Design optimization of corona ring and grading ring for a 400kV Tension insulator

doi:10.21203/rs.3.rs-2370067/v1

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Design optimization of corona ring and grading ring for a 400kV Tension insulator

https://doi.org/10.21203/rs.3.rs-2370067/v1

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The design of polymer insulator depends on the surface electric field gradient. Increased electric field distribution generates corona discharge and leads to breakdown. Corona discharge has become an important factor not only because of corona losses but also due to electromagnetic interferences. Hence proper design optimization is necessary while designing the corona ring and grading ring which is employed at the critical region of the insulator to reduce the corona discharge. In this paper, optimized ring designs are identified for a 400kV tension type insulator. Three phase tension insulator along with the tower model is selected and its electric field distribution is calculated using finite element analysis. A 3D model design is developed using FEM based software. Seven structure parameters of the corona and grading rings are varied and the electric field is calculated. The optimized ring design is then achieved using multi-objective genetic algorithm. The obtained corona ring and grading ring parameters are compared with the simulated values and the error is less than 3%. Hence the proposed methodology can be used for prediction of corona ring and grading ring design, as the electric field is below the critical value.

Corona discharge

Tension insulator

Corona ring

Grading ring

Finite element method

Optimization

The increase in power transfer and improvement in the efficiency of power delivery over a limited right of way led to the modelling of UHV and EHV transmission lines. High voltage insulators take major part in maintaining the reliability of the transmission lines. Failure in insulators occurs due to aging, improper material design, flashover, corona discharge. EHV and UHV transmission lines are exposed to high electric fields which produce corona discharge that is responsible for audible noise, radio interferences, degradation of the insulating material, and also flashover when the electric field is very high [1]-[3]. External metal rings known as corona rings and grading rings are installed to minimize the electric field density thereby mitigating corona discharge.

Corona rings can be used for several benefits they can reduce the electric field strength, provide even electric field distribution, reduce TV and radio interferences [4]. Polymer insulators are preferred nowadays in transmission lines as they have many merits over ceramic insulators. Polymer insulators are less in weight, have high tensile strength, provide good hydrophobicity, resistant to vandalism [5]-[7]. The major disadvantages of polymer insulators are: the electric field concentration is uneven due to its structural limitations. The electric field throughout the length of the insulator should be even which is taken care of by the grading ring. The electric fields around a clean and dry polymer insulator as per the standards: Around the triple junction it should not exceed 0.45 kV/mm, at grading ring the electric field should be less than 2.1 kV/mm and at corona ring the field should not go beyond 2.1 kV/mm [8].

Installation of the Corona rings and grading rings are performed to minimize the field density. But proper standards are not laid down for the dimensions of the rings. Therefore, in this paper, an optimum ring parameter is designed by varying the radius of corona ring (Rc), Thickness of corona ring (rc), Height of corona ring (Hc), Height of grading ring (Hg), Radius of grading ring (Rg), Thickness of grading ring (rg), Length of grading ring (Lg). Many studies are being carried out for optimizing the ring dimensions and most of the study focuses on the design parameters for optimization [9]. The seven critical design parameters which are considered for analyses are illustrated in Fig. 1. There is only less research work performed in the optimization of rings in stress insulators. Hence an initiative for finding optimum design parameters for a 400kV stress type high voltage insulator is selected for the analysis.

The analysis is performed using a cup-shaped tower and three-phase conductors. The variation in electric distribution along the insulator is more evident with the inclusion of the tower, three phase conductors and hardware fittings. In order to incorporate the practical scenario, the model is simulated with polymer insulators along with the tower, three-phase conductors and hardware fittings. The front view and side view of the entire structure along with the three phase insulators and conductor lines are shown in Fig. 2. The top view of the whole model is shown in Fig. 3.

The three phase conductors along with 12 corona rings and 6 grading rings are shown in Fig. 4. Each phase carries two corona rings and two grading rings at the high voltage end which is shown in Fig. 5. Two corona rings are installed at the low voltage end for each phase.

A 400 kV tension type insulator with two conductor bundles is chosen for the analysis. IEC 120 standard is followed for the dimension of the hardware fittings of the insulator. The conductor length is chosen such that it is 1.5 X the length of the insulator. The center phase carries peak value of the working voltage, whereas the outer two phases operates with half of the negative values of the center phase. Silicone rubber material is assigned for the sheds in ANSYS with permittivity of 4.3. Fiber reinforced plastic epoxy is assigned for the fiber rod with permittivity 5.0. The electric field value remains the same despite reducing the sheds. By reducing the shed number, the simulation time reduces drastically. The insulator is simulated with reduced sheds at high voltage side – 5 sheds and low voltage side – 2 sheds [10]. The dimensions of the insulator and the rings are given in Table 1.

Table 1

Dimensions of insulator and rings
Sectional length (mm)		4105
Dimensions of corona ring at H.V (mm)	r_c	25
	R_c	135
	h_c	160
Dimensions of grading ring at H.V (mm)	r_g	200
	R_g	250
	h_g	190
Dimensions of corona ring at L.V (mm)	r	25
	R	100
	H	3253

As mentioned earlier, the electric field is at its peak at three critical regions. As the input voltage is the peak voltage, the critical limits at peak values are,

At triple junction , electric field should be less than 0.64 kV/mm
Around corona and grading ring, electric field should be less than 2.97kV/mm.

Computation is performed for 400kV tension insulator at the three critical regions to find the maximum electric field. ANSYS (Finite Element Method) based software is utilized to compute the electric field distribution. Table 2 summarizes the maximum electric field at the critical regions. It can be inferred that, the electric field around the corona ring and the grading ring are within the critical limits, whereas the electric field at the triple junction region is greater than the stipulated critical limits. The corona ring and grading ring has reduced the electric field but not below the limits. Therefore it is understood that the dimension of the rings has a major effect in the influence of the electric field.

Table 2. Electric field values after computation.

Three regions	Region of interest	Maximum electric field (kV/mm)
Critical region 1	At triple junction region	0.7007
Critical region 2	Around Corona ring	1.189
Critical region 3	Around Grading ring	2.394

Figure 6 and Figure 7 depicts the electric field at critical region 1 and critical region 3.

Misplaced rings can increase the field intensity and leads the degradation of the insulating material. Hence, the electric fields should be kept in track while varying the dimension of the rings. The simulation is carried by varying one critical parameter at a time. Initially, the height of corona ring (H_c) is varied in steps while the other six parameters are kept constant. Next, the radius of corona ring is varied (R_c) in steps and the electric field at the three critical regions are analyzed. Similarly r_c, H_g, R_g, r_g, L_g are varied in steps [11].

The analyzed results are portrayed as graphs which are shown in Fig. 6. It is evident from the results that,

The electric field at the critical region 2 and 3 are within the critical limit (< 2.97 kV/mm) when the seven critical parameters are varied. Therefore, the electric field around the rings is not considered for further analyses.

The electric field exceeds the critical limit (> 0.64kV/mm) at critical region 1, when the seven critical parameters are varied. Hence, the electric field at the triple junction region is the region of interest which has to be minimized.

It is inferred from the above simulations that there are many combinations of critical parameters involved which change the electric field. Hence, the optimization process is indispensable to find the optimum dimensions. For optimization procedure, OPTIMTOOL is used in MATLAB.

Initially, a mathematical equation is derived between the maximum electric field and ring parameters using Non-linear curve fitting software. Eq. (1) denotes the mean electric field at the triple junction for 400kV tension insulator. E is the function of all seven critical parameters.

E (H_c,R_c,r_c,H_g,R_g,r_g,L_g) = 7.801 + 1.864 x 10^− 6 x₁^2.5-0.251 x₁^0.5+6.811 x 10^− 3x₂ − 4.89 x10^− 8 x₂³ − 2.859 x 10^− 2 x₃ + 5.55 x 10^− 6 x₃³ + 3.758 x 10^− 7 x₄² − 8.458 x 10^− 4x₄ − 2.851 x 10^− 9 x₅³ + 2.81 x 10^− 6x₅² − 8.77x10^− 4x₅ -1.871x10^− 6x₆²

The mathematical equation is used in MATLAB to predict the optimum dimensions by genetic algorithm (GA) optimization technique. The objective functions are mentioned below

Triple junction - min E(H_c,R_c,r_c,H_g,R_g,r_g,L_g) ≤ 0.64

Corona ring - min E(H_c,R_c,r_c,H_g,R_g,r_g,L_g) ≤ 2.97

Grading ring - min E(H_c,R_c,r_c,H_g,R_g,r_g,L_g) ≤ 2.97

The limits are increased in ascending order and stopped when the electric field values exceeds the limit. The finial upper limit and lower limit of the rings for 400 kV tension insulators are shown in Table 3.

Table 3

Lower limit and upper limit of the ring dimensions
Constraints
Lower Limit	Upper Limit
[50,110,5,0,200,100,200]	[250, 180, 45, 1000, 700, 400,1000]

The optimized dimensions are predicted in MATLAB and listed in Table 4. The electric field are observed to be less than the limits in the three region of interest.

Table 4

Ring dimensions predicted by Genetic algorithm optimization technique
H_c (mm)	R_c (mm)	r_c (mm)	H_g (mm)	R_g (mm)	r_g (mm)	L_g (mm)
137	143	39	181	403	293	810

The above mentioned predicted ring dimensions are simulated in ANSYS. The electric field obtained are observed to be within the critical limits and are compared with the predicted values. The percentage difference is found out to be -2.672 as shown in Table 5.
As the percentage difference is less than 3%, this methodology is a reliable prediction method and can be used for the prediction of the optimized dimensions rather than using the trial and error method which is time-consuming. The maximum electric field at critical region 1 with optimum ring dimensions is shown in Fig. 8.

Table 5

Difference in predicted and simulated electric field
Voltage ratings (kV)	Predicted electric field by (kV/mm)	Simulated electric field in ANSYS (kV/mm)	%Difference in electric field
Triple junction	0.6083	0.625	-2.672

The electric field along the polymer insulator is highly non-linear compared to ceramic types. A 400 kV tension insulator along with the tower, three phase conductors and hardware fittings are simulated using FEM based software ANSYS. The electric fields in three critical regions are higher than their critical limits and highly non-linear. Corona ring and grading rings mitigates the peak electric fields. The optimum dimensions of the rings are identified by the proposed methodology. The seven critical parameters are selected and varied one by one, and a mathematical equation is derived as the electric field is the function of the six critical parameters. Using this equation in OPTIMTOOL optimized dimensions are predicted. The obtained optimized dimensions are compared with the simulated values and it is found that the error is negligible. This technique can be used as a systematic approach to find out the optimized ring dimensions. The future scope of the work is to find a general algorithm for optimized dimensions of the rings for all voltage classes.

Ethics Approval and Consent to Participate:

No participation of humans takes place in this implementation process

Human and Animal Rights:

No violation of Human and Animal Rights is involved.

Funding:

No funding is involved in this work.

Conflict of Interest:

Conflict of Interest is not applicable in this work.

Authorship contributions:

There is no authorship contribution

Acknowledgement

There is no acknowledgement involved in this work

.Code Availability:

There is no code availability.

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No competing interests reported.

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Design optimization of corona ring and grading ring for a 400kV Tension insulator

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Version 1

Abstract

Figures

1. Introduction

2. Structural Parameters Of Tension Insulator And Tower Used For Study

3. Simulation Studies

4. Study Of Variation Of Electric Field In The Three Region Of Interest

5. Optimum Dimensions Of The Rings

6. Conclusion

Declarations

References

Additional Declarations

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