i
`
`1;_.wejs-t.nghause_
`'
`'Eust‘Pi‘nssbu'rg'h, ‘Pehh-syliah'd .'
`
`GE 2016
`Vestas v. GE
`IPR2018-01015
`
`i
`
`

`

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

`

`348
`
`7‘ Application
`
`Chapter 11
`
`C
`
`i
`
`Relay and'cacmt—Breake
`the faulted phase only is in phase with the zero—sequenCe
`current.
`Individual overcurrent elements in the three
`be used for this selection as all three
`phases could not
`would pick up for a single line—to-ground fault on many
`solidly—grounded systems.
`
`.
`1‘
`0
`3
`
`1
`
`
`33
`
`_,
`
`,
`'
`
`
`3. A-C Generators
`
`Most a—c generators above 1000 kva and many smaller
`.
`machines are equipped with differential protection an
`ranged to trip if the currents at the two ends of each phase
`_
`
`,
`winding differ. This scheme is shown in Fig. 3.
`Smaller machines are sometimes operated without dif-
`ferential protection, but if paralleled with larger machines _
`
`EI cos (0+20 degrees) is used to re—
`12 operating against
`strict the tripping area to assist other relays in differenti—
`ating heavy load swings from faults. A reactance element,
`(x), is obtained similarly with the phase—shift devices ar—
`ranged so that the maximum—torque line is along the as
`(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 balance—beam im-
`Balance-Beam
`pedance element is shown in (i), a balance occurring for
`E/I =Z0. For higher impedances than Z0 (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
`of minor consequence, and the trip—
`voltage and current islotted on an R and X diagram is
`ping characteristic, p
`substantially a circle.
`stiC——The circu-
`Modified—Impedance Characteri
`be shifted by some circuits auxiliary
`lar characteristic may
`der to provide better
`to the element as shown in (Ir), in or
`d swing
`discrimination between fault currents and load an
`The
`currents on long, heavily—loaded transmission lines.
`al characteristic to the relay in
`shifting imparts a direction
`gion to more nearly
`addition to narrowing its tripping re
`just that required for faults.
`Circuits—~It may be
`Networks and Auxiliary
`relay elements cer—
`noted that in discussing fundamental
`ernal to the mechanical relay
`tain auxiliary circuits ext
`phase shifter; in (j), the
`have been introduced: in (g), the
`ork to produce in the
`Rectox; and in (k), a full fledged netw
`s a trend
`relay element proper, the desired currents. This i
`e as time goes on, as
`of which we shall certainly see mor
`mple current out-
`static circuits are devised to produce a si
`arious line
`put proportional to
`currents and voltages.
`11+K10’The
`Sequence—Segregating Networks,
`nts has been the key
`method of symmetrical compone
`ber of the aforemen-
`that has unlocked the door to a num
`illustrated in (r),
`tioned possibilities, some of which are
`and zero-sequence netw0rk in‘
`(8), and (t). The positive-
`d in pilot-wire relaying, where it iswhich
`(r)
`is commonly use
`the wires only one quantity,
`desired to compare over
`current irrespective of what
`is a good measure of the fault
`is A—B, A-Grd, ABC. The
`kind of fault it may be, that
`endent and widely different
`relay can be given almost indep
`using the single
`settings for phase faults and ground faults,
`be set for one ampere
`relay element. For example, it may
`itivity, but for
`ctions for one phase using the percen
`of ground fault to provide the requisite sens
`Fig. 3——Conne
`elay for generator protection.
`tion on loads.
`current to avoid Opera
`ential r
`(8).
`ten amperes of 3—phase
`'s shown in
`A negative-sequence directional element 1
`or with a system, they may be arranged to tri
`ement for ground faults on
`It is an adequate directional el
`two
`reversed flow of pOWer into the machine.
`reasonably Well—grounded systems, and requires only
`ther than three as with usual
`For differential protection the Type CA norm
`potential transformers ra
`d in the
`
`,_
`Another novel application,
`(If), is the phase—selector re— induction,
`ratio—type relays are use
`residual- directional relays.
`layto determinewhichphaseisfaulted. This information
`jority of cases, their speed (about 0.1 secondrelay“If:
`is necessary in single-pole tripping and reclosing schemes.
`severefaults) beingadequatetopreventseriousburmfi
`
`symmetrical— the iron in nearly all cases. However, a high-Spee‘i.
`e HA”, is available pm.
`
`It is predicated on the knowledge, from
`that the negative-sequence current in
`
`components theory,
`
`
`
`
`II. PROTECTIVE SCHEMES
`Protective schemes may be conveniently clasSified as
`follows :
`1. Apparatus Protection
`2. Bus Protection
`3. Line Protection
`Thus, in Fig. 1, generator and transformer protection
`come under the “Apparatus” classification; generator
`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.
`
`CURRENT TRANSFORMER
`
`
`
`
`
`THREE PHASE A-C
`GENERATOR
`
`TYPICAL PHASE ONLY SHOWN
`
`crater-differential relay, Typ
`
`tagedifi
`
`

`

`Chapter 11
`
`Relay and Circuit-Breaker Application
`
`349
`
`
`4337019 protection and is being used with 100 per cent suc-
`
`Iess in a number of important applications.
`
`'The relay is usually arranged to trip the generator, field
`
`ircui’fl, and neutral circuit breakers (if any) simultaneously
`
`y-a manually—reset lockout relay in new installations.
`
`Frequently the relay also trips the throttle and admits
`
`00,1901“ fire prevention. For example it may be required to
`
`cordinate with other high speed relays or to reduce the
`
`hock to the systems.
`
`If a Single—winding generator (or equivalent) is con—
`
`ected to a double bus through two breakers, a current
`
`ransformer matching problem is introduced. The cur-
`
`ent transformers in the connections to the busses may
`
`Harry large currents from one bus to the other in addition
`
`'0 the generator current. Thus, matching is not assured
`
`y 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 CO relay is also used for generator differential
`
`r'otection. It provides straight differential protection, as
`
`o'ntrasted with percentage differential, the diagram being
`
`he same as Fig. 3 without the restraining coils. Its setting
`
`must be considerably coarser than that of the CA relay be-
`
`ause there are no restraining coils to desensitize it when
`
`'_i_gh-through—fault currents are flowing.
`
`:_ Double-Winding and Multiple-Winding Gener-
`
`ators—The differential protection scheme of 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-
`
`Vi'de 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
`
`. one branch. The differential relays, Type CA or HA,
`
`Tan 'be arranged to detect shorted turns, grounds* or
`
`phase-to-phase faults, by placing one current transformer
`
`11 the neutral end of one of the parallel windings, and one
`
`(if double ratio at the line end in the combined circuit. The
`
`{hoice 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
`asetight bushings only with considerable difficulty, and
`
`ally there is no space for transformers inside the hydro-
`
`
`
`
`
`
`Efiect of the Method of Grounding—The method
`grounding the generator neutral affects the protection
`Orded by differential relays. For example, if sufficient
`unding impedance is used so that a ground fault at the
`nerator terminals draws full load current, then for a
`It at the midpoint of the winding, where the normal
`tags to ground is half as great, the fault current will be
`proximately one—half the full load current. When a
`11nd fault occurs 10 percent from the neutral end of the
`
`lidlng, the fault current, being limited largely by the
`
`litral impedance, is about 10 percent of full load current.
`1's corresponds to the sensitivity of a 10 percent differ—
`tlal relay and, therefore, represents the limit of protec—
`I.1 for phase to ground faults with such a relay. For
`With the same limitations as for a singlewinding 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
`methods of grounding is given in Chap. 19.
`Solidly Grounded and Low Resistance or React-
`ance Grounded Machineulf 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—arethosegroundedonlythrough
`the natural capacitance from the metallically connected
`windings, buswork, and cables to ground. The potential
`transformer from neutral to ground, if properly appliedT,
`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 i1-
`lustrated in Fig. 29 of Chap. 19.
`Indication from avolt-
`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 coarser trip, 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 one or two short feeder
`cables. A limited amount of selectivity is possible by the
`use of a polarized relay, such as the CWP—l, which obtains
`most of its energy from a potential coil in parallel with the
`grounding resistor. 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
`TSee also Light-Resistance—Grounded Generators.
`
`

`

`358
`
`Relay and Circuit-Breaker Application
`
`Chapter 11
`
`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 3—RELAY SYMBOLS
`
`(a) SYMBOLS FROM THE ASA STANDARDS.
`OVERCURRENT
`4—- DIRECTIONAL OVERGURRENT ——->
`OVERVOLTAGE
`
`
`
`UNDERVOLTAGE
`
`DISTANCE
`
`BALANCED OR
`
`OVER FREQUENCY
`
`UNDER FREQUENCY
`
`OVER TEMPERATURE
`
`BALANCED PHASE
`
`PILOT WIRE (CURRENT
`DIFFERENTIAL)
`
`PILOT WIRE (DIRECTIONAL
`COMPARISON)
`
`CARRIER PILOT
`
`-a
`
`s.WWhummuswrw-Wlwwxm”calculusnun.
`
`Relative Number of different kinds of faults\
`The relative numbers of different types of faults vary Wide
`1y with such factors as relative insulation to ground and
`between phases, circuit configuration, the use of ground
`wires, voltage class, method of grounding, speed of fault
`clearing, isokeraunic level*, atmospheric conditions, qua}-
`ity of construction and local conditions. Thus the figures
`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
`
`The general plan of coordination with overcurrent relays
`on a radial system is shown in Fig. 13. The time shown in
`each case is the fastest operating time for a fault at the 10-
`cation of the next device in sequence. At lighter generat-
`ing capacity the fault currents are reduced and all Operat-
`
`.
`
`(IO-0.5 Sec.
`CO~0;__5.SBC. c...-
`7] *
`CO-1.Q§ec.
`O-
`
`
`
`H
`
`CO~0‘.7—5’Sec_.
`
`g
`
`CO-0.§—§CC.
`
`' }Feeders
`
`S C Inst.
`
`GROUND DIRECTIONAL WITH INSTANTANEOUS ATTACHMENT
`DIRECTIONALLY CONTROLLED
`
`Fig. 13—Coordination of overcurrent protection on a radial
`power system.
`
`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 symbol
`thus:-
`
`Residual Overcurrenf -i||¢-——— Directional Residuai 0vercurrent~rtl—————>
`
`Other prefixes such as ® and GD 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
`
`BUS GROUND DIFFERENTIAL
`
`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 llO-kv
`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
`
`
`
`
`
`
`ing times increase, but because of the inverse time charac-
`teristics of the relay the margins between successive relays _
`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.83 Several
`
`characteristic curve shapes are available in different 66-
`
`signs of the induction-type overcurrent relays as illustrated:
`
`in Fig. 14. These provide latitude in selecting the relayg.
`
`'
`that coordinates best with the fuse curves at the current
`
`involved.
`
`The definite minimum time characteristic provides a.
`ready means for coordinating several relays in series w1th
`
`.
`only an approximate knowledge of the maximum current,
`and results in relatively small increase in the relay time as
`the fault current is lowered. It is used in the maJ'oritY_9_f
`overcurrent relay applications. The inverse and very 1n-'
`verse characteristics are sometimes more favorable Where
`close coordination with fuses is required. They also .make
`it possible to take advantage of the reduction of maXIImlm
`
`fault current as distance from the power source increases
`
`Several relays in series can be set for the same time for
`
`*Number of storm-days per year
`
`
`
`
`
`
`
`
`

`

`Chapter 11
`
`Relay and Circuit-Breaker Application
`
`359
`
`
`
`WIIIII:
`IflflIIIII
`. IIIIIIIII
`II
`
`IHNIIII
`II
`IHWIIIIII
`IflHIIII
`II
`II
`IHIIIII
`IMIRIIII
`I
`IHEHIIIIIIIIIIIIIIII
`IIHIEIQIIIIIIIIIIIII
`III-==III-====!!!lll
`
`
`
`
`
`
`
`TimeinSeconds
`
`
`
`
`
`
`12
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`Immediately beyond the relay and still provide the
`(3025 second or more margin for fault beyond the
`:ay'beeause 0f 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 used1n series While still having
`
`d margin between successive relays if the fault
`opped1n the ratio 7 to 4 between successive loca-
`
`
`
`
`
`
`
`
` .500-
`
`1000
`
`1500
`
`
`2000
`
`Fig. l4—Characteristics of various induction type overcurrent relays.
`
`Percent of Pick Up Current
`
`--a)' Type OOH.
`) Very inverse-low energy relay, Type CO.
`
`nice of relaysis also influencedin certain cases by
`' urden of the “low energy” and “very inverse”
`
`aleSpeed Impedance Relay*
`'—d.iStance tripping characteristic of the Type
`peed directional distance relay1s illustrated1n
`ch shows a number of line sections in series.
`ually well be a loop, the two ends of the section
`at the same supply point. The tripping time
`increasesin direct proportion to the distance
`Y to the fault, except that the minimum time
`mind for a fault at the relay. Each relay1s
`OWard the high-speed impedance relay describedIn
`mter'mediate voltage transmission lines.
`
`
`(c) Inverse—10W energy relay, Type CO.
`(d) Standard, definite minimum time, Type CO relay.
`
`Trip Time for Bkr. fit 1
`
`
`
` Distan ce—p—
`
`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 Mr sec.
`
`adjusted to trip in approximately % 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 N o. 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
`
`Original Author:
`R. L. Witzke
`
`Revised by:
`
`R. L. Witzke
`
`FOR manyyears it was commonpractice tobase the
`
`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 components1 (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 grounding 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 producedunder fault conditions
`are a function of the type of fault and the ratios of the
`sequence impedances. The effect 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, Z2, and Z, for
`
`.
`3 PHASE FAULT
`“-‘L‘L 0R 31"“
`
`7
`SINGLE LINE-T07 GROUND
`FAULT (L's)
`
`
`
`.
`
`496
`
`
`.
`LINE_TO_UNE FAULT--
`DOUBLE L|NE_T0_GR'OUND
`(L—L)
`.
`FAULT (n-6,
`
`'
`'
`Fig. l—Types of faults on three-phase systems; I
`.
`
`.
`--
`-
`-
`the positive—, negative-, and zero-sequence netWOl'kSi If?"
`
`spectively. In the present analysis the fault-'reslstance- 15"
`represented by R and is not included in Z0. 'Zo 11101119135 3‘.
`3
`
`zero-sequence resistance 130 the point 0f fault but (1065;12:011-
`include the fault resistance. It is further assumed that“
`
`
`the generated emfs can be reduced to a single 903E ‘57
`sequence emf, E
`
`2- Formulas
`.
`_
`.
`
`In Tables 1 and 2 are given the formulasl‘ for'caflfi"
`the line currents and line—to—ground voltages for the
`
`illustrated in Fig. 1. These formulas are 99111131109“
`such an extent that it is difficult to Vis_uallZ§3'1_"_3
`
`currents and voltages that can be produced 113d?
`conditions for ranges of system constants. For '13.-
`
`the currents and voltages have been malculated.f‘;J
`*Formulas taken from pages 224 and 226 of referel_1_0_e -
`
`
`
`

`

`Chapter 14
`
`Power System Voltages and Currents During Abnormal Conditions
`
`497
`
`
`
`
`
`ratios of system constants and the results are presented as
`a series of curves.
`
`3. Range of Sequence Impedances Considered
`
`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-
`
`The principal impedances that usually apply to tran-
`
`sient conditions are the positive—sequence impedance Z1,
`
`the negative-sequence impedance Z2, and the zero—sequence
`impedance Z0, each consisting of a resistance and a react-
`
`ance component.
`In general, the positive—sequence resist—
`ance R1 and the negative—sequence resistance R2 are small
`
`in comparison to the positive— and negative—sequence re-
`actances. Consequently, the effect of these two resistances
`
`on the magnitude of the voltages and currents during fault
`conditions is small. For this reason and because of compli—
`
`cations introduced by considering positive— and negative—
`sequence resistances, these factors will be neglected. Zero—
`
`sequence resistance R0 and zero—sequence reactance X0 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 whether or not the initial
`
`high decrement component of the current is to be consid—
`
`ered or neglected. The ratio of X2 to X1 for commercial
`
`machines usually lies between 0.5 and 15, although with
`' special machines it is possible to exceed this range. The
`
`higher ratios of X2 to X1 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 assume a ratio of X2/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 X2 to X1 within the range of 0.5 to 1.5; the formulas
`In Tables 1 and 2 can be used for ratios outside of this
`
`2.0
`
`1.8
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`
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`L-G short-circui't X1(X =0.5"I.0" 1.5 '
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`l
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`2
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`Rad-i0 Xq/Xg
`
`4
`
`5
`
`6 CD
`
`Fig. 2—Curves of fault currents vs. system reactances for
`single and double line-to—ground faults. Each curve is labeled
`to indicate the type of fault and the ratio of Xg/Xl. All cur-
`rents are expressed as a ratio to the three-phase short-circuit
`current. For these curves, all resistances are assumed equal
`to zerol.
`
`ground voltages respectively for single and double line-to—I
`ground faults for ratios of Xo/X1 from zero to six. The
`ranges of fault current and fault voltages for ratios of
`X2/X1 between 0.5 and 1.5 are shown in Fig. 4.
`.
`R
`The ranges of fault current for ratlos of X2 between zero
`1
`and six are given in Fig. 5. In this figure the ratio X2/X1
`
`
`
`
`
`
`
`
`TABLE 1~FAULT CURRENTS
`
`Au=X1X2+Xo(X1~I—X2)
`
`
`Type of fault
`Vector expression, effect of fault resistance included
`Milfiggriiggfisfi Euérsrgs 1V(1)1en
`_
`_
`_ _ g _
`
`Three— h
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`= Er;
`= = =E$
`p ase
`Ia Z1+
`Is.
`It
`Io X1
`
`_
`_ —j\/§Eg
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`e-to—hne ................
`Ib‘zl+zg+R
`1b=102fl
`—
`X1+X2
`Ic -— -—Ib
`
`€19 line—to—ground ........
`Ia =4E’g—
`= ——'3-Eg—
`Zo+zl+zz+3R
`1“ xo+xl+x2
`
`_
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`— 3E
`—
`-.———
`1. = Tip{van—42L) +1(220+zz+3RL—-6R.>]
`1b =1. = “if vXa+XoX2+X§
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`— $14]
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`3E
`lZI:\/3(Z2 RL)
`Ic— 21/311
`J<2Z° I Z2+3RL“6Rg):I
`Ig=A_MgX2
`Ig=1b+Ic=3lo
`
`—3E
`= A1) g(Z2 +RL)
`Av‘(Z1 I RL)(Z2 I RI.) I (Z1 I Z2 I 2RL)(Z0 I RL I 3Rg)
`
`-
`
`,
`uble line-to—ground .......
`
`
`
`figsitive-sequence impedance to the point of fault
`gatlve—sequence impedance to the point of fault
`
`zero'SGQUence impedance to the point of fault and does not include any fault resistance
`99 Fig. 1 for definitions of R, RL and R.
`
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