# Industrial Power Systems Handbook Donald Beeman Pdf 12 ##BEST##

Short-circuit-current CalculatingProceduresFUNDAMENTALS OF A-CSHORT-CIRCUIT CURRENTSThe determination of short-circuit currentsin power distribution systems is just as basic and important as thedetermination of load currents for the purpose of applying circuitbreakers, fuses, and motor starters. The magnitude of theshoncircuit current is often easier to determine than the magnitudeof the load current. Calculating procedures have been so greatlysimplified compared with the very complicated procedures previouslyused that now only simple arithmetic is required to determine theshort-circuit currents in even the most complicated powersystems.SHORT-CIRCUIT CURRENTS AND THEIR EFFECTS

## Industrial Power Systems Handbook Donald Beeman Pdf 12

Synchronous motors are constructed substantially likegenerators; i.e., they have a field excited by direct current and astator winding in which alternating current flows. Normally,synchronous motors draw a-c power from the line and convertelectric energy to mechanical energy. However, the design of asynchronous motor is so much like that of a generator that electricenergy can be produced just as in a generator, by driving thesynchronous motor with a prime mover. Actually, during a systemshort circuit the synchronous motor acts like a generator anddelivers shortcircuit current to the system instead of drawing loadcurrent from it (Fig. 1 4 . .) As soon as a short circuit isestablished, the voltage on the system is reduced to a very lowvalue. Consequently, the motor stops delivering energy to themechanical load and starts slowing down. However, the inertia ofthe load and motor rotor tends to prevent the motor from slowingdown. In other words, the rotating energy of the load and rotordrives the synchronous motor just as the prime mover drives agenerator.

In the usual industrial power systems the applied or generatedvoltages are of sine-wave form. When a short circuit occurs,substantially s i n e wave short-circuit currents result. Forsimplicity, the following discussion assumes sine-wave voltages andcurrents. In ordinary power circuits the resistance of the circuitis negligible compared with the reactance of the circuit. Theshort-circuit-current power factor is determined by the ratio ofresistance and reactance of the circuit only (not of the load).Therefore the short-circuit current in most power circuits lags theinternal generator voltage by approximately 90" (see Fig. 1.13).The internal generator voltage is the voltage generated in thestator coils by the field flux. If in a circuit mainly containingreactance a short circuit occurs at the peak of the voltage wave,the short-circuit current would start at zero and trace a sine wavewhich would be symmetrical ahout the zero axis (Fig. 1.14). This isknown as a symmetrical short-circuit current. If in the samecircuit (i.e., one containing a large ratio of reactance toresistance) a short circuit occurs at the zero point of the voltagewave, the current will start a t zero but cannot follow a sine wavesymmetrically about the zero axis because such a current would bein phase with the voltage. The wave shape must be the same as thatof voltage hut 90' behind. That can occur only if the current isdisplaced from the zero axis, as shown in Fig. 1.15. In thisillustration the current is a sine wave and is displaced 90' fromthe voltage wave and also is displaced from the zero axis. The twocases shown in Figs. 1.14 and 1.15 are extremes. One shows asymmetrical current and the other a completely asymmetricdcurrent.

The total symmetrical short-rirruit current is made up ofcurrents from several sourves, Fig. 1.23. At the top of the figureis shown the shortcircuit current from the utility. This act,uallycomes from ut,ility generators, but generally the industrial systemis small and remote electrically from the utility generators sothat the Symmetrical short-rircuit current is substant,iallyconstant,. If there are generators in the indust,rial plant, thenthey cont,ribute a symmet,rical short-circuit rurreiit which forall practical purposes is constant over the first few cycles. Thereis, however, a slight decrement, as indicated in Fig. 1.23. Theother sources are synchronous motors which act something like plantgenerators, except that t,hey have a higher rate of decay of thesymmetriral component, and induction motors whirh have a very rapidrate of dccay of the symmetrical component of current. When allthese currents are added, the total symmetrical short-circuitrurrent is typical of that shown a t the bottom of Fig. 1.23. Themagnitude of the first few cycles of the t,otal symmetricalshortcircuit, current is further increased by the presence of a d-ccompouent, Fig. 1.24. The d-c component, offsets the a-c ware and,therefore, makes it asymmetrical. The d-c component decays t o zerowithin a few cycles in most indust,rial power systems. It is thistotal rms asymmetrical short-circuit current, as shown in Fig.1.24, that must he determilied for short-circuit protective-dericeappliration. The problem of doing this has been simplified bystandardized procedures to a poiut xhere t o determine the rmsasymmetriral current one need only divide t,he line-to-neutralroltage by the proper reactance

variation in the circuit-breaker operating speed, power circuitbreakers have been grouped into classes, such as eight-cycle,five-cycle, three-cycle circuit breakers, etc. It is assumed forshort-circuit-calculation purposes that circuit breakers of allmanufacturers, in any one speed grouping, operate substantially thesame with regard to contact parting time. Instead of specifying atime a t which the short-circuit current is to he calculated, it isdetermined by the simpler approach of specifying the generator andmotor reactances and using multiplying factors. These factors arelisted in Table 1.2. In industrial plants, eight-cycle circuitbreakers are generally used. Normally, the induction-motorcontribution has disappeared, and that of the synchronous motorshas changed from the subtransient to the transient condition beforethe contacts of these circuit breakers part. Therefore, incalculating the interrupting duty on commonly used power circuitbreakers, generator subtransient reactance and synchronous-motortransient reactance are used and induction motors are neglected.The elapsed time is so long that usually all the d-c component hasdisappeared. What d-c component is left is more than offset by thereduction in a-c component due to the increase in reactance of thegenerators. Hence, a multiplying factor of one (1) is used. In verylarge power systems, when symmetrical short-circuit interruptingduty is 500 mva or greater, there is an exception to this rule. Insuch large power systems, the ratio of reactance to resistance isusually so high that there may be considerable d-c component leftwhen the contacts of the standard eight-cycle circuit breaker part.To account for this, the multiplying factor of 1.1is used indetermining the total rms short-circuit mva that a circuit breakermay have to interrupt in these large systems. The multiplyingfactor of 1.1 is not applied until the symmetrical shortcircuitvalue reaches 500 mva. High-voltage Fuses. High-voltage fuses areeither of the currentlimiting type, Fig. 1.26, which open thecircuit before the first current peak, or of thenon-current-limiting type, which open the circuit within one or twocycles after the inception of the short circuit. For the sake ofstandardization, all fuse-interrupting ratings are on the basis ofmaximum rms current that will flow in the first cycle after theshort circuit occurs. This is the current that will flow if thefuse did not open the circuit previously, i.e., fuses are rated interms of available short-circuit current. To determine theavailable short-circuit current a t the first cycle for theapplication of high-voltage fuses, use the subtransient reactancesof all generators, induction motors, synchronous motors, andutility sources and allow for the maximum d-c component. Themultiplying factor for allowing for d-c component is 1.6, the sameas for allowing for d-c compo-

nent when determining the momentary duty on a power circuitbreaker (see Table 1.2). The interrupting rating of fuses inamperes is exactly parallel, in so far as short-circuit+urentcalculations are concerned, to the momentary rating of powercircuit breakers. The ampere interrupting rating of high-voltagefuses is the only rating that has any physical significance. Forthe sake of simplicity of application in systems with power circuitbreakers, some fuses are given interrupting ratings in three-phasemva. The three-phase mva interrupting rating has no physicalsignificance, because fuses are single-phase devices, each fusefunctioning only on the current which passes through it.WAVE OFAVAILABLE

Three-phase Short Circuits Generally Considered. I n mostindustrial systems, the maximum short-circuit current is obtainedwhen a three-phase short circuit occurs. Short-rircuit-currentmagnitudes are generally less for line-to-neutral or line-to-lineshort circuits than for the three-phase short circuits. Thus, thesimple three-phase short-circuitcurrent calculations will sufficefor application of short-circuit protective devices in mostindustrial systems. Unbalanced Short Circuits in Large PowerSystems. In some very large systems where the high-voltage-systemneutral is solidly grounded, maximum short-circuit current flowsfor a single phase-to-ground short rircuit. Such a system might beserved from a large delta-Y transformer bank or directly from theplant generators. Hence the only time that single-phaseshort-circuit-current calculations need be made is on largehigh-voltage systems (2400 volts and above) with solidly groundedgenerator neutrals or where main transformers that supply a plantfrom a utility are ronnected in delta on the highvoltage side(incoming line) and in Y with solidly grounded neutrals on thelow-voltage (load) side. The calculations of unbalancedshort-circuit currents in large power systems can best be done bysymmetrical components, see Chap. 2. Normally, generator and largedelta-Y transformer secondaries are grounded through a reactor orresistor to limit the short-circuit current for a singleline-to-ground short circuit on the system to letis than the valueof short-circuit current for a three-phase short circuit. BoltedShort Circuits Only Are Considered. Several tests have been made toevaluate the effect of arc drop at the point of short circuit inreducing the short-circuit-current magnitude. It was felt by someengineers that the current-limiting effect of the arc waspronounced. These tests showed, however, that for circuit voltagesas low as 300 volts