During the assessment of the electromagnetic emissions of wind turbines (WTs), the aspects of measurement uncertainty must be taken into account. Therefore, this work focuses on the measurement uncertainty which arises through distance errors of the measuring positions around a WT.

The measurement distance given by the corresponding standard is 30

Every electrical system emits electromagnetic fields. Since these fields
could disturb or harm other electrical systems, given limits have to be met.
In the case of wind turbines (WTs), these limits are defined in the CISPR 11
(CISPR 11, 2015). For reproducible measurement results, not only are the
limits defined, but also the measurement positions and frequency ranges.
These definitions are further specified in a technical guideline
(FGW/TR 9, 2016). For the measurement a minimum of 4 measuring positions at
a distance of

Measuring positions according to FGW/TR 9 (2016).

When measuring the electromagnetic fields, one has to keep in mind, that every measuring result is afflicted by an expanded uncertainty. Therefore, the standard uncertainty has to be determined according to the “Guide to the Expression of Uncertainty” (GUM, 2008). To calculate the standard uncertainty, information about the uncertainty contributions are needed which had to be characterised for the in situ measurement. In previous works the contribution to the measurement uncertainty of the wind and of the undefined ground had already been investigated (Koj et al., 2018). In this contribution the influence of the uncertainty of the distance is presented.

Since WTs are tested in situ, there are various causes for the uncertainty of the distance. WTs are most often located in areas used for agriculture, the ground around the WT is uneven. This leads to an inaccurate placement of the antenna due to unsuitable ground at the determined measuring position or because of inaccuracies while measuring the distance to the WT due to the given circumstances. Furthermore, the measuring equipment itself can be the cause of some inaccuracies, e.g. the antenna phase centre of a logarithmic periodic antenna that is wandering with respect to the frequency. All these factors add up to the measurement uncertainty. This aspect is investigated in this work.

Therefore, in Sect. 2 the limits for the far field are considered for electrical small and for electrical large radiators. Following, in Sect. 3 the field distribution around a wind turbine is analysed based on simulation results in hindsight of the influence of the distance uncertainty to the WT. Thereafter, a method to minimize this uncertainty contribution is presented in Sect. 4. The conclusion in Sect. 5 gives a short summary of the most important insights of this contribution.

As mentioned before, the frequency range for the measurement stretches from
150

Field impedance of a Hertzian dipole for different distances (Koj, 2019).

Figure 2 shows the calculated wave impedance for distances of 20, 30 and
40

These results apply to electric elementary radiators and can also be used
for small electric radiators. A radiator is electric small if the largest
dimension

With a tower height of

With these different definitions of the far field distance, a closer investigation for the case of a WT is done. Therefore, various distances are examined.

Simulation model of a monopole fed at the bottom over PEC.

Investigated distances

In order to investigate which of those definitions best suits the WT, a
simulation model is built to investigate four different distances. The model
shown in Fig. 3 consists of a monopole with the length

Field impedance of a monopole over PEC for varying
distances, frequency range from 150

Field impedance of a monopole over PEC for varying
distances, frequency range from 30

Magnetic field strength over the distance for discrete
frequencies up to 3

Magnetic field strength over the distance for discrete
frequencies above 3

Figures 4 and 5 show that for the distance

Electric field strength over the distance for discrete
frequencies up to 150

Electric field strength over the distance for discrete
frequencies above 150

In order to determine the uncertainty contribution of the distance error as
described previously, the field distribution around a WT is investigated by
the model shown in Fig. 3. In contrast to the previous simulations, now
discrete frequencies are investigated over a varying distance

In order to investigate the distribution of the electric field strength,
simulations for distances

With the knowledge of the field distribution, the influence of the distance
error on the measurement uncertainty of the field strength can be explained.
For example, the electric field strength distribution at 300

If a logarithmic periodic dipole antenna (LPDA) is used for the measurement
of the electric field strength, a distance error of

Uncertainty contribution caused by distance errors for the magnetic field strength (Koj, 2019).

Uncertainty contribution caused by distance errors for the electric field strength (Koj, 2019).

Since the wavelength decreases with increasing frequency, the error made becomes greater with increasing frequency. Therefore, a way to minimize the uncertainty contribution caused by distance error is needed and is treated in the following section.

The goal of this chapter is to define a method which allows a reduction of
the measurement uncertainty described above, the influence of the frequency
and of the tower height

Field distribution for different tower heights at 30

Field distribution for 30

Figure 13 shows the magnetic field distribution at 30

The idea of reducing the influence of the distance errors and the
measurement uncertainty of the magnetic and electric field strength is based
on the

This work describes the contribution of distance errors to the measurement
uncertainty during in situ tests of electromagnetic emissions of wind
turbines (WTs). In order to investigate the far field region, a simple model
of a WT is set up and numerically analysed. The simulation results show that
at the normative required distance of

Therefore, the field distribution near a WT is calculated. It can be shown
that at those frequencies, where the WT model is an electrical small
radiator, the field distribution shows a monotonically decreasing dependence
on the distance

In order to reduce the measurement uncertainty at electrical large
radiators, the dependence of the field distribution from the frequency and
the tower height is investigated. It is shown that the distance between two
maxima of the field distribution decreases with increasing frequency. The
location of a local maximum also depends on the tower height. However, the
simulation results show that the levels of the local maxima decrease with
distance

Using the presented results, the measurement uncertainty of in situ tests of radiated electromagnetic emissions from WTs can be described. With the knowledge of this uncertainty a serial release of WTs is possible. The assessment of WTs becomes more time and cost effective.

The data are available from the corresponding author upon request.

All authors contributed to the design and implementation of the research, the analysis of the results and the writing of the manuscript.

The authors declare that they have no conflict of interest.

This article is part of the special issue “Kleinheubacher Berichte 2018”. It is a result of the Kleinheubacher Tagung 2018, Miltenberg, Germany, 24–26 September 2018.

The publication of this article was funded by the open-access fund of Leibniz Universität Hannover.

This paper was edited by Thorsten Schrader and reviewed by two anonymous referees.