# Experimental Investigation of the Spatial and Temporal Evolution of the Tangential and Normal E-Field Components along the Stress Grading System of a Real Stator Bar

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## Abstract

**:**

_{t}) and normal (E

_{n}) E-field components along the stress grading system (SGS) of a real stator bar (Roebel type) for different AC 60 Hz applied voltages. These measurements were made with a new electro-optic system allowing for the study of both spatial distributions of two E-field components along the bar and their temporal evolution at critical points. The results obtained allowed us to calculate the correlation between the distribution of E

_{n}and E

_{t}along the SGS. In particular, it was demonstrated that the E

_{n}distribution presents a characteristic minimum, which can be used to identify the zone of partial discharge inception. Moreover, it was possible to observe an enlargement of the E

_{t}component distribution followed by a saturation in magnitude with the applied voltage increase. Moreover, the results have demonstrated that the waveform of the E

_{n}component is mostly affected by the SG material used, producing a greater distortion in its waveform than those obtained for the E

_{t}component. The more significant distortion was obtained at the end of the outer corona protection (OCP) material, corresponding to the first maximum of the E

_{n}component and characterized by the appearance of a third harmonic of large amplitude.

## 1. Introduction

_{t}) by inverse calculation. This can be a source of error in the case of fast spatial variation of the surface potential. However, another prototype of EO sensor has been proposed which permits to measure only the tangential component of the E-field at the surface of the SGCs, in a direct manner [10]. Finally, the recent development of a new noninvasive E-field sensor based on microelectro-mechanical system (MEMS) with remarkable spatial resolution could be an accurate solution for E-field component scanning at the surface of a stress grading systems [11,12].

_{t}and E

_{n}and then obtain the E-field resultant. Such information can be of great interest to characterize the efficiency of the SGCs and reduce the E-field strength below the dielectric rigidity of the surrounding medium. In addition, this information is helpful to validate the different numerical simulations dedicated to SGC modelling where generally only E

_{t}is verified due to the restrictions of the experimental measurement methods [1,9,10].

_{t}and E

_{n}along the SGCs present on a real stator bar of a HV hydro-generator. The proposed method is based on the use of a compact size EO E-field system [13,14], which provides unidirectional E-field measurement. The small size (millimeter sized transversally) of the EO probe allows E

_{n}and E

_{t}measurements close to the surface of the stator bar. Thanks to the metrological capabilities of this EO E-field system, the distribution of E

_{t}and E

_{n}have been determined as a function of applied voltage. The results obtained permitted to highlight the correlation between the two E-field components as function of the position along the stress grading system and particularly in the region of OCP and SGC overlapping. Moreover, the EO E-field system has permitted to study the influence of the OCP and SGC coatings on the temporal waveform shape of the E-field components by performing a harmonic analysis as a function of the position along the bar.

## 2. Materials and Methods

#### 2.1. Model of the Stator Bar

_{ECP}(S/m), measured directly on the stator bar based on ASTM standards [15,16], can be expressed as a function of the E-field E (V/m) as follow:

#### 2.2. Electro-Optic E-Field System

^{−1}) provided in real-time by the optoelectronic convertor. The manufacturer calibrates each EO probe in order to obtain the most accurate antenna factor.

#### 2.3. Experimental Setup

_{n}and E

_{t}were performed at the middle of the stator bar (central line in Figure 5) extended from the OCP to the bar bend. All the measuring points on each line are distant of 1 cm. For all measurements, the bottom of the EO probe was positioned at 2 mm from the surface of the stress grading system.

## 3. Experimental Results

#### 3.1. EO E-Field System Calibration

^{−1})).

#### 3.2. Distributrions of the Tangential E-Field Component

_{t}distributions obtained for an applied voltage of 8 kV

_{rms}((13.8/√3) kV

_{rms}) and 16 kV

_{rms}, respectively, along the central line illustrated in Figure 5. Figure 8 presents the corresponding normalized E

_{t}distributions obtained by dividing, for each applied voltage, the E-field strength at each measuring point by the strength obtained at the maximum of the distribution.

_{t}distributions with strength expressed in p.u. and presented in Figure 8 are very interesting on several aspects. First, the results clearly demonstrate that the maximum strength of E

_{t}is not reached at the end of the OCP coating. The maximum strength is obtained in a 1 cm zone width (zone 2 on Figure 8 and Figure 9) located at about 1.5 cm from the OCP end. It can be noticed that this zone of maximum strength is independent of the applied voltage. However, the maximum strength of E

_{t}shows an increase of about 57% when the applied voltage goes from 8 kV

_{rms}to 16 kV

_{rms}. Moreover, from the results of Figure 8, it can be observed that the increase in applied voltage leads to an expansion of the E

_{t}distribution. As illustrated in Figure 8 and Figure 9, the distribution at 16 kV

_{rms}starts to expand at the end of Zone 1, which corresponds to the beginning of the stator bar bend. In order to quantify this enlargement, it was decided to compute the width of the distributions at 50% of the maximum value. For 8 kV

_{rms}, a width of 60.0 mm was obtained against 92.0 mm for 16 kV

_{rms}, which represents an increase of 53%.

#### 3.3. Distributrions of the Normal E-Field Component

_{n}distributions were measured along the same references lines used for the tangential component (see Figure 4) for the same applied voltages.

_{n}distributions obtained at 8 kV

_{rms}and 16 kV

_{rms}and expressed in kV

_{rms}/mm and in p.u., respectively. In Figure 10, it is possible to visualize for the first time the experimental distribution of E

_{n}at the surface of a stress grading system. As it can be observed, this distribution’s behavior is significantly different from those obtained for E

_{t}. As observed with E

_{t}in Figure 7, the magnitude of the normal component increases with the applied voltage, increasing to a first maximum at the end of the OCP, as shown in Figure 10. At this particular point, E

_{n}increases by around 46% as the applied voltage goes from 8 kV

_{rms}to 16 kV

_{rms}. Notice that this increase is of the same magnitude that observed for E

_{t}.

_{n}can also be observed in Figure 11 where the E

_{n}strength is expressed in p.u. As it can be seen, the distribution of the normalized E

_{n}remains the same until it reaches 61 mm. At this point, the normalized E

_{n}at 16 kV

_{rms}becomes lower by an average of 16% than those obtained at 8 kV

_{rms}until position 110 mm where its strength begins to be higher. This behavior can be compared to the average 40% increase of the normalized E

_{t}obtained from 81 mm, as observed in Figure 8.

_{n}is higher than E

_{t}, as expected at the surface of a conductive layer. It can be observed that the definition of Zone 1 width, identified in Figure 7 and Figure 8, can be obtained in Figure 11 at 8 kV

_{rms}as it is clearly delimited by the two points where the normal component magnitude equals the tangential one. This zone, with a width of around 30 mm, is principally characterized by a tangential component magnitude greater than the normal one. In the same way, it can be observed that inside Zone 2, previously identified in Figure 7 and Figure 8, E

_{n}reaches a minimum in magnitude whereas for the same point, E

_{t}is at a maximum. Finally, for distances greater than 81 mm, which corresponds to the beginning of the stator bar bend, E

_{t}decreases rapidly and E

_{n}increases until reaching its maximum strength.

#### 3.4. Distribution of the Tangential and Normal E-Field Components at 35 kV_{rms}

_{n}and E

_{t}obtained for an applied voltage of 35 kV

_{rms}compared to those at 16 kV

_{rms}. It is interesting to note that E

_{t}is not significantly affected by the applied voltage increase from 16 to 35 kV

_{rms}in comparison to E

_{n}until the Zone 2 (see Figure 12). When the Zone 2 is reached, E

_{t}is more affected by the applied voltage increase than E

_{n}. These results can be compared to those of Figure 7 and Figure 10 where an increase of about 50% was observed for the E-field component magnitude when the voltage was increased from 8 to 16 kV

_{rms}.

#### 3.5. Waveforms of the Tangential and Normal E-Field Components

_{rms}.

_{t}and its corresponding Fast Fourier Transform (FFT). From these figures, it can be seen that the tangential instantaneous E-field along the bar presents (Figure 14b–d) a slight distortion characterized by the appearance of the third harmonic (Figure 15b–d) with a magnitude between 10% to 15% of the fundamental harmonic. The distortion in the harmonic content comes principally from the physical response of the silicon carbide material and not form the HV test set itself. Indeed, if this would be the case, the distortion would be observed in every location, at the different voltage and for the two components of the E-field. Deeper investigation are in progress to complete the understanding of the material response of the grading coating. The large distortion obtained at 41 mm (Figure 14a) is principally due to the low magnitude of E

_{t}at the surface of the OCP. As no averaging was used in the waveform recording, the signal-to-noise ratio becomes significant which causes several harmonics to appear (Figure 15a). As the EO E-field system presents a sensitivity of 500 mV/m as specified by the manufacturer, the oscillations in the snapshot of Figure 14a can be attributed to the noise of the HV source and experimental setup.

_{n}, as illustrated in Figure 16 and Figure 17. Along the OCP, the instantaneous normal E-field remains rather sinusoidal for measurement points below 51 mm (Figure 16a,b) as the harmonics are lower than 5% (Figure 17a,b). This indicates that E

_{n}is governed principally by the conductivity of the OCP. From the OCP/SG junction at 51 mm, however, there is a large deformation in the instantaneous E

_{n}form, as shown in Figure 16c,d. Indeed, the waveform of E

_{n}changes from a quasi-sinusoidal shape (51 mm) to triangular (81 mm) one. The distortion of the waveform of E

_{n}seems more significant at the measurement point located at 61 mm (Figure 16c), as it corresponds to the minimum of E

_{n}and the maximum of E

_{t}, as shown in Figure 12. As expected, at 61 mm, the normal component presents a third harmonic amplitude of around 31% of its fundamental (Figure 17c), which decreases to 15.5% at 81 mm (Figure 17d).

## 4. Discussion

#### 4.1. Tangential E-Field Component

_{rms}/mm for 8 kV

_{rms}and 16 kV

_{rms}, respectively situated at around 15 mm from the end of the OCP. Moreover, Staubach et al. also found that the tangential component distribution expanded with the increase of the applied voltage. This enlargement, determined by calculating the width of the distributions at 50% of the maximum value, can be estimated to 37 mm at 11.55 kV to 65 mm at 30 kV, an increase of 80.5%. The results of the present study with those of Staubach et al. are in close agreement as for E

_{t}distributions which are similar in terms of maximum values and spatial distribution. The differences between the two studies can be attributed to the different conductivity of the material tape used for the SG and its application along the stator bar.

#### 4.2. Normal E-Field Component

_{n}presented in Figure 10, Figure 11 and Figure 12, some interesting findings can be extracted from the distributions obtained. Firstly, the E

_{n}distribution present a first maximum, which corresponds exactly to the end of the OCP. Such information can be used during inspection procedure to control the manufacturing process and the quality of the stator bars before their installation. In the same way, the fact that the minimum of the distribution corresponds to the maximum of E

_{t}can be used to evaluate the zone where the partial discharge has a significant probability of occurrence.

_{n}at different characteristic points along the stator bar. The results clearly showed the particular behavior of E

_{n}, which presents a strong distortion at the surface of the SG material and particularly at the junction OCP/SG where E

_{t}is maximum. From these results, it is possible to confirm the influence of the semi-conductivity of the SG, mainly on E

_{n}as compared to E

_{t}. This result is very interesting in the sense that it can also be used to identify the position of the maximum tangential E-field magnitude, which corresponds to the beginning of the possible zone where the partial discharges can develop. Another interesting aspect is that the third harmonic amplitude of the instantaneous normal electric field can be linked to the non-linearity property of the SG material. The authors have verified this assumption by simulations and the results obtained will be presented in a future paper. In this way, the study of the third harmonic of the normal component could be a potential tool to verify the degradation of the SG electrical properties caused by local discharges, temperature, and aging. This assumption should be verified in future work.

#### 4.3. Dependency of the Tangential and Normal E-Field Components on the Applied Voltage

_{n}at 51 mm (first maximum) and at 61 mm for E

_{t}(first maximum) as a function of the applied voltage. As can be observed, from 8kV

_{rms}to 16 kV

_{rms}(increase by a factor 2), E

_{t}increases by a factor 1.57, and E

_{n}by a factor of 1.46. When the voltage increases from 16 kV

_{rms}to 35 kV

_{rms}, E

_{n}increases by a factor 1.16 whereas E

_{t}does not change and seems saturated.

_{n}, can be mainly explained by the behavior of the SG material, as discussed in [3,4,5,6,7,8]. From these papers, it was established that the grading behaviour of the SG material, at fixed service frequency (here 60 Hz) is governed by the permittivity (εω) of the SG material at low E-field magnitude and by the conductivity (σ(E)) for high E-field magnitude. In other word, at low E-field, the SG acts as capacitive and resistive grading for higher E-field magnitude [3,4,5,6,7,8]. For higher E-field values, the resistive grading of the SG material results on a more uniform distribution of the surface potential on the SG surface, leading to a more uniform distribution of the tangential component. This can explain, in the first step, the observed expansion of the tangential component distribution along the SG (Figure 7 and Figure 13) as applied voltage is increased.

_{rms}and the resulting saturation of the tangential component. As explained in [3], a dielectric material with non-linear E-field dependent conductivity presents a limiting E-field E

_{lim}when σ(E

_{lim}) = εω [3]. When the E

_{lim}value inside the SG material is reached, the dielectric relaxation time constant becomes comparable with the time constant of the applied voltage, leading to the formation of space charges inside the material, which becomes the limiting factor of E-field magnitude inside the SG as well as outside, as demonstrated in Figure 13.

## 5. Conclusions

_{n}and E

_{t}at the surface of the stress-grading system (SGS) of a real stator bar for the first time, as used in large hydro generators. These measurements, performed for different AC applied voltages, also permitted us to study the temporal evolution of the two E-field components at different critical points along the SGS.

_{n}and E

_{t}and clearly identify the zone of possible partial discharge for which E

_{n}present a minimum and E

_{t}a maximum. This indicates that the partial discharge appearance can be mainly attributed to E

_{t}. The use of it means that the two component distributions could be used as a quality control tool of stator bars before their installation.

_{n}is more affected by the SG material with a greater distortion in its waveform than those obtained for E

_{t}. A most significant distortion was obtained at the end of the OCP material, corresponding to the first maximum of E

_{n}, and was characterized by the appearance of a third harmonic of large amplitude. This result is important as the study of the E

_{n}third harmonic could easily be used to evaluate the degradation of the SG material over time. Future researches should be undertaken to verify this assumption.

_{t}distribution. For higher applied voltage, the effect of the space charge limited field (SCLF) in the SG material causes a limitation of the amplitude increase of E

_{t}, limitation which is less significant for E

_{n}.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Illustration of the insulation system of a typical stator bar used in large high-voltage (HV) hydro-generators.

**Figure 3.**Illustration of the electro-optic (EO) E-field system: (

**a**) the EO probe and (

**b**) optoelectronic convertor.

**Figure 4.**Experimental setup built and installed at the IREQ (Institut de Recherche d’Hydro-Québec) laboratory for the E-field mapping.

**Figure 5.**Closed view of the EO probe at the surface of the stress grading system with the referenced measuring points and E-field component orientation.

**Figure 6.**Results of the calibration of the EO E-field system obtained at 60 Hz using a two plane-to-plane circular electrode configuration.

**Figure 7.**Distributions of the E

_{t}obtained at the surface of the stress grading system for an applied voltage of 8 kV

_{rms}and 16 kV

_{rms}.

**Figure 8.**Comparison of the normalized E

_{t}distributions (in p.u.) obtained at the surface of the stress grading system for an applied voltage of 8 kV

_{rms}and 16 kV

_{rms}.

**Figure 9.**Close view of the stress grading system with the identification of the outer corona protection (OCP) end and the possible corona appearance zone.

**Figure 10.**Distributions of the absolute value of E

_{n}obtained at the surface of the stress grading system for applied voltages of 8 kV

_{rms}and 16 kV

_{rms}.

**Figure 11.**Comparison of the normalized absolute value of E

_{n}(in p.u.) obtained at the central line on the surface of the stress grading system for applied voltages of 8 kV

_{rms}and 16 kV

_{rms}.

**Figure 12.**Comparison of the normalized E

_{n}(absolute value) and normalized E

_{t}(in p.u.) obtained at the central line on the surface of the stress grading system for applied voltages of 8 kV

_{rms}and 16 kV

_{rms}.

**Figure 13.**Comparison of E

_{n}and E

_{t}obtained at the central line on the surface of the stress grading system for an applied voltage of 35 kV

_{rms}.

**Figure 14.**Comparison of the tangential E-field snapshot for applied voltages of 8 kV

_{rms}and 16 kV

_{rms}obtained at different measuring points along the stress grading system for (

**a**) 41 mm, (

**b**) 51 mm, (

**c**) 61 mm, and (

**d**) 81mm.

**Figure 15.**Harmonic analysis of the tangential E-field waveforms for an applied voltage of 8 kV

_{rms}obtained along the stress grading system at (

**a**) 41 mm, (

**b**) 51 mm, (

**c**) 61 mm, and (

**d**) 81 mm.

**Figure 16.**Comparison of the normal E-field snapshot for an applied voltage of 8 kV

_{rms}obtained along the stress grading system at (

**a**) 41 mm, (

**b**) 51 mm, (

**c**) 61 mm, and (

**d**) 81 mm.

**Figure 17.**Harmonic analysis of the normal E-field waveforms for an applied voltage of 8 kV

_{rms}obtained along the stress grading system at (

**a**) 41 mm, (

**b**) 51 mm, (

**c**) 61 mm, and (

**d**) 81 mm.

Applied Voltage (kV_{rms}) | Normal E-field (kV_{rms}/mm) | Tangential E-field (kV_{rms}/mm) |
---|---|---|

8 | 0.13 | 0.21 |

16 | 0.19 | 0.33 |

35 | 0.22 | 0.33 |

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**MDPI and ACS Style**

Koné, G.; Volat, C.; Hudon, C.; Bernier, S.
Experimental Investigation of the Spatial and Temporal Evolution of the Tangential and Normal E-Field Components along the Stress Grading System of a Real Stator Bar. *Energies* **2020**, *13*, 534.
https://doi.org/10.3390/en13030534

**AMA Style**

Koné G, Volat C, Hudon C, Bernier S.
Experimental Investigation of the Spatial and Temporal Evolution of the Tangential and Normal E-Field Components along the Stress Grading System of a Real Stator Bar. *Energies*. 2020; 13(3):534.
https://doi.org/10.3390/en13030534

**Chicago/Turabian Style**

Koné, Gbah, Christophe Volat, Claude Hudon, and Simon Bernier.
2020. "Experimental Investigation of the Spatial and Temporal Evolution of the Tangential and Normal E-Field Components along the Stress Grading System of a Real Stator Bar" *Energies* 13, no. 3: 534.
https://doi.org/10.3390/en13030534