This paper presents a complete assessment to the interferences caused in the nearby radio systems by wind turbines. Three different parameters have been considered: the scattered field of a wind turbine, its radar cross-section (RCS), and the Doppler shift generated by the rotating movements of the blades. These predictions are very useful for the study of the influence of wind farms in radio systems. To achieve this, both high-frequency techniques, such as Geometrical Theory of Diffraction/Uniform Theory of Diffraction (GTD/UTD) and Physical Optics (PO), and rigorous techniques, like Method of Moments (MoM), have been used. In the analysis of the scattered field, conductor and dielectric models of the wind turbine have been analyzed. In this way, realistic results can be obtained. For all cases under analysis, the wind turbine has been modeled with NURBS (Non-Uniform Rational B-Spline) surfaces since they allow the real shape of the object to be accurately replicated with very little information.

In the last decade, the interest in renewable energy has increased as a consequence of the climate change and the diminishing of fossil fuel. In particular, the use of wind turbines as electric generators has grown about 20% annually [

The aspect of wind turbines is quite characteristic. They are made up of a tower and three blades joined by a rotor. The size of these structures is usually very large. The height of the tower is around 80 meters and the length of the blades is around 40 meters. Hence, the total height of the wind turbine is around 120 meters. It must be considered that the shape of the tower is not a cylinder since its diameter is larger at the bottom than at the top. As a result of their large dimensions, they can interfere with many services such as TV broadcast [

Many of these effects have been extensively introduced in the previous literature. For instance, the EM scattering of different scaled models for wind turbines is characterized in [

The large size and rotational movement of the turbine blades produces a shift on the frequency of electromagnetic signals. This causes serious distortion on telecommunication systems. For this reason, it is quite interesting to study the Doppler features of wind turbines [

In this paper, three different analyses have been conducted to study the effects caused by a wind turbine in telecommunication systems located in its neighborhood.

Scattered field: to implement this kind of analysis, both high-and-low frequency techniques, such as GTD/UTD and MoM, respectively, have been used. Nevertheless, due to the tremendous size of this kind of structure [

Radar cross-section: for the purpose of analyzing the RCS of a wind turbine, MoM is applied too. In the group of asymptotic techniques, several studies such as [

Doppler spectra: as in the analysis of the scattered field, UTD, MoM, and MoM-PO have been used to compute the Doppler shift caused by a wind turbine.

For all these cases, the geometrical model plays an important role. The structure under study is modeled using parametric surfaces, Non-Uniform Rational B-Spline (NURBS) [

All the analyses here presented have been performed with NewFasant [

This paper is organized as follows: Section

As mentioned above, this paper presents several analyses to characterize the interferences caused by a wind turbine on radio systems located in its vicinity. This section shows the study of the scattered field of a wind turbine, in which the ground reflection has not been taken into account, considering the object as a static one.

Before starting the computation of the scattered field of a wind turbine or any other analysis, it is necessary to follow some initial steps. First, the geometrical model of the object must be obtained. As it has been mentioned in Section

Geometrical model of a wind turbine.

Frequently, a simplified model of a wind turbine is created considering that it is only composed of perfect conductors. This model is itself very interesting because it is considered a worst case for system analyses. However, a real model of a wind turbine must be generated considering that the blades are composed of different dielectric materials with two plates inside them to provide rigidity to the structure, as shown in Figure

Dielectric model of a blade.

Hence, to perform the analysis of the test case of these two models, Figure

Description of the scene for the analysis of the scattered field.

Two different geometrical models of the wind turbine have been compared.

The first model is a turbine made of conductor, exclusively. We call it conductor model.

The second one is a turbine with a metallic tower and with its blades made of a dielectric material, to consider the case of a real turbine which is not only composed of conductor. We call it dielectric model.

For both models, three different techniques have been applied.

MoM, a rigorous technique that tries to solve directly the Maxwell equations by dividing the geometry in small parts [

PO and MoM-PO solutions have been included to speed up the computation of the electrical field when the simulation is performed at high frequency. In the MoM-PO solution, the current on the metallic parts of the wind turbine is obtained using MoM and ignoring the dielectric parts of the turbine. The equivalent-induced current in the dielectric parts is computed using PO considering the incident field and the field due to the currents on the metallic parts.

Uniform Theory of Diffraction (UTD), an asymptotic technique introduced by Pathak and Kouyoumjian in [

For the computation of the scattered field at the observation points shown in Figure

Comparison of the scattered field at 700 MHz between the conductor and dielectric models.

Comparison of the scattered field at 1300 MHz between the conductor and dielectric models.

As shown in Figures

To obtain the electrical field scattered by the wind turbine applying rigorous techniques, we shall obtain first the induced currents on the geometry. Figure

Current density on the wind turbine at 1300 MHz.

Additionally, both models have been analysed applying the GTD/UTD technique at 700 MHz and 1300 MHz obtaining the results presented in Figures

Comparison of the scattered field at 700 MHz between the conductor and dielectric models.

Comparison of the scattered field at 1300 MHz between the conductor and dielectric models.

From Figures

Ray-tracing representation for two observation points.

To compare the analysis performed by MoM and GTD/UTD, Figures

Comparison of the scattered field at 700 MHz between MoM and GTD/UTD.

Comparison of the scattered field at 1300 MHz between MoM and GTD/UTD.

As it can be observed from Figures

Considering the dielectric model of the wind turbine, the scatter field obtained with MoM-PO and GTD has been compared in Figures

Comparison of the scattered field at 700 MHz between MoM-PO and GTD/UTD.

Comparison of the scattered field at 1300 MHz between MoM-PO and GTD/UTD.

As it can be observed from Figures

Nonetheless, the CPU time and memory resources required by GTD/UTD are less than in the case of MoM. Table

CPU time and memory requirements for the scatter field of the conductor model.

GTD/UTD (8 processors) | MoM (8 processors) | |||
---|---|---|---|---|

700 MHz | 1300 MHz | 700 MHz | 1300 MHz | |

CPU time | 8 min. 18 s. | 8 min. 18 s. | 1 h. 3 min. 45 s. | 1 h. 8 min. 5 s |

Memory resources | 538 KB | 538 KB | 723 MB | 2.5 GB |

Table

CPU time and memory requirements for the scattered field of the dielectric model.

GTD/UTD (16 processors) | MoM (16 processors) | |||
---|---|---|---|---|

700 MHz | 1300 MHz | 700 MHz | 1300 MHz | |

CPU time | 14 min. 35 s. | 14 min. 35 s. | 2 h. 18 min. 4 s. | 7 h. 13 min. 7 s. |

Memory resources | 382 KB | 382 KB | 520 MB | 1.9 GB |

The second analysis presented in this paper is the study of the RCS of a wind turbine to characterize the impairment caused to services like meteorological radar or aerial radio navigation systems. As in the scattered field case, there are numerous techniques to perform this kind of analysis. These can be classified in two different groups.

High-frequency techniques these techniques are applied to analyze electrically large bodies. Techniques such as Geometrical Optics (GO) [

In this section, a hybrid method combining GO and PO [

Rigorous techniques, such as Method of Moments (MoM) [

The bistatic RCS of the metallic wind turbine has been computed applying PO and MoM at the same frequency, 1300 MHz. The results obtained by these two methods, for the cut

Comparison between the results obtained applying PO and MoM for the bistatic RCS at 1300 MHz (dBsm: decibel measure of the RCS of the target relative one square meter).

From the graphic presented in Figure

CPU time and memory requirements for the calculation of the bistatic RCS.

PO (8 processors) | MoM (8 processors) | |
---|---|---|

CPU time | 11 min. 41 s. | 1 h. 32 min. 9 s. |

Memory | 123 MB | 3 GB |

In Figure

3D representation of the RCS of the wind turbine at 1300 MHz applying MoM.

As in the analysis of the scattered field applying MoM, this technique calculates the currents on the metallic wind turbine to compute its RCS. Figure

Current density on the wind turbine at 1300 MHz applying MoM.

Finally, the scatter map of the metallic wind turbine at 3 GHz has been obtained applying PO, since this analysis lets the parts with a higher contribution to the RCS to be identified. The results for the monostatic case for the incidence angle

Scatter map of a wind turbine at 3 GHz.

The computation of the bistatic RCS and the scatter map have been run in a 2.0 GHz Quad Intel Xeon with 24 GB of RAM. Only two processors have been used for the scatter map computation.

One of the main interference problems in the deployment of wind turbine farms in the vicinity of radio communication systems is due to Doppler frequency spectrum spreading and Doppler frequency shift generated by the rotation of the blades. In this way, the third and last analysis presented in this paper is the study of the Doppler spectra. The analysis of this effect is quite interesting since the detection of moving targets, such as planes, can be interfered by this movement. Moreover, the information provided by Doppler spectra can be used in target identification applications [

Therefore, an efficient method has been developed for both asymptotic techniques, like GTD, as rigorous techniques, like MoM, to compute the Doppler spectrum of the scattering of wind turbines. This new method has been implemented following these steps: read input data, set linear velocity, and compute the Doppler frequency. With this approach it is easier to obtain the Doppler shift generated by a moving target or by some moving parts of a target.

The first step to obtain the Doppler spectrum is to compute the linear velocity of points of the rotating parts of the wind turbines, in this case the blade. This speed in a given point is computed as follows:

Once the linear velocity has been calculated, it is very simple to obtain the Doppler frequency shift due to the linear speed of the point using the following expression:

We obtain the Doppler spectrum using MoM or PO considering a filter of 1.0 Hz of bandwidth, say we split the frequency band in windows (bins) of 1.0 Hz of width. The total field in a given frequency bin is due to all the MoM or PO subdomains that in accordance with (

Using GTD, the complex spectral response is obtained as a discrete series of impulses, each impulse due to a ray-path. The frequency of each impulse is computed considering the reflection/diffraction point to obtain the Doppler shift in (

The differences between the spectral responses of MoM and GTD are due to the fact that in GTD, the spectral response is a series of impulses, each one of them associated to a reflection or diffraction point over the wind turbine, while in MoM the spectral response is computed considering the contribution of each MoM subdomain of the induced currents on the wind turbine. Each impulse of the GTD spectral response is due to the current in a surface around the reflection/diffraction point that gives the reflected/diffracted value. This surface can be large in terms of wavelengths. The GTD impulse is located in a single frequency bin. For the current in the same area, the MoM computes for each subdomain (that is electrically small) its contribution to the spectral response; therefore, the spectral response, appears “nearly” a continuous function because there will be contribution in all the bins around the bin in which the GTD impulse is located. Speaking roughly, the GTD approach could be equivalent to make a filtering of the MoM complex spectral response, making a filtering around the bin associated to each reflection/diffraction point. From the previous explanation it is obvious that the MoM solution is quite more accurate.

It is important to realize that with the algorithm presented above, the Doppler spectra of a wind turbine considering several rotation axes can be analysed. In this way, for each axis the surfaces rotating around it must be associated to that axis. Then, this previous formulation will be applied for each group of surfaces and rotation axis to obtain the Doppler frequency for each of them.

The scenario shown in Figure

Description of the scene for the analysis of the Doppler spectra.

The analysis of the Doppler spectra has been run in a 2.6 GHz AMD Opteron with 256 GB of RAM, using 16 processors and obtaining the graphics shown in Figures

Comparison between the results obtained applying MoM and PO approximation for the Doppler spectra of a wind turbine.

Doppler spectra of a wind turbine applying GTD/UTD.

To undertake the analysis of possible interferences caused by a wind turbine, three different parameters have been examined (scattered field, RCS, and Doppler shift), applying asymptotic techniques as well as rigorous techniques included in NewFasant [

Before installing a wind farm in a specific location, it is necessary to undertake a study of the impairment caused to telecommunication systems in its vicinity analyzing the scatter field, the RCS, and the Doppler shift as it has been presented in this paper. Therefore, these results may be used as a guideline to predict these interferences. This kind of study will serve to conclude whether or not it is possible to install the wind farm.

This work has been supported in part by the Comunidad de Madrid Project S-2009/TIC1485, the Castilla-La Mancha Project PPII10-0192-0083, the Spanish Department of Science, Technology Projects TEC2010-15706 and CONSOLIDER-INGENIO no. CSD-2008-0068, and a contract from NewFasant.