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Industrial Power Systems. Short-circuit-current Calculating. The determination of short- circuit currents in power distribution sys- tems is just as basic and important as the determination of load currents for the purpose of applying circuit breakers, fuses, and motor starters.

The magnitude of the shoncircuit current is often easier to determine than the magnitude of the load current. Calculating procedures have been so greatly simplified compared with the very complicated procedures previously used that now only simple arithmetic is required to determine the short-circuit currents in even the most complicated power systems. If adequate protection is to he provided for a plant electric system, the size of the electric power system must also be considered to determine how much short-circuit current it will deliver.

This is done so that cir- cuit breakers or fuses may he selected with adequate interrupting capac- ity IC. This interrupting capacity should be high enough to open safely the maximum short-circuit current which the power system can cause to flow through a circuit breaker if a short circuit occurs in the feeder or equipment which it protects. The magnitude of the load current is determined by the amount Of work that is being done and hears little relation to the size of the system supplying the load.

However, the magnitude of the short-circuit current is somewhat independent of the load and i s directly related to the size o r. The larger the apparatus which supplies electric power to the system, the greater the short-circuit current will be. Take a simple case: A volt three-phase lo-lip motor draws about 13 amp of current at full load and will draw only this amount whether supplied by a 25 - kva or a - kva transformer bank. So, if only thc load currcnts arc considered when selecting motor branch circuit break-.

However, the. Hence, a much. A simple mathematical example is shown in Fig. These numbers. El IOOV. I A. Illustrotion showing that copocity of power source has more effect on rhort-. The impedance, limiting the flow of load current, consists mainly of the 20 ohms apparent impedance of the motor. If a short circuit occurs at F, the only impedance to limit the flow of short-circuit current is the transformer impedance 0.

Unless circuit breaker A can open amp, the short-circuit current will continue to flow, doing great damage. Suppose the plant grows and a larger transformer, one rated at amp, is substituted for the amp unit. A short circuit at F , bottom in Fig. Although the load current i s still 5 amp, the short- circuit current will now he 10, amp, and circuit breaker A must be able to open that amount.

Consequently it is necessary to coiisider the size of the system supplying the plant a s well a s the load current, to be sure that circuit breakers or fuses are selected which have adequate interrupting rating for stopping the f l o w of the short-circuit current. Short - circuit and load currents are analogous to the flow of xvater in a hydroelectric plant, shoivn in Fig.

The amount of water that flows. Within limits, it makes little difference whether the reservoir behiiid the dam is large or small. This flow of water is comparable to the flow of load current in the distribution system in a factory.

On the other hand, if the dam breaks, the amount of water that will flow will depend upon the capacity of the reservoir and will bear little. Whether the reservoir is large or. This flow of water is. The load currents do useful work, like the water that flows down the penstock through the turbine water wheel. The short-circuit currents produce unwanted effects, like the torrent that rushes madly downstream when the dam breaks. When determining the magnitude of short - circuit currents, it is extremely important that all sources of short-circuit current he considered and that the reactance characteristics of these sources be known.

There are three basic sources of short-circuit current:. Generators 2. Synchronous motors and synchronous condensers 3. Induction motors. All these can feed shorecircuit current into a short circuit Fig. Generators are driven by turbines, diesel engines, water wheels, or other types of prime movers.

When a short circuit occurs on the circuit fed by a generatar, the generator continues to produce voltage because the field excitation is maintained and the prime mover drives the generator at substantially normal speed.

The generated voltage produces a short- circuit current of a large magnitude which flows from the generator or generators to the short circuit. This flow of short-circuit current is limited only by the impedance of the generator and of the circuit between the generator and the short circuit.

For a short circuit at the terminals of the generator, the current from the generator is limited only by its own impedance. Normal load and short-circuit currents are analogous to the conditions shown in.

Generators, synchronous motors, and induction motors all produce short-circuit. Synchronous motors are constructed substantially like generators; i. Normally, synchronous motors draw a-c power from the line and convert electric energy to mechanical energy.

However, the design of a synchronous motor is so much like that of a generator that electric energy can be produced just as in a generator, by driving the synchronous motor with a prime mover. Actually, during a system short circuit the synchronous motor acts like a generator and delivers shortcircuit current to the system instead of drawing load cur- rent from it Fig.

As soon as a short circuit is established, the voltage on the system is reduced to a very low value. Consequently, the motor stops delivering energy to the mechanical load and starts slowing down. However, the inertia of the load and motor rotor tends to prevent the motor from slow- ing down. In other words, the rotating energy of the load and rotor drives the synchronous motor just as the prime mover drives a generator. The synchronous motor then becomes a generator and delivers short- circuit current for many cycles after the short circuit occurs on the system.

Figure 1. The amount of current depends upon the horsepower, voltage rating, and reactance of the synchronous motor and the reactance of the system to the point of short circuit. SHORT '. The inertia of the load and rotor of an induction motor has exactly the same effect on an induction motor as on a synchronous motor; i. There is one major difference. The induction motor has no d-c field winding, but there is a flux in the induction motor during normal operation.

This flux acts like flux produced by the d-c field winding in the synchronous motor. The field of the induction motor is produced by induction from the stator rather than from the d-c winding. The rotor flux remains normal as long as voltage is applied to the stator from an external source. How- ever, if the external source of voltage is removed suddenly, as it is when a short circuit occurs on the system, the flux in the rotor cannot change instantly. Since the rotor flux cannot decay instantly and the inertia drives the induction motor, a voltage is generated in the stator winding causing a short-circuit current to flow to the short circuit until the rotor flux decays to zero.

To illustrate the short-circuit current from an induction motor in a practical case, oscillograms were taken on a wound- rotor induction motor rated hp, volts, 60 cycles, three phase, ten poles, rpm. The external rotor resistance was short- circuited in each case, in order that the effect might he similar to that which would he obtained with a low-resistance squirrel-cage induction motor.

The current shown is measured on the motor side of the short circuit; so the short- circuit current contribution from the source of power does not appear, but only that contributed by the motor. Similar tests made with the machine initially running at full load show that the short-circuit current produced. Note that the maximum current occurs in the lowest trace on the oscillogram and is about ten times rated full-load current.

The current vanishes almost completely in four cycles, since there is no sustained field current in the rotor to provide flux, as in the case of a synchronous machine. The flux does last long enough to prodnce enough short-circuit current to affect the momentary duty on circuit breakers and the interrupting duty on devices which open within one or two cycles after a short circuit.

Hence, the short-circuit current produced by induction motors must he considered in certain calculations. The magnitude of short-circuit cur- rent produced by the induction motor depends upon the horsepower, voltage rating, reactance of the motor, and the reactance of the system to the point of short c.

The machine impedance, effective at the time of short circuit, cmesponds closely with the impedance at standstill. Consequently, the i iitial symmetrical value of Short-circuit current is approximately equnl to the full-voltage starting current of the motor. Transformers are often spoken of as a source of short-circuit current. Strictly speaking, this is not correct, for the transformer merely delivers the short-circuit current generated by generators or motors ahead of the transformer.

Transformers merely change the system voltage and mag;. The short-circuit current deliv-. The reactance of a rotating machine is not one simple value as it is for a transformer or a piece of cable, but is complex and variable with time. For example, if a short circuit is applied to the terminals of a generator, the short-circuit current behaves as shown in Fig. The current starts out at a high value and decays to a steady state after some time has elapsed from the inception of the short cirroit.

Since the field excitation voltage and speed have remained snbstantially constant within the short interval of time considered, a change of apparent react,ance of the machine.

The expression of such variable reactance at any instant after the. For the sake of simplification in short-cir- cuit calculating procedures for circuit-breaker and relay applications, three values of reactance are assigned to generators and motors, viz.

The three reactances can be briefly described as follows:. Subtransient reactance Xy is the apparent reactance of the stator winding at the instant short circuit occurs, and it determines the current Row during the first few cycles of a short circuit. Transient reactance Xi is the apparent initial reactance of the stator winding, if the effect of all amortisseur windings is ignored and only the field winding considered. This reactance determines the cur- rent following the period when subtransient reactance is the controlling value.

Transient reactance is effective up to 4 5 see or longer, depending upon the design of the machine. Synchronous reactance Xd is the apparent reactance that deter- mines the current flow when a steady-state condition is reached. It is not effective until several seconds after the short circuit occurs; consequently, it has no value in short-circuit calculations for the application of circuit breakers, fuses, and contactors but is useful for relay-setting studies.

Previous loading has an effect on the total magnitude of short-circuit. Trace of orcillograrn of hart-circuit current produced by a generator.

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