Analysis on corona discharge electrical characteristics of wind turbine blades

Abstract

Corona plays an important role in both initiation and development process of leaders around wind turbine blades. In this paper, based on laboratory experiments and numerical simulation, the corona triggering tests are performed by analyzing corona discharge characteristics of wind turbine blades. The corona threshold voltage and the corona current are measured. The corona environmental threshold and the corona triggering threshold are evaluated and discussed in detail. The influence of blade lengths, rotational angles and rotational speeds is analyzed. The results show that the corona trigger threshold obtained is a constant and is about 321.29 kV/m, which appears to be some fluctuations due to atmospheric conditions and charged ions. In addition, through analysis the corona triggering threshold of different rotational angles and the corona environmental threshold of different rotational speeds, rotational wind turbine blades affect the electric field near the blades by varying the blade height and the charged ions distribution at the tip of the blades where the altered blade height accounts for the dominant factor. The above research results are valuable for the understanding of the initiation and development of leaders around the wind turbine blades.

Keywords

Wind turbine blades electric field distortion corona discharge corona triggering threshold corona environmental threshold

1. Introduction

As a renewable energy source, wind energy is strongly advocated for its environmentally friendly characteristic [1]. However, during the development of wind power, wind turbines are mostly built on the wilderness and people find that they are vulnerable to lightning [2–4]. Coupled with the ever-increasing scale of wind turbines and the increasing tower height of wind turbines, the menace of lightning is increasing. Research results show that wind turbine blades are the most vulnerable part to lightning [5]. Once the wind turbine blades are damaged, it will not only reduce the power generation efficiency, but also raise the cost of equipment running [6]. In recent years, the development of wind power has been restricted due to the damage caused by lightning strikes [7]. The corona can change the electric filed around the tip of wind turbine blades, which affects the process of lightning flashes triggered [8,9].

Recently, lots of researches have been conducted by scholars at home and abroad on flashes around wind turbines [10–14]. Wang D et al. [15] and Wilson N et al. [16] found that a wind turbine and a tower of the similar height, rotating wind turbine blades tend to have a bigger chance to initiate an upward leader. Based on simulation observation of 2-dimension random model of lightning leader, Li Dang [17] claimed that the probability of lightning striking the wind turbine blades is much higher than other components of the wind turbine, possibly because the electric field distortion caused by the blade is beneficial to trigger the upward leader. JMAR Williams [18] found that the rotational blades have higher probability of upward leaders triggering with 3-D Lightning Mapping Array and high-speed video. However, the corona discharge electrical characteristics of wind turbine blades have been little addressed through experiments and numerical calculation in previous papers.

In order to explore the corona discharge electrical characteristics of wind turbine blades, corona triggering experiments were carried out with negative high voltage applied in the tests. The corona threshold voltage and the corona current are measured, where the corona threshold voltage is the actual voltage of the upper plate when the corona is initially generated. The electric field is calculated by numerical simulation, and the maximum electric field is the corona triggering threshold. In addition, the electric field in the absence of the wind turbine is also calculated, which is the corona environmental threshold. The influence of blade lengths, rotational angles and rotational speeds is analyzed. By comparing the variation of corona triggering threshold and corona environmental threshold under different conditions, the results are obtained and discussed in detail. The results are valuable for the understanding of the initiation and development of leaders around the wind turbine blades.

2. Theoretical analysis of the corona triggering threshold

When the wind turbine is exposed to the electric field, the electric field near wind turbine blades will be strongly distorted, which will accelerate electrons. If the intensity of the electric field distorted is serious enough, the kinetic energy of the electrons would exceed the ionization energy of the air, and high-speed electrons collide with air molecules near wind turbine blades to generate new electrons. A corona will occur when new electrons continue to collide which lead to electronic avalanche growth [19]. In this paper, the electric field around the wind turbine blades is used to estimate the generation of corona. The electric field is difficult to measure by the instrument; however, it can be calculated by numerical simulation. This paper calculates the corona triggering threshold under a uniform electric field background.

2.1. Calculation of a uniform electric field

Due to the edge effect of the two aluminum plates in the experiment, the electric field between the two plates is not evenly distributed. The uniform electric field between the two plates is actually smaller than the ratio of the voltage U between the two plates of the distance d. Therefore, the formulation of the uniform electric field can be described mathematically: $\begin{eqnarray}\displaystyle E_{0}={\alpha}U/d & & \displaystyle\end{eqnarray}$ (1) Where correction coefficient 𝛼 = 0.91 [20].

2.2. Calculation of the corona triggering threshold

The Poisson equation is solved in a 2D uniform electric field, which is shown as below [20] $\begin{eqnarray}\displaystyle {\nabla}^{2}{\varphi}=-{\rho}/{\varepsilon} & & \displaystyle\end{eqnarray}$ (2) Where 𝜑 is the potential, 𝜌 is the density of free charge, and ϵ is the permittivity.

Equation (2) can also be transformed into Laplace’s equation when corona ions are ignored in the air. The equation can be described as. $\begin{eqnarray}\displaystyle {\nabla}^{2}{\varphi}=0 & & \displaystyle\end{eqnarray}$ (3) Where the potential of upper plate is U _a, the potential of lower plate and wind turbine is 0, and side boundaries are Robin condition.

The electric field is solved according to the potential solved by Eq. (3), noted as $\begin{eqnarray}\displaystyle E=-{\nabla}{\varphi} & & \displaystyle\end{eqnarray}.$ (4)

3. Test and analysis

3.1. Test model

The model of the corona triggering tests is shown in Fig. 1, which consists mainly of a high voltage generator, a parallel capacitor plate and a wind turbine model. The parameters are listed as follows: YDJ-60: YDJ series oil immersed test transformer, R1 and R2: Protection resistance, D: Diode, C: Capacitor, S: Switch. The radius of the plates is 75 cm, and the distance between two aluminum plates is 90 cm. The high voltage generated by the high voltage generator is applied to the upper plate, and the lower plate is grounded. The electric field between two plates is approximately a uniform electric field. The wind turbine is positioned on the middle of the lower plate.

Fig. 1.

The model of the corona triggering test.

In the experiment, the negative high voltage is applied on the upper plate. When the voltage of the upper plate is charged to the set voltage, it drops at a rate of 0.1 kV/s. With decrease of the voltage on the upper plate, the number of corona current pulse showing on the oscilloscope will reduce and eventually disappears. When the final corona current pulse disappears, the actual voltage on the upper plate is collected, noted as corona threshold voltage. And the corona current also is measured by the oscilloscope, where the sampling resistance is 10 MΩ. Corona triggering tests were carried out on different blade lengths, rotational angles and rotational speeds. And the parameters in tests are listed as follows: (1) The pole height of the wind turbine is 40 cm, (2) blade lengths are adopted in the analysis that is 5.5 cm, 11 cm and 22 cm, (3) rotational angles are adopted that is 0°, 30°, 45° and 60°, (4) rotational speeds are adopted that is 0 r/min, 12 r/min, 30 r/min and 75 r/min. Finally, the data collected by the test is affected by atmospheric conditions. Therefore, it should be collected under the same atmospheric conditions as much as possible.

3.2. Test results and discussion of corona current

Waveforms of corona current are shown in Fig. 2. It consists of many pulses, and each pulse represents a corona triggering process. The peak of corona current is about 1 μA −2 μA. With decrease of the voltage on the upper plate, the number of corona current pulse decreases and eventually disappears. When the final corona current pulse disappears, the actual voltage on the upper plate is noted as corona threshold voltage.

Fig. 2.

Corona current with 11 cm blade and 0° rotational angle. (a) −26.5 kV high voltage. (b) −26.0 kV high voltage. (c) −25.5 kV high voltage. (d) −25.1 kV high voltage.

3.3. Test results and discussion corona triggering threshold with different Rotational angles

As is shown in Fig. 3, at rotational angles outside range from 0° to 60°, symmetric or uniform blade attitudes can be found within range from 0° to 60°. Therefore, the influence of rotational angles in Fig. 3 is analyzed.

Fig. 3.

The attitude diagram of the wind turbine blades with different rotational angles.

Corona threshold voltages with different blade lengths and 0° rotational angles are shown in Fig. 4. The longer is the blade length; the lower is its corona threshold voltage. It also can be found with other rotational angles.

Fig. 4.

Corona threshold voltages with different blade lengths and 0° rotational angle.

In the experiment, corona threshold voltages with different rotational angles are obtained. As showed in Table 1, when the blade length is 5.5 cm, at rotational angles the range of 0° to 60°, the corona threshold voltage increases with increase of the rotational angle. The reason is perhaps that the height of the highest blade relative to the ground decreases with increase of the rotational angle. The results also can be found when the blade lengths are 11 cm and 22 cm respectively, and their data are illustrated in Table 2 and Table 3 respectively.

Table 1

Corona threshold voltages with 5.5 cm blade and different Rotational angles (kV)

Rotational angle	First times	Second time	Third time	Fourth times	Fifth times	Average
0°	31.7	31.8	31.5	31.7	31.6	31.66
30°	32.1	32.1	32.3	32.2	32.1	32.16
45°	33.2	33.3	33.1	33.3	33.2	33.22
60°	35.8	35.8	36.0	35.7	35.9	35.84

Table 2

Corona threshold voltages with 11 cm blade and different Rotational angles (kV)

Rotational angle	First times	Second time	Third time	Fourth times	Fifth times	Average
0°	25.3	25.3	25.4	25.4	25.3	25.34
30°	26.1	26.1	26.1	26.0	26.1	26.08
45°	27.4	27.4	27.4	27.3	27.3	27.36
60°	30.4	30.5	30.4	30.2	30.3	30.36

Table 3

Corona threshold voltages with 22 cm blade and different Rotational angles (kV)

Rotational angle	First times	Second time	Third time	Fourth times	Fifth times	Average
0°	19.5	19.5	19.4	19.5	19.6	19.50
30°	20.7	20.7	20.6	20.8	20.6	20.68
45°	21.6	21.7	21.7	21.7	21.7	21.68
60°	25.3	25.2	25.4	25.3	25.2	25.28

In order to discuss the relationship between the electric field and the corona triggering, this paper uses formula (4) to calculate the electric field when the corona is initially triggered. As showed in Fig. 5, The strongest distortion of the electric field occurs at the tip of the highest blade. It also can be discovered by other scholar [17]. In addition, as changing of the rotational angle, the strongest distortion of the electric field always occurs at the tip of the highest blade. The maximum electric field strength is noted as corona triggering threshold, and it has little change with the varying of rotational angles.

Fig. 5.

Electric field with 11 cm blade length and different rotational angles. (a) 0° rotational angle. (b) 30° rotational angle. (c) 45° rotational angle. (d) 60° rotational angle.

The electric field in the absence of the wind turbine is approximately a uniform electric field noted as the corona environmental threshold which is calculated by formula (1). As showed in Fig. 6, the corona environmental threshold is proportional to the blade length. In addition, at rotational angles range from 0° to 60°, the corona environmental threshold increases with the increase of the rotational angle. The above result indicates that the corona environmental threshold become smaller when the highest blade rotates to higher position.

Fig. 6.

Corona environmental threshold of wind turbine blades.

Corona triggering thresholds with different blade lengths and different rotational angles are calculated and are shown in Table 4. As shown in Fig. 4 and Table 4, at rotational angles range from 0° to 60°, the corona environmental threshold increases with the increase of the rotational angle, but their corona triggering threshold has little change with the varying of the rotational angle. In other word, with the increase of the rotational angle, when the corona is triggered, the environmental electric field becomes larger; the actual electric field near the tip of the blade has little change. The paper uses the relative error formula to calculate concentration of the data in Table 4, which is shown as below $\begin{eqnarray}\displaystyle {\delta}=\displaystyle \frac{|E_{\text{ci}}-\overline{E_{\text{c}}}|}{\overline{E_{\text{c}}}}\times 100\% & & \displaystyle \nonumber\end{eqnarray}$ Where the average value of corona triggering thresholds for the same blade length is E _c, and the corona triggering threshold with different blades and different rotational angles is E _ci.

Table 4

Corona triggering thresholds with different blade lengths and different rotational angles

Rotational angle	5.5 cm blade length	11 cm blade length	22 cm blade length
0°	349.69	332.21	325.62
30°	358.56	320.87	318.52
45°	361.60	322.85	320.64
60°	368.62	322.34	312.31

Relative errors of corona triggering thresholds with the same blade length are illustrated in Table 5. The maximum relative error of the corona triggering threshold is 2.76%, less than 3%. Therefore, this paper claimed that triggering threshold has little change with the varying of the rotational angle. The result indicates that the corona occurs when the electric field around wind turbine blades reaches the corona triggering threshold.

Table 5

Relative errors of corona triggering thresholds with the same blade length

Rotational angle	5.5 cm blade length	11 cm blade length	22 cm blade length
0°	2.76%	−2.35%	−1.99%
30°	0.29%	1.14%	0.24%
45°	−0.55%	0.53%	−0.43%
60°	−2.50%	0.69%	2.18%

As showed in Table 4, the corona triggering threshold decrease slightly with the increase of the blade length. Actually, the corona triggering threshold has little change with the varying of the blade length. The explanations are as follows. Changing the rotational angle changes the height of blades. The previous analysis also shows that with the varying of rotational angles the corona triggering threshold has little change. This error is probably caused by the limitation of the calculation method. In the calculation of the electric field, this paper assumes that there is no charged ion in the space. However, in the actual environment, there are charged ions in the space. These charged ions weaken the electric field near the blades, which lead to the calculated results become larger than the actual electric field strength. According to the bar-plate gap discharge theory, the smaller is the gap between the blade-plate, the less is corona ions accumulated between the blade and the plate [21]. In other word, in this experiment, the longer is the blade length, the less is the corona ions between the blade and the upper plate, and the smaller is the charged ions weakening electric field near the blade. Therefore, in the case of ignoring the charged ions in the air, the longer is the length of the blade, the smaller is the error between the electric field calculated and the actual value. Based on the above analysis, the problems with the data of Table 4 can be reasonably explained. Therefore, the corona triggering threshold has little change with the varying of the blade length. According to the concentration of the data, the average corona triggering threshold of 11 cm blades and 22 cm blades is able to represent the corona triggering threshold of the wind turbine blades, which is about 321.29 kV/m.

3.4. Test results and discussion of corona environmental threshold with different rotational speeds

The corona environmental threshold with different rotational speeds is calculated. As illustrated in Table 6, when the blade move from stationary to dynamic, the corona environmental threshold decreases rapidly, but it has little change with the increase of the rotational speed. In other word, the rotational blades are beneficial to corona discharge than stationary blades. The explanations are as follows. When the blade is stationary, the tip of the blade accumulates a large amount of the charged ions to form a shielding layer which weakens the electric field. When the blade starts to rotate, the shielding layer is broken. During the rotational process, the shielding layer has been broken and the corona environmental threshold is little affected by the magnitude of the rotational speed. Due to the computational complexity, the corona trigger threshold of wind turbine blades with different rotational speeds could not be calculated. The above result agrees well with the conclusion of JMAR Williams [18]. Therefore, the result of this paper is very reasonable.

Table 6
Corona environmental thresholds with different rotational speeds (kV/m)

Rotational speed (r/min) 5.5 cm blade length 11 cm blade length 22 cm blade length

0 19.96 25.76 32.13

12 19.21 22.59 31.71

30 19.11 22.43 31.38

75 19.13 22.33 31.38

Rotational speed (r/min)	5.5 cm blade length	11 cm blade length	22 cm blade length
0	19.96	25.76	32.13
12	19.21	22.59	31.71
30	19.11	22.43	31.38
75	19.13	22.33	31.38

According to the above experimental results when upper plate is negatively charged, based on the corona triggering principle between the rod and the plate, this paper infers that when the upper plate is positively charged, the corona triggering threshold of wind turbine blades is basically unchanged, but the corona environmental threshold become higher. The explanations are as follows. When a negative voltage is applied to the upper plate, the tip of the blade has a positive potential, electrons will be absorbed by blades and thus many compensating positive ions are left around the tip of the blade. Although these positive ions move toward to the upper plate, their velocity is very slow, they are approximate to staying near the blade. These ions enhance the electric field between the positive ions zone and the plate. But when a positive voltage is applied to the upper plate, the tip of the blade has a negative potential. At this time, the electron avalanche will initiate from the surface of blades, moving fast to the upper plate, and these electrons will weaken the electric field between the electron zone and the plate.

4. Conclusion

By analyzing and discussing the corona trigger test results of wind turbine, the following conclusions are reached:

(1) The strongest distortion of the electric field always occurs at the tip of the highest blade. In addition, the longer the wind turbine blade length is, the larger the distortion of the electric field, and the smaller the corona environmental threshold of the blade. The effect of the rotational angle on the corona environment threshold is reflected in the height of the blade. In other word, the higher is the position while the wind turbine blade rotates, the smaller the corona environmental threshold.

(2) The corona triggering threshold has little change with varying of the blade length and the rotational angle. The corona trigger threshold obtained in this test is about 321.29 kV/m, which appears to be some fluctuations due to atmospheric conditions and charged ions.

(3) The corona environment threshold of the rotational wind turbine blades is lower than the corona environmental threshold of the static wind turbine blades, and the corona environmental threshold of the dynamic wind turbine is a little affected by the rotational speed. The result indicates that the rotational blade is beneficial to corona triggering than the static blade. The reason is that the shielding layer formed by the charged ions at the tip of the blade is broken by the dynamic wind turbine blades, which reduce the weakening of the electric field by charged ions.

In short, rotational wind turbine blades, to affect the electric field near the blades by varying the blade height and the charged ions distribution at the tip of the blades, with the altered blade height accounting for the dominant factor. The results are valuable for the understanding of the initiation and development of leaders around the wind turbine blades.

Footnotes

Acknowledgements

These works were financially supported by the Postgraduate Research & Practice Innovation Program of Jiangsu Province (Grants No. KYCX18_1033), the Natural Science Foundation of Jiangsu Province (Grants No. BK20150903) and the Natural Science Fundamental Research Project of Jiangsu Higher Education Institutions of China (Grants No. 15KJB170010).

References

Abdelli

Sareni

and Roboam

, Optimization of a small passive wind turbine generator with multiobjective genetic algorithms, International Journal of Applied Electromagnetics and Mechanics 26(3-4) (2007), 175–182.

Cerveira

Baptista

and Pires

E.J.

, Wind farm distribution network optimization, Integrated Computer-Aided Engineering 23(1) (2016), 69–79, doi:10.3233/ICA-150501.

Abdi

Moradi

and Saleh

, Optimal unit commitment of renewable energy sources in the micro-grids with storage devices, Journal of Intelligent & Fuzzy Systems 28(2) (2015), 537–546, doi:10.3233/IFS-141330.

Zhang

Cui

Wang

Zhao

Zou

and Zou

, Optimal layout of wind farm for lightning protection based on lightning leader development model, The Journal of Engineering 2017(13) (2017), 2261–2265, doi:10.1049/joe.2017.0733.

Liu

Polinder

Abrahamsen

A.B.

Stehouwer

Hendriks

and Magnusson

, Optimization and comparison of superconducting generator topologies for a 10 MW wind turbine application, International Journal of Applied Electromagnetics and Mechanics 53(S2) (2017), S191–S202, doi:10.3233/JAE-140161.

Garolera

A.C.

Cummins

K.L.

Madsen

S.F.

Holboell

and Myers

, Multiple lightning discharges in wind turbines associated with nearby cloud-to-ground lightning, IEEE Transactions on Sustainable Energy 2015 6(2) (2015), 526–533, doi:10.1109/TSTE.2015.2391013.

Miki

Mik

Wada

and Wada

, Observation of lightning flashes to wind turbines, in: International Conference on Lightning Protection, Cagliari, 2010.

Rachidi

Rubinstein

Montanya

and Bermúdez

, A review of current issues in lightning protection of new-generation wind-turbine blades, IEEE Transactions on Industrial Electronics 55(6) (2008), 2489–2496, doi:10.1109/TIE.2007.896443.

Y.F.

Zhang

and Yan

J.Y.

, Inception mechanism of lightning upward leader from the wind turbine blade and a proposed critical length criterion, Proceedings of the CSEE 36(21) (2016), 5975–5982+6042, doi:10.13334/j.0258-8013.pcsee.152350.

10.

Naka

Vasa

N.J.

Yokoyama

Wada

Asakawa

Honda

Tsutsumi

and Arinaga

, Study on lightning protection methods for wind turbine blades, IEEJ Transactions on Power and Energy 125(10) (2005), 993–999, doi:10.1541/ieejpes.125.993.

11.

Shi

Ren

Yao

Yuan

and Li

, Research advances and trends of lightning protection for offshore wind turbines, in: Chinese Automation Congress, Jinan, China, 2017.

12.

Muljadi

Zhang

Y.C.

and Gevorgian

, Understanding dynamic model validation of a wind turbine generator and a wind power plant, in: Energy Conversion Congress and Exposition, Milwaukee, U.S.A, 2016.

13.

Holboell

Madsen

S.F.

and Henroiksen

, Discharge phenomena in the tip area of wind turbine blades and their dependency on material and environmental parameters, in: International Conference on Lightning Protection, Kanazawa, Japan, 2006, pp. 1503–1508.

14.

Yao

Kaifang

Tong

and Liang

, Dynamic striking distance and electrical geometrical model of wind turbine blades based on lightning physics, The Journal of Engineering 13 (2017), 2298–2302, doi:10.1049/joe.2017.0740.

15.

Wang

Takagi

and Watanabe

, Observed characteristics of upward leaders that are initiated from a windmill and its lightning protection tower, Geophysical Research Letters 35(2) (2008), 196–199, doi:10.1029/2007GL032136.

16.

Wilson

Myers

and Cummins

, Lightning attachment to wind turbines in central Kansas: Video observations, correlation with the NLDN and in-situ peak current measurements, in: EQEA, The European Wind Energy Association, Vienna, Austria, 2013.

17.

, 3D simulation of the lightning leader and its application, M.S. Dissertation, Chinese Academy of Meteorological Sciences, 2013.

18.

Williams

J.M.A.R.

, Lightning discharges produced by wind turbines, Journal of Geophysical Research Atmospheres 119(3) (2014), 1455–1462, doi:10.1002/2013JD020225.

19.

Radičević

B.M.

and Savić

M.S.

, Experimental research on the influence of wind turbine blade rotation on the characteristics of atmospheric discharges, IEEE Transactions on Energy Conversion 26(4) (2011), 1181–1190, doi:10.1109/TEC.2011.2162240.

20.

Zhang

L.C.

and Xu

, Application of Finite Element Method in Electromagnetic Calculation, China Railway Publishing House, 1996, pp. 154–185.

21.

Miao

J.S.

Chen

Zhang

and Jin

Z.G.

, Comparison of positive and negative IONIC Wind in needle-to-plate corona discharge, Transactions of Beijing Institute of Technology 37(01) (2017), 61–66, doi:10.15918/j.tbit1001-0645.2017.01.013.

Analysis on corona discharge electrical characteristics of wind turbine blades

Abstract

Keywords

1. Introduction

2. Theoretical analysis of the corona triggering threshold

2.1. Calculation of a uniform electric field

3.1. Test model

Table 6 Corona environmental thresholds with different rotational speeds (kV/m) Rotational speed (r/min) 5.5 cm blade length 11 cm blade length 22 cm blade length 0 19.96 25.76 32.13 12 19.21 22.59 31.71 30 19.11 22.43 31.38 75 19.13 22.33 31.38

Footnotes

Acknowledgements

References

Table 6
Corona environmental thresholds with different rotational speeds (kV/m)

Rotational speed (r/min) 5.5 cm blade length 11 cm blade length 22 cm blade length

0 19.96 25.76 32.13

12 19.21 22.59 31.71

30 19.11 22.43 31.38

75 19.13 22.33 31.38