Estimaciones y juicios contables significativos

GENERATOR

. . FT.

AND RESISTANCE OF THESE IN GENERAL USF REACTANCE

CIRCUIT ELEMENTS.

SHORT CIRCUIT CURRENT CONSIDERING REACTANCE ONLY : AMPERES SHORT CIRCUIT CURRENT CONSIDERING REACTANCE OF ALL PARTS PLUS RESISTANCE OF COW VOLTAGE CABLE

FT

FIG. 1.31 One-line diagram showing effect of resistance in cable circuits.

impedance diagram. T h e example of Fig. 1.31 shows the error that might result in neglecting cable resistance.

I n secondary network systems of 600 volts and less, the resistance as well as the reactance of the tie-cable circuits between substation buses should be included in the impedance diagram. The example of Fig. 1.32 shows the effect of resistance in reducing short-circuit current in a typical industrial network.

n n

SHORT CIRCUIT CURRENT USING REACTANCE ONLY 51000 AMPERES, SHORT CIRCUIT CURRENT USING REACTANCE PLUS RESISTANCE OF T I E C I R C U I T = 41000 AMPERES.

T I E CIRCUITS

200 FT 2 - 250 3 CONO. CABLES

I N PARALLEL

200 F T

FIG. 1.32

resistance of cable tie circuits.

of low-voltage network showing effect of

Where to Use Exact Multiplying Factors. I n low-voltage systems having considerable lengths of the ratio may be so low that the 1.25 multiplying factor would be considerably in error. in these systems where resistance is considered, determine the correct

ratio and then minimum multiplying

GUIDE FOR REPRESENTING THE REACTANCE O F A GROUP O F M O T O R S

A group of motors fed from one substation or from one generating station bus may range in rating from fractional to several thousand horse- power per motor. All motors t h a t are running at the time a short circuit occurs in the power system contribute short-circuit current and therefore should be taken into consideration.

I n t h a t portion of the power sys- tem operating at 600 volts or less, there are generally numerous small

Motors Roted 600 Volts and Below.

SHORT-CIRCUIT-CURRENT PROCEDURES A?

motors, under about 50 hp. I t becomes impractical to represent each small motor in the impedance diagram. These motors are con- stantly being turned off and so it is practically impossible to predict which ones will be on the when a short circuit occurs. Furthermore, it would be impractical to obtain the characteristics of each small motor and to account for the of the impedance of their leads.

Where more accurate data are not available, the following procedure may be used with satisfactory results for representing the combined 240-, 480-, or 000-volt systems. Hence in systems where more accurate data are not available, assume a t each generator and/or

SHORT EQUIVALENT MOTOR

CIRCUIT 7 5 0

any one time is equal 50 per cent of the combined rating of all step- down and/or generators supplying power to that one Fig. 1.33. For large commercial buildings the 50 per cent figure may be too low. Check carefully the load on all large

systems.

I n generalized rases referred t o in paragraphs and 2 , no specific ratio of induction t o synchronous motors or no specific of motors which prcduce unusually high short-circuit has been set T o account for these variables, a n average motor

leads is assumed t o be 25 per cent for the purpose of preparing application tables like Table 1.5 and in making short-circuit where no more data are available. It will he noted t h a t the average motor reactance of per cent is based on the transformer or supply-generator kva rating. This figure is between the values of 28 per cent for induc- tion and 21 per cent for synchronous motors given in 1.14.

Where the division between synchronous and motors is

then more accurate calculations can be made by using the assumed motor reactances of Table 1.14. T h e reactances given in 1.14 are based on motor kva ratings and not supply transformer or generator ratings.

750 KVA

500 KVA 750 KVA

500 KVA

EQUIVALENT MOTORS WOULD 250 KVA AND

FOR VOLT SECONDARY SYSTEM

375 K VA

480 VOLTS

FIG. 1.34 Diagram illustrating how lo include in network

SHORT-CIRCUIT-CURRENT PROCEDURES 49

Although a portion of the load connected to a bus rated GOO or less may be heaters, lights, a-c welders, appliances, arid other devices which produce no short-circuit the total installed horsepower of motors connected such a bus is much greater than the kva rating of the supply transformers and generators.

ever, for diversity, generally the total horsepower of all running a t one time produce short-cir- cuit currents i n excess of the values obtained when using the assumptions.

I n systems of volts or the large motors

order of several hundred are usually number and represent only a small portion of the connected horsepower; there- fore, these larger motors are generally lumped in with the motors and the complete group is represented as one equivalent motor the impedance diagram.

Synchrouous and induction motors not be segregated when com- bining the motors these low-voltage systems, because lorn-voltage air circuit breakers operr so that only the current the first half cycle is considered; only reactances of

are considered.

Motors Rated above 600 ^Volts. High-voltage motors (rated 2200 volts and ahove) are generally larger horsepower rating motors on systems operating under volts. These motors may a much more on short-circuit-current magnitudes

smaller motors, and, therefore, more exact determinatiou of the reactances of larger motors is in order. Therefore, it is often

t o represent each large high-voltage motor individually the impedance diagram.

However, in large like steel mills, paper mills, etc., where there are numerous motors of several huridred horsepower each, it is often desirable t o group these larger motors iii one group arid represent by one in the impedance diagram. Individual motors of

several thousand should be individually and

their reactances accurately determined starting the short-circuit Whether considering motors individually or in groups, regardless of voltage rating of the motors, it is necessary t o obtain equivalent kva rating of individual or group of motors. This done precisely for large motors by Eq. (1.9) or can be approximated hy

or when the full-load current is not known. The latter equations are used when considering a single reactance t o represent a group of miscellaneous motors.

study.

I n high-voltage systems, complete motor data may not be available.

Lacking these data, the connected is assumed to he equal t o the generator and/or transformer capacity supplying a

voltage

If the reactance of the leads between the transformer and/or gen- erator and the motors is significant, the reactanre of these leads should be included.

MAKING THE IMPEDANCE DIAGRAM

After it has decided what elements of the one-line diagram are to be considered in the impedance diagram, the mechanirs of making the impedance diagram and of determining the short-circuit-current magnitude are as follows.

Treatment of Sources of Short-circuit Current. The generators and motors are treated as if they comprised a

of zero reactance an external reactor to represent the reactance of the machine windings, Fig. 1.35. The first

REPRESENT IMPEDANCE OF step in making an impedance diagram

GENERATOR OR MOTOR. is torepresent every generator and motor or groups of motors and utility supply

FIG. 1.35 One-line representation by a reactance connected to a im-

of generator or motor in impedance ped_ance

Fig. This represents the ternal voltage of the generators and motors.

The second step is to add the reactance of cables, buses, transformers, current transformers, circuit

GENERATOR OR OF ZERO IMPEDANCE

Completing the Impedance Diagram.

1.36

shown in one-line diagram form in Fig. 1.28.

Representation of of generators, motors, and utility of

SHORT-CIRCUIT-CURRENT PROCEDURES 51

breakers, switches, etc., in their proper location to complete the imped- ance diagram, top of Fig. 1.37.

The next step is to decide whether to ohms, per cent ohms, or per-unit ohms to represent the various circuit impedances in the impedance diagram.

Choice of Ohms, Per Cent Ohms, or Per-unit Ohms Method.

INFINITE BUS

SHORT INFINITE BUS CIRCUIT

STEP NO i COMBINE SERIES REACTANCES

H

+ +

^J

STEP COMBINE PARALLEL REACTANCES F,G AND

F G

I I

+

2.783 X

STEP N 0 . 3 COMBINE SERIES REACTANCES

+

^E

STEP NO. 4 COMBINE PARALLEL REACTANCES . B . AND

XI A C+D 0 2 5 2.0 0.19

I - + - + - + -

4

RESULTANT SINGLE REACTANCE 0.0805

FIG. 1.37

bining o single value.

Complete for system in Fig. 1.28. ^Steps for

Ohms are generally not used because of the difficulty of converting ohms from one voltage base t o another without error because of the very small numbers, which make accurate and easy calculation more difficult the per cent or per-unit system.

I n many of the examples in this book, the assumed or given impedance or reactance data are listed in per cent, hut in the reactance dia, these are converted t o per-unit. N o notation will he made when that is done as it will be obvious.

Equations (1.1) to (1.4) show how to convert ohms t o per cent ohms, ohms t o per-unit ohms.

The Per-unit System for Electrical Calculations.* A per-unit system is a means of expressing numbers for ease in comparing them. A per-unit value is a ratio:

a number Per-unit =

base number ^(1.21)

The base number is also called unit value since in the per-unit system Thus, base voltage is also called unit

CALCULATING PROCEDURES 53

For numbers that are similarly related to two different base numbers.

example :

A

2300 460

during starting 2020 420

The above figures in themselves have little significance they are compared each with its normal condition as follows:

during starting of normal 0.91

Per Cent. Obviously per cent and per-unit systems are similar.

per cent system is obtained by multiplying the per-unit value arbitrarily by 100 to keep many frequently used per-unit values expressed as whole integers. By definition,

x

100

The per cent system is somewhat more difficult to work with and more subject to possible error since it must always be remembered that the numbers have been arbitrarily multiplied by For a simple example, money may draw interest a t the rate of 4 per cent per year. Early in arithmetic one learns to determine the interest by multiplying the princi- pal by 0.04. It is thus necessary to remember t o convert to the per-unit value before using the figure. a complex calculation, this repeated conversion may invite errors. In effect it is safer and more convenient to say that interest is a t the rate of 0.04 per-unit.

I t is usually convenient t o convert these figures immediately to per-unit by dividing by and thereafter do all calculating in terms of per-unit rather than attempt t o remember always during the calculations whether a number should or should not be multiplied or divided by 100 to obtain the value.

Just as the per cent system has a symbol t o desig- nate that a given number is expressed in terms of per cent (as 6%) so also does the per-unit system have a symbol. The symbol for per-unit is I n a per-unit system as used for expressing electrical quantities of voltage, current, and impedance, it is necessary to select numbers arbitrarily for the following:

Impedances of electric apparatus are usually given in per cent.

Symbol.

Thus 0.06 per-unit is written as 0.06 Selection of Base Number.

Base volts Base amperes

54

Using the selected base values, all parts of an electric circuit or system may be expressed in per-unit terms as follows:

(1.24)

The base values of other are thus automatically fixed.

for a single-phase system,

Hence,

where base kva is single-phase kva and base volts is single-phase volts.

base volts where base kva is three-phase kva, base volts is line-to-line, and hase ohms is per phase.

Per-unit Ohms. I n practice i t is desirable t o convert directly from ohms t o per-unit ohms, without first determining base ohms. By Ohm’s law,

SHORT-CIRCUIT-CURRENT CALCULATING PROCEDURES

where base kva is single-phase and base kv is single-phase kv.

When dealing with a three-phase system, i t is usual to select three-phase kva and line-to-line volts for the base values. Convert the above expres- sions to these bases to obtain

where ohms are per phase, kva is three-phase kva, and kv is line-to-line voltage.

Usual Base Numbers for System Studies. If per cent per-unit ohms reactance is used, the next step is to choose a kva base.

In system studies it is usually desirable t o select as the base voltage nominal-system voltage or the voltage rating of the generators and supply transformers. Base kva will usually be selected as the kva rating of one of the machines or transformers in the system, or a convenient round number such as 1000, or After choosing the kva base, convert ohmic reactance of cables, wires, current transformers, etc., to per cent or per-unit ohms reactance on the chosen base, using Eq. (1.1) or (1.2) or Table 1.3.

If ohms reactance is used, convert all per cent reactances to ohms by Eq. (1.3).

Where two systems of differing voltage are interconnected through a

In document Informe de Auditoría de Laboratorios Farmacéuticos Rovi, S.A. (página 116-119)