Actually, all the flux will not link all the turns of both coils. With current in coil 1 only, the linkages of both coils will be less than that given by eqs. This ratio is the same no matter which of the two windings is the primary. The tighter the coupling, the smaller is the leakage coefficient.
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Rapid clearing of faults promotes power-system stability. As shown in Fig. I, the transient stability power limit, or power which can be transmitted without loss of synchronism during a fault, is greater the more rapidly the fault is cleared.
Indeed, increasing the speed of fault clearing is often the most effective and most economical way of improving the transient stability of a power system or of increasing its stability limit. Rapid fault clearing is desirable for additional reasons. It lessens annoyance to electric-power customers from flickering of lamps due to voltage dips and from shutting down of motors through operation of undervoltage tripping devices.
It also decreases the damage to overhead transmission-line conductors and insulators at the point of fault. Such damage is most likely to occur if the fault current is great: then, with slow clearing, conductors may burn down or in- sulators may crack from the heat of the arc, giving rise to a permanent fault.
With rapid clearing, on the other hand, the conductor is hardly damaged, and the line can be put back into service immediately. The great majority of transmission-line faults originate as one-line-to- ground faults. High-speed clearing decreases the likelihood of such faults developing into more severe types, such as two-line-to-ground or three-phase, through the arc being carried by the wind from one conductor to another.
Since rapid fault clearing is so important for increasing stability and for other reasons, it is fitting to consider the circuit breakers and relays, the function of which is to clear faults. Circuit breakers serve to open the faulted circuit and thereby to sever it from the sound part of the power system.
They are required to interrupt abnormally large currents. Protective relays serve to detect the presence of faults, to determine their locations, and to initiate the opening of the proper circuit breakers. To isolate a fault with the least interruption of service to customers and with the least shock to the synchronous machines, only the faulted circuit-and no other-should be discon- nected.
In addition, both the relays and the circuit breakers should act as rapidly as possible consistent with selectivity. It is better to open the right breakers with some delay than to open the wrong breakers immediately. Most of the faults on overhead transmission lines are caused by lightning. Such faults usually do no permanent damage.
After the line has been disconnected by the circuit breakers the arc goes out, and in a short while the arc path becomes deionized and recovers its insulating strength.
Then the line may be re-energized without caus- ing the arc to restrike. Putting the line back into service immediately is advisable, not only to restore service to loads if any which are solelydependent upon the particular line, but also to render the system less vulnerable to any fault which may occur later. Furthermore, rapid reclosureof the circuit breakers, accomplishedwhilethe machines are still swinging apart in consequence of the fault, increases the restoring forces and thus increases the stability limit of the system.
Manual reclosure is too slow to have any effect on the stability limit, but high-speed automatic reclosure has a marked effect. Methods of analyzing the effect of high-speed reclosing on stability are considered in Chapter XI. Speeds of circuit breakers and relays. For the reasons stated in the preceding section, high-speed clearing of faults is necessary or desirable in many cases, and the added feature of high-speed automatic reclosing is frequently desirable.
Circuit breakers and relays, according to their speed and according to whether or not reclosing is employed, may be divided into the following classes: 1. Slow-speed circuit breakers and relays. High-speed circuit breakers and relays. High-speed reclosing circuit breakers and relays. The usual fault-clearing times for all classes and the reclosing times for the last class will now be discussed. The clearing time is the sum of the relay time and the breaker interrupting time.
The relay time is the elapsed time from the instant when a fault occurs until the instant when the relay contacts close the trip circuit of the circuit breaker. It is the sum of the breaker opening time the time required to part the breaker contacts and the arcing time.
Reclosing time is the elapsed time from the instant of energizing the trip circuit, the breaker being in the closed position, until the instant when the breaker arcing contacts touch on the reclosing stroke; it includes breaker opening time and time during which the breaker is open. All these times, if short, are customarily expressed in cycles on the basis of the usual power-system frequency of 60 cycles per second. Before breakers having interrupting times of 15 to 30 cycles and relays having times of 6 to cycles were generally used.
The resultant clearing times were from 21 to cycles. With such slow clearing, the power limits were but little higher than. Many slow- speed breakers and relays are still in use where rapid clearing is not necessary. As the importance of faster clearing to stability became recognized, higher-speed circuit breakers and relays were developed.
In , 8-cyclebreakers were introduced; and, in , 8 cycles became the standard breaker speed. Three- cycle breakers were first developed for the kv. In , the standard interrupting time for kv. Undoubtedly, the trend toward higher breaker speeds will continue; 5-cycle and 3-cycle breakers may be expected to become more common, and breakers of even higher speeds will probably be developed.
Many of the slow-speed circuit breakers have been rebuilt or can be rebuilt to make them faster. At least 8-cycle operation, and often 5-cycle or better, can be obtained by rebuilding. If both slow-speed breakers and slow-speed relays are used, the speed of clearing can usually be increased more economically by changing to high-speed relays than by rebuilding or replacing the circuit breakers.
Present high-speed relays operate in from 1 to 3 cycles. In most cases 1 cycle can be relied upon. The use of high-speed relays, there- fore, gives a clearing time of 9 to 11 cycles if 8-cycle breakers are used, or 6 to 8 cycles if 5-cycle breakers are used.
However, this clearing time cannot be achieved for all fault locations on a transmission line unless a pilot channel, such as carrier current, connecting the two ends of the line, is usedto supplement the relays. Although the final clearing time is long with this relaying scheme, the rapid opening of the first breaker materially improves the stability situation, for the fault is left connected to the system radially through the impedance of nearly the whole length of the line.
Further improvement may be obtained-at additional expense, of course-by the use of a pilot-wire or carrier-current channel to secure simultaneous high-speed opening of the breakers at both ends. Little, if any, increase in relay speeds over those now obtainable with carrier current can be expected because at least half a cycle of single- phase current and voltage appears to be necessary for obtaining reliable operation of the directional relay elements.
High-speed-reclosing circuit breakers and relays. High-speed reclosing has become common at the higher voltages, and the standard reclosing time of breakers for this service is 20 cycles. Such breakers are usually opened and closed by pneumatic mechanisms. Somewhat higher speeds of reclosure may be expected in the future, though the permis- sible speed is limited by the necessary "dead time" required for deioniza- tion of the arc path see Chapter XI. High-speed carrier-pilot relaying having relay time of 1 cycle is always used with high-speed-reclosing breakers.
Low voltage-up to volts a-c. Medium-low voltage and interrupting rating Medium-high voltage and interrupting rating to High voltage kv. Low-voltage circuit breakers are used for light and power circuits in buildings and in industrial plants, for electric railways, and for low- capacity power-station auxiliaries. Nearly all of them are air circuit breakers. CIRCUIT BREAKERS 5 Circuit breakers of the last three classes were once exclusively oil circuit breakers, but, since many air circuit breakers of these classes have been installed, the term power circuit breakers has been applied to both oil and air circuit breakers in these classes.
Medium-low-voltage circuit breakers are used in small power stations, including municipal and industrial plants, in steel mills, and for high- capacity auxiliaries in large power stations. Although many oil circuit breakers are still in service, the trend is toward air circuit breakers, especially those of the magnetic-blowout type. Medium-high-voltage circuit breakers are found in important sub- stations and in the generator-voltage circuits in large power stations.
The commonest voltage class is Here again, many oil circuit breakers are employed; but, since , air-blast breakers, which had already been developed in Europe, have become widely used in the United States, most new installations being of this type. For kv. High-voltage circuit breakers are used on important transmission lines.
Incidentally, there is a notable trend toward the elimination of generator-voltage switchgear in large generating stations which do not have a large local load but which transmit bulk power over high- voltage transmission lines. In such stations each generating unit, consisting of a generator and a step-up transformer, is connected through a high-voltage circuit breaker to a high-voltage bus or, some- times, to one high-voltage line. In the high-voltage class, oil circuit breakers of the outdoor floor-mounted steel-tank type have remained in favor in the United States and have been greatly improved as to speed, interrupting capacity, and compactness.
Low-oil-content porcelain-clad impulse circuit breakers have been employed to a lesser extent. High-voltage air-blast circuit breakers are in general use in Europe, and, though there are few of them in the United States at present , it seems likely that their importance will increase. High-voltage circuit breakers have large interrupting capacities and short interrupting times. The greatest interrupting rating increased from 2, Mva. The types of circuit breaker used in the high- and medium-high- voltage classes, being those of most concern in stability studies, will be described in some detail.
Oil circuit breakers-description. In oil circuit breakers, the current is interrupted in oil, which, by its cooling effect, helps to quench the arc that forms when the contacts part, and which, because of its insulating properties, permits closer spacing of live parts than would be permissible in air.
Power system stability
Power System Stability (IEEE Press Series on Power Engineering) (Volumes II)