22-10-2012, 01:40 PM
Calculation of short-circuit currents
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Introduction
Electrical installations almost always require
protection against short-circuits wherever there
is an electrical discontinuity. This most often
corresponds to points where there is a change
in conductor cross-section. The short-circuit
current must be calculated at each level in the
installation in view of determining the
characteristics of the equipment required to
withstand or break the fault current.
The flow chart in Figure 1 indicates the
procedure for determining the various shortcircuit
currents and the resulting parameters for
the different protection devices of a low-voltage
installation.
In order to correctly select and adjust the
protection devices, the graphs in Figures 2, 3
and 4 are used. Two values of the short-circuit
current must be evaluated:
c The maximum short-circuit current, used to
determine
The breaking capacity of the circuit breakers
The making capacity of the circuit breakers
The electrodynamic withstand capacity of the
wiring system and switchgear
The maximum short-circuit current corresponds
to a short-circuit in the immediate vicinity of the
downstream terminals of the protection device.
It must be calculated accurately and used with a
safety margin.
Development of the short-circuit current
A simplified network comprises a source of
constant AC power, a switch, an impedance Zsc
that represents all the impedances upstream of
the switch, and a load impedance Zs
(see Fig. 6 ).
In a real network, the source impedance is made
up of everything upstream of the short-circuit
including the various networks with different
voltages (HV, LV) and the series-connected
wiring systems with different cross-sectional
areas (A) and lengths.
In Figure 6, when the switch is closed and no
fault is present, the design current Is flows
through the network.
When a fault occurs between A and B, the
negligible impedance between these points
results in a very high short-circuit current Isc that
is limited only be impedance Zsc.
Basic assumptions
To simplify the short-circuit calculations, a
number of assumptions are required. These
impose limits for which the calculations are valid
but usually provide good approximations,
facilitating comprehension of the physical
phenomena and consequently the short-circuit
current calculations. They nevertheless maintain
a fully acceptable level of accuracy, “erring”
systematically on the conservative side.
Advantages of this method
Calculation using symmetrical components is
particularly useful when a three-phase network is
unbalanced, because, due to magnetic
phenomena, for example, the traditional
“cyclical” impedances R and X are, normally
speaking, no longer useable. This calculation
method is also required when:
c A voltage and current system is not
symmetrical (Fresnel vectors with different
moduli and imbalances exceeding 120°).This is
the case for phase-to-earth or phase-to-phase
short-circuits with or without earth connection
c The network includes rotating machines and/or
special transformers (Yyn connection, for
example)
This method may be used for all types of radial
distribution networks at all voltage levels.
Symmetrical components
Similar to the Leblanc theorem which states that
a rectilinear alternating field with a sinusoidal
amplitude is equivalent to two rotating fields
turning in the opposite direction, the definition of
symmetrical components is based on the
equivalence between an unbalanced threephase
system and the sum of three balanced threephase
systems, namely the positivesequence,
negative-sequence and zerosequence
(see Fig. 23 ).