PROCEEDINGS of the
23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Measurement and simulation of vibration acceleration of a highvoltage three-phase gapped-core reactor
BART VAN DER AA1; BART WIJNHOVEN1; TIMO OVERBOOM1; LUC DORPMANNS1
1

Royal SMIT Transformers (SGB-SMIT Group), Large Power Transformers, Nijmegen, The Netherlands

ABSTRACTIn this work, vibration acceleration of a high-voltage three-phase gapped-core shunt reactor is studied. The
active part is oil-immersed, has three wound limbs, and two flux return limbs. Measurements are done using
fibre optical accelerometers, which allows one to install sensors at locations otherwise not accessible forconventional piezoelectric accelerometers due to presence of high electromagnetic fields. Measured results
are compared to simulation results, where forcing of the structure is assumed to be dominated by Maxwell
forces. The study shows good qualitative agreement at twice the power frequency. Results obtained giveinsights in the dynamic behaviour of the gapped-iron core, which can be used for optimization of noise andvibration behaviour.
Keywords: Power Transmission, Shunt Reactor, Gapped-Core Reactors, Vibration, Maxwell forces, Fibre
Optical Sensors

1. INTRODUCTION
Gapped core reactors are electrical components mainly used in electrical transmission networks.
Their function is to stabilize the grid voltage by consuming reactive power of overhead lines in low
load conditions, e.g. during night time. High quality and long term stability of such components is
crucial for a reliable transmission network, but next to that low noise and vibration levels are often
required by customers. The current trend is that even lower noise and vibration levels than today’s
standard are requested, and all manufactures are confronted to meet these challenging demands.
Noise emission by gapped-core shunt reactors and other electrical components such as (large)
power transformers has a tonal character. This can be perceived as more annoying than broadband
noise with the same equivalent sound levels (1). Primary sources of noise and vibration of gappedcore reactors are linked to the iron-core and current conducting windings. Three different source
mechanisms can be distinguished: i) Lorentz forces acting on the windings, ii) Maxwell forces at theinterface between core-steel and air, and iii) magnetostriction which is a property of all ferromagnetic
materials. Because all phenomena are simultaneously present the determination of the main source ofvibration and noise can be challenging. In various studies, researchers came to the conclusion that forsome designs core vibration is dominated by Maxwell forces (2), whereas for other configurations
magnetostriction dominates the response at twice the power frequency (3). Further, it was shown thatfor a two-legged gapped core reactor with a small gap, i.e. approximating an ordinary transformer
core, magnetostriction dominates the overall vibration response, but by increasing the total gap length
the Maxwell force component will increase and eventually dominates the overall response (4). In (5)a direct comparison was made between two cores of the same global dimensions, where an gap of 2
mm was created in the middle limb of one core. It was found that the peak-to-peak vibration
acceleration of the reactor core was three times higher than the transformer core , which can be
attributed to Maxwell forces (5). The optimal choice of spacer material, i.e. the non-conducting
material which create the gaps, was also investigated in relation to noise and vibration. In (6) it was
shown that optimizing the modulus of elasticity of the spacers can significantl y lower the vibration
response, which was also reported in (2).
1bart.van.der.aa@sgb-smit.group4219

It should be noted that the above mentioned results are obtained for model scale cores operated at
a few hundred volts maximum. The active part of these reactors is therefore surrounded by air, as
opposed to high voltage equipment where oil is normally used as di-electric insulation and coolingmedium. The dynamic mechanical response of a structure immersed in oil will however be modified
by a fluid loading phenomenon in such a way that the natural frequencies are altered from their invacuum values (7). In addition, it can be shown that model scale cores with length scales in the orderof decimetres have eigen-frequencies at higher frequencies than high-voltage units where lengthscales are in the order of meters. Tank vibrations and sound levels of an oil-immersed high-voltage
single phase gapped-core reactor was studied in (8). It was reported that the eigen-frequency of theso-called the box-mode was altered by 10 Hz due to fluid loading (8), which shows that a fully coupledanalysis is needed when considering an oil-immersed active part. Further, it was reported that Maxwell
forces are the dominant source of vibration in (high-voltage) reactors (9). Direct comparison of themeasured and simulated on-load vibration response has, to the best of our knowledge, not beenreported for high-voltage oil-immersed shunt reactors.
In this work, vibration acceleration of a high-voltage three-phase gapped-core shunt reactor isstudied numerically and experimentally. Simulation results are compared against measured results attwice the power frequency. It is assumed that core vibration is dominated by Maxwell forces, which
implies that magnetostriction is neglected in the numerical analysis. Measured results are obtainedusing fibre-optical sensors, which allows one to install sensors at locations otherwise not accessible
for conventional piezoelectric accelerometers. The reactor considered is a three-phase, five-legged
design with a nominal voltage of 400 kV, and 150 MVAr reactive power. Its oil-filled weight is in theorder of a few hundred metric tons, and typical length scales of the active part are in the order ofmeters in all directions.

2. THE MODEL
2.1 Basic Description of a Gapped-Core Reactor
A gapped-core reactor basically consist of a magnetic iron-core with current conducting windings.
In case of a fixed power reactor, each phase is equipped with a single winding, but designs withmultiple windings per phase are also possible and are referred to as variable power shunt reactors(VSR’s). Depending on the application and design philosophy a single or three-phase concept is used,
where the latter can have three or five limbs. With a five limb layout, which is studied here, the outer
two approximately rectangular limbs are referred to as flux return limbs. The wound limbs, on theother hand, are cylindrically shaped and built up by radially stacked packets, see Figure 1.

A3

A1
A2

A4

U

V

W

Figure 1: Illustration of three-phase 5-legged gapped-core active part (left), and close-up of a gapped-corelimb with steatite spacer discs (right).
Between the three phases the magnetic flux is carried by the top- and bottom yokes. Together with24220

the flux return limbs the yokes form a low reluctance path for the magnetic flux. The radially stacked
core packets are separated by non-magnetic steatite disks, which create the gaps. The total gap createdis an important design parameter of a gapped-core reactor and mainly determines, next to the crosssectional area of the limb, the impedance of the device. The core is built up from thin sheets of grainoriented electrical steel and can contain thousands of laminations per sub-component. The assembled
yokes and flux return limbs gain its stability and stiffness from a clamping construction which acts inthe direction of lamination (not shown here). Such a laminated structure is very strong and canwithstand large in-plane loads. This property is needed, as the forces to clamp the gapped-core limbs
and windings are transferred from the tie-rods to the bridges to the yokes. A well-balanced pressure
exerted on the gapped-core limbs is needed to minimize vibration levels due to high dynamic forces
acting on the core.
2.2 Electromagnetic Force Model
It is assumed that vibration at twice the power frequency of a high-voltage gapped-core reactor isdominated by Maxwell forces, which can be interpreted as attractive forces that try to minimize thegap length. In order to calculate the Maxwell forces that act on the individual c ore-packets a twodimensional axis-symmetric electromagnetic model based on Rabin’s method is utilized (10). The
magnetostatic harmonic model gives an analytical solution to the 2d-vector potential ‫ ܣ‬in the ‫ݖݎ‬plane, by solving a truncated set of boundary conditions. Using ‫ܣ‬ሺ‫ݎ‬ǡ ‫ݖ‬ሻ the axial component of theflux density ‫ܤ‬௭ , and the radial component of the flux density, ‫ܤ‬௥ can be obtained. Using the computed‫ܤ‬-field, peak axial forces, ‫ܨ‬௭ , are here calculated at the top and bottom surface of each packet andyoke:ோ‫ܤ‬௭ ሺ‫ݎ‬ሻଶ‫ݎ݀ݎ‬ǡ‫ݑ‬଴଴‫ܨ‬௭ ൌ  േߨ න

where, ‫ݑ‬଴ is the magnetic permeability in vacuum, and ܴ the radius of the gapped-core limb.
In the context of this work, results are obtained for a fictive single-phase configuration, where
geometrical properties of one gapped-core limb with yokes and flux return limbs, are taken into
account. Hence, it is assumed that three-dimensional effects have only a marginal impact on thecomputed Maxwell forces acting on the surface of each core-packet, which has been verified bycomparing three-dimensional simulations using Ansys Maxwell. It was found that the difference
between the computed peak forces of the analytical approach and 3D-FEM was maximum 10%, where
the analytical approach typically results in a somewhat higher value. The same discrepancy between
analytical and numerical results were reported in (8).
The computed normal forces acting on the top- and bottom surfaces of the gapped-core packets areshown in Figure 2.

Figure 2: Flux lines (left), and axial forces acting on the gapped-core limbs and yokes (right). Positive
forces are linked to the top faces of the packets, whereas negative forces are linked to the bottom faces.
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In addition, the net normal force acting on the individual packets are also shown. It can be seenthat forces acting on the top- and bottom faces of an isolated packet are in opposite direction and haveapproximately the same magnitude, resulting in a near-to-zero net force acting on each packet. This
holds, except for the two outer most packets, where a difference in gap-height and geometricalconfiguration ultimately leads to a deviation of the axial force component of the top and bottom faces.
Further, it can be seen that the forces between the yokes and end-packets are biggest, and the peakvalues are in the order of a few hundred kilo newton for this configuration. The direction of theseforces is always inwards, i.e. the normal forces are pointing towards the geometrical centre of thestructure, at half-height of the limb.
2.3 Vibroacoustic Model
To simulate the vibration response of a gapped-core active part, a fully coupled vibroacoustic
harmonic model is setup in Ansys Workbench. Details about the setup and main assumptions are
discussed below.
Mechanical Model
The active part of the gapped-core reactor is immersed in oil and enclosed by the reactor tank. The
stiffened tank structure is geometrically simplified by leaving out e.g. the bushings, the conservatortank, and radiators. In addition, small-scale details such as flanges, control-cabinets, and otheraccessories are also left out. This will by definition have an effect on the eigen -frequencies of thecomplete system, but as measurements are performed on the active part, the impact to the simulated
response is considered minor.
The solid mechanical model, i.e. all non-fluid domains, comprises of three basic materials. The
components forming the tank are modelled as construction steel with a density of ߩ ൌ7850 kg/m3,
Young’s modulus of ‫ ܧ‬ൌ2e11 Pa, and a Poisson’s ratio of ߭ ൌ0.3. All core steel components, i.e.
yokes, limbs and return limbs, are assumed to have isotropic properties with a density of ߩ ൌ7650
kg/m3, a Young’s modulus of ‫ ܧ‬ൌ1.1e11 Pa, and a Poisson’s ratio of ߭ ൌ0.3. The non-magnetic
steatite spacer disks are assumed to have a density of ߩ ൌ2650 kg/m3, a Young’s modulus of ‫ ܧ‬ൌ7e10 Pa, and a Poisson’s ratio of ߭ = 0.24. To reduce computational efforts and minimize small scaledetails in the computational mesh, regions with steatite spacer disks are substituted by anhomogeneous cylinder with equivalent material properties ‫ܧ‬௘௙௙  and ߩ௘௙௙ , as suggested in (7).
Practically speaking more material is introduced, which is compensated by lowering the Young’s
modulus and density through multiplication with the filling factor of the air-gap, ݂݂, being 0.55 inthis case.
In this paper, it is further assumed that the active part and tank are only coupled via the enclosed
fluid, which means that direct structural coupling paths are neglect in the analysis. The active part is
fixated in the fluid domain by imposing a fixed support condition at the imprint faces of the lower
support bridges. Other components to pre-stress the structure, i.e. upper bridges and tie-rods, are also
omitted from the analysis.
Mechanical Excitation
The structure is mechanically excited by the calculated Maxwell forces as described in section 2.2,
which are imported as nodal forces acting on the top- and bottom surface areas of each gapped-core
packet. The applied force is divided by the number of nodes, which effectively results in a
homogeneous force distribution. Further, it shall be noted that the Maxwell forces are proportional to
the squared values of ‫ܤ‬௭ ǡ which implies that for a harmonically oscillating ‫ܤ‬-field, the resulting force
is non-zero crossing. In other words, the polarity of the force is not changing during a full (sinusoidal)
period of the applied magnetic field. Using a harmonic solver, applied loads are by nature of themethod oscillating around zero, and hence polarity of the force vectors are changing after half a periodof the excitation frequency. To simulate the true, non-zero crossing force function, a transient solver
has to be used. However, the same acceleration response can be obtained by using a harmonic solver
if the peak amplitude of the harmonic force function is set to ‫ܨ‬௭ /2, which is utilized here.
In a three-phase AC-system the U, V, and W lines will produce an equal magnitude voltage withan equally spaced mutual phase angle at +/- 120˚ form a reference line at a given frequency. The
instantaneous Maxwell forces acting on the three gapped-core limbs also experience the same phaseshift. However, as the axis-symmetric electromagnetic model is only laid out for a single phase
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configuration no (computed) mutual phase information is available. Here, forces applied to the U, V
and W phases are given an exact mutual phase-shift of 120˚.
Fluid Structure Interaction
Having a vibrating structure surround by a heavy fluid such as oil, the response of the system isaltered due to a fluid-loading phenomenon. In the simplified case that pressure waves radiate toinfinity and do not reflect back on the surface of the structure, the fluid exerts a constant force field
to the structure which can be seen as an added mass. However, when the fluid is contained by e.g. atank, acoustic waves reflect upon the boundaries and can interfere with intersecting pressure waves,which may lead to acoustic modes. From literature it is known that a contained fluid exhibits aresonant acoustic behaviour, producing a strongly frequency dependent response (7). This, in
combination with a narrowband excitation mechanism is best solved by a fully coupled formulation.
Coupling of the structural domains and the fluid domain is done at the outside surfaces of the coreand inside surfaces of the tank. To do that, two coupling boundary conditions are imposed. The first
coupling condition states that vibration velocity of the mechanical structure normal to the surface
shall match the surface normal velocity of the fluid, whereas the second coupling condition states thatan acoustic pressure wave will introduce mechanical stress to the solid. The combination of the firstand second coupling condition assures a feedback mechanism, which enables vibrational energy to betransferred to acoustic energy and back to vibrational energy again.
In this work, the speed of sound in oil is assumed to be 1400 m/s, whereas the density of oil isassumed to be 850 kg/m3.

3. MEASUREMENTS
On-load vibration measurements of the gapped-core shunt reactor has been performed in the highvoltage laboratory of Royal SMIT Transformers. To energize the reactor at rated voltage and rated
current the unit has been connected to a step-up transformer.
To measure on-load vibration of high-voltage electrical components, ordinary piezo-electricalaccelerometers which are resistant to oil, solvents and other liquids are available on the market.
However, the drawback is that these piezo-electrical sensors are sensitive to external magnetic fields,
and their co-axial cables cannot be routed through zones where high electrical field strengths arepresent. To mitigate these shortcomings custom-made single-axis fibre-optical accelerometers havebeen implemented, which are manufactured from non-magnetic non-conducting materials.
The basic principle of the fibre-optical vibration measurement technique used here is to track the
dynamic displacement of an optical resonator. By application of a given vibration signal the sensor
response will exhibit a continuous shift of the measured optical resonance peak around a known
optical resonance frequency. In a post-processing step the transient optical displacement response ofeach sensor is translated into a transient acceleration signal, which in a second post-processing step
is translated to the frequency domain using FFT. A vibration acceleration level is than obtained
through ܸ‫ ܮܣ‬ൌ ʹͲ ଵ଴ ሺȁܽȁȀܽ଴ሻ, where ܽ is the measured acceleration, and ܽ଴ is the reference
acceleration here set to 1e-6 m/s2 .
Here, four single-axis fibre-optical accelerometers have been fixed to the active part of the gappedcore reactor, see Figure 1 for the schematic locations. Sensors A1 and A2 are mounted to the flux
return limb, with their principle measurement axis placed parallel to the y-axis of the global domain,which is shown in Figure 1. Sensors A3 and A4, on the other hand, have their principle measurement
axis placed parallel to the z-axis. An example of a fibre-optical accelerometer mounted on the gappedcore limb is shown in Figure 3.
Now, energizing the reactor at 50 Hz will lead to Maxwell forces at twice the power frequency, i.e.
100 Hz in this case. In absence of other excitation mechanisms, the measured vibration response will
display a distinct peak at 100 Hz similar to the one shown in Figure 3.

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Figure 3: Fiber-optical acceleration sensor at outer edge of gapped-core packet (left). typical response
spectrum for a system operated at 50 Hz power frequency (right).

4. RESULTS
4.1 Simulated Forced Response
The total, and y-component, of the modelled vibration acceleration at 100 Hz with phase angles of
0˚ and +180˚ are shown in Figure 4. It can be seen that phase U at 0˚ phase angle displays a peak intotal acceleration, and simultaneously the neighbouring flux return limb exhibits its maximum
acceleration with positive slope in the y-direction. This happens when the applied force field to phase
U is at its maximum and is pointing inwards. Now, at +180˚phase angle the flux return limb has its
maximum acceleration with negative slope, which happens when the force field is at its minimum andis pointing outwards. In both cases, the flux return limb next to phase W experience only a very small
acceleration. The acceleration of the flux return limb next to phase W is at is maximum atapproximately +90˚ and +270˚ phase angle. Due to the three-phase excitation mechanism the vibration
response appears to travel from phase W to phase U, which obviously would be revered by swapping
the phase angles of the both phases. The oil pumping effect of the flux return limb is considered to be
an important source of transmitted vibrations to the tank, as was also addressed by (8).

z
U

V

W

y

U

V

W

Figure 4: Total vibration acceleration of gapped-core reactor at 100 Hz and a phase angle of +0˚ (top-left),and +180˚ (top-right). Vibration acceleration, y-component , at 100 Hz and a phase angle of +0˚ (bottomleft), and +180˚ (bottom-right). The acceleration response is projected on a deformed frame.
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4.2 Multiple Frequency Excitation
With a fine enough spatial resolution it is possible to visualize the measured operational deflection
shape at the driving frequency. This is not possible with the set of accelerometers used here. However,to display the underlying mechanical response at the measurement locations, it is possible to drive thesystem at a variable frequency with constant force. This can be done by means of a constant frequency
approach, i.e. by treating each frequency as a separate test. In this work, a discrete multiple frequency
excitation is executed in a range from 48 to 52 Hz in steps of 1 Hz. This results in Maxwell forces
appearing at 96 to 104 Hz in steps of 2 Hz.
The measured vibration acceleration levels of sensors A1 to A3 are compared against the simulated
vibration acceleration in Figure 5. To give an impression of the response outside the measured range,
the simulated frequency range has been extended to +/- 10 Hz around the 100 Hz frequency component.
It can be seen that the simulated response is in the order of 6 dB higher than the measured values,
which holds for all three sensor locations. Further, it can be seen that the overall increasing trend withfrequency is captured well.

Figure 5: Comparison of measured and simulated Vibration Acceleration Levels at locations A1 to A3.
As phase information is not available between individual measurements, e.g. using a continuous
reference signal, comparing the computed and simulated phase angles for a given sensor is notpossible. By comparing the transfer functions between different sensors, the mutual phase lag canhowever still be recovered. The computed and measured phase difference from A1 to A3, and A1 to
A2 are shown in Figure 6. As sensors A1 and A2 are both located on the flux return limb it is expectedthat the phase difference is small, which is confirmed by the measurements. The simulated angulardifference from A1 to A2 is approaching zero, suggesting the model results are nearly symmetric
about the middle axis. Comparing the computed and simulated angular difference from A1 to A3 it
can be seen that measured results tend to +180˚, whereas the model predicts an angular difference ofapproximately +120˚.

Figure 6: Measured versus simulated angular difference between sensor A1-A3 (left), and A1-A2 (right).

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5. CONCLUSIONS
Vibration acceleration of a high-voltage three-phase gapped-core shunt reactor was studied in thiswork. Measurements obtained by fibre-optical accelerometers were compared to simulation results,
where forcing of the structure was assumed to be dominated by Maxwell forces. The study shows
good qualitative agreement at twice the power frequency for a small range of measured frequencies
around the 50 Hz component. The fibre-optical technique has proven to give valuable insight in the
dynamic mechanical behaviour of a three-phase gapped-core shunt reactor, which can be used for
optimization of noise and vibration behaviour.

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