Rotor Fig. 10. Watthour-meter structure. Induction-Cup and Double-Induction-Loop Structures. These two structures are shown in Figs. I I and 12. They most closely stationary, only the rotor-conductor portion being free to rotate. The cup structure Stationar Fig. 11. Induction- cup structure employs a hollow cylindrical rotor, whereas the double-loop structure employs two loops at ight angles to one another. The cup structure may have additional poles between those shown in Fig. I l. Functionally, both structures are practically identical These structures are more efficient torque producers than either the shaded-pole or the watthour-meter structures, and they are the type used in high-speed relays Single-Induction-Loop Structure. This structure, shown in Fig. 13, is the most efficient torque- producing structure of all the induction types that have been described. However, it has the rather serious disadvantage that its rotor tends to vibrate as previously described for a relay in which the actuating force is expressed by only one component inside the brackets of equation 2. Also, the torque varies somewhat with the rotor position 26 FUNDAMENTAL RELAY-OPERATING PRINCIPLES AND CHARACTERISTICS
26 FUNDAMENTAL RELAY-OPERATING PRINCIPLES AND CHARACTERISTICS Induction-Cup and Double-Induction-Loop Structures. These two structures are shown in Figs. 11 and 12. They most closely resemble an induction motor, except that the rotor iron is stationary, only the rotor-conductor portion being free to rotate. The cup structure employs a hollow cylindrical rotor, whereas the double-loop structure employs two loops at right angles to one another. The cup structure may have additional poles between those shown in Fig. 11. Functionally, both structures are practically identical. These structures are more efficient torque producers than either the shaded-pole or the watthour-meter structures, and they are the type used in high-speed relays. Single-Induction-Loop Structure. This structure, shown in Fig. 13, is the most efficient torqueproducing structure of all the induction types that have been described. However, it has the rather serious disadvantage that its rotor tends to vibrate as previously described for a relay in which the actuating force is expressed by only one component inside the brackets of equation 2. Also, the torque varies somewhat with the rotor position. Fig. 10. Watthour-meter structure. Fig. 11. Induction-cup structure
Rotor Loop Pivot Fig. 12. Double-induction-loop structure Fig. 13. Single- induction-loop structure ACCURACY The accuracy of an induction relay recommends it for protective-relaying purposes Such relays are comparable in accuracy to meters used for billing purposes. This accuracy is not a consequence of the induction principle, but because such relays invariably employ jewel bearings and precision parts that minimize friction SINGLE-QUANTITY INDUCTION RELAYS A single-quantity relay is actuated from a single current or voltage source. Any of the induction-relay actuating structures may be used. The shaded-pole structure is used only for single-quantity relays When any of the other structures is used, its two actuating circuits are connected in series or in parallel; and the required phase angle between the two fluxes is obtained by arranging the two circuits to have different X/R(reactance-to-resistance) ratios by the use of auxiliary resistance and/ or capacitance in combination with one of the circuits. Neglecting the effect of saturation, the torque of all such relays may be expressed as: T=K1l2-Ks where I is the rms magnitude of the total current of the two circuits. The phase angle between the individual currents is a design constant, and it does not enter into the lication of these relays If the relay is actuated from a voltage source, its torque may be expressed as: T=KIV2-K2 where V is the rms magnitude of the voltage applied to the relay FUNDAMENTAL RELAY-OPERATING PRINCIPLES AND CHARACTERISTICS 27
FUNDAMENTAL RELAY-OPERATING PRINCIPLES AND CHARACTERISTICS 27 ACCURACY The accuracy of an induction relay recommends it for protective-relaying purposes. Such relays are comparable in accuracy to meters used for billing purposes. This accuracy is not a consequence of the induction principle, but because such relays invariably employ jewel bearings and precision parts that minimize friction. SINGLE-QUANTITY INDUCTION RELAYS A single-quantity relay is actuated from a single current or voltage source. Any of the induction-relay actuating structures may be used. The shaded-pole structure is used only for single-quantity relays. When any of the other structures is used, its two actuating circuits are connected in series or in parallel; and the required phase angle between the two fluxes is obtained by arranging the two circuits to have different X/R (reactance-to-resistance) ratios by the use of auxiliary resistance and/or capacitance in combination with one of the circuits. Neglecting the effect of saturation,the torque of all suchrelays may be expressed as: T = K1 I 2 – K2 where I is the rms magnitude of the total current of the two circuits. The phase angle between the individual currents is a design constant, and it does not enter into the application of these relays. If the relay is actuated from a voltage source, its torque may be expressed as: T = K1V 2 – K2 where V is the rms magnitude of the voltage applied to the relay. Fig. 12. Double-induction-loop structure. Fig. 13. Single-induction-loop structure
TORQUE CONTROL orque Figs. 10, Il 19 is obtained simply by ries with circuits if they are in parallel, or in serie with a portion of a circuit if they are in EFFECT OF FREQUENCY The effect of fi kup of single-quantity relay is Frequency, cycles per second qualitatively by Fig. 14. So far as a single-quantity induction relay lowest pickup at its rated frequency. The effect of slight changes in frequency normally encountered in power-system operation may be neglected. However, distorted wave form may produce significant changes in pickup and time characteristics. This fact is particularly important in testing relays at high currents; one should be sure that the wave form of the test currents is as good as that obtained in actual service, or else inconsistent results will be obtained g EFFECT OF D-C OFFSET The effect of d-c offset may be neglected with inverse-time single relays. High-speed relays may or may not be affected, depending on the characteristics of their circuit elements Generally, the pickup of high-speed relays is made high enough to compensate for any tendency to"overreach, "as will be seen later, and no attempt is made to evaluate the effect of d-c offs RATIO OF RESET TO PICKUP The ratio of reset to pickup is inherently high in induction relays; because their operation does not involve any change in the air gap of the magnetic circuit. This ratio is between 95% and 100% friction and imperfect compensation of the control-spring torque being the only things that keep the ratio from being 100%. Moreover, this ratio is unaffected by the pickup adjustment where tapped current coils provide the pickup adjustment. RESET TIME Where fast automatic reclosing of circuit breakers is involved, the reset time of an inverse time relay may be a critical characteristic in obtaining selectivity. If all relays involved do not have time to reset completely after a circuit breaker has been tripped and before the breaker recloses, and if the short circuit that caused tripping is reestablished when the breaker recloses, certain relays may operate too quickly and trip unnecessarily. Sometimes the drop-out time may also be important with high-speed reclosing 28 FUNDAMENTAL RELAY-OPERATING PRINCIPLES AND CHARACTERISTICS
28 FUNDAMENTAL RELAY-OPERATING PRINCIPLES AND CHARACTERISTICS TORQUE CONTROL Torque control with the structures of Figs. 10, 11, 12, or 13 is obtained simply by a contact in series with one of the circuits if they are in parallel, or in series with a portion of a circuit if they are in series. EFFECT OF FREQUENCY The effect of frequency on the pickup of a single-quantity relay is shown qualitatively by Fig. 14. So far as possible, a relay is designed to have the lowest pickup at its rated frequency. The effect of slight changes in frequency normally encountered in power-system operation may be neglected. However, distorted wave form may produce significant changes in pickup and time characteristics. This fact is particularly important in testing relays at high currents; one should be sure that the wave form of the test currents is as good as that obtained in actual service, or else inconsistent results will be obtained.3 EFFECT OF D-C OFFSET The effect of d-c offset may be neglected with inverse-time single relays. High-speed relays may or may not be affected, depending on the characteristics of their circuit elements. Generally, the pickup of high-speed relays is made high enough to compensate for any tendency to "overreach," as will be seen later, and no attempt is made to evaluate the effect of d-c offset. RATIO OF RESET TO PICKUP The ratio of reset to pickup is inherently high in induction relays; because their operation does not involve any change in the air gap of the magnetic circuit. This ratio is between 95% and 100% friction and imperfect compensation of the control-spring torque being the only things that keep the ratio from being 100%. Moreover, this ratio is unaffected by the pickup adjustment where tapped current coils provide the pickup adjustment. RESET TIME Where fast automatic reclosing of circuit breakers is involved, the reset time of an inversetime relay may be a critical characteristic in obtaining selectivity. If all relays involved do not have time to reset completely after a circuit breaker has been tripped and before the breaker recloses, and if the short circuit that caused tripping is reestablished when the breaker recloses, certain relays may operate too quickly and trip unnecessarily. Sometimes the drop-out time may also be important with high-speed reclosing. Fig. 14. Effect of frequency on the pickup of a single-quantity induction relay
TIME CHARACTERISTICS Inverse-time curves are obtained with relays whose rotor is a disc and whose actuating structure is either the shaded-pole type or the watthour-meter type. High-speed operation is obtained with the induction-cup or the induction-loop structures DIRECTIONAL INDUCTION RELAYS Contrasted with single-quantity relays, directional relays are actuated from two different independent sources, and hence the angle 0 of equation 3 is subject to change and must be considered in the appliation of these relays. Such relays use the actuating structures of Figs.10,11,12,or13 TORQUE RELATIONS IN TERMS OF ACTUATING QUANTITIES Curment-Cument Relays. A current-current relay is actuated from two different current transformer sources. Assuming no saturation, we may substitute the actuating currents for the fluxes of equation 3, and the expression for the torque becomes T=K1l112 sin 6-Kg where I1 and 12=the rms values of the actuating currents 8=the phase angle between the rotor-piercing fluxes produced by I and 12. An actuating current is not in phase with the rotor-piercing flux that it produces, for the same reason that the primary current of a transformer is not in phase with the mutual flux. (In fact, the equivalent circuit of a transformer may be used to represent each actuating circuit of an induction relay. But in some relays, such as the induction cylinder and double-induction-loop types, the rotor-piercing(or mutual)fluxes are at the same phase angle with respect to their actuating currents. For such so-called"symmetrical"structures, 8 of equation 4 may be defined also as the phase angle between the actuating currents. For the wattmetric type of structure, the phase angle between the actuating currents may be nificantly different from the phase angle between the fluxes For the moment, we shall assume that we are dealing with symmetrical structures, and that 8 may be defined as the phase angle between 1 and l2 of equation 4 However, it is usually desirable that maximum torque occur at some value of 0 other than 90. To this end, one of the actuating coils may be shunted by a resistor or a capacitor Maximum torque will still occur when the coil currents are 90 out of phase; but, in terms of the currents supplied from the actuating sources, maximum torque will occur at some angle other than90° Figure 15 shows the vector relations for a relay with a resistor shunting the I coil. II will now be defined as the total current supplied by the source to the coil and resistor parallel. If the angle 0 by which I2 leads I is defined as positive, the angle o by which the coil component of 11 lags 11 will be negative, and the expression for the torque will be: 12 sin(0-0)-K2 FUNDAMENTAL RELAY-OPERATING PRINCIPLES AND CHARACTERISTICS
FUNDAMENTAL RELAY-OPERATING PRINCIPLES AND CHARACTERISTICS 29 TIME CHARACTERISTICS Inverse-time curves are obtained with relays whose rotor is a disc and whose actuating structure is either the shaded-pole type or the watthour-meter type. High-speed operation is obtained with the induction-cup or the induction-loop structures. DIRECTIONAL INDUCTION RELAYS Contrasted with single-quantity relays, directional relays are actuated from two different independent sources, and hence the angle θ of equation 3 is subject to change and must be considered in the appliastion of these relays. Such relays use the actuating structures of Figs. 10, 11, 12, or 13. TORQUE RELATIONS IN TERMS OF ACTUATING QUANTITIES Current-Current Relays. A current-current relay is actuated from two different currenttransformer sources. Assuming no saturation, we may substitute the actuating currents for the fluxes of equation 3, and the expression for the torque becomes: T = K1I1I2 sin θ – K2 (4) where I1 and I2 = the rms values of the actuating currents. θ = the phase angle between the rotor-piercing fluxes produced by I1 and I2. An actuating current is not in phase with the rotor-piercing flux that it produces, for the same reason that the primary current of a transformer is not in phase with the mutual flux. (In fact, the equivalent circuit of a transformer may be used to represent each actuating circuit of an induction relay.) But in some relays, such as the induction cylinder and double-induction-loop types, the rotor-piercing (or mutual) fluxes are at the same phase angle with respect to their actuating currents. For such so-called "symmetrical" structures, θ of equation 4 may be defined also as the phase angle between the actuating currents. For the wattmetric type of structure, the phase angle between the actuating currents may be significantly different from the phase angle between the fluxes. For the moment, we shall assume that we are dealing with symmetrical structures, and that θ may be defined as the phase angle between I1 and I2 of equation 4. However, it is usually desirable that maximum torque occur at some value of θ other than 90°. To this end, one of the actuating coils may be shunted by a resistor or a capacitor. Maximum torque will still occur when the coil currents are 90° out of phase; but, in terms of the currents supplied from the actuating sources, maximum torque will occur at some angle other than 90°. Figure 15 shows the vector relations for a relay with a resistor shunting the I1 coil. I1 will now be defined as the total current supplied by the source to the coil and resistor in parallel. If the angle θ by which I2 leads I1 is defined as positive, the angle φ by which the coil component of I1 lags I1 will be negative, and the expression for the torque will be: T = K1I1I2 sin (θ – φ) – K2
SItIon ximum positi l2 Resiste of I1 Fig. 15. Vector diagram for maximum torque in a current-current induction-type directional relay For example, if we let 6-45 and o--30, the torque for the relations of Fig. 15 will b T=K11lsin75°-K2 The angle t of Fig 15 is called the "angle of maximum torque" since it is the value of e at which maximum positive torque occurs. It is customary to specify this angle rather than o when describing this characteristic of directional relays. The two angles are directly related by the fact that they add numerically to 90 in symmetrical structures such as we have assumed thus far. But, if we use t as the design constant of a directional relay rather than o, we can write the torque expression in such a way that it will apply to all relays whether symmetrical or not, as follows: T=Kilo cos(8-t)-K2 where t is positive when maximum positive torque occurs for I2 leading 11, as in Fig. 15 Or the torque may be expressed also as T=K1h1l2 cos B where, is the angle between I2 and the maximum-torque position of 12, or, B-(8-T) sh,se two equations will be used from now on because they are strictly true for any If a capacitor rather than a resistor is used to adjust the angle of maximum torque, it may be connected to the secondary of a transformer whose primary is connected across the coi and whose ratio is such that the secondary voltage is much higher than the primary voltage. The purpose of this is to permit the use of a small capacitor. Or, to accomplish the same purpose, another winding with many more turns than the current coil may be put on the same magnetic circuit with the current coil, and with a capacitor connected across this di 30 FUNDAMENTAL RELAY-OPERATING PRINCIPLES AND CHARACTERISTICS
30 FUNDAMENTAL RELAY-OPERATING PRINCIPLES AND CHARACTERISTICS For example, if we let θ = 45° and φ = –30°, the torque for the relations of Fig. 15 will be: T = K1I1I2 sin 75° – K2 The angle "τ" of Fig. 15 is called the "angle of maximum torque" since it is the value of θ at which maximum positive torque occurs. It is customary to specify this angle rather than φ when describing this characteristic of directional relays. The two angles are directly related by the fact that they add numerically to 90° in symmetrical structures such as we have assumed thus far. But, if we use τ as the design constant of a directional relay rather than φ, we can write the torque expression in such a way that it will apply to all relays whether symmetrical or not, as follows: T = K1I1I2 cos (θ – τ) – K2 where τ is positive when maximum positive torque occurs for I2 leading I1, as in Fig. 15. Or the torque may be expressed also as: T = K1I1I2 cos β – K2 where, β is the angle between I2 and the maximum-torque position of I2, or, β = (θ – τ). These two equations will be used from now on because they are strictly true for any structure. If a capacitor rather than a resistor is used to adjust the angle of maximum torque, it may be connected to the secondary of a transformer whose primary is connected across the coil and whose ratio is such that the secondary voltage is much higher than the primary voltage. The purpose of this is to permit the use of a small capacitor. Or, to accomplish the same purpose, another winding with many more turns than the current coil may be put on the same magnetic circuit with the current coil, and with a capacitor connected across this winding. Fig. 15. Vector diagram for maximum torque in a current-current induction-type directional relay