The electromagnetic (EM) emissions of wind energy
conversion systems (WECS) are evaluated in situ. Results of in situ tests,
however, are only valid for the examined equipment under test (EUT) and
cannot be applied to series production as samples, as the measurement
uncertainty for in situ environment is not characterized. Currently
measurements must be performed on each WECS separately, this is associated
with significant costs and time requirement to complete. Therefore, in this
work, based on the standard procedure according to the “Guide to the
Expression of Uncertainty” (GUM, 2008) the measurement uncertainty is
characterized. From current normative situation obtained influences on the
measurement uncertainty: wind velocity and undefined ground are evaluated.
The influence of increased wind velocity on the measurement uncertainty is
evaluated with an analytical approach making use of the dipole
characteristic. A numerically evaluated model provides information about the
expected uncertainty due to reflection on different textures and varying
values of relative ground moisture. Using a classical reflection law based
approach, the simulation results are validated. Thanks to the presented
methods, it is possible to successfully characterize the measurement
uncertainty of in situ measurements of WECS's EM emissions.
Introduction and Motivation
In order to meet the goal of the 2015 Paris agreement, it is necessary to
reduce the amount of carbon dioxide emissions currently being produced
(UNFCC, 2015). The reduction of carbon dioxide emissions is a movement
towards power generation systems with renewable energy sources instead of
fossil ones. One approach is to operate wind energy conversion systems
(WECS). Like all other industrial, scientific and medical (ISM) devices,
WECS must be assessed and evaluated regarding their radiated electromagnetic
(EM) emissions based on international standards (CISPR 11, 2015). Due to
their geometrical size, WECS cannot simply be installed and tested at a
defined test site such as an open area test site (OATS). Instead, they need
to be tested in situ. The problem is, that for equipment under test (EUT),
evaluated in situ only, compliance with these standards can be proven for
this specific EUT, but not for the whole product line. In order to reduce
the effort and costs, it is always aimed for a series release. However, a
series release is only possible with the knowledge of the measurement
uncertainty, determined according to the “Guide to the Expression of
Uncertainty in Measurement” (GUM, 2008). The measurement uncertainty for in
situ tests of WECS is not specified yet. Therefore, the goal of this work is
to define and characterize possible contributions to uncertainty during in
situ measurements of EM emissions from WECS. The normatively given limit
values as well as the causes of the EM emissions are not focus of this
article. The latter are discussed e.g. in Koj et al. (2017) and Fisahn et
al. (2017).
This paper explains the measurement of EM emissions of WECS according to the
normative situation in the second Chapter. Subsequently, Sect. 3 describes
the standard procedure for the determination of the measurement uncertainty
according to GUM. In Sect. 4 the normative situation on determination of
the uncertainty in EM emission tests is analysed. The comparison between
OATS and in situ leads to two main emphases: the deflection of the antenna
due to wind velocity and the reflection of EM waves on different grounds.
The numerical and analytical evaluation of the antenna deflection is
presented in Sect. 5 and the influence of the ground reflections is
discussed in Sect. 6 respectively. A conclusion of the significant results
completes this article.
In Situ Measurements on WECS
In this chapter the determination of the EM emissions of WECS according to
the normative situation is roughly sketched. Further, more detailed
considerations on this topic can be found in e.g. Koj et al. (2016a, b).
WECS, also known as wind turbines (WTs), have to be evaluated with respect
to their radio frequency (RF) disturbances respectively as well as the
radiated emissions from other ISM (industrial, scientific and medical)
electrical and electronic equipment. Therefore, the proof of compliance
according to the Directive 2014/30/EU with the national implementation of
this directive (e.g. the EMC Law, 2016 in Germany), must be provided. The standard
CISPR 11 deals with the measurement methods and limits for the RF
disturbances of ISM equipment. With respect to this standard, WTs must be
classified into Group 1 and Class A, since the WT forms an unintentional
radiator (Group 1) that is always located and operated out of living areas
(Class A). Because of the enormous geometrical dimensions of a WT with a
typical height of more than 100 m, the only practical way to assess the
device is to perform an in situ measurement, even though equipment that is
classified into Group 1 could be tested either on a test site or in situ.
Thus, the radiated emissions have to be determined solitarily in order to be
evaluated. Therefore, the emission measurements have to be carried out with
an antenna and an EMI receiver according to CISPR 16-1-1 (2015), CISPR
16-1-4 (2010), CISPR 16-2-3 (2010), CISPR 16-4-2 (2011) and CISPR/TR
16-2-5 (2008) so as to measure the magnetic field strength in the
frequency range from 150 kHz to 30 MHz (CISPR Band B) respectively the
electric field strength in the range from 30 MHz to 1 GHz. The latter
frequency range corresponds to the CISPR Bands C (30–300 MHz) and D (300 MHz–1 GHz).
Figure 1 shows examples of standard compliant antennas. Using
the loop antenna, the recorded magnetic field strength and the biconical
antenna, the electric field strength can be measured. The above mentioned
standards also allow the use of a logarithmic periodic dipole antenna (LPDA)
for the electric field strength measurement, whereby both polarizations of
the electric field strength shall be measured, the horizontal and the
vertical.
Example antennas for measuring the radiated RF emissions of wind
turbines.
Further information about a measurement campaign at a WT can be found in the
technical guideline FGW/TR 9, 2014. This guideline describes the procedure
for the uniform definition of measuring positions, where the RF emissions
shall be measured. An example of this is shown in Fig. 2. The field
measurements must be carried out on at least four measuring positions,
whereby the distance between the outer tower wall and the measuring position
should be 30 m each. In order to ensure the reproducibility of the measuring
positions, there should be a fixed reference point chosen, e. g. the tower
door of the WT. At each of the measuring positions, the WT must be measured
in at least two modes: when the WT is in power harvesting mode, and when the
WT is turned off. Further modes can be found in the FGW/TR 9. The measured
field strength values of each measuring position should be rated using the
limit values given by CISPR 11. If the measured radiated emissions are below
these frequency dependent limits, the wind turbine will pass the test,
otherwise it will fail.
Top view on a wind turbine (WT). The measuring positions (MP) are
located around the WT (FGW/TR 9, 2014). The tower door sets the orientation
of the reference frame.
Procedure for determining the measurement uncertainty according to
GUM (Sommer and Siebert, 2004).
A general explanation of the uncertainty of measurement will be discussed in
the following chapter.
Determining the Measurement Uncertainty According to GUM
A measurement result is only complete with inclusion of the associated
measurement uncertainty. In order to determine the measurement uncertainty,
the method according to GUM, which has been established in recent years, is
utilized. This method is described in detail in various publications, for
example in Sommer and Siebert (2004). Therefore, in this chapter, the
standard GUM procedure is only succinctly explained. The procedure requires
a model equation for the measurand Y:
Y=f(X1,X2,…,XN).
The measurand Y, also referred to as output value shown in Fig. 3, is
dependent on input values Xi, with i={1,2,…,N, such as the quantities as well as the probability density function
(PDF).
In most cases it is not possible to specify the input values exactly. With
knowledge of the limitation of the possible input values ξi of
Xi and with the associated PDF, the input values can be characterized
by their expected values
xi=E[Xi]
and standard uncertainties
uxi={EXi-xi2}1/2.
Using the Gaussian uncertainty propagation, the output value Y can be
characterized by the expected value
y=EY=f(x1,x2,…,xN)
and the associated standard uncertainty
uy=∑i=1N∂f∂xi2uxi2+2∑i=1N-1∑j=i+1N∂f∂xi∂f∂xjuxixj1/25=∑i=1Nci2uxi2+2∑i=1N-1∑j=i+1Ncicjuxixj1/2
where
uxixj=uxi⋅uxj⋅rxi;xj is estimated covariance associated with
xi and xj and
rxi;xj is the correlation coefficient.
For a complete measurement result Y=y±Uy(P), the expanded measurement uncertainty
UyP=kp⋅uy is required.
UyP indicates the interval in which the value of the
measurand is located with a probability P. The coverage factor kp
depends on the PDF of the output value Y. Usually, a normal
PDF, a probability P=95 % and thus kp=2 is
assumed.
This work focuses in the definition and on the characterization of the input
values according to Fig. 3. For this purpose, the following chapter
considers the normative situation for measurement uncertainty in other test
sites.
Overview of standards with information on measurement uncertainty
in EM emission measurements.
Challenges in Determining the Measurement Uncertainty in In Situ Tests of
WECS
As shown in Fig. 4, CISPR 11 refers to the CISPR 16-2-3, CISPR/TR 16-2-5 and
CISPR 16-4-2 standards in terms of measurement uncertainty. CISPR 16-2-3
contains general advice about performance of measurement campaign. In the
annexes informations and specifications for measurements in the presence of
environmental interferences can be found.
While CISPR/TR 16-2-5 defines requirements to in situ measurement in
general, of interest is in particular the demand to carry out in situ
measurement campaign at wind velocities below 10 m s-1 and in “dry weather”.
Finally, CISPR 16-4-2 establishes terms of references on uncertainty in
measurements of EM emissions for various test environments, except in situ.
Comparing in situ to other test sites covered in the CISPR 16-4-2, it can be
said that the OATS is most similar to the in situ environment. The terms of
reference in CISPR 16-4-2 contain the model equation for determining the
field strength (measurand) and standard uncertainties of the input values,
which can be divided into three groups:
Measuring equipment,
Test setup,
Measurement environment.
The “measuring equipment” (receiver display, antenna factor) used on OATS
and in situ is the same, thus all input values are conform and can be
adopted to in situ measurement.
For the category “test setup” the influence of the wind velocity has to be
investigated (the other measurement uncertainty aspects can be adopted). The
requirement of the CISPR/TR 16 2-5 to carry out the measurements at wind
velocity below 10 m s-1 is of no use evaluating WECS, because usually their
rated power is reached at this wind velocity. The author's experience of
various measurement campaigns is, that higher wind velocities causes
deflection of the antenna tripod. Therefore, the resulting standard
uncertainty is evaluated in Sect. 5.
The category “measurement environment” shows the biggest differences
between the OATS and in situ environment. OATS should be placed
(theoretically) far away from sources of interference and the ground should
be (perfectly) conductive in order to enable reproducible measurement
results. In contrast, WECS are often installed in industrial environments,
where the presence of other sources of interference must be expected.
Furthermore, the electromagnetic properties of the soil around a WT depends
on the local texture (clay, sand) and also varies in time due to weather
conditions (moisture). In order to deal with environmental EM disturbances
in the vicinity of WECS, the instructions of CISPR 16-2-3 can be consulted.
Approaches to deal with uncertainties due to undefined ground conditions
around a WT are presented in Sect. 6.
Contribution of the Wind Velocity to the Measurement Uncertainty
The impact of wind velocity on the measurement uncertainty is evaluated in
two steps. First, numerical simulations and an analytical approach relate
the antenna deflection with the field deviation. Second, the wind related
uncertainty is estimated relating measurement deviation and the wind
velocity.
Antenna Deflection and Corresponding Deviation
Taking into account the CISPR 11 Bands the evaluation is divided in three
parts: Band B, C and D. As CISPR 16-2-3 instructs to use a loop antenna to
measure the magnetic field component at a height h1=1 m above ground
(in Band B), no relevant deflection of the tripod can be observed during
measuring campaigns using a standard tripod. The electric field has to be
measured according to CISPR 16-2-3 at a height h2=2 m above ground
using a biconical antenna for measurements in Band C and a LPDA for
measurements in Band D. Due to the height and larger wind exposed areas of
the electrical antennas, their deflection of approx. φ=7∘ on a standard tripod can be observed during both polarization
measurements, horizontal and vertical. To evaluate this impact on the
results simulations with the field simulator for radio emission problems
“Concept II” are set-up. For the CISPR Band C a biconical antenna is
modeled and for the CISPR Band D ten adapted dipoles are modeled in the CAD
tool provided by ”Concept II”. In the simulation those antennas are tilted
in a plain wave field as shown in Fig. 5 (here for an LPDA) while feed point
voltage is detected. In order to calculate the deviation
DW=20logUφU0
the feed point voltage of the tilted antenna Uφ is divided by
the feed point voltage U0 at tilting angle of zero. As shown in Fig. 7
the deviation at each angle is constant over the frequency spectrum.
Furthermore, it can be seen that same deviation occurs at the same angle for
both, the biconical antenna and LPDA.
Tilted LPDA in plain wave field.
Dipole characteristic. φ is
the deflection angle.
Simulated deviation of feed point voltage for different antenna
tilting angles.
By approximating the behavior of the antennas by an adapted dipole of which
the directional pattern has a well-known torus geometry C(θ)=sin(θ) (Balanis, 2005), shown in Fig. 6, the deviation
DW can be calculated with
DW=20logsin(|90∘-φ|)sin(90∘)=20|log(cos(φ))|
The deviation derived from simulation and the deviation evaluated
analytically are equivalent and plotted in Fig. 8 over the tilting angle.
Thanks to the dipole characteristic, the deviation can be described
analytically by Eq. (7). In a next step, the relation between the wind
velocity and the wind related deviation will be deduced.
Analytically calculated deviation over the tilting angle of the
dipole.
Antenna tripod modelled as a bending beam strained by wind
force FW.
Realistic Wind Velocities and Standard Uncertainty
The tilting angle of the antenna is caused by the deflection of the tripod
due to wind force, therefore the tripod is modeled as a bending beam, shown
in Fig. 9. In order to evaluate the deviation of antenna directivity by wind
velocity the tilting angle is related to the wind force FW by
φ=arctanFWl26EI
where l is antenna tripod height, E is the modulus of elasticity and I
is the tripod inertia (Gross et al., 2005).
The following Eq. (9)
FW=AScpρ2v2
relates the wind force FW and the wind velocity v, where
AS is wind-exposed area, cp is the pressure
coefficient and ρ is the atmospheric pressure (Blohm, 1975).
By inserting Eqs. (8) and (9) in Eq. (7) and taking into account the
parameters of a typical wooden antenna tripod, the wind caused deviation
DW can be given as a function of wind velocity. According to
FGW/TR 9, WECS are operating at wind velocities between 3 and 27 m s-1
what leads to maximum deviation DW,max=0.06 dB, as shown in
Fig. 10. Hence, the standard uncertainty uW caused by wind
velocity can be calculated assuming a rectangular distribution between 0 and
0.6 dB with
uW=DW(27ms-1)23=0.02dB
In this way, the wind velocity related standard measurement uncertainty can
be characterized. The analysis of the presented mechanical antenna model is
based on the assumption that the antenna structure is in a homogeneous and
laminar wind field. Thus, the resulting uncertainty is assumed for both, the
horizontal and the vertical orientation of the electrical antenna. In the
next chapter the uncertainty of field reflection on undefined ground is
considered.
Analytically calculated deviation over the wind velocity. At wind
velocity of 27 m s-1, WECs are turned off.
Influence of the Ground on the Measurement Uncertainty
The evaluation of the reflected EM field on undefined ground is approached
in two ways. A numerical one – explained in Sect. 6.1 – uses a
simplified model of a WT to calculate the EM fields above the ground. The
ground properties are simulated by varying EM parameters of electrical
conductivity and relative permittivity. And a conservative one – explained
in Sect. 6.2 – known from the law of reflection. The grounds chosen
are electrically neutral (free space) and PEC. The obtained standard
uncertainty follows a worst case scenario, thus used for validation of the
simulation results.
Numerical Simulation
Of all the possible grounds WECS can be built on, sand has the lowest
conductivity while clay has the highest; therefore, those textures are
considered the two extremes (Hippel, 1995). In order to evaluate the
reflection of WT's EM emission on undefined ground a simulation is set-up in
FEKO, a field simulator by Altair. As shown in Fig. 11, a l=100 m
long bottom loaded monopole, approximating a WT, is placed above an
infinitive extended ground.
The ground relative permittivity εr and conductivity κ meets with either sand or clay with varying moisture rate. The frequency
depended values are taken from Hippel (1995). As an example, the values for
10 MHz are shown in Table 1.
Bottom loaded monopole as a simplified model of a WT.
Exemplary parameters for clay at 10 MHz (Hippel, 1995).
Relative moisture rateεrtanδκ in S m-10 %2.440.045.43×10-520.09 %21.61.72.04×10-2
Carrying out the simulation the field is detected corresponding to CISPR
16-2-3 in r=30 m distance and h2=2 m above the ground (Fig. 11). In
order to validate the model, the simulation is run in free space and with
perfect electric conducting (PEC) ground. The field strength with PEC is for
the entire spectrum lower than the doubled field strength in free space, as
shown in Fig. 12. Thus, the model can be assumed correct.
Validation of the simulation model. Electric field strength
calculated in free space and over PEC.
Magnetic field strength calculated over sand ground with various
relative moisture rate.
Magnetic field strength calculated over clay ground with various
relative moisture rate.
In order to evaluate the impact on measurement uncertainty due to undefined
ground the spectrum is divided into three parts based on the CISPR Bands B,
C and D. Shown as an example, for the magnetic field with sand in Fig. 13
and with clay in Fig. 14 it is observed that the amplitude increases with
increasing moisture rate, resonances occur proportional to the monopole`s
length and the curve progression is similar for all moisture rates and both
textures.
In order to differ between the texture's and the moisture rate's influence
they are considered separately in the following. For the texture the
deviation DT is calculated by
DT=20logFS,0FC,0
the field strength FS,0 over sand as ground is dived by the
field strength FC,0 over clay as ground at zero moisture rate
in each case. The deviation DM of the moisture rate is
calculated by Eq. (12), the field strength FC,20 at maximum
moisture rate (20.09 %, saturated ground) is divided by the field
strength at zero moisture rate, of clay as ground.
DM=20logFC,20FC,0,
While the deviation DT due to different texture is low and has
not to be regarded any further the deviation DM due to
different moisture rate is high, shown in Fig. 15 for the magnetic field and
in Fig. 16 for the electric field.
Standard measurement uncertainties caused by field reflection on
undefined ground.
Approach typeCISPR Band BCISPR Band CCISPR Band D(150 kHz–30 MHz)(30–300 MHz)(300 MHz–1 GHz)Simulation1.67 dB1.41 dB1.13 dBConservative1.73 dB
Deviation of the magnetic field strength.
Deviation of the electric field strength.
Supposing rectangular distribution, the uncertainty due to different
moisture rate can be calculated by Eq. (13) taking each maximum deviation
DM,max occurring in the three frequency bands into account.
uM=DM,max23
The results for the magnetic field strength (CISPR Band B) and the electric
field strength divided in CISPR C and D Band are shown in Table 2.
Validation with a Conservative Approach
As shown in Sect. 6.1, the relative moisture rate is a significant
factor for the measurement uncertainty. In consideration of extreme EM
properties, ground with the relative humidity of zero percent, is assumed EM
neutral behaviour, i.e. the WT is in free space. The field strength detected
at this state corresponds to the value F1 in Fig. 17. Taking into
account the other extreme, ground is very wet or even seawater (offshore
WT), i.e. the WT is on PEC. The field strength detected at this state
corresponds to the value F2 in Fig. 17. It is assumed that the field
strengths F1 and F2 are detected at the same observation point and
that the EM emissions of the WT remain the same for both scenarios.
According to the law of reflection, the field strength F2 can be
considered a superposition of a direct field component and a indirect field
component reflected at the PEC plane. Of interest in this consideration is
only the constructive overlay, leading to a field increase and in worst case
exceed the limits. In the scenario sketched, the field strength F2 can
be at twice as large as the field strength F1, leading to a
deviation of 6 dB. Assuming a rectangular distribution, this approach leads
to a standard uncertainty of 1.73 dB.
Field strength PDF according to the conservative approach.
Table 2 summarizes the values of the standard measurement uncertainties due
to undefined ground, derived in this work. It can be seen that the
numerically obtained standard uncertainties are always smaller than the
conservative uncertainty, validating the simulation results. However, it
should be noted that the simulation results are only applicable to onshore
WECS, but the conservative standard uncertainty is a general valid
assumption, hence applicable to both, onshore and offshore installations.
Conclusions
The electromagnetic (EM) emissions of wind energy conversion systems (WECS)
are evaluated in situ. Results of in situ tests, however, are only valid for
the examined equipment under test (EUT) and cannot be applied to series
production as samples, as the measurement uncertainty for in situ
environments is not characterized. Currently measurements must be performed
on each WECS separately, that is associated with significant costs and time
requirement to complete.
Therefore, this work, explains the measurement of EM emissions of WECS.
Evaluating the normative situation on the determination of EM emissions of
WECS results in the definition of the magnetic (CISPR Band B) and the
electric field strength (CISPR Bands C and D) as measurand.
In order to evaluate the measurement uncertainty, the measurands are
described using model equations, based on the standard procedure according
to the “Guide to the expression of uncertainty” (GUM). To determine the
expected value and the associated measurement uncertainty of the measurand,
knowledge of the so-called input values of the model equation is necessary.
Evaluation of the normative situation on measurement uncertainty of EM
emission measurements leads to the result that open area test site (OATS) is
the most similar test-site to in situ environment. Model equations for the
measured field strength and input values specified for OATS can be adopted.
Taking a closer look on the input values, two aspects occur with the need to
further evaluation: the deflection of the antenna caused by wind velocity,
and the reflection of EM fields on undefined ground.
In order to evaluate the deflection of the antenna tripod, caused by wind
velocity, common antennas are simulated under different tilting angles in a
plain wave field. The antenna foot point voltage, which directly relates to
the EM field, is observed. By calculating the force necessary to tilt a
common antenna tripod up to a certain angle and using the analytical
characteristic of a dipole, the relation between wind velocity and deviation
of the EM field is established. The EM field of tilted and not tilted
antenna is compared and the impact on the standard measurement uncertainty
is presented.
The reflection of the EM waves on undefined grounds is evaluated in two
approaches. In the first one, a simplyfied model of a WECS is simulated
above infinite extended ground with different EM characteristics. The
observed EM fields of the extremes in texture and moisture are compared.
This shows that the influence of varying ground moisture has a much higher
influence on the measurement uncertainty than the variation of the texture.
Therefore, a second, conservative approach assessing the measurement
uncertainty is derived from the law of radiation, taking the relative soil
moisture into account. In summary, it can be said that the numerically
obtained standard uncertainties are always smaller than the conservative
uncertainty, validating the simulation results. However, it should be noted
that the simulation results are only applicable to onshore WECS, but the
conservative standard uncertainty is a general valid assumption, hence
applicable to both, onshore and offshore installations. Thanks to the
achievements made in this contribution it is possible to determine the
measurement uncertainty of radiated EM emissions during WECS evaluation.
Data availability
No data sets were used in this article.
Competing interests
The authors declare that they have no conflict of
interest.The publication of this article was funded by the open-access fund of Leibniz Universität Hannover.
Edited by: Thorsten Schrader
Reviewed by: Kevin Herrling and one anonymous referee
References
Balanis, C. A.: Antenna Theory, 3rd Edition, John Wiley & Sons, New
Jersey, USA, 2005.
Blohm, O.: Natur- und Modelluntersuchungen von Wind, Wellen und Winddruck am
Leuchtturm, Alte Weser, Germany, 1975.
CISPR 11:2015: Industrial, scientific and medical equipment –
Radiofrequency disturbance characteristics, Limits and methods of
measurement, 2015.
CISPR 16-1-1:2015: Specification for radio disturbance and immunity measuring
apparatus and methods – Part 1-1: Radio disturbance and immunity measuring
apparatus, Measuring apparatus, 2015.CISPR 16-1-4:2010 + A1:2012: Specification for radio disturbance and
immunity measuring apparatus and methods – Part 1-4: Radio disturbance
and immunity measuring apparatus – Antennas and test sites for radiated
disturbance measurements, 2010.CISPR 16-2-3 + A1:2010 + A2:2014: Specification for radio
disturbance and immunity measuring apparatus and methods – Part 2-3:
Methods of measurement of disturbances and immunity, Radiated disturbance
measurements, 2010.CISPR 16-4-2:2011 + A1:2014: Specification for radio disturbance and
immunity measuring apparatus and methods – Part 4-2: Uncertainties,
statistics and limit modelling, Measurement instrumentation uncertainty,
2011.
CISPR/TR 16-2-5:2008: Specification for radio disturbance and immunity
measuring apparatus and methods Part 2–5: In situ measurements of disturbing
emissions produced by physically large equipment, 2008.
Directive 2014/30/EU of THE EUROPEAN PARLIAMENT AND OF THE COUNCIL of 26
February 2014 on the harmonization of the laws of the Member States relating
to electromagnetic compatibility, 2014.
EMC Law: Gesetz über die elektromagnetische Verträglichkeit von
Betriebsmitteln (EMVG), 14 December 2016.
FGW/TR 9: Technical Guidelines for Wind Turbines (FGW Guideline) Part
9:2014, Rev. 1, Determination of High Frequency Emissions from Renewable
Power Generating Units, 2014.
Fisahn, F., Koj, S., and Garbe, H.: Modelling of Multi-Megawatt Wind Turbines
for EMI and EMS Investigations by a Topological Approach, in: Proceedings of
the XXXIInd International Union of Radio Science General Assembly and
Scientific Symposium (URSI 2017 GASS), Montréal, Canada, August 2017,
E9-2, 2017.
Gross, D., Hauger, W., Schnell, W., and Schröder, J.: Technische
Mechanik, Band 2: Elastostatik, 8th Edition, Springer-Verlag, Berlin,
Heidelberg, Germany, 2005.
GUM: JCGM 100: Evaluation of measurement data, Guide to the
expression of uncertainty in measurement, 2008.
Hippel, v. A. R.: Dielectric Materials and Applications, Artech House Inc.,
1995.
Koj, S., Fisahn, S., and Garbe, H.: Untersuchungen zur Bestimmung von
hochfrequenten elektromagnetischen Emissionen von Windkraftanlagen, in:
Tagungsband Intern. Fachmesse und Kongress EMV, Duesseldorf, Deutschland,
Februar 2016, 327–334, 2016a.
Koj, S., Fisahn, S., and Garbe, H.: Determination of Radiated Emissions from
Wind Energy Conversion Systems, International Symposium on Electromagnetic
Compatibility, in: Proceedings of the International Symposium on
Electromagnetic Compatibility (EMC EUROPE), Wroclaw, Poland, September 2016,
188–192, 2016b.Koj, S., Reschka, C., Fisahn, S., and Garbe, H.: Radiated Electromagnetic
Emissions from Wind Energy Conversion Systems, in: Proceedings of the 2017
IEEE International Symposium on Electromagnetic Compatibility, Signal and
Power Integrity (EMC+SIPI 2017), Washington D.C., USA, August 2017,
243–248, 2017.Sommer, K.-D. and Siebert, B. R. L.: Praxisgerechtes Bestimmen der
Messunsicherheit nach GUM, Technisches Messen, 7, 52–66, 2004.
UNFCC: UN/FCCC/CP/ 2015/L.9/Rev.1: Adoption of the Paris Agreement, Paris,
30 November to 11 December 2015.