TRANSMISSION AND DISTRIBUTION
Short-circuit current limitation
by series reactors
by Oswald Mendrock, Trench, Austria
Safe and reliable supply of electric power is a prerequisite for continuation and growth of prosperity in any country.
As shown in the past there are
circumstances which require a substantial
adaptation of the power systems to new
conditions. For example, changes in the
political conditions in Europe at the end
of the 1980s have resulted in a massive
restructuring of the power systems in
Central and Eastern Europe. In addition,
the liberalisation of the power industr y,
which started globally in the nineties of the
last century, caused substantial changes
to the power systems because of new
reference conditions, in particular by
intensifying electric power trading. A further
important factor influencing extension of
power grids is the growing imperatives for
electric power which is increasingly being
met by renewable energy sources. The
integration of new energy sources, e.g.
wind energy with large block units into
the grid, or the connection of distributed
small power producers into the distribution
network, will lead to major changes in the
infrastructure of power systems. Changes
of sites for large power production and
consumption may result in the need to
completely change the original grid plans.
These new system conditions result in the
need to extend the existing network and
coordinatenew networks withexisting ones.
Management and control of increased
short-circuit currents resulting from these
conditions is a major requirement.
In many cases the use of series reactors
to limit the short-circuit power is not
only economical, but the only possible
technical solution to the problem for a
given plant design, as this allows the use
of existing equipment without modification
and without replacement of switchgear.
Grid planning has to integrate the networks
of low-power consumers with high-power
networks. It is not economical to design the
equipment of such consumers to cater for
the short-circuit current of the high power
network, but the use of current-limiting
reactors allows the equipment to be rated
for nominal current and this is usually the
best and most economical solution.
The function of a current-limiting reactor is
to increase the impedance in a possible
short-circuit loop. The short-circuit current
driven by the voltage source in the faulty
circuit is reduced by the reactance of the
coil. During normal operation, any increase
in reactance results in an increase of the
Fig. 1: Relationship between system voltage drop, reactor short circuit voltage, and power factor.
voltage drop in the network. In general, this
does not represent a particular problem
for the grid operation since the voltage
drop at the reactor is geometrically
subtracted from the supply voltage, and
is therefore a function of the power factor.
The system voltage drop as the result of a
series reactor is calculated as a function
of cosφ as follows:
ฬ
οܷ
ฬ ൌ ͳ െ
ܷே
ͳ
ටͳ ൅ ʹ ȉ ‫ݑ‬௞ ξͳ െ ܿ‫ ݏ݋‬ଶ ߮ ൅ ܷ௞ଶ
(1)
where U k is the short-circuit voltage of the
reactor
For example, a short-circuit voltage of
a reactor of 5% and a power factor of
0,9 leads to a drop insystem voltage of
only 2,23%. Fig. 1 shows the relationship
between the system voltage drop, the
short-circuit voltage of the reactor, and
the power factor.
Main parameters of short-circuit current
and of the current-limiting reactor
Short-circuit current parameters are given
in national and international standards
(e.g. IEC 60909-0 or DIN EN 60909-0) and
are listed briefly here
Initial symmetrical short-circuit current: IK"
The AC component of the current flowing
at the beginning of a short-circuit is
called the initial symmetrical short-circuit
current. The AC component is not constant
energize - October 2009 - Page 45
with time, and it decays due to the
armature reaction of the generators. The
AC component reduces towards the end
of the short-circuit duration to become:
Steady-state short-circuit current: I KD
T h e r e l a t i o n s h i p b e t w e e n I K" a n d I KD
depends (among other factors) on the
type of the fault, the location of the fault,
and the type of generator. The steady-state
short-circuit current determines the thermal
loading of the system components in the
event of a short circuit.
Peak short-circuit current: l KS
If the short-circuit begins at an instant
near to the voltage zero crossing, a DC
component is present in addition to the
AC current. This,together with the initial
symmetrical short-circuit current form
the peak short-circuit current, which is
reached at the first maximum of the
AC current after the short-circuit has
occurred. The peak short-circuit current
determines the dynamic loading of the
system components through which the
short-circuit current passes.
Peak factor: k
This is the ratio between IKS and √2.IK" and is
called the peak factor. It depends on the
ratio of the reactance to the resistance
in the short-circuit loop and is usually
TRANSMISSION AND DISTRIBUTION
the short-circuit and the generators,
the armature reaction is not significant
This situation is refered to as a far-fromgenerator short-circuit.
Single or multiple fault
In contrast to single faults, multiple faults
have at least two fault locations which
result in a short circuit. One type of multiple
fault is the double earth fault. As long
as both fault locations are on the same
side of the current-limiting reactor the
short-circuit currents can be expected
to be smaller than for the three-phase
short-circuits (at the same location). If the
two fault locations are at different sides of
the reactor, the short-circuit current of the
double earth fault can exceed that for a
three-phase fault.
Fig. 2: Example calculation.
assumed to have a value of 1,8.
Reactor parameters for current-limiting
Short-circuit power: N K
The short-circuit power in a network is
calculated by:
 ൌξ͵ȉ ȉ
(2)
Short-circuit voltage of a reactor – U K
The short-circuit voltage of a reactor,
which is usually given as a percentage is
calculated by:
ܷ௞ ൌ where
ͳͲͲ ȉ ξ͵ ȉ ‫ܫ‬ே ȉ ܺ
Ψ
ܷே Fig. 3: Short-circuit current-limiting reactor.
(3)
X is the reactance of the reactor.
UN is the rated voltage of the network (see
IEC 60038: IEC Standard voltages).
IN is the rated continuous current of
the coil.
Types of fault
For the calculation of short-circuit currents,
information on the type of the fault
is required in addition to the network
parameters. Faults are classified into
various types:
Symmetrical or asymmetrical fault
An asymmetrical fault is present when
the symmetrical short-circuit current is
of a different magnitude in the three
phases. All single and two-phase faults
a r e a s y m m e t r i c a l f a u l t s, w h e r e a s a
three-phase short-circuit is a symmetrical
fault. This is the most easily calculated
case and is specifically considered for
network planning and dimensioning of
the current-limiting reactor. For networks
with an isolated or resonance grounded
neutral the three-phase short-circuit results
in the highest short-circuit current (except
for special cases of double line-to-ground
faults.)
Near–to–generator or far–from–generator
short-circuit
Armature reaction of the generators results
in a reduction of the AC current provided
by the generator. If there is sufficient
impedance between the location of
The three-phase short-circuit is usually the
only case considered in the specification
of parameters for a current-limiting reactor.
The starting point for the specification
is the initial short-circuit current I K". With
the exception of reactors installed in the
immediate vicinity of a generator, the
initial short-circuit current is considered
to be equal to the steady-state shortcircuit current for practical purposes. The
short-circuit duration depends mainly
on the protection system and the type
of switchgear. In most standards the
maximum duration is assumed to be two
seconds. Peak current is determined from
the initial symmetrical short-circuit current
by applying the peak factor k, usually
assumed to be 1,8. The peak short-circuit
current is then calculated by:
‫ܫ‬௄ௌ ൌ ξʹ ȉ ͳǡͺ ȉ ‫ܫ‬௄ ̶ ൌ ʹǡͷͷ ȉ ‫ܫ‬௄ ̶ 4)
Once the inductance L, the initial or the
steady-state short-circuit current, I K" or I KD,
the short-circuit duration and the peak
short-circuit current l KS are set, the design
of the series reactor is fully determined.
Reactors are designed according to
IEC 60076-6: "Reactors" and they must
withstand the rated short-circuit currents.
If the short-circuit power of the supply
network is large compared to the shortcircuit power after the coil, the symmetrical
short-circuit current is solely determined by
the reactance of the coil and is calculated
by:
‫ܫ‬௄஽ ൌ ‫ܫ‬ே ȉ ͳͲͲ
ܷ௄
(5)
If the short-circuit power of the supply
network is of the same order of magnitude
as that of the network to be protected,
the short-circuit impedance of the supply
network may be taken into consideration
for dimensioning the reactor. Precise
calculation of short-circuit currents is
not particularly easy because of several
system parameters which may have an
influence, and for this reason simplified
c a l c u l a t i o n m e t h o d s a r e u s e d. T h e
approximate calculation of the shortcircuit current is described in detail in IEC
60909-0: "Short-circuit currents in threeenergize - October 2009 - Page 46
phase AC systems – Part 0, Calculation of
currents". For this calculation the relevant
components of the network, including
all power sources, are modeled in the
form of impedances. At the fault location
an equivalent voltage source c.U N/√3 is
inserted. The voltage factor which covers
various uncertainties in the calculation is
usually assumed to be 1,1. Using this the
short-circuit current is determined from the
equivalent voltage and the impedances
of the equivalent system.
A problem with this method is the necessity
of converting the impedances to a
reference voltage level (usually the voltage
at the fault location). This is avoided in
a more simple procedure, called the
"Method of calculation with reduced
percentage short-circuit voltages" [1]. This
method uses the network voltage drops
of the impedances, i.e. the short-circuit
voltages which are arbitrarily related to a
rated transmission power of 1 MVA . The
formulae used for this method are:
‫ݑ‬ᇱ ൌ ܷ௄
ܰ௡
ͳͲͲ
ᇱ
‫ ݑ‬ൌ
where
ܰ௄
(6)
(7)
u' = reduced, percentage voltage drop
U K =short-circuit voltage in percent
Nn =rated transmission power in MVA
N K =short-circuit power in MVA
Values of the reduced percentage voltage
drop in series are summed, values in
par al l el are cal cu l ated l i ke parallel
connected resistors.
Series connection
‫ݑ‬ᇱ ൌ ‫ݑ‬Ԣଵ ൅ ‫ݑ‬Ԣଶ
(8)
Parallel connection
‫ݑ‬ᇱ ൌ ‫ݑ‬Ԣଵ ȉ ‫ݑ‬Ԣଶ
‫ݑ‬Ԣଵ ൅‫ݑ‬Ԣଶ
(9)
TRANSMISSION AND DISTRIBUTION
Fig. 5a and Fig. 5b Reactor in the supply feeder.
Applying equation (6) for the transformer:
ܷԢଶ ൌ ܷ௄் ͳͲ
ൌ
ൌ ͲǡʹͷΨ
ܰ௡் ͶͲ
For calculation of the short-circuit power at
the 30 kV busbar u'1 and u'2 are added:
Fig. 4: Stacked three-phase reactor.
The following example illustrates the
calculation of the design parameters of
a current-limiting reactor by this method.
(See Fig. 2).
The short-circuit power of a 30 kV feeder
at a 30 kV busbar (Fig. 2) must not exceed
200 MVA. The short-circuit power of the
220 kV system is 1000 MVA, the transformer
has a rated power of 40 MVA and a
short-circuit voltage of 10%. The required
short-circuit voltage of the reactor is
unknown, the rated current of the feeder is
400 A corresponding to 20,8 MVA .
The following symbols are used:
U n = nominal voltage, in kV
NK1 220 kV network short-circuit power, in
MVA
N nT rated power of the transformer, in
MVA
U KT transformer short-circuit voltage, in
percent
NK2 short-circuit power at the 30 kV busbar,
in MVA
UKD short-circuit voltage of the reactor, in
percent
NnD rated through-put power of the reactor,
in MVA
N K3 short-circuit power after the reactor,
in MVA
u' 1 ...u' 5 reduced percentage voltage
drop at the corresponding locations, in
percent
Applying equation (7) for the 220 kV
network:
‫ݑ‬Ԣଵ ൌ ͳͳͲ
ͳͳͲ
ൌ
ൌ ͲǡͳͳΨ
ܰ௄ଵ
ͳͲͲͲ
‫̶ݑ‬ଷ ൌ Ͳǡͳͳ ൅ Ͳǡʹͷ ൌ Ͳǡ͵͸Ψ
ͳͲͲ ͳͳͲ
ൌ
ൌ ͵Ͳͷ‫ܣܸܯ‬
‫̶ݑ‬ଷ Ͳǡ͵͸
using equation (7)
Fig. 6: Feeder reactors.
ܰ௄ଶ ൌ The short-circuit power at the feeder after of
the reactor must not exceed 200 MVA; thus:
‫ݑ‬Ԣହ ൌ
ͳͳͲ ͳͳͲ
ൌ
ൌ ͲǡͷͷΨ
ܰ௄ଷ ʹͲͲ
winding which can withstand the forces
occurring during a short-circuit.
Fig. 3 shows the layout of a typical air-core
dry-type current-limiting reactor.
The percentage voltage drop of the
reactor is:
The main advantages of an air-core
reactor are as follows:
u'4 (coil) = U' 5 - U'3 = 0,55 - 0,36 = 0,19%
l
Constant inductance, even for the
short-circuit current, with no saturation
effects
l
No insulating oil and therefore no risk
of a possible contamination of the
ground, and negligible fire hazard
when compared to oil immersed
reactors
l
Simple insulation to ground, provided
by support insulators
The required short-circuit voltage for the
reactor, using equation (6) is:
UKD =U'4 • NnD= 0.19
•
20,8=3,95%
A 4 % c o i l i s u s e d. T h e s y m m e t r i c a l
short-circuit current I KD of the reactor is
calculated by equation (2):
ൌ
͵
ʹͲͲ
ൌ
ൌ3,85 A
 ȉξ͵ ͵Ͳȉξ͵
This corresponds to 3850/400 = 9,65 times
the rated current.
Design of current-limiting reactors
Air-core, dry-type current-limiting reactors,
being robust and having a simple design
have been used almost exclusively for
decades. Compared to oil-immersed
coils with an iron-core, an air-core reactor
requires considerably lower investment
costs.
An air-core reactor is a cylindrical winding
mounted on a number of insulators.
Since windings made of copper are
heavier and more expensive and do
not offer any technical advantages vs.
aluminum windings, aluminum is used
almost exclusively as the material for the
windings. The turn's insulation consists of a
combination of insulation film and glass
cloth tape. Impregnation with epoxy
resin results in a compact, self-supporting
energize - October 2009 - Page 48
Since dry type reactors do not have an ironcore or an iron screen, the magnetic field
spreads into the surrounding environment.
This must be taken into account particularly
for three-phase air-core reactance coils
with stacked phase windings.
Three-phase stacked reactors will exhibit
time var ying axial forces between the
phase coils during a two-phase or threephase short-circuit. As the short-circuit
force depends on the distance between
the coils, the force from the center to
the outward coils is much higher than
between the two outward coils. Reversing
the winding direction of the center coil
with respect to the outward coils, causes
the neighboring coils to be attracted to
each other when the time varying force
reaches its maximum during a threephase short-circuit. This contraction force
is absorbed by the supporting insulators
between the coils.
Further, the magnetic coupling between
the coils results in an increase of the
effective inductance of the center coil. This
TRANSMISSION AND DISTRIBUTION
are loaded symmetrically, the magnetic
coupling in the two half coils will reduce
the effective reactance and therefore
the voltage drop. In the event of a shortcircuit the full reactance of the half coil
is effective.
Fig. 7a: Bus tie reactors.
Fig. 7b: Duplex reactor.
can be compensated for by a reduction
of the self inductance of the center
phase by reducing the number of turns
accordingly.
feeder, the same reactance (not the same
short-circuit voltage) must be provided in
each short-circuit path, i.e. the inductance
of the reactor in the incoming feeder
and that of each outgoing feeder must
be the same. As the unit power rating of
a reactor is proportional to the square of
the current (N = X • IN2), the total power of
n reactors (of identical power) is only the
nth part of the unit power rating of a single
reactor applied in the incoming feeder.
Furthermore, splitting into several reactors
with lower current but the same reactance
leads to lower voltage variations at the
consumers, and less impact by one feeder
on the voltage of other feeders.
Examples of application of current-limiting
reactors
The application of current-limiting reactors
is illustrated in a simple circuit. Three
arrangements of the reactor are shown
(Fig. 5a, 5b, 6, 7a, 7b).
The short-circuit power at the outgoing
feeders of the simple circuit consisting of
a feeder transformer and a busbar with
eight outgoing feeders should be reduced
accordingly. Depending on the location
of the reactor, the following cases are
classified:
The reactor in the supply feeder
This has the lowest investment cost, as a
large unit is cheaper than several smaller
units. Further advantages are a lower space
requirement and thus less installation cost.
A disadvantage compared to the other
options is higher losses and larger voltage
variations at the busbar between full load
and reduced load. This option should not
be employed if a large power consumer
with strongly varying load is connected
at one of outgoing lines, which would
reduce the voltage quality for all other
consumers.
Coils in busbars (Fig. 7a and 7b).
A further option for reducing the shortcircuit power in the sample circuit is the
installation of bus tie reactors (Fig. 7a). If
the two coils are combined to form a joint
reactor with the center terminal connected
to the supply transformer, one obtains a socalled duplex-coil. If the busbar sections
The options shown in Fig. 5a and Fig. 5b
only differ in the location of the reactor,
either upstream or downstream of the
transformer. If a possible fault between the
coil and the transformer is considered and
the transformer is not short-circuit-proof
(e.g. autotransformer), the reactor has to
be installed upstream of the transformer.
If the transformer is short-circuit-proof the
choice of location of the coil is open and
be may be made according to space or
best price conditions.
Reactors in outgoing feeders (Fig. 6)
The possible impact on the quality of
the busbar voltage can be avoided
by providing reactors in the individual
outgoing feeders. However, it must be
ensured that the equipment before the
feeder reactors is short-circuit-proof.
Further it may be noted that the unit power
of all feeder reactors together is less than
the unit power rating of one single reactor
at the incoming line. If the short-circuit
power should be the same at any outgoing
energize - October 2009 - Page 49
If each busbar is supplied by a separate
transformer, the reliability of voltage
supply may be improved by coupling
the two busbars with a bus tie reactor.
Assuming that the two busbars are loaded
symmetrically, no current flows in the
bus tie reactor and therefore no losses
and voltage drops occur. If one of the
transformers fails, the associated busbar is
still live but it is supplied at reduced power
through the bus tie reactor. The short-circuit
power of each busbar is of course higher
due the connection via the bus tie reactor
as compared to fully separated busbars.
It is, however, less than the short-circuit
power of firmly connected busbars. Usually
the specified current rating of the bus tie
reactors is approx. 50% of the rated current
of the transformers.
References
[1] P Steglich, "Kurzschlussberechnung mit Hilfe von
reduzierten prozentualen Spannung-sabfällen"
(Short-circuit calculation by means of reduced
percentage voltage drops), in German, ETZ Nr.
63, Heft 43/44
Contact Oswald Mendrock, Trench Austria,
oswald.mendrock@trench-group.com v