Mason C. Russell. The art and science of protective relaying

Подождите немного. Документ загружается.

VOLTAGE TRANSFORMERS 131

Similarly,

= (1– a

) V

+ (1– a) V

= a

(1– a

) V

+ a(1– a) V

= (a

– a) V

+ (a – a

) V

— —

= –j

√

+ j

√

= (1– a

) V

+ (1– a) V

= a(1– a

) V

+ a

(1– a) V

= (a – l) V

+ (a

– l) V

—

= (– – + j

√

3/2

) V

+ (– –– j

√

3/2

) V

2 2

It will be observed that these relations are similar to those obtained for the output currents

of the delta-connected CT's of Chapter 7, Fig. 7.

LOW-TENSION VOLTAGE FOR DISTANCE RELAYS

The potential transformers must be connected to the low-voltage source in such a way that

the phase-to-phase voltages on the high-voltage side will be reproduced. The connection

that must be used will depend on the power-transformer connections. If, as is not usually

the case, the power-transformer bank is connected wye-wye or delta-delta, the potential-

transformer connections would be the same as though the potential transformers were on

the high-voltage side. Usually, however, the power transformers are connected wye-delta or

delta-wye.

Fig. 8. Three-phase voltages for standard connection of power transformers.

132 VOLTAGE TRANSFORMERS

First, let us become acquainted with the standard method of connecting wye-delta or delta-

wye power transformers. Incidentally, in stating the connections of a power-transformer

bank, the high-voltage connection is stated first; thus a wye-delta transformer bank has its

high-voltage side connected in wye, etc. The

standard method of connecting power

transformers does not apply to potential

transformers (which are connected as

required), but the technique involved in

making the desired connections will apply

also to potential transformers. The standard

connection for power transformers is that,

with balanced three-phase load on the

transformer bank, the current in each

phase on the high-voltage side will lead by

30° the current in each corresponding

phase on the low-voltage side. Also, the no-load phase-to-phase voltages on the high-

voltage side will lead the corresponding low-voltage phase-to-phase voltages by 30°. For this

to be true, the three-phase voltages must be as in Fig. 8, where a´ corresponds to a, b´ to b,

and c´ to c. The numbers on the voltage vectors of Fig. 8 designate the corresponding ends

of the transformer windings, 1-2 designating the primary and secondary windings of one

transformer, etc. Now, consider three single-phase transformers as in Fig. 9 with their

primary and secondary windings designated 1-2, etc. If we assume that the transformers

are rated for either phase-to-phase or phase-to ground connection, it is only necessary to

connect together the numbered ends that are shown connected in Fig. 8, and the

connections of Fig. 10 will result.

Fig. 9. Numbering the ends of the transformer

windings preparatory to making three-phase

connections.

Fig. 10. Interconnecting the transformers of Fig. 9 according to Fig. 8 to get standard connections.

VOLTAGE TRANSFORMERS 133

We can now proceed to examine the connections of potential transformers on the low-

voltage side that are used for the purpose of supplying voltage to distance relays. Figure 11

shows the connections if the power transformers are connected wye-delta. Figure 12 shows

the connections if the power transformers are connected delta-wye.

For either power-transformer connection, the phase-to-phase voltages on the secondary

side of the potential transformers will contain the same phase-sequence components as

those derived for the connections of Fig. 7, if we neglect the voltage drop or rise owing to

load or fault currents that may flow through the power transformer. If, for one reason or

another, the potential transformers must be connected delta-delta or wye-wye, or if the

voltage magnitude is incorrect, auxiliary potential transformers must be used to obtain the

required voltages for the distance relays.

The information given for making the required connections for distance relays should be

sufficient instruction for making any other desired connections for phase relays. Other

application considerations involved in the use of low-voltage sources for distance and other

relays will be discussed later.

Fig. 11. Connections of potential transformers on low-voltage side of wye-delta power transformer

for use with distance relays.

134 VOLTAGE TRANSFORMERS

CONNECTIONS FOR OBTAINING POLARIZING VOLTAGE FOR

DIRECTIONAL-GROUND RELAYS

The connections for obtaining the required polarizing voltage are shown in Fig. 13. This

is called the "broken-delta" connection. The voltage that will appear across the terminals

nmis as follows:

= V

+ V

= (V

+ V

) + (V

+ V

) + (V

+ V

)

= V

+ V

= 3V

In other words, the polarizing voltage is 3 times the zero-phase-sequence component of the

voltage of any phase.

The actual connections in a specific case will depend on the type of voltage transformer

involved and on the secondary voltage required for other than ground relays. If voltage for

distance relays must also be supplied, the connections of Fig. 14 would be used.

If voltage is required only for polarizing directional-ground relays, three coupling

capacitors and one potential device, connected as in Fig. 15 would suffice. The voltage

obtained from this connection is 3 times the zero-phase-sequence component.

Fig. 12. Connections of potential transformers on low-voltage side of delta-wye power transformer

for use with distance relays.

VOLTAGE TRANSFORMERS 135

The connection of Fig. 15 cannot always be duplicated with bushing potential devices

because at least some of the capacitance corresponding to the auxiliary capacitor C

might

be an integral part of the bushing and could not be separated from it. The capacitance to

ground of interconnecting cable may also have a significant effect.

Fig. 13 The broken-delta connection.

Fig. 14. Potential-transformer connections for distance and ground relays.

136 VOLTAGE TRANSFORMERS

The three capacitance tape may be connected together, and a special potential device may

be connected across the tap voltage as shown in Fig. 16, but the rated burden may be less

than that of Table 1.

Incidentally, a capacitance bushing cannot be wed to couple carrier current to a line

because there is no way to insert the required carrier-current choke coil in series with the

bushing capacitance between the tap and ground, to prevent short-circuiting the output of

the carrier-current transmitter.

Fig. 16. Connection of three coupling capacitors and one potential device for providing polarizing

voltage for directional-ground relays.

Fig. 16. Use of one potential device with three capacitance bushings.

VOLTAGE TRANSFORMERS 137

PROBLEM

1. Given a wye-delta power transformer with standard connections. According to the

definitions of this chapter, draw the connection diagram and the three-phase voltage

vector diagram for the HV and the LV sides, labeling the HV phases a, b, and cand the

corresponding LV phases a´, b´, and c´, (1) for positive-phase-sequence voltage applied to

the HV side, and (2) for negative-phase-sequence voltage applied to the HV side. When

positive-phase-sequence voltage is applied to the HV side, the phase sequence is a-b-c.

When negative voltage is applied, there is no change in connections, but the phase

sequence is a-c-b.

BIBLIOGRAPHY

1. "American Standard Requirements, Terminology, and Test Code for Instrument

Transformers," Publ. C57.13-1954,American Standards Association, Inc., 70 East 45th

Street, New York 17, N. Y.

2. "Outdoor Coupling Capacitors and Capacitance Potential Device," Publ. 31,American

Institute of Electrical Engineers, 33 West 39th Street, New York 18, N. Y.

"Standards for Coupling Capacitors and Potential Devices," Publ. 47-123,National

Electrical Manufacturers Association, 155 East 44th Street, New York 17, N. Y.

3. "Application of Capacitance Potential Devices," by J. E. Clem, AIEE Trans., 48(1939),

pp. 1-8. Discussions, pp. 8-10.

4. Transient Performance of Electric Power Systems,by R. Rudenberg, McGraw-Hill Book Co.,

New York, 1950.

5. "The Effects of Coupling-Capacitor Potential-Device Transients on Protective-Relay

Operation," AIEE Committee Report, AIEE Trans., 70(1951), pp. 2089-2096. Discussions,

p. 2096.

"Transient and Steady-State Performance of Potential Devices," by E. L Harder, P. O.

Langguth,, and C. A. Woods, Jr., AIEE Trans., 59(1940), pp. 91-99 Discussions, pp. 99-102.

138 METHODS FOR ANALYZING GENERALIZING, AND VISUALIZING RELAY RESPONSE

METHODS FOR ANALYZING GENERALIZING,

AND VISUALIZING RELAY RESPONSE

The material that has been presented thus far will enable one to translate power-system

currents and voltages into protective-relay response in any given case. From that stand-

point, the material of this chapter is unnecessary. Nor is this chapter intended to teach one

how to determine these currents and voltages by the methods of symmetrical compo-

nents,

1,2

since it is assumed that this is known. The purpose of this chapter is best

explained by a simple example.

In Chapter 7, we learned that a relay coil connected in the neutral lead of three wye-

connected current transformers would have a current in it equal to 3

. Assuming that

this is an overcurrent relay, we can immediately say that this relay will respond only to zero-

phase-sequence current. This is important and useful knowledge, because we then know

that the relay will respond only to faults involving ground. Furthermore, we do not have to

calculate the positive- and negative-phase-sequence components of current in the circuit

protected by the relay; all we need to know is the zero-phase-sequence component.

Moreover, merely by looking at the phase-sequence diagram for any fault, we can tell

whether this relay will receive zero-phase-sequence current, and how the magnitude and

direction of this current will change with a change in fault location. Therefore, it is evident

that we have at our disposal a much broader conception of the response of this relay than

merely knowing that it will operate whenever it receives more than a certain magnitude of

current. The value of being able to visualize and generalize relay response will become even

more evident in the case of any relay that responds to certain combinations of voltage, cur-

rent, and phase angle.

THE R-X DIAGRAM

The R-X diagram was introduced in Chapter 4 to show the operating characteristics of

distance relays. Now, we are about to use it to study the response of distance-type relays

to various abnormal system conditions. With this diagram, the operating characteristic of

any distance relay can be superimposed on the same graph with any system characteristic,

making the response of the relay immediately apparent.

A distance relay operates for certain relations between the magnitudes of voltage, current,

and the phase angle between them. For any type of system-operating condition, there are

certain characteristic relations between the voltage, current, and phase angle at a given

distance-relay location in the system. Thus, the procedure is to construct a graph showing

the relations between these three quantities (1) as supplied from the system, and (2) as

required for relay operation.

METHODS FOR ANALYZING GENERALIZING, AND VISUALIZING RELAY RESPONSE 139

PRINCIPLE OF THE R-X DIAGRAM

As described in Chapter 4, the basis of the R-X diagram is the resolution of the three vari-

ables–voltage, current, and phase angle–into two variables. This is done by dividing the

rms magnitudeofvoltagebythe rms magnitude ofcurrent and callingthis animpedance “Z.”

(For the moment, let us not be concerned with the significance of this impedance.)

Then, the resistance and reactance components of Z are derived, by means of the familiar

relations R = Z cos

and X = Z sin

. We shall call

positive when I lags V, assuming certain

relay connections and references. These values of R and X are the coordinates of a point

on the R-X diagram representing a given combination of V, I, and

. R and X may be pos-

itive or negative, but Z must always be positive; any negative values of Z obtained by

substituting certain values of

in an equation should be ignored since they have no

significance.

Figure 1 shows the R-X diagram and a point P representing fixed values of V, I, and

, when

I is assumed to lag V by an angle less than 90°. A straight line drawn from the origin to P

represents Z, and

is the angle measured counterclockwise from the + R axis to Z.

It is probably obvious that P can be located from a knowledge of Z and

without deriving

the R and X components. Or, by calculating the complex ratio of V to I, the values of R and

X can be obtained immediately without consideration of

. If V, I, and

vary, several points

can be plotted, and a curve can be drawn through these points to represent the character-

istic.

Fig. 1. The R-X diagram.

140 METHODS FOR ANALYZING GENERALIZING, AND VISUALIZING RELAY RESPONSE

CONVENTIONS FOR SUPERIMPOSING RELAY AND SYSTEM CHARACTERISTICS

In order to superimpose the plot of a relay characteristic on the plot of a system charac-

teristic to determine relay operation, both plots must be on the same basis. A given relay

operates in response to voltage and current obtained from certain phases.

Therefore, the

system characteristic must be plotted in terms of these same phase quantities as they exist

at the relay location. Also, the coordinates must be in the same units. The per unit or per-

cent system is generally employed for this purpose. If actual ohms are used, both the

power-system and the relay characteristics must be on either a primary or a secondary

basis, taking into account the current- and voltage-transformation ratios, as follows:

Secondary ohms = Primary ohms ×

CT ratio

VT ratio

Finally, both coordinates must have the same scale, because certain characteristics are

circular if the scales are the same.

It is necessary to establish a convention for relating a relay characteristic to a system char-

acteristic on the R-X diagram. The convention must satisfy the requirement that, for a

system condition requiring relay operation, the system characteristic must lie in the oper-

ating region of the relay characteristic. The convention is to make the signs of R and X

positive when power and lagging reactive power flow in the tripping direction of the dis-

tance relays under balanced three-phase conditions. Lagging reactive power is here

considered to flow in a certain direction when current flows in that direction as though

into a load whose reactance is predominantly inductive. It is the practice to assume “delta”

(defined later) currents and voltages as the basis for plotting both system and relay char-

acteristics when phase distance relays are involved, or phase current and the

corresponding phase-to-ground voltage (called “wye” quantities) when ground distance

relays are involved. In either case, three relays are involved, each receiving current and

voltage from different phases. Either the delta or the wye voltage-and-current combina-

tions will give the same point on the R-X diagram under balanced three phase conditions.

Fig. 2. Illustration for the convention for relating relay and system

characteristics on the R-X diagram.