# PROTECTIVE RELAYING THEORY AND APPLICATIONS PDF

Donald Reimert. Protective Relaying: Principles and Applications, Third. Edition, J. Lewis Blackburn and Thomas J. Domin ß by Taylor & Francis Group. Protective Relaying Theory and bestthing.info - Ebook download as PDF File . pdf), Text File .txt) or read book online. bestthing.info TLFeBOOK - Free ebook download as PDF File .pdf), Text File .txt) or read book online for.

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Edition Download Pdf, Free Pdf Protective Relaying Principles Applications Edition. Download. Protective Relaying: Principles And Applications protective. W. A. Elmore, Protective Relaying Theory and Applications, Marcel Decker, NY, 2. submit all work as a single PDF file electronically on Canvas, unless a . The art of public speaking / Stephen Lucas. i 10th ed. p. cm. sequently, one of the first tasks in any public speaking Giancoli – Physics Principles with.

There are three classes of grounding: An ungrounded system is connected to ground through the natural shunt capacitance, as illustrated in Figure see also Chap. In addition to load, small usually negligible charging currents ow normally.

In a symmetrical system, where the three capaci- tances to ground are equal, g equals n. If phase a is grounded, the triangle shifts as shown in Figure Consequently, V bg and V cg become approximately.

In contrast, a ground on one phase of a solidly grounded radial system will result in a large phase and ground fault current, but little or no increase in voltage on the unfaulted phases Fig.

Arc resistance is seldom an important factor in phase faults except at low system voltages. The arc does not elongate sufciently for the phase spacings involved to decrease the current ow materially. In addition, the arc resistance is at right angles to the reactance and, hence, may not greatly increase the total impedance that limits the fault current. Figure Phasor diagram for the ground directional relay connection shown in Figure Phase a-to-ground fault is assumed on a solidly grounded system.

Figure Voltage plot for a solid phase a-to-ground fault on an ungrounded system. Figure Voltage plot for a solid phase a-to-ground fault on a solidly grounded system. Also, the relatively high tower footing resistance may appreciably limit the fault current.

Arc resistance is discussed in more detail in Chapter The diagrams shown are for effectively grounded systems. In all cases, the dotted or uncollapsed voltage triangle exists in the source the generator and the maximum collapse occurs at the fault location. The voltage at other locations will be between these extremes, depending on the point of measurement. Among the operating conditions to be considered are maximum and minimum generation, selected lines out, line-end faults with the adjacent breaker open, and so forth.

With this information, the relay engineer can select the proper relays and settings to protect all parts of the power system in a minimum amount of time. Three-phase fault data are used for the application and setting of phase relays and single- phase-to-ground fault data for ground relays. The method of symmetrical components is the foundation for obtaining and understanding fault data on three-phase power systems. Formulated by Dr. Fortescue in a classic AIEE paper in , the symmetrical components method was given its rst practical application to system fault analysis by C.

Wagner and R. Evans in the late s and early s. Lewis and E. Harder added measurably to its development in the s. Today, fault studies are commonly made with the digital computer and can be updated rapidly in response to system changes. Manual calculations are practical only for simple cases. A knowledge of symmetrical components is impor- tant in both making a study and understanding the data obtained.

It is also extremely valuable in analyzing faults and relay operations. A number of protective relays are based on symmetrical compo- nents, so the method must be understood in order to apply these relays successfully.

In short, the method of symmetrical components is one of the relay engineers most powerful technical tools. Although the method and mathematics are quite simple, the practical value lies in the ability to think and visualize in symmetrical components. This skill requires practice and experience. Figure Phasor diagrams for the various types of faults occurring on a typical power system.

Phasors, Polarity, and Symmetrical Components 21 the positive, negative, and zero sequence components. This reduction can be performed in terms of current, voltage, impedance, and so on.

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The positive sequence components consist of three phasors equal in magnitude and out of phase Fig. The negative sequence components are three phasors equal in magnitude, displaced with a phase sequence opposite to that of the positive sequence Fig.

The zero sequence components consist of three phasors equal in magnitude and in phase Fig. Note all phasors rotate in a counterclockwise direction. In the following discussion, the subscript 1 will identify the positive sequence component, the subscript 2 the negative sequence component, and the subscript 0 the zero sequence component.

For example, V a1 is the positive sequence component of phase-a voltage, V b2 the negative sequence component of phase-b voltage, and V c0 the zero sequence component of phase-c voltage. All components are phasor quantities, rotating counterclockwise. Since the three phasors in any set are always equal in magnitude, the three sets can be expressed in terms of one phasor. For convenience, the phase-a phasor is used as a reference. Note that the b and c components always exist, as indicated by Eq.

Note that dropping the phase subscripts should be done with great care. Where any possibility of misunderstanding can occur, the additional effort of using the double subscripts will be rewarded.

## Protective Relaying Principles and Applications 4th Edition By J Lewis Blackburn and Thomas J Domin

Equations to can be solved to yield the sequence components for a general set of three-phase phasors: If any sequence component exists by measure- ment or calculation in one phase, it exists in all three phases, as shown in Eq. Neutral is established by connecting together the terminals of three equal resistances as shown with each of the other resistor terminals connected to one of the phases.

Substituting Eq. V 0 V ng Neutral and ground are distinctly independent and differ in voltage by V 0. Grounding and its inuence on relaying are discussed in Chapters 7 and Interconnections of the three sequence networks allow any series or shunt disconti- nuity to be investigated. For the rest of the power- system network, it is assumed that the impedances in the individual phases are equal and the generator phase voltages are equal in magnitude and displaced from one another.

Based on this premise, in the symmetrical part of the system, positive sequence current ow produces only positive sequence voltage drops, negative sequence current ow produces only negative sequence voltage drops, and zero sequence current ow produces only zero sequence voltage drops. For an unsymmetrical system, interaction occurs between components. For a particular series or shunt discontinuity being repre- Figure Power system neutral.

Phasors, Polarity, and Symmetrical Components 23 sented, the interconnection of the networks produces the required interaction. Any circuit that is not continuously transposed will have impedances in the individual phases that differ.

This fact is generally ignored in making calculations because of the immense simplication that results. From a practical viewpoint, ignoring this effect, in general, has no appreciable inuence. Except in the area of a fault or general unbalance, each sequence impedance is con- sidered to be the same in all three phases of the symmetrical system.

A brief review of these quantities is given below for synchronous machinery, transfor- mers, and transmission lines. X 00 d indicates the subtransient reactance, X 0 d the transient reactance, and X d the synchronous reactance. These direct-axis values are necessary for calculating the short-circuit current value at different times after the short circuit occurs.

Since the sub- transient reactance values give the highest initial current value, they are generally used in system short-circuit calculations for high-speed relay applica- tion. The transient reactance value is used for stability consideration and slow-speed relay application.

The unsaturated synchronous reactance is used for sustained fault-current calculation since the voltage is reduced below saturation during faults near the unit. The negative sequence reactance of a turbine generator is generally equal to the subtransient X 00 d reactance. X 2 for a salient-pole generator is much higher.

The ow of negative sequence current of opposite phase rotation through the machine stator winding produces a double frequency component in the rotor. As a result, the average of the subtransient direct-axis reactance and the subtransient quadrature- axis reactance gives a good approximation of negative sequence reactance. Since the machine is braced for only three-phase fault current magnitude, it is seldom possible or desirable to ground the neutral solidly.

The armature winding resistance is small enough to be neglected in calculating short-circuit currents. This resistance is, however, important in determining the dc time constant of an asymmetrical short-circuit current. Typical reactance values for synchronous machin- ery are available from the manufacturer or handbooks. However, actual design values should be used when available. Values are available from the nameplate. The zero sequence reactance is either equal to the other two sequence reactances or innite except for the three-phase, core-type transformers.

In effect, the magnetic circuit design of the latter units gives them the effect of an additional closed delta winding. The resistance of the windings is very small and neglected in short-circuit calculations. The sequence circuits for a number of transformer banks are shown in Figure The impedances indicated are the equivalent leakage impedances between the windings involved. For two-winding transformers, the total leakage impedance Z LH is measured from the L winding, with the H winding short-circuited.

Z HL is measured from the H winding with the L winding shorted. Except for a 1: For three-winding and autotransformer banks, there are three leakage impedances: In the rst convention, the windings are labeled H high , L low , M medium ; in the second H high , L low , and T tertiary.

Unfortu- nately, the L winding in the second convention is 24 Chapter 2 equivalent to M in the rst. The tertiary winding voltage is generally the lowest. On a common kVA base, the equivalent wye leakage impedances are obtained from the following equations: The wye is a mathematical equivalent valid for current and voltage calculations external to the transformer bank.

The junction point of the wye has no physical signicance. One equivalent branch, usually Z M Z L , Figure Equivalent positive, negative, and zero sequence circuits for some common and theoretical connections for two- and three-winding transformers.

Phasors, Polarity, and Symmetrical Components 25 may be negative. On some autotransformers, Z H is negative. The equivalent diagrams shown in Figure are satisfactory when calculations are to be made relative to one segment of a power system. However, a more complex representation is required when phase cur- rents and voltages are to be determined at points in the system having an intervening transformer between them and the point of discontinuity being examined. For delta-wye transformers, a phase shift must be accommodated.

For ANSI standard transformers, the high-voltage phase-to-ground voltage leads the low- voltage phase-to-ground voltage by , irrespective of which side the delta or wye is on. This phase shift may be included in the equivalent per unit diagram by showing a 1 The phase shift in the negative sequence network for the delta-wye transformer is the same amount, but in the opposite direction, to that in the positive sequence network.

The phase shift then, for an ANSI standard transformer, would be 1 The phase shift must be used in all the combinations of Figure where a wye and delta winding coexist. This effect is extremely important when consideration is being given to the behavior of devices on both sides of such a transformer.

As a rule of thumb, the Hz reactance is roughly 0: The zero sequence impedance is always different from the positive and negative sequence impedances. Zero sequence impedance can vary from 2 to 6 times X 1 ; a rough average for overhead lines is 3 to 3. The resistance terms for the three sequences are usually neglected for overhead lines, except for lower- voltage lines and cables. In the latter cases, line angles of 30 to may exist, and resistance can be signicant.

A good compromise is to use the impedance value rather than reactance and neglect the angular differ- ence in fault calculations. This yields a lower current to assure that the relay will be set sensitively enough. This mutual impedance becomes an increasingly important factor as more lines are crowded into common rights of way.

Thus, three network diagrams are required to separate the three sequence compo- nents for individual consideration: These sequence network diagrams consist of one phase to neutral of the power system, showing all the compo- nent parts relevant to the problem under considera- tion.

Typical diagrams are illustrated in Figures through The positive sequence network Fig. Balanced loads may be shown from any bus to the neutral bus. Generally, however, balanced loads are neglected. Compared to the system low-impedance high-angle quantities, they have a much higher impedance at a Figure Example system and positive sequence network. In short, balanced loads complicate the calculations and generally do not affect the fault currents signicantly.

With two exceptions, the negative sequence network Fig. For all practical calculations involving faults or discontinuities remote from the generating plant, however, X 1 is assumed to be equal to X 2.

The zero sequence network Fig. First of all, it has no voltage: Rotating machinery does not produce zero sequence voltage. Also, the transformer connections require special consideration and grounding impe- dances must be included.

Figure shows the zero sequence circuits for many transformers. A three-line system diagram is usually not required to determine the zero sequence network, but if a question arises as to the ow of zero sequence currents, the three-line diagram can be useful. From this three- phase system diagram, the zero sequence network requirements can be resolved by determining whether or not equal and in-phase currents can exist in each of the three phases.

If the zero sequence current component can ow, the zero sequence network must reect its path. For simplicity, Figure shows the generators solidly grounded. In practice, however, solid ground- ing is used only in very special cases. Current reference direction in any circuit element must be the same in all three networks to avoid confusion. Current ow in one or more of the networks may reverse for some types of unbalances, particularly if the networks are complex.

Reverse ow should be treated as a negative current to ensure that it will be properly subtracted when determining the phase currents. Each sequence network is, of course, a per unit diagram representing one of the three phases of the symmetrical power system. Therefore, a resistor reactor, impedance connected between the system neutral and ground, as shown in Figure , must be multiplied by 3 as indicated. In the system, 3I 0 ows through R; in the zero sequence network, however, I 0 ows through 3R, producing an equivalent voltage drop.

Figure Negative sequence network for example system. Figure Zero sequence network for example system. Figure Example system generators shown solidly grounded for simplication. Phasors, Polarity, and Symmetrical Components 27 5. In such areas, negative and zero sequence voltages are generated, as previously described.

Sequence network connections for various types of common faults are shown in Figures through From the three-phase diagrams of the fault area, the sequence network connections representing the fault can be derived.

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These diagrams do not show fault impedance, and fault studies do not include this effect except in very rare cases. The single-sequence impedance Z 1 ; Z 2 ; Z 0 practically equivalent to X 1 ; X 2 ; X 0 shown in the gures is the net impedance between the neutral bus and selected fault location. Based on zero load, all generated voltages V AN are equal and in phase.

Since the three-phase fault is balanced, symmetrical components are not required for this calculation. However, since the positive sequence network repre- sents the system, the network can be connected as shown in Figure to represent the fault. For a phase-a-to-ground fault, the three networks are connected in series Fig. Figure illustrates a phase-b-c-to-ground fault and its sequence network interconnection.

The phase-b-to-phase-c fault and its sequence connections are shown in Figure Fault studies normally include only three-phase faults and single-phase-to-ground faults. Three-phase faults are the most severe phase faults, whereas single- phase-to-ground faults are the most common. Studies of the latter faults provide useful information for ground relaying. A fundamental study of both series and shunt unbalances was made by E.

Harder in The shunt unbalances summarized in Figure are taken from Harders study. Note that all the faults shown in Figures through are also represented in Figure Figure Sequence network connections and voltages. Figure Three-phase fault and its network connection. Figure Phase-to-ground fault and its sequence net- work connections. Inside the topmost box for each shunt condition is a four-line representation of the shunt to be connectedtothe systemat point x.

The three lower boxes for each shunt condition are the positive, negative, and zero sequence representations of the shunt.

The sequence connections for the series unbalances, such as open phases and unbalanced series impe- dances, are shown in Figure As before, these diagrams are taken from E. Harders study. Here again, the diagrams inside the topmost box for each series condition represent the area under study, from point x on the diagrams left to point y on the right.

The power system represented by the box is open between x and y to insert the circuits shown inside the box. Points x and y can be any distance apart, as long as there is no tap or other system connection between them. The positive, negative, and zero sequence interconnections for the discontinuity shown in the top box are illustrated in the three boxes below it. Simultaneous faults require two sets of interconnec- tions from either Figures or or both.

As shown in Figure , ideal or perfect transformers can be used to isolate the two restrictions. It is sometimes necessary to use two transformers as shown in Figure f. In this case, the rst transfor- mer ratios 1: These can be replaced by an equivalent transformer with ratios 1: Figure a, for example, represents an open phase-a conductor with a simultaneous fault to ground on the x side.

The sequence networks are connected for the open conductor according to Figure j, with three 1: The manual calcula- tions required, which involve the solution of simultaneous equations, may be quite tedious. To simplify this reduction, with negligible effect on the results, the following basic assumptions are some- times made: All generated voltages are equal and in phase.

All resistance is neglected, or the reactance of machines and transformers is added directly with line impedances. All shunt reactances are neglected, including loads, charging, and magnetizing reactances. All mutual reactances are neglected, except on parallel lines.

By using these assumptions, the positive sequence network can be drawn with a single-source voltage V an connected to the generator impedances by a bus. If voltages are different, either the voltages must be retained in the network or Thevenin theorem and superposition must be used to reduce the network and calculate fault currents and voltages. Note that for the series unbalances of Figure , a difference in Figure Double phase-to-ground fault and its sequence network connections.

Figure Phase-to-phase fault and its sequence network connections. Phasors, Polarity, and Symmetrical Components 29 voltageeither magnitude, phase angle, or bothis required for current to ow. The single-sequence impedances Z 1 , Z 2 and Z 0 of Figures through will be different for each fault location because of the different network reduc- tions.

During the network reduction, the distribution of currents in the various branches should be calculated, both as a check and to determine the current ow through the relays involved in a fault. These distribu- tion factors are calculated with the assumption that 1 per unit current ows in these single-sequence impe- dances at the fault or point of discontinuity. Network reduction calculations for the system of Figure are illustrated in Figures , , and 2- In these gures, X 1 , X 2 , and X 0 are the impedances between the neutral bus and the fault at bus G.

I 1 , I 2 , and I 0 are all assumed to be equal to 1 per unit. Analog or digital studies should be tailored to produce outputs that allow each branch current in Figure Sequence network interconnections for shunt balanced and unbalanced conditions. For single-phase-to- ground faults, 3I 0 is required for relays. When using the computer for sequence network reduction, the impedance data are input for the positive and zero sequence networks, along with bus and fault node points.

The network is then solved for three-phase and single-phase-to-ground faults. Tabu- lated printed data are provided for phase-a fault current and three-phase fault voltages, along with the corresponding 3I 0 , 3V 0 values for the phase-to-ground fault. I 2 and V 2 values should also be obtained for negative sequence relays.

These voltage and current values are needed for not only faults near the relay, but also those several buses or lines away. Among the operating conditions normally considered are maximum and minimum generation, selectedlines out of service, andline-end faults where the adjacent breaker is open. This information allows the correct relay types and settings to be selected in a minimal amount of time for the entire power system.

The following steps must be performed for calculat- ing fault currents and voltages: Obtain a complete single-line diagram for the entire system, including generators, transformers, and transmission lines, along with the positive, negative, and zero sequence impedances for each component.

Prepare a single-line impedance diagram from the system diagram or establish the nodes in a digital study for the positive, negative, and zero sequence networks. Reduce the impedance values of all network branches to a common base. Values may be expressed as per unit on a common kVA base or as ohms impedance on a common voltage base. Figure Sequence network interconnections for series balanced and unbalanced conditions. Phasors, Polarity, and Symmetrical Components 31 Obtain, or have the computer obtain, the equivalent single impedance of each sequence network, current distribution factors, and equivalent source voltage for the positive-phase sequence network.

All quantities must be referred to the proper base. Interconnect the networks or utilize the computer program to represent the fault type involved, and calculate the total fault current at the fault. Determine the current distribution and voltages as required in the system.

Total fault current is seldom of use as relays generally see a fraction of that current except for radial circuits. Alternatively, they Figure Representations for simultaneous unbalances. All the impedances have been reduced to a common base, as indicated in the diagram.

The positive sequence network for this system is shown in Figure , the zero sequence network in Figure The negative sequence network is equal to Figure , except that V an is not present. To perform this sample calculation of a phase-to- ground fault on the bus at station D, the networks must be reduced to a single reactance value between the neutral bus and fault point.

Of the several delta loops, at least one must be converted to wye-equivalent in order to reduce the networks. After one loop is chosen arbitrarily , the equivalent X, Y, Z branches for an equivalent wye are dotted in as shown in Figures and The X, Y, Z conversion from delta to wye- equivalent is a simple process: The X branch of the wye-equivalent is the product of the two delta reactances on either side divided by the sum of the three delta impedances.

The same relation applies to Figure Network reduction for example system Figure fault at bus G.

Figure Network reduction and current distribution. Figure Final network reduction for fault at bus G in Figure Figure Single line diagram for a typical loop-type power system. Thus, in Figures and , the networks are reduced as follows: Positive and negative sequence networks Zero sequence network X 1 62 j Since the two upper branches of each network are in parallel, they can be reduced as follows: Positive and negative sequence networks Zero sequence network 0: Figure Zero sequence network reduction for the system of Figure The remaining branches are in parallel and can also be reduced: These factors are expressed as the ratio of each term in the numerator and denominator.

Determining these fac- tors provides a convenient check on the calculations, since the sum of the two fractions must be 1. Distribution factors can be determined by working back through the reduction. The factors should be written on the diagrams as shown in Figure The distribution factors for the upper parallel branches of Figure c are determined as follows: Positive sequence network The delta current distribution factors are obtained from the X, Y, Z equivalents. The conversion technique is straightforward: The voltage drop across two of the wye branches is equivalent to the drop across the delta branch.

Calculating from Figure c, we obtain Positive sequence network 0: The three networks are connected in series for the phase-to-ground fault Fig. For convenience, the sequence currents are calculated in per unit values: Figure Per unit current distribution for AG fault at D. These currents may be expressed in either per unit or ampere values. Currents in the fault are calculated for each phase as follows: I 1 I 0 0 For each branch, the per unit positive, negative, and zero sequence currents can then be used to determine the individual phase currents by using Eqs.

These are recorded in Figure Next, the sequence and phase voltages at each bus are determinedas inFigure It is convenient tocalculate the voltages in per unit values. Note that the impedances listed in Figure appear in percent, rather than ohms, and may be converted easily to per unit. In the following calculations, the values in parenth- eses are volts, converted from the per unit values for the kV system of Figure V line-to-neutral 1: V ag j0: All the distributed current and voltage values for the system are displayed in Figure In this example, only a kV system fault, with its currents and voltages, was involved.

The effect of the phase shift through the transformer banks could not, however, have been neglected if currents and voltages were required for the opposite side of the power transformers. If the transformer bank is wye-connected on the high-voltage side, as shown in Figure , the general equations for one phase are I A nI a I c V an nV An V Bn nV AB The lowercase subscripts represent high-side quantities and the capital letter subscripts low-side quantities.

In Figure Current and voltage distribution for a single phase-to-ground fault at bus D of the system of Figure Phasors, Polarity, and Symmetrical Components 37 the balanced or symmetrical transformer bank, the sequences are independent. Consequently, positive sequence only is rst applied to Eqs.

If a power transformer bank is connected delta on the high-voltage side, as shown in Figure , the general equations for one phase are I a 1 n I A I B V A 1 n V a V c Applying only positive sequence quantities to Eqs. In either case, the positive sequence quantities are shifted in one direction, while the negative sequence quantities are shifted in the opposite direction. Zero sequence quantities are not affected by phase shift. These either pass directly through the bank or, more commonly, are blocked by the connections.

Thus, in a wye-delta bank, zero sequence current and voltage on one side cannot pass through the bank to the other side. With a ground fault, current ows in not only the faulted phase a, but also the unfaulted b and c phases. The positive and zero sequence distribution factors on any loop system will be different.

Conse- quently, the positive, negative, and zero sequence currents will not add up to zero in the unfaulted phases. On a radial system one with a source at one end only for both the positive and zero sequences , the three network distribution factors will all be equal to 1.

For a phase-a-to-ground fault on these circuits, I b equals I c , which equals 0. In practice, only 3I 0 and related 3V 0 ; V 2 , and I 2 values would be recorded for a phase-to-ground fault. The phase currents and voltages shown in Figure were provided for academic purposes.

The reason for showing 3I 0 , rather than the faulted phase current, can be seen from Figure In most circuits, there is a signicant difference between the I a and 3I 0 currents in any loop network. In a radial system, however, I a is equal to 3I 0 and ground relays operate on 3I 0. On phase-to-ground faults, the phase relays will receive current and may start to operate. Coordination between ground and phase relays is usually not necessary.

The principal reason there are so few coordination problems is that phase relays must be set above load 5 A secondary , whereas ground relays are conventionally set at 0. Phasors, Polarity, and Symmetrical Components 39 not miscoordinate with the phase relays. If higher ground settings are used, the likelihood of miscoordi- nation is increased. Under any fault condition, the total current owing into the ground must equal the total current owing up the neutrals. With an autotransformer, however, current can ow down the neutral.

In this case, the fault current plus the autotransformer neutral current equals the current up the other transformer neutrals. The convention that current ows up the neutral when current is owing down into the earth at the fault has given rise to the idea that the grounded wye-delta transformer bank is a ground source, a source of zero sequence current. This long-established idea is not, in fact, correct. The fault is the true source. It is a converter of positive sequence into negative sequence and, for ground faults, into zero sequence current.

This is illustrated by a voltage plot for various faults on a simple system Fig. For simplicity, assume Z 1 equals Z 2 equals Z 0. During faults, the voltage inside the generators does not change unless the fault persists long enough for the internal ux to change.

No appreciable voltage change should occur in high- or medium-speed relaying. For a solid three-phase fault, the voltage at the fault is zero. Therefore, high positive sequence-phase currents ow to produce the gradient shown in the plot of Figure For a phase-to-phase fault, negative sequence voltage is produced by the fault itself.

Negative sequence current, then, ows through- Figure Voltage gradient for various types of faults. The same general conditions also apply to phase-to-ground faults, except that since V a is zero, V 2 and V 0 are negative.

In summary, the positive sequence voltage is always highest at the generators or sources and lowest at a fault.

In contrast, negative and zero sequence voltages are always highest at the fault and lowest at the sources. The phasor diagrams of Figure illustrate the same phenomena, from a different viewpoint. In a three-phase fault, the voltages collapse symmetrically, except inside the generator.

The three currents have a large symmetrical increase and lagging shift of angle. Other phase faults shown in Figure are characterized by the relative collapse of two of the phase-to-neutral voltages, compared to the relatively normal third phase-to-neutral voltage. Two of the phase currents have a large lagging increase. For a single-phase-to-ground fault, on the other hand, one phase-to-neutral voltage is collapsed relative to the other two phases.

Similarly, one phase current has a large value and lags the line-to-ground voltage. With wye-delta transformers between the fault and measurement point, the positive sequence quantities shift in one direction, and the negative sequence quantities shift in the opposite direction. As a result, a phase-to-ground fault on the wye side of a bank has the appearance of a phase-to-phase fault on the delta side. Figures and offer a nal look at sequence currents and voltages for faults. Note that the positive sequence currents and voltages, shown in the left-hand columns, have approximately the same phase relations Figure Sequence currents for various faults.

Figure Sequence voltages for various faults. Phasors, Polarity, and Symmetrical Components 41 for all types of faults. At the fault are various nonsymmetrical currents and voltages, as shown in the far right-hand column. The negative and, some- times, the zero sequence quantities provide the transi- tion between the symmetrical left-hand column and nonsymmetrical right-hand column.

These quantities rotate and change to produce the nonsymmetrical, or unbalanced, quantity when added to the positive sequence.

These phasors can be constructed easily by remembering which fault quantity should be mini- mum or maximum. In a phase c-a fault, for example, phase-b current will be small. Thus, I b2 will tend to be opposite I b1. Since phase-b voltage will be relatively uncollapsed, V b1 and V b2 will tend to be in phase. After one sequence phasor is established, the others can be derived from Eq. A number of other protective relays use combinations of the sequence quantities, as summar- ized in Table A zero sequence 3I 0 current lter is obtained by connecting three current transformers in parallel.

A zero sequence 3V 0 voltage lter is provided by the wye-grounded-broken-delta connection for a voltage transformer or an auxiliary. Positive and negative sequence current and voltage lters are described in Chapter 3. Because a number of these fault-detecting or decision units are used in a variety of relays, they are called basic units.

Basic units fall into several categories: Combinations of units are then used to form basic logic circuits applicable to protective relays. When the current or voltage applied to the coil exceeds the pickup value, the plunger moves upward to operate a set of contacts.

The force F which moves the plunger is proportional to the square of the current in the coil. The plunger units operating characteristics are largely determined by the plunger shape, internal core, magnetic structure, coil design, and magnetic shunts. Plunger units are instantaneous in that no delay is purposely introduced. Typical operating times are 5 to 50 msec, with the longer times occurring near the threshold values of pickup.

The unit shown in Figure a is used as a high- dropout instantaneous overcurrent unit. The steel plunger oats in an air gap provided by a nonmag- netic ring in the center of the magnetic core. When the coil is energized, the plunger assembly moves upward, carrying a silver disk that bridges three stationary contacts only two are shown.

A helical spring absorbs the ac plunger vibrations, producing good contact action. The pickup range can be varied from a two-to-one to a four-to-one range by the adjusting core screw. The more complex plunger unit shown in Figure b is used as an instantaneous overcurrent or voltage unit.

An adjustable ux shunt permits more precise settings over the nominal four-to-one pickup range. This unit is relatively independent of frequency, operating on dc, Hz, or nominal Hz frequency. It is available in high- and low-dropout versions. The armature is hinged at one side and spring-restrained at the other. When the associated electrical coil is energized, the armature moves toward the magnetic core, opening or closing a set of contacts with a torque proportional to the square of the coil current.

The pickup and dropout values of clapper units are less accurate than those of plunger units. Four clapper units are shown in Figure Those illustrated in Figures a and b have the same general design, but the rst is for dc service and the second for ac operation. In both units, upward movement of the armature releases a target, which drops to provide a visual indication of operation the target must be reset manually.

The dc ICS unit Fig. The ac IIT unit Fig. It is equipped with a lag-loop to smooth the force variations due to the alternating current input. Its adjustable core provides pickup adjustment over a nominal four-to-one range. The SG Fig. The SG has provisions for four contacts two make and two break , and the MG will accept six. The AR clapper unit Fig. Figure Plunger-type units. Figure Four clapper units. A permanent magnet across the structure polarizes the armature-gap poles, as shown.

The nonmagnetic spacers, located at the rear of the magnetic frame, are bridged by two adjustable magnetic shunts. This arrangement enables the magnetic ux paths to be adjusted for pickup and contact action.

With balanced air gaps Fig. With the gaps unbalanced Fig. The resulting polarization holds the armature against one pole with the coil deener- gized. The coil is arranged so that its magnetic axis is in line with the armature and at a right angle to the permanent magnet axis.

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Current in the coil magnetizes the armature either north or south, increasing or decreasing any prior polarization of the armature. If, as shown in Figure b, the magnetic shunt adjust- ment normally makes the armature a north pole, it will move to the right.

Direct current in the operating coil, which tends to make the contact end a south pole, will overcome this tendency and the contact will move to the left. Depending on design and adjustments, this polarizing action can be gradual or quick.

The left-gap adjustment Fig. Some units use both an operating and a restraining coil on the armature. The polarity of the restraint coil tends to maintain the contacts in their initial position. Current of sufcient magnitude applied to the operating coil will provide a force to overcome the restraint, causing the contacts to change position. A combination of normally open or normally closed contacts is available.

These polar units operate on alternating current through a full-wave rectier and provide very sensitive, high-speed operation on very low energy levels. The operating equation of the polar unit is K 1 I op K 2 I r K 3 f where K 1 and K 2 are adjusted by the magnetic shunts; K 3 is a design constant; f is the permanent magnetic ux; I op is the operating current; and I r is the restraint current in milliamperes.

The induction disc unit Fig. The cylinder unit see Fig. Modern units, however, although using the same operating principles are quite different. All operate by torque derived from the interaction of uxes produced by an electromagnet with those from induced currents in the plane of a rotatable aluminum disc. The E unit in Figure a has three poles on one side of the disc and a common magnetic member or keeper on the opposite side.

The main coil is on the center leg. Current I in the main coil produces ux, which passes through the air gap and disc to the keeper. A small portion of the ux is shunted off through the side air gap.

A short- circuited lagging coil on the left leg causes f L to lag both f R and f T , producing a split-phase motor action. The phasors are shown in Figure Flux f T is the total ux produced by main coil current I.

The three uxes cross the disc air gap and induce eddy currents in the disc. These eddy currents react with the pole uxes and produce the torque that rotates the disc. With the same reference direction for the three uxes as shown in Figure b, the ux shifts from left to right and rotates the disc clockwise, as viewed from the top. There are many alternative versions of the induction disc unit.

The unit shown in Figure , for example, may have a single current or voltage input. The disc always moves in the same direction, regardless of the direction of the input. If the lag coil is open, no torque will exist. Other units can thus control torque in the induction disc unit. Most commonly, a directional unit is connected in the lag coil circuit. When the directional units contact is closed, the induction disc unit has torque; when the contact is open, the unit has no torque.

Induction disc units are used in power or directional applications by substituting an additional input coil for the lag coil in the E unit. The phase relation between the two inputs determines the direction of the operating torque. A spiral spring on the disc shaft conducts current to the moving contact.

This spring, together with the shape of the disc an Archimedes spiral and design of the electromagnet, provides a constant minimum operating current over the contact travel range.

A permanent magnet with adjustable keeper shunt Figure Induction disc unit. Figure Phasors and operations of the E unit induction disc. The spring tension, damping magnet, and magnetic plugs allow separate and relatively independent adjustment of the units inverse-time current characteristics.

Shown in Figure , the basic unit used for relays has an inner steel core at the center of the square electromagnet, with a thin-walled aluminum cylinder rotating in the air gap. Cylinder travel is limited to a few degrees by the moving contact attached to the top of the cylinder and the stationary contacts. A spiral spring provides reset torque. Operating torque is a function of the product of the two operating quantities applied to the coils wound on the four poles of the electromagnet and the sine of the angle between them.

The torque equation is T KI 1 I 2 sin f 12 K s where K is a design constant; I 1 and I 2 are the currents through the two coils; f 12 is the angle between I 1 and I 2 ; and K s is the restraining spring torque. Different combinations of input quantities can be used for different applications, system voltages or currents, or network voltages.

DArsonval Units In the DArsonval unit, shown in Figure , a magnetic structure and an inner permanent magnet form a two-pole cylindrical core. A moving coil loop in the air gap is energized by direct current, which reacts with the air gap ux to create rotational torque. The DArsonval unit operates on very low energy input, such as that available from dc shunts, bridge networks, or rectied ac.

The unit can also be used as a dc contact-making milliammeter or millivoltmeter. As the temperature changes, the different coefcients of thermal expansion of the two metals cause the free end of the coil or strip to move.

A contact attached to the free end will then operate based on temperature change. These networks, also known as sequence lters, are widely used. Basic Relay Units 47 I b , and I c inputs.

Similarly, the secondaries of three- phase voltage transformers, connected in series with the primary in grounded wye, provide 3V 0. By using Thevenins theorem, these three-phase networks can be reduced to a simple equivalent circuit, as shown in Figure b.

V F is the open circuit voltage at the output, and Z the impedance looking back into the three-phase network. Z s is the self-impedance of the three-winding reactors secondary with mutual impedance X m. The open circuit voltage Fig. In some applications, the currents I b and I c are interchanged, changing Figure DArsonval-type unit. Figure Composite sequence current network. With switch r closed and switch s open, the zero sequence response of Eq. The switches r and s are used in Figure as a convenience for description only.

Several typical sequence network combinations are given in Table A network in common use is shown in Figure Since this network is connected phase to phase, there is no zero sequence voltage effect. The network is best explained through the phasor diagram Fig. By design, the phase angle of Z R is lagging. For convenience, consider switches s to be closed and switches r open.

Impedance Z R is thus connected across voltage V ab , and the autotrans- former across voltage V bc. With only positive sequence voltages Fig. The drop V by1 across the auto- transformer to the tap is in phase with voltage V bc across the entire transformer.

The tap is chosen so that jV xb1 j jV by1 j. The lter output V xy V F is the phasor sum of these two voltages. With only negative voltages applied Fig.

Figure Sequence voltage network. Figure Phasor diagrams for the sequence voltage network of Figure with s closed and r open. Thus, this is a positive sequence net- work. A negative sequence network can be made by reversing the b and c leads or, in Figure , by opening s and closing r.

Then Figure a conditions apply to a negative sequence, giving an output V F ; Figure b conditions apply to a positive sequence with V F 0. This interchange of b and c leads to either the current or voltage networks offers a very convenient technique for checking the networks.

## Frontiers in Massive Data Analysis

For example, the negative sequence current network should have no output on a balanced power-system load but by interchanging the b and c leads it should produce full output on test. These components have been designed into logic units used in many relays.

Before these logic units are described in detail, the semiconductor components and their characteristics will be reviewed Fig. Relays use silicon-type components almost exclusively because of their stability over a wide temperature range. The device manifests a voltage drop for conduction in the forward direction of approximately 0.

The limit of voltage to be applied in the reverse direction is dened by the rating of the diode. Failure of the diode is expected if a voltage in excess of the rating is applied in the reverse direction. These devices are used in dc circuits to block interaction between circuits, for ac test circuits to generate a half-wave rectied current wave shape, or as a protective device around a coil to minimize the voltage associated with coil current interruption. If the current is limited to within rated values, the diode recovers its nonconducting characteristics when the reverse voltage falls below the zener value.

They are used for surge protection, voltage-regulating functions, and other applications in which a distinct conduction level is desired. Where conduction is desired in both directions with a threshold at a level at which conduction occurs, the back-to-back zener Fig. The characteristics of these devices are essentially the same in both the forward and reverse direction. It has a voltage-dependent nonlinear charac- teristic. The thermistor depicted in Figure e is a nonlinear device whose resistance varies with tempera- ture.

For this function, it is shifted from a nonconducting to conducting state by the base current I b. The transistor Figure Semiconductor components and their charac- teristics. The emitter current I e is the sum of I b and I c. Very small values of I b are able to control much larger values of I c and I e Fig. The thyristor is also known as a silicon-controlled rectier SCR.

With forward vol- tage applied, the thyristor will not conduct until gate current I g is applied to trigger conduction. The higher the gate current, the lower the anode-to-cathode voltage V F required to start anode conduction. After conduction is established and the gate current is removed, the anode current I F continues to ow.

The minimum anode current required to sustain conduc- tion is called the holding current I H. When V e reaches the peak value V p , the device conducts and passes current I e. Current will continue to ow as long as V e does not fall below the minimum value V v. The unijunction transistor is used for oscillator and timing circuits. Figure The transistor and equivalent electrical sym- bols. Figure Typical characteristic curves of transistor.

Figure The thyristor and its characteristics. Basic Relay Units 51 4. A logic unit has only two states: Two logic conventions are used to indicate the voltages associated with the 0 and 1 states. In normal logic, 0 is equivalent to zero voltage and 1 to normal voltage.

In reverse logic, the corresponding voltage equivalents are reversed; 0 is equivalent to normal voltage and 1 to zero voltage. In positive logic, inputs and outputs are positive; in negative logic, both inputs and outputs are negative. Relay systems normally use positive logic, although some elements may use negative signal inputs and outputs. Logic units are shown diagrammatically in their quiescent state, that is, the normal or at-rest state.

The quiescent state corresponds to the normally deenergized representation in electromechanical relay circuitry. Two sets of symbols are in common use in the United States. The European practice is similar to this. Convention dictates that inputs are shown on the left-hand side and outputs on the right-hand side.

## Protective Relaying: Principles and Applications

When a logic function has only two inputs, its output is usually simple to determine. For three or more inputs, particularly with combination logic functions, a logic or truth table offers a convenient method of determining the output. A logic table for a function with three inputs and one output is shown in Figure The table lists all possible combinations of zeros and ones for the inputs.

Each output could be 0 or 1, depending on the function. Properly speaking, the protective relaying system includes circuit breakers and current transformers cts as well as relays. Relays, cts, and circuit breakers must function together. There is little or no value in applying one without the other.

Protective relays or systems are not required to function during normal power system operation, but must be immediately available to handle intolerable system conditions and avoid serious outages and damage. Thus, the true operating life of these relays can be on the order of a few seconds, even though they are connected in a system for many years. In practice, the relays operate far more during testing and main- tenance than in response to adverse service conditions.

In theory, a relay system should be able to respond to an innite number of abnormalities that can possibly occur within the power system. In practice, the relay engineer must arrive at a compromise based on the four factors that inuence any relay application: Economics. Initial, operating, and maintenance Available measures of fault or troubles. Fault magnitudes and location of current transformers and voltage transformers Operating practices.

Conformity to standards and accepted practices, ensuring efcient system operation Previous experience. History and anticipation of the types of trouble likely to be encountered within the system The third and fourth considerations are perhaps better expressed as the personality of the system and the relay engineer.

Since it is simply not feasible to design a protective relaying system capable of handling any potential problem, compromises must be made. In general, only 2 Chapter 1 those problems that, according to past experience, are likely to occur receive primary consideration.

Natu- rally, this makes relaying somewhat of an art. Different relay engineers will, using sound logic, design sig- nicantly different protective systems for essentially the same power system. As a result, there is little standardization in protective relaying. Not only may the type of relaying system vary, but so will the extent of the protective coverage. Too much protection is almost as bad as too little. Nonetheless, protective relaying is a highly specia- lized technology requiring an in-depth understanding of the power system as a whole.

The relay engineer must know not only the technology of the abnormal, but have a basic understanding of all the system components and their operation in the system. Relay- ing, then, is a vertical speciality requiring a horizontal viewpoint. This horizontal, or total system, concept of relaying includes fault protection and the performance of the protection system during abnormal system operation such as severe overloads, generation deciency, out-of-step conditions, and so forth.

Although these areas are vitally important to the relay engineer, his or her concern has not always been fully appreciated or shared by colleagues. For this reason, close and continued communication between the planning, relay design, and operation departments is essential. Frequent reviews of protective systems should be mandatory, since power systems grow and operating conditions change.

A complex relaying system may result from poor system design or the economic need to use fewer circuit breakers. Considerable savings may be realized by using fewer circuit breakers and a more complex relay system. Such systems usually involve design compro- mises requiring careful evaluation if acceptable protec- tion is to be maintained. It should be recognized that the exercise of the very best relaying application principles can never compensate for the absence of a needed circuit breaker.

The application logic of protective relays divides the power system into several zones, each requiring its own group of relays. In all cases, the four design criteria listed below are common to any well-designed and efcient protective system or system segment. Since it is impractical to satisfy fully all these design criteria simultaneously, the necessary compromises must be evaluated on the basis of comparative risks.

Dependability is the degree of certainty of correct operation in response to system trouble, whereas security is the degree of certainty that a relay will not operate incorrectly.

Unfortunately, these two aspects of reliability tend to counter one another; increasing security tends to decrease depend- ability and vice versa.In practice, communications channel between stations. If the a input is reduced to 0 through Rin Fig. The factors should be written on the diagrams as shown in Figure There are many alternative versions of the induction disc unit.

For an unsymmetrical system, interaction occurs between components. Current of sufcient magnitude applied to the operating coil will provide a force to overcome the restraint, causing the contacts to change position.

Network reduction calculations for the system of Figure are illustrated in Figures , , and 2- Such systems usually involve design compro- required a trip-out. No single technological breakthrough has been more inuential in generating change than the microprocessor.