MB30-CS datasheet(102/105 Pages) MITSUBISHI

102 / 105 page

101

Ias = Is ·

{

1 + 2e

+ 2

1 +

} =

Is · K3

πR

–

πR

–

that is: K3 =

{

1 + 2e

+ 2

1 +

}

πR

–

πR

–

K3 is the asymmetrical coefficient, derived from the

symmetrical value and the circuit power factor.

3. Peak Value of Asymmetrical Short-Circuit Current

This value (

Ip in Fig. 9.3) depends upon the phase

angle at short circuit closing and on the circuit power

factor; it is maximum when

θ = 0. It will reach peak

value in each case,

ωt

ϕ after the short circuit

occurrence. It can be computed as before, by means

of the circuit power factor and the symmetrical short-

circuit current.

Ip = Is [1 + sin

ϕ·e

] =

Is · Kp

–(

ϕ)·

thus: Kp =

2 [1 + sin

ϕ·e

]

–(

ϕ)·

Kp, the peak asymmetrical short-circuit current coeffi-

cient, is also known as the closing-capacity coefficient,

since

Ip is called the closing capacity. Thus, in each

case, the asymmetrical coefficients can be derived

from the symmetrical values and the circuit power fac-

tor. These coefficients are shown Fig. 9.4.

1/2 Cycle

Fig. 9.3 Short-Circuit Current

9.4 Classification of Short-Circuit Current

A DC current (Fig. 9.3) of magnitude determined by

the voltage phase angle at the instant of short circuit

and-the circuit power factor will be superimposed on

the AC short-circuit current.

This DC component will rapidly decay; however,

where a high-speed circuit-interruption device such

as an MCCB or fuse is employed, the DC component

must be considered. Further, the mechanical stress

of the electric circuit will be affected by the maximum

instantaneous short-circuit current; hence, the short-

circuit current is divided, as below.

1. RMS Symmetrical Short-Circuit Current (

Is)

This is the value exclusive of the DC component; it is

As/M2 of Fig. 9.3.

2. RMS Asymmetrical Short-Circuit Current (

Ias)

This value includes the DC component. It is defined

as:

Ias =

)2 + Ad2

(

Accordingly, when the DC component becomes maxi-

mum (i.e.,

θ – ϕ = ±

, where the voltage phase angle

at short circuit is

θ, and the circuit power factor is cosϕ),

Ias will also become maximum

1 cycle after the short

circuit occurs, as follows:

Ias = Is ·

1 + 2e

Is · K1, that is: K1 =

1 + 2e

πR

–

πR

–

where K1 is the single-phase maximum asymmetrical

coefficient, and

Ias can be calculated from the asym-

metrical value and the circuit power factor. In a 3-

phase circuit, since the voltage phase angle at switch-

on differs between phases,

Ias will do the same. If the

average of these values is taken

1 cycle later, to give

the 3-phase average asymmetrical short-circuit cur-

rent, the following relationship is obtained:

3.0

2.0

1.0

2.0

1.9

1.8

1.7

1.6

1.5

1.4

1.3

1.2

1.1

1.0

10 8 7 6

2.5

1.5

0.5

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

K1: Single-phase maximum

asymmetrical coefficient

K3: 3-phase asymmetrical coefficient

Kp: Closing capacity coefficient

Power factor

Fig. 9.4 Short-Circuit Current Coefficients

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