has been used for many years now in high-
`speed distance measuring relays.
`basic pbalance-beam im-
`Balance-Beam Element—The
`pedance element is shown in (4), a balance occurring for
`E/I=Z. For higher impedances than Zo (current rela-
`tively lower) the contacts remain open, whereas for lower
`impedances (relatively higher currents) they close quickly.
`Since the balance is mechanical, the phase angle between
`voltage and current qs of minor consequence, and the trip-
`ping characteristic, plotted on an R and X diagram is
`substantially a circle.
`Modified-Impedance Characteristic—The circu-
`lar characteristic may be shifted by some circuits auxiliary
`to the element as shown in (i), in order to provide better
`discrimination between. fault currents and load and swing
`currents on long, heavily-loaded transmission lines. The
`shifting imparts a directional characteristic to the relay in
`addition to narrowing its tripping region to more nearly
`just that required for faults.
`Circuits—It may be
`Networks and Ausxiliary
`noted that in discussing fundamental relay elements cer-
`tain auxiliary circuits external to the mechanical relay
`have been imtroduced:in (g), the phaseshifter; in (7), the
`Rectox; and in (fk), a full fledged networkto producein the
`relay element proper, the desired currents. This is a trend
`of which we shall certainly see more as time goes on, as
`static circuits are devised to produce a simple current out-
`put proportional to the desired function of the various line
`currents and voltages.
`gating Networks, L.4Ki,—tThe
`Sequence-Segre
`method of symmetrical components has been the key
`that has unlocked the door to a number of the aforemen-
`tioned possibilities, some of which are illustrated in (7),
`(s), and (é). The positive- and gero-sequence network in
`(r)
`is commonly used in pilot-wire relaying, where it is
`desired to compare over the wires only one quantity, which
`d measure of the fault current irrespective of what
`kind of fault it may be, that is A-B, A-Grd, ABC. The
`relay can be given almost independent and widely different
`settings for phase faults and ground faults, using the single
`example, 1t may be set for one ampere
`relay element. Yor
`of ground fault to provide the requisite sensitivity, but for
`ten amperes of 3-phase current to avoid operation onloads.
`A negative-sequence directional element is shownin (s).
`It is an adequate directional element for ground faults on
`reasonably well-grounded systems, and requires only two
`potential transformers rather than three as with usual
`residual-directional relays.
`is the phase-selector re-
`Another novel application,
`(E),
`d. This information
`lay to determine which phase is faulte
`is necessary in single-pole tripping and reclosing schemes.
`It is predicated on the knowledge, from symmetrical-
`components theory, that the negative-sequence current in
`
`is a Zoo
`
`348
`
`Chapter 11
`
`Relay and Circuit-Breaker Application
`the faulted phase only is in phase with the zero-sequence
`current.
`Individual overcurrent elements in the three
`phases could not be used for this selection as all three
`would pick up for a single line-to-ground fault on many
`golidly-grounded systems.
`Il. PROTECTIVE SCHEMES
`Protective schemes may be conveniently classified as
`
`follows:
`1. Apparatus Protection
`2. Bus Protection
`3, Line Protection
`in Fig. 1, generator and transformer protection
`Thus,
`atus” classification, generator
`come under the “Appar
`buses, high-voltage buses, and substation buses, under the
`second classification; and high-voltage transmission lines
`and feeders under “Line Protection.”
`The relay application chart, Table 2, has been included
`for ready reference in determining the operating principles
`and application of various specific relay types referred to
`throughout this chapter.
`3. A-C Generators
`erators above 1000 kva and many smaller
`Most a-c gen
`d with differential protection ar
`machines are equippe
`3 at the two ends of each phase
`ranged to trip if the current:
`winding differ. This scheme is shown in Fig. 3.
`Smaller machines are sometimes operated without dif -
`ferential protection, but if paralleled with larger machines -
`
`
`
`
`
`THREE PHASE A-C
`
`GENERATOR
`TYPICAL PHASE ONLY SHOWN
`ctions for one phase using the percen
`Fig. 3—Conne
`elay for generator protection.
`ential r
`
`they may be arranged to trip of ©
`or with a system,
`
`ower into the machine.
`protection the Type CA normals?
`reversed flow of p
`For differential
`sed in the large
`induction, ratio-type relays are U
`1 second relay tw
`
`jority of cases, their speed (about 0.
`severe faults) being adequate to prevent geriouspu?
`the iron in nearly all cases. However, @ high-speet.
`
`erator-differential relay, Type HA™,is available pr"
`
`
`CURRENT TRANSFORMER
`
`
`
`OPERATING
`WINDING
`
`
`
`

`

`Relay and Circutt-Breaker Application
`
`849
`
`
`-eycle protection and is being used with 100 per cent suc-
`
`egg in a number of important applications.
`
`“The relay is usually arranged to trip the generator, field
`
`srcuit, and neutral circuit breakers Gf any) simultaneously
`
`ya manually-reset lockout relay in new installations.
`
`Frequently the relay also trips the throttle and admits
`
`CO;for fire prevention. For example it may be required to
`
`oordinate with other high speed relays or to reduce the
`
`hock to the systems.
`
`Jf a single-winding generator (or equivalent) is con-
`
`ected to a double bus through two breakers, a current
`
`ransformer matching problem is imtroduced. The cur-
`
`ent transformers in the connections to the busses may
`
`arry large currents from one bus to the other in addition
`
`o the generator current. Thus, matching is not assured
`
`Me identical current transformers as in the simpler case of
`
`Fig. 3, and consequently,
`the Type HA relay is pre-
`
`erred for this case because of its superior discriminating
`
`qualities.
`
`‘The Type COrelay is also used for generator differential
`
`rotection. It provides straight differential protection, as
`
`entrasted with percentage differential, the diagram being
`
`he same as Fig. 3 without the restrainingcoils. Its setting
`
`must be considerably coarser than that of the CA relay be-
`
`sause there are no restraining coils to desensitize it when
`
`nighthrough-fault currents are flowing.
`
`_Double-Winding and Multiple-Winding Gener-
`
`ators—The differential protection schemeof Fig. 3 does
`
`not detect turn-to-turn short circuits within the winding
`
`because the entering and leaving currents of a phase re-
`
`main equal. Double and multiple winding machines pro-
`
`
`vide a means for obtaining such protection in the larger,
`
`more important generators. The currents in the parallel
`
`branches, become unequal when turns are short circuited
`
`none branch. The differential relays, Type CA or HA,
`
`can be arranged to detect shorted turns, grounds* or
`
`phase-to-phase faults, by placing one current transformer
`
`in the neutral end of one of the parallel windings, and one
`
`of double ratio at the line end in the combinedcircuit. The
`
`choice of schemes depends somewhat on the facility with
`
`which leads can be brought out and the necessity of over-
`
`ping the generator breaker. With hydrogen cooling
`additional leads can be brought out through the necessary
`as-tight bushings only with considerable difficulty, and
`
`ally there is no space for transformers inside the hydro-
`
`gen compartment.
`Effect of the Method of Grounding—The method
`
`grounding the generator neutral affects the protection
`orded by differential relays. For example, if sufficient
`unding impedanceis used so that a ground fault at the
`
`nerator terminals draws full load current, then for a
`li at the midpoint of the winding, where the normal
`
`tage to groundis half as great, the fault current will be
`
`proximately one-half the full load current. When a
`und fault occurs 10 percent from the neutral end of the
`
`ding, the fault current, being limited largely by the
`
`Uutral impedance, is about 10 percent of full load current.
`
`1S corresponds to the sensitivity of a 10 percent differ-
`tial relay and, therefore, represents the limit of protec-
`1 for phase to ground faults with such a relay. For
`With the same limitations as for a single. winding generator.
`
`
`lower impedance grounding the differential relay protects
`closer to the neutral. With higher impedance grounding,
`the limit of protection for ground faults is farther from
`the neutral end, and for an ungrounded machine,
`the
`differential protection is ineffective against ground faults.
`The protection afforded for phase-to-phase, double-phase-
`to-ground, or three-phase faults is relatively unaffected by
`the method of grounding. A complete discussion of the
`methodsof groundingis given in Chap. 19.
`Solidly Grounded and Low Resistance or React-
`ance Grounded Machine—If the generator is solidly
`grounded, or grounded through a reactor or resistor, draw-
`ing at least full-load current for a ground fault at a line
`terminal, the usual 10 percent differential relay operates
`for practically any short circuit within the machine and
`for grounds to within 10 percent of the neutral, or closer
`if the ground current is higher.
`Ungrounded, and Potential-Transformer-
`Grounded Generators—arethosegrounded onlythrough
`the natural capacitance from the metallically connected
`windings, buswork, and cables to ground. The potential
`transformer from neutral to ground, if properly appliedf,
`serves as a measuring device only. To insure that this is
`so, it must be liberally designed so that under no condition
`will its exciting current become appreciable compared with
`the charging current to ground. Otherwise, ferro-reso-
`nance may occur. Usually a full line-to-line rated trans-
`former will suffice. The potential transformer and a volt-
`age relay such as the SV (instantaneous) or CV (inverse
`time) may be used to initiate an alarm or optionally to
`trip. Or, on lower voltages, a static voltage unbalance
`indicator may be used connected directly to the primary
`circuit. Such an instrument is the Type G. These devices
`supplement the generator differential protection to provide
`indication or tripping for ground faults. Light resistance
`grounding as covered in the next section is generally pre-
`ferred to ungrounded operation.
`Light-Resistance-Grounded Generators — This
`scheme and an associated protective arrangement is il-
`lustrated in Fig. 29 of Chap. 19.
`Indication from a volt-
`age relay, connected in parallel with the resistor as shown,
`or from a current relay, such as the Type BG, connected
`in series with the resistor, may be used to sound an alarm
`or to trip, depending on the application. Combinations
`of sensitive alarm and coarsertrip, or of alarm and time-
`delay trip, have also been used. The latter gives time
`to transfer the load to another machine at the hazard of
`operating with a fault on one phase.
`This scheme was designed primarily for the unit station
`arrangement in which a generator and step-up transformer
`are operated as a unit without an intervening bus. How-
`ever, it can also be used where an intervening bus carries
`the station service transformer and oneor two short feeder
`cables. A limited amountofselectivity is possible by the
`use of a polarized relay, such as the CWP-1, which obtains
`most of its energy from a potential coil in parallel with the
`groundingresistor. Such a relay used in the station-service
`feed, for example, can detect a ground on that circuit.
`Field Protection—While a large number of machines
`still operate without any protective relays to function on
`{See also Light-Resistance-Grounded Generators.
`
`

`

`358
`
`Relay and Circuit-Breaker Application
`
`Chapter 14
`
`notations as to relay types and settings, these symbols
`compress the otherwise complicated picture of complete
`system protection into a form that can be readily visual-
`ized. The standard symbols are given in Table 3. Their
`use has been illustrated in Fig. 12.
`
`TABLE 8— RELAY SYMBOLS
`
`(0) SYMBOLS FROM THE ASA STANDARDS.
`OVERGURRENT
`<— DIRECTIONAL OVERGURRENT| ——»
`OVERVOLTAGE
`ye
`
`UNDERVOLTAGE
`
`Py
`
`DISTANGE
`
`<—Z- [DIRECTIONAL DISTANCE —z»
`
`POWER DIRECTIONAL
`
`iit
`
`BALANGED OR
`DIFFERENTIAL CURRENT] <—%—»
`
`OVER FREQUENCY
`
`UNDER FREQUENCY
`
`ote
`
`|e
`
`OVER TEMPERATURE
`
`|<+—t»
`
`+—g—= PHASE ROTATION
`PILOT WIRE (DIRECTIONAL
`+>, [COMPARISON)
`CARRIER PILOT
`Where the operation of a relay is conditional upon the flow of ground
`current (residual or zero sequence) this shall be indicated by prefixing
`the ground symbo!
`thus:-
`
`—fo
`
`Sy
`
`Ne
`BUS GROUND DIFFERENTIAL
`
`Relative Number of different kinds of faults—
`Therelative numbersof different types of faults vary wide.
`ly with such factors as relative insulation to ground ang
`between phases, circuit configuration, the use of ground
`wires, voltage class, method of grounding, speed of fay}
`clearing, isokeraunie level*, atmospheric conditions, qual.
`ity of construction and local conditions. Thus thefigures
`given below serve merely to indicate the order of preva,
`lence and emphasize that there are usually a great many
`more line-to-ground faults than faults of other types.
`Three-Phase Faults
`5 percent
`‘Two-Line-to-Ground Faults
`10 percent
`Line-to-Line Faults
`15 percent
`Line-to-Ground Faults
`70 percent
`Total
`100 percent
`
`10. Overcurrent Protection
`Thegeneralplan of coordination with overcurrentrelays
`on a radial system is shown in Fig. 18. The time shown in
`each case is the fastest operating timefor a fault at the lo.
`cation of the next device in sequence. At lighter generat-.
`ing capacity the fault currents are reduced andall operat
`
`alishisSeadCRUaRLaOruUeerGk
`
`|
`
`CO-0.5 Set.
`P
`CO-0.5 Sec. ait
`CO-1.0See.g,,
`
`So Load " c0-0.3 Sec. tho
`
`SC Inst.
`
`Fig. 13—Coordination of overcurrent protection on a radial
`power system,
`
`ing times increase, but because of the inverse time charac-
`teristics of the relay the margins between successiverelays _
`also increase.
`Relays used with feeder circuit breakers must be coor |
`dinated with fuses of distribution transformers and with
`the main and branch line sectionalizing fuses.® Several
`
`characteristic curve shapes are available in different de-
`
`signs of the induction-type overcurrent relays as illustrated.
`
`in Fig. 14. These provide latitude in selecting the relay _
`
`that coordinates best with the fuse curves at the current
`
`involved.
`
`The definite minimum time characteristic provides a
`ready meansfor coordinating several relays in series with
`
`_
`only an approximate knowledge of the maximum current,
`and results in relatively small increase in the relay time 4%
`
`the fault current is lowered. It is used in the majority, al
`
`overcurrent relay applications. The inverse and very =
`verse characteristics are sometimes more favorable where
`
`close coordination with fuses is required. They also make
`
`it possible to take advantageof the reduction of maximu®
`
`fault current as distance from the power source increase:
`
`Several relays in series can be set for the same time for
`
`*Numberof storm-days per year
`
`
`
`
`
`
`
`BALANCED PHASE
`PILOT WIRE (CURRENT
`DIFFERENTIAL)
`
`Residual Overcurrent «le——* Directional Residuat Overcurrent «t}-——o
`Other prefixes such os @) and ®) to indicate operation on positive
`or negative phase sequence quantities, and suffixes to indicate the
`relay types,
`inclusion of
`instantaneous trip attachments, etc. may be
`added at
`the discretion of
`the user.
`
`(b) FREQUENTLY USED VARIATIONS OF THE STANDARD SYMBOLS.
`OVERCURRENT GROUND WITH INSTANTANEOUS ATTACHMENT
`
`GROUND DIRECTIONAL WITH INSTANTANEOUS ATTACHMENT
`DIRECTIONALLY CONTROLLED
`
`POWER DIRECTIONAL WITH INSTANTANEOUS ATTACHMENT
`DIRECTIONALLY CONTROLLED
`
`BUS CURRENT DIFFERENTIAL
`
`9. Fault Frequency and Distribution
`About 300 disturbances (or one per ten miles) occurred
`per year in a typical system operating 3000 miles of 110-ky
`circuit. This system used mostly overcurrent and direc-
`tional relays, and in a 4-year period experienced 2800 relay
`operations of which
`92.2 percent were correct and desired
`5.3 percent were correct but undesired
`2.1 percent were wrong tripping operations
`0.4 percent were failure to trip
`The faults were as follows:
`56 percent
`Lightning
`Sleet, Wind, Jumping Conductors 11 percent
`Apparatus Failure
`11 percent
`Close-in on Fault
`11 percent
`Miscellaneous
`11 percent
`
`

`

`Chapter 11
`
`Relay and Circuit-Breaker Application
`
`359
`
`
`
`Pitte?tttttet
`NETtt
`
`
`
`PL)AAT|
`
`
`PIMAAEEEE
`P|NoiNNTPPte
`
`
`PNAOe
`Ft St —
`
`
`
`
`0
`_l
`
`1000
`
`1500
`
`2000
`
`
`
`12
`
`TimeinSeconds
`
`
`
`
`mmediately beyond the relay andstill provide the
`e 0.25 second or more margin for fault beyond the
`lay because of the lower current value for fault in-
`ation. For example the timing on curve (b), Fig.
`
`bles when the current is reduced from 700 percent
`
`ercent of pick-up value. Several settings of 0.3 sec-
`
`0 percent could be usedin series, whilestill having
`d margin between successive relays if the fault
`Spped iin the ratio 7 to 4 between successive loca-
`
`oice of relays iis also influenced in certain cases by
`burden of the “low energy” and “very inverse”
`
`al-Speed Impedance Relay*
`-distance tripping characteristic of the Type
`peed directional distance relayis illustrated in
`ch shows a numberof line sections in series.
`
`ually well be a loop, the two endsof the section
`at the same supply point. Thetripping time
`increases in direct proportion to the distance
`yto the fault, except that the minimum time
`
`cond for a fault at the relay. Hach relay is
`oward the high-speed impedancerelay described in
`intermediate voltage transmission lines.
`
`
`
`
`
`
`Fig. 14—Characteristics of various induction type overcurrentrelays.
`
`Percent of Pick Up Current
`
`(a) Type COH.
`) Very inverse-low energy relay, Type CO.
`
`
`
`(c) Inverse-low energy relay, Type CO.
`(d) Standard, definite minimum time, Type COrelay.
`
`Trip Time for Bkr. #1
`
`
`Distance—»
`
`~+Time~
`
`Fig. 15—Time-distance curves of the Type CZ relay. The slope
`of the curve is changed by varying the resistance in series with
`the potential coil, The minimum operating time with zero
`voltage on the relay is about 14 sec.
`
`adjusted to trip in approximately 34 second for a fault at
`the next bus, except as will be noted.
`It is essential that for a fault near bus 4, breaker No. 3
`be tripped in preference to breaker No. 1. Thus the oper-
`ating time of relay No. 1 must exceed that of relay No. 3
`for fault at location No. 4 by one circuit breaker operating
`time plus margin. For 8-cycle breakers a reasonable break-
`er time plus margin is 0.4 second.
`
`

`

`CHAPTER 14
`
`POWER SYSTEM VOLTAGES AND CURRENTS DURING
`ABNORMAL CONDITIONS
`
`Revised by:
`
`R. L. Witzke
`
`3 PHASE FAULT
`(L-L-L OR 3L-G)
`
`SINGLE LINE-TO- GROUND
`FAULT (L-G}
`
`
`
`Original Author:
`R. L. Witzke
`
`P=:manyyearsitwascommonpracticetobasethe
`
`requirements of system apparatus on normal load
`conditions and on three-phase short circuits. More
`or less empirical multiplying factors were sometimes used
`to predict the probable ground-fault currents from the
`three-phase fault currents. However,
`this procedure is
`unsatisfactory because the relations between three-phase
`and ground-fault currents vary greatly between systems.
`In some systems the current for a single line-to-ground
`fault is less than normal load current, whereas, in other
`systems, or at other locations in the same systems, the
`current for a single line-to-ground fault is larger than the
`three-phase fault current. The analysis of power systems
`by symmetrical components! (see Chap. 2) has made pos-
`sible the accurate calculation of fault currents and voltages
`for unsymmetrical faults directly from system constants.
`Under many conditions the voltages present on a power
`system may be higher than those calculated for steady-
`state conditions. These higher voltages are usually of a
`transient nature and exist during the transition from one
`steady-state condition to another. Transient voltages can
`be produced by simple circuit changes such as the opening
`of a circuit breaker or the erounding of a conductor, or
`they can be produced by an intermittent arc in a circuit
`breaker or in a fault. Usually the higher voltages are
`associated with intermittent arcs rather than with simple
`circuit changes without arcing. Most transient voltages
`are not of large magnitude but may still be important
`because of
`their effect on the performance of circuit-
`interrupting equipment and protective devices. An appre-
`ciable number of these transient voltages are of sufficient
`magnitude to cause insulation breakdown.
`The various factors that determine the magnitudes of
`currents and voltages in power systems during abnormal
`conditions will be discussed in this chapter.
`I. STEADY-STATE VOLTAGES AND CURRENTS
`DURING FAULT CONDITIONS
`
`1. Assumptions
`Voltages and currents produced under fault conditions
`are a function of the type of fault and the ratios of the
`sequence impedances. The effeet of these factors on the
`voltages and currents produced can be shown by sets of
`curves as will be done here. The four types of faults il-
`lustrated in Fig. 1 will be considered. It is assumed that
`the network is symmetrical to the point of fault, F’, and.
`can be reduced to series impedances, Z1, Zo, and Zo for
`
`-
`
`
`
`
`
`LINE-TO-LINE FAULT.
`(L-t)
`
`DOUBLE LINE-TO- GROUND
`FAULT (2L-6)
`]
`Fig. 1—Types of faults on three-phase systems.
`
`
`the positive-, negative-, and zero-sequence networks, 1
`spectively. In the present analysis the faultresistance ©
`represented by R andis not included in Zo. Zo includes al
`zero-sequence resistance to the point of fault but doesnot
`include the fault resistance. It is further assume t al : ul
`
`the generated emfs can be reduced to a single posit a
`
`sequence emf, Ey.
`
`2. Formulas
`In Tables 1 and 2 are given the formulas* forcalet
`
`the line currents and line-to-ground voltages for the
`
`illustrated in Fig. 1. These formulas are complica
`such an extent that it is difficult to visualize re
`
`unde
`currents and voltages that can be produce
`conditions for ranges of system constants. For tn
`
`the currents and voltages have beencalculatedfo
`*Hormulas taken from pages 224 and 226 of referen®® :
`
`496
`
`
`
`

`

`
`
`
`
`Chapter 14
`
`Power System Voltages and Currents During Abnormal Conditions
`
`A497
`
`ratios of system constants and the results are presented as
`a series of curves.
`
`4. Fault Current and Voltage Curves
`Curves prepared in accordance with the preceding dis-
`cussion are plotted in Figs. 2 to 6 inclusive. In these figures
`the fault current is plotted as a ratio of the three-phase
`short-circuit, and the line-to-ground and line-to-line volt-
`ages are plotted as a ratio to their respective normal values.
`In Figs. 2, 3, and 4 all resistances are equal to zero.
`Figs. 2 and 3 show the ranges of line currents and line-to-
`
`20
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`2L-G short-circuit serls
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`L-G short-circuit als =05°107151
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`3. Range of Sequence Impedances Considered
`
`The principal impedances that usually apply to tran-
`sient conditions are the positive-sequence impedance “i,
`
`the negative-sequence impedance Zs, and the zero-sequence
`impedance Zo, each consisting of a resistance and a react-
`
`ance component.
`In general, the positive-sequenceresist-
`ance Jt; and the negative-sequence resistance Ry are small
`
`in comparison to the positive- and negative-sequence re-
`actances. Consequently, the effect of these two resistances
`
`on the magnitudeof the voltages and currents during fault
`conditionsis small. For this reason and because of compli-
`
`cations introduced by considering positive- and negative-
`sequenceresistances, these factors will be neglected. Zero-
`
`sequence resistance 2) and zero-sequence reactance Xo can
`vary through wide ranges depending on the type of system
`grounding used, hence the curves are arranged to cover a
`wide range of zero-sequence resistance and zero-sequence
`
`reactance.
`The positive-sequence reactance that applies to tran-
`
`sient conditions may be either the sub-transient or the
`
`transient reactance depending on whetheror not theinitial
`
`high decrement componentof the current is to be consid-
`
`ered or neglected. The ratio of X», to X: for commercial
`
`machines usually lies between 0.5 and 1.5, although with
`special machines it is possible to exceed this range. The
`
`higher ratios of X, to Xi are in machines without dampers
`
`_whereas the lower ratios are in machines with dampers
`
`or their equivalent.
`In general calculations it is usually
`
`permissible to assumea ratio of X./X1 of unity especially
`
`if an appreciable percentage of the negative-sequence re-
`
`actance to the point of fault is in static apparatus or trans-
`mission lines. The general curves are limited to ratios
`of X. to X, within the range of 0.5 to 1.5 ; the formulas
`in Tables 1 and 2 can be used for ratios outside of this
`
`
`
`
`
`
`
`
`
`
`
`Magnitudeof currents aeen
`Vector expression, effect of fault resistance included
`Type of fault
`=R,=R,=R=R,=
`
`=I=1.=
`ae
`Three-phase................
`Li
`Lp
`I, X
`I, ZAR
`pha;
`x
`_ —jV/3E.
`.
`Tya1,=oe
`ly=FATR
`e-to-line... 000.0... le,
`=
`Xi4+X,
`I,= —Iy
`
`
`
`gle line-to-ground........ Ta =,Me___= ee_
`ZotZ,+Z,+3R
`f
`fa Xo+Xi +X
`
`
`—V3E. v3.PILPL= . _
`
`
`
`
`TyNSEVBE+Rs) +4Qho+Zs+3Ri+6R)|
`[y=1-288 VPRO
`
`
`uble line-to-ground.......
`Tom Me |viz: Rr)
`~J2Zo4 Z,+3R,+6Re)|
`bey
`
`Fig. 2—Curves of fault currents vs. system reactances for
`single and double line-to-ground faults. Each curveis labeled
`to indicate the type of fault and the ratio of X,/X:. All cur-
`rents are expressed as a ratio to the three-phase short-circuit
`current. For these curves, all resistances are assumed equal
`to Zero!”
`
`ground voltages respectively for single and double line-to-
`ground faults for ratios of Xo/Xi from zero to six. The
`ranges of fault current and fault voltages for ratios of
`X2/X1 between 0.5 and 1.5 are shownin Fig. 4.
`.
`R
`The ranges of fault current for ratios of ¥ between zero
`1
`and six are given in Fig. 5. In this figure the ratio X./X1
`
`TABLE 1—FAULT CURRENTS
`
`—-V8E.
`
`.
`
`3H
`
`L,=Ih+I,=381
`
`—8E,
`= §(Z.+-Rx)
`Av=(Z1+Rr)(4.+R1) +(Z+2,+2R1)(Zo+Ri+3R,)
`Positive-sequence impedance to the point of fault
`
`:
`ative-sequence impedance to the point of fault
`2ero-seque
`nee impedance to the point of fault and does not include any fault resistance
`ee Fig. { for definitions of R, Ri and R,
`
`
`
`Am =XiX24X0(Xi+X.)
`
`