International audienceUnder high-supply current, residual circuit breakers are subject to abnormal tripping, caused by false residual currents. Geometric or magnetic anomalies in the circuit breaker ring core seem to be responsible for these abnormal currents. This paper studies a few anomalies (spiral shape effect, conductor eccentricity, lamination effect) and calculates different contributions using the finite element simulations. The results show that the ring core, made of thin wound magnetic tape, is particularly sensitive to primary conductor eccentricity

Chillet, Christian

Colin, Bruno

Kedous-Lebouc, Afef

Mas, Patrick

English

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https://hal.archives-ouvertes.fr/hal-00192256
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Distributed under a Creative Commons Attribution| 4.0 International License
Effects of magnetic core geometry on false detection in
residual current sensor
Bruno Colin, Christian Chillet, Afef Kedous-Lebouc, Patrick Mas
To cite this version:
Bruno Colin, Christian Chillet, Afef Kedous-Lebouc, Patrick Mas. Effects of magnetic core geometry
on false detection in residual current sensor. Journal of Magnetism and Magnetic Materials, Elsevier,
2006, pp.804-806. ￿10.1016/j.jmmm.2006.02.273￿. ￿hal-00192256￿
Effects of magnetic core geometry on false detection in residual
current sensor
Bruno Colina,b,, Christian Chilleta, Afef Kedous-Lebouca, Patrick Masb
aLaboratoire d’Electrotechnique de Grenoble INPG UJF-CNRS UMR 5529, 38400 Saint Martin d’Heres, France
bSchneider-Electric, Rue Pierre Mende`s France, 38320 Eybens, France
Abstract
Under high-supply current, residual circuit breakers are subject to abnormal tripping, caused by false residual currents. Geometric or 
magnetic anomalies in the circuit breaker ring core seem to be responsible for these abnormal currents. This paper studies a few 
anomalies (spiral shape effect, conductor eccentricity, lamination effect) and calculates different contributions using the ﬁnite element 
simulations. The results show that the ring core, made of thin wound magnetic tape, is particularly sensitive to primary conductor 
eccentricity.
PACS: 85-70 Ay
Keywords: Differential circuit breaker; Ring core; Nuisance tripping
1. Introduction
Residual current device must ensure the users safety
against electrical shocks without disturbing normal opera-
tions of electrical installations. It must detect residual
current in the installation supply and trigger the opening of
the installation circuit breaker when this current exceeds a
given threshold (typically 30mA). It is composed of:
 A 40mm wide, 1.5mm thick, 10mm high magnetic core
of a high-permeability material which surrounds the
supply conductors.
 A short circuited secondary coil wound around the core
which picks up the ﬂux created by the conductors.
In theory, the device works as a current transformer and
should detect only residual current in the primary
conductors. In practice, even under normal conditions, a
false residual current (FRC) is measured and leads to
abnormal tripping. The current standards [1] impose the
circuit breakers to be immune to the nuisance tripping
under six times the nominal current (several hundreds
Amperes). To achieve that, partial solutions, like external
shielding or compensation coils, are used today [2].
This paper is focused on the different sources of FRCs
using the ﬁnite element simulations and more speciﬁcally
on the analysis of the effect of the shape of magnetic ring
core and on the impact of the conductor eccentricity. The
impact of a non-uniform secondary winding will not be
studied here, even though experimental data show a
signiﬁcant contribution to FRCs.
The ring core is made of a wound thin high permeability
magnetic ribbon. The ribbon ends, placed inside and outside
the core, create an asymmetry in the core which generates
FRCs in the secondary winding (the spiral shape effect).
Moreover, the thin layers of air gaps between layers of the
core cause a shielding phenomenon and concentrate the ﬂux
to the ﬁrst layers of the core, which are oversaturated.
2. Simulation conditions
To study the effect of the magnetic ring core separately,
the ﬁnite element simulations have been carried out (Flux
Corresponding author. Laboratoire d’Electrotechnique de Grenoble
INPG UJF-CNRS UMR 5529, 38400 Saint Martin d’Heres, France.
E-mail address: bruno.colin@leg.ensieg.inpg.fr (B. Colin).
1
software). To simplify the problem and to avoid the edge
effects a two-dimensional single phase residual circuit
device was modelled (Fig. 1).
Simulations have been achieved under a step-by-step
time mode, using sinusoidal current sources and the
following conditions:
 The secondary winding is modelled by two current
layers placed inside and outside of the core. An electrical
circuit coupled with the model connects the two coils
with a 26O resistance.
 The magnetic core is modelled either as a wound spiral
or as an assembly of concentric layers. The number of
magnetic layers is variable, core and air layer thickness
remaining constant, 30 by default. The magnetic
material uses an isotropic non-linear BðHÞ law. The air
layers in the magnetic core are represented by a linear
region with vacuum magnetic properties.
 For a spiral shape core, the angular positions of two
ends are deﬁned by bint and bext (Fig. 2).
3. Results and discussion
Fig. 3 shows the effect of the spiral shape. Indeed, to
avoid the ribbon end, the ribbon ﬁrst layer ﬂux gradually
goes through the second layer. This leads to an asymme-
trical saturation of the second layer, which causes FRCs.
The impact of the ribbon extremities decreases with the
layer thickness. Indeed, a core composed from an inﬁnite
number of layers should tend towards an ideal ring. This
has been conﬁrmed by simulation.
This asymmetrical effect is more or less important and
depends on the ribbon extremities position. Figs. 4 and 5
represent the FRC as a function of bint and bext, with,
respectively, bext ¼ 0 and bint ¼ 0.
It shows that an optimum conﬁguration of the cores
exists that minimizes the FRCs. However, this is not valid
for a three phase device because of the rotating magnetic
ﬁeld.
The shielding effect of the internal layers saturates the
material. This phenomenon ampliﬁes the effects of primary
conductors eccentricity. Under normal conditions, the core
and the conductors are centered. Thus, the core saturation
is perfectly symmetrical (not considering spiral shape
effect). If any eccentricity exists (Fig. 6), the ﬂux is
distributed asymmetrically in the two halves of the core.
The shielding effect enhances this unbalance.
This effect not only depends on the layer thickness and
conductor eccentricity but also on the primary current level
(non-linear phenomena). To separate this effect from that
of the spiral shape, simulations were conducted on a
concentric ring core.
Fig. 7 presents, for 0, 0.6 and 1mm eccentricity, a
comparison between the normalized FRC with a spiral or a
concentric layers ring core as a function of the normalized
primary current. For a given eccentricity the difference
between the two curves corresponds exactly to the spiral
effect. This conﬁrms that the tape ends and the shielding
effects are additive.
Sec. winding
Core
Conductorsy
x
Fig. 1. Simulated model.
βext
βint
Fig. 2. Angular position of ends.
Fig. 3. Spiral effect.
Inside extremity
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
-180 -120 -60 0 60 120 180
Beta int (¡)
N
or
m
al
iz
ed
 F
al
se
 R
es
id
ua
l C
ur
re
nt
Fig. 4. Inﬂuence of angular position on FRCs: inside extremity. The FRC
is normalized to 30mA.
2
The shielding effect increases highly the circuit breaker
sensitivity to the conductor eccentricity. At low current level
(less than two times the nominal current) the spiral shape
effects are preponderant whereas for high currents, domi-
nates the shielding effect, even with a small eccentricity.
4. Conclusion and future developments
The FRCs are a serious nuisance tripping source for the
residual current circuit breakers. The magnetic and
geometric anomalies can cause the asymmetry in the ﬂux
distribution within the core.
Using the ﬁnite element simulations, it has been shown
that the ring core was particularly sensitive to primary
conductor eccentricity. The two-dimensional simulation
allowed different FRCs to be sorted but could not give a
precise estimation of the real FRC levels. A three-
dimensional analysis is necessary to complete this numer-
ical study.
The previous results make necessary to take into account
the internal shielding in any new model of a magnetic ring
core. Unfortunately, the ﬁnite element simulation and
modelling of the spiral shape and internal layers is very
time and memory consuming. Thus, the work today is
focused on a new modelling of the wound magnetic cores
by a bulk model considering an apparent anisotropy in
BðHÞ law.
An elliptic permeability model could be a simple an
convenient way to achieve this [3].
It is an important step to employ the three-dimensional
simulations which will allow the edge effects to be taken
into account and therefore should be more realistic.
References
[1] IEC Standard 947-2.
[2] M.S. Zhou, FR Patent 2 799 840, 1999.
[3] J.M. Dedulle, G. Meunier, A. Foggia, J.C. Sabonnadiere, D. Shen,
IEEE Trans. Magn. 26 (2) (1990).
Outside extremity
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
-180 -120 -60 0 60 120 180
Beta ext (¡)
N
or
m
al
iz
ed
 F
al
se
 R
es
id
ua
l C
ur
re
nt
Fig. 5. Inﬂuence of angular position on FRCs: outside extremity.
Fig. 6. Conductors eccentricity.
0
1
2
3
4
5
0 3
Normalized primary current
1 mm Spiral Shape
1 mm Concentrical layers
0.6 mm Spiral Shape
0.6 mm Concentrical layers
0 mm Spiral Shape
0 mm Concentrical layers
N
or
m
al
iz
ed
 F
al
se
 R
es
id
ua
l C
ur
re
nt
1 2 4 5 6
Fig. 7. Comparison concentric/spiral models for a given eccentricity.
3


Effects of magnetic core geometry on false detection in residual current sensor

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Effects of magnetic core geometry on false detection in residual current sensor

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