Optimum Cable Bonding with Pareto Optimal and Hybrid Neural Methods to Prevent High-Voltage Cable Insulation Faults in Distributed Generation Systems

Abstract

The high voltage, current and harmonic distortion in high-voltage cable metal sheaths cause cable insulation faults. The SSBLR (Sectional Solid Bonding with Inductance (L) and Resistance) method was designed as a new cable grounding method to prevent insulation faults. SSBLR was optimized using multi-objective optimization (MOP) with the prediction method (PM) to minimize these factors. The Pareto optimal method was used for MOP. The artificial neural network, hybrid artificial neural network and regression methods were used as the PM. When the artificial neural network–genetic algorithm hybrid method was used as the PM, and the genetic algorithm was used as the optimization method, the voltage and current were significantly reduced in the metal sheath of the cable.

1. Introduction

High-voltage cable faults are an important factor in terms of the sustainability of electrical energy. High-voltage cables consist of different layers. These layers are shown in Figure 1 [1]. The most important layer is the insulation layer because the insulation layer prevents short circuits by insulating the phase conductor.

However, an increase in the temperature of the insulation layer weakens the electric strength of the insulation material [2]. If the insulation material in the insulation layer weakens, it can be punctured by the electrical field. Hence, a cable insulation fault occurs [3,4,5].

The insulation layer is covered with a metal sheath as shown in Figure 1. If the current flows through the metal sheath, the temperature of the insulation layer increases. The metal sheath is grounded to restrict high electrical stress. However, when the metal parts of the cable are grounded the sheath current (SC) flows in these metal parts. Also, the SC can be up to 50% of line current. The unbalanced line current is one of the most important factors in the formation of the sheath current. The unbalanced current flows from the neutral points of the transformers to the ground and is called zero sequence current.

The cable configuration is another factor in the formation of the zero sequence current. Even if the line currents are balanced, the zero sequence current occurs in the metal parts of the cable owing to the cable configuration. For example, an 800 A sheath current occurs in the metal part of 30 km high-voltage cable in wind farm [6,7,8]. The cable configurations shown are trefoil and flat. These arrangements are shown in Figure 2.

In addition, when phase-to-ground short circuit faults or unbalanced line currents occur between the transformer substations, the zero sequence current flows between the neutral points of the transformers. If there is high-ground resistance between the transformer substations, the zero sequence current flows in the metal sheath of the cable instead of the ground. This situation is shown in Figure 3.

As can be seen from Figure 3, high-voltage cables are grounded at the line’s head and end. In this case, the zero sequence current flows through the metal sheath of the high-voltage cables, so the sheath voltage increases at the cable termination points. Thus, a potential tent occurs at the cable termination points. If the grounding resistances of the line head and the line end are different from each other, the potential tents in these regions are different from each other. Therefore, the high voltage is carried to the line head or line end as potential drift. This case causes a lot of energy loss on the high-voltage line, and it also causes an increase in temperature in the cable [9]. The cable temperature according to the SC is shown in

Table 1. SC and the cable temperature.

SC (A)	0	10	20	30	40
CT (°C)	43.1	54.4	74.2	119.0	184.1

.

In particular, if there are current harmonics in the sheath current, the temperature of the insulation layer increases excessively because of the high-frequency current harmonics [10]. Namely, one of the most important factors in the increase in the temperature of cable insulation is the current harmonics. In addition, harmonics cause resonance and a high voltage in the insulation layer [11].

The main reason for harmonic distortion in electrical networks is the use of power electronic elements. Renewable energy sources are the most important harmonic sources because power electronic elements are used for the conversion of DC/AC in renewable energy sources. Renewable energy sources can be photovoltaic power plants, wind power plants and biofuel facilities. Distributed generation plants (DGPs) are formed by using these facilities together. Distributed generation plants play an important role in the stability of electrical networks. However, distributed generation plants cause current and voltage harmonics [12,13,14,15,16,17].

In electricity networks, third harmonics, fifth harmonics, seventh harmonics and ninth harmonics occur due to DGPs and the total harmonic distortion is 20% [18]. Generally, fifth harmonics and seventh harmonics occur in wind farms. Third harmonics and ninth harmonic occur due to unbalanced loading [19,20,21,22,23]. In photovoltaic systems, third harmonics, seventh harmonics and ninth harmonics are dominant and the total harmonic distortion is 20% [24]. While fifth harmonics and seventh harmonics have a positive component character, third harmonics and ninth harmonics have a zero sequence character [25]. The DGP is connected to the electricity network using a high voltage power cable (HVPC). Thus, HVPC faults are an important issue for DGP.

PVC and XLPE insulation materials are generally used in HVPC. The endurance temperature of XLPE insulation material is 90 °C. The endurance temperature of PVC insulation material is 70 °C. As can be seen from Table 1, the insulation materials will be damaged at such a high SC. In addition, the SC and harmonic currents increase the cable temperature. And, current harmonics occur due to parallel resonance. Thus, an extremely high voltage occurs on the metal sheath owing to the parallel resonance.

Cable faults generally occur on the high voltage-cable accessory points [26]. The cable joints and cable terminations are the most important cable accessories. The single-point bonding, the solid bonding and the cross bonding methods are used in today’s practice for grounding of the high-voltage cable metallic parts to prevent cable insulation faults. However, since these grounding methods are not sufficient in systems owing to the high harmonic and zero sequence currents because these factors were not considered when these methods are designed. Therefore, cable faults cannot be sufficiently prevented in distributed generation systems [27].

In Section 2, the methods used in this article are explained. Section 2 consists of two parts. First, the SSBLR method developed for grounding high-voltage cables is explained. In the SSBLR method, the cable sheath was divided into pieces of certain lengths and grounded via inductances and resistors in order to reduce the current, voltage and harmonic distortion in the cable sheath. Second, the optimum parameter values of these elements were determined. The estimation methods and multi-objective optimization methods used for this purpose are explained. In Section 3, simulations of the proposed methods are performed. The obtained results were compared with the results of the methods used in the literature, and the conclusion section is presented in Section 4.

2. Materials and Methods

In this study, we aimed to minimize the voltage, current and harmonic distortion in the high-voltage cable metal sheath. In particular, the aim was to reduce the voltage on the metal sheath to below 70.71 V, which is the touch voltage limit value. In this study, Section 2 consists of two parts. First of all, a grounding method was introduced to prevent insulation failures in the high-voltage cable; then, the proposed grounding method was optimized with artificial intelligence methods.

2.1. The Suggested High-Voltage Cable Grounding Method

In this study, the SSBLR (Sectional Solid Bonding with Inductance (L) and Resistance) method is developed as a new high-voltage power cable grounding method to prevent the effects of current and voltage, harmonic current, and zero sequence current on the sheath. This cable grounding method is shown in Figure 4.

The minor part parameters are the minor part length (L), the grounding resistances (Rg₁ and Rg₂) and the grounding inductances (Lg₁ and Lg₂).

In the SSBLR method, the total cable length is called the major part, and the major part occurs due to the minor parts. Each minor part is grounded separately. The values of the circuit elements in the grounding method must be determined correctly. These determined values must prevent insulation faults in the high-voltage cable. In the SSBLR method, inductances Lg₁ and Lg₂ are used to suppress harmonics and prevent parallel resonance. The Rg₁ and Rg₂ resistors are used to prevent the potential drift.

Since these parameter values vary according to the line length, type of load and the condition of the ground transition resistance, the most suitable minor part parameters can be determined using optimization methods. There are three optimization problems involved in determining the optimum minor part parameters. These optimization problems are the minimization of current harmonic distortion (MHC), the minimization of the induced voltage (MV) the and minimization of the induced current (MC) on the metal parts of the cable. The minimizations of these parameters provide reductions in the cable temperature and the metal sheath voltage.

2.2. Optimization Process for the Suggested High-Voltage Cable Grounding Method

The optimization of the minor part parameters is a multi-objective optimization problem. The multi objective optimization methods are the Pareto optimal, the Scalarization method and the Vector Computational Genetic Algorithm [28,29,30]. In this study, the Pareto optimal method was used as the multi-objective optimization method. In the Pareto optimal method, there are dominant and non-dominant solutions. These solutions are shown on the Pareto front. This Pareto front is shown in Figure 5 [31]. In this study, many optimal solutions were obtained, and the most suitable solution was determined using the Pareto optimal method.

These solutions were classified as the dominant and non-dominant solutions in the Pareto optimal method. The most suitable solution was determined on the Pareto front. The minimum MV, MC and MHC values that were determined according to optimum minor part parameters (L, Rg₁, Rg₂, Lg₁ and Lg₂ values) were used for the determination of Pareto front.

When the optimization problems are solved, an objective function is determined. This objective function is expressed mathematically as an equation. In the equation, there are dependent and independent variables. The dependent variable is the parameter to be optimized.

$$a=\left(b+c\right)\ast d$$

(1)

For example, Equation (1) shows an objective function. In this objective function, a is the dependent variable. The b, c and d parameters are independent variables. Here, the optimum value of the parameter will be investigated according to the values of the b, c and d parameters. Then, the optimization process can be started by determining the limits of the independent variables in the objective function. Minimization or maximization operations are performed according to the purpose of the optimization.

In this study, the objective function was determined according to the current and voltage on the metal sheath on the high-voltage cable. There are many factors involved in the formation of the current and voltage on the sheath, but it is very difficult to determine them. In other words, expressing the objective function mathematically is a difficult process and its accuracy is low. Therefore, in this study, the prediction methods were used as the objective function. Firstly, different high-voltage cable lines were created and simulations of these lines were carried out using variable working conditions. These estimation methods were trained with the data obtained from the simulation results and the methods that provided the highest estimation accuracy were used as the objective function. Namely, the prediction methods were used as the objective function to solve the optimization problems in this study. The minor part parameter values were used as the input parameters, and the predicted MV, MC and MHC values were used as the output parameters.

2.3. Use of the Prediction Methods in the Optimization Process

The prediction methods used in this study were the artificial neural network, the hybrid artificial neural network and the regression method. These methods were used as the objective function because these methods are widely used in forecasting studies in electrical engineering. Artificial neural networks (ANN) are widely used in forecasting studies. A fundamental characteristic of ANNs is that they are based on human learning, and this process is modeled with a mathematical model. ANNs include an input layer, hidden layer and output layer, and these layers consist of neurons. Neurons are the basic elements in ANNs, and neurons work as a transfer function in Equation (2) [32,33,34,35,36,37,38].

$$y_i=f_i({\displaystyle \sum _{j=1}^n{w}_{ij}\times x_j}+b_i)$$

(2)

where x_j is the input, w_ij is weight, b_i is bias, f_i is the transfer function, and y_i is the output of the neuron. Training and forecasting errors were calculated using the mean square error (MSE) method, and the equation for MSE is shown in Equation (3).

$$E(t)={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n{(p(i)-o(i))}^2}$$

(3)

where E(t) is the forecasting error at tth iteration, p(i) is the desired value for the ith output and o(i) is the real value for ith output. The weights in ANN must be updated to reduce the training error. The weights in a classic ANN are updated by Equation (4).

$$w_i\left(t+1\right)=w_i\left(t\right)+\Delta w_i\left(t\right)$$

(4)

Specifically, in the hybrid artificial neural network method, the weights of the ANN are updated by optimization methods instead of Equation (4). The hybrid artificial neural network algorithm is shown in Figure 6 [39]. The prediction methods were trained with the training data to predict the MV, MC and MHC values. The training data were the input and output matrices.

In this study, there are three optimization problems, and each prediction method was trained for each optimization problem. Namely, the prediction methods were trained for the prediction of MV, MC and MHC separately. Thus, there are three output matrices for MV, MC and MHC in the training of the prediction method. In addition, the input matrix is the same for each optimization problem.

The input matrix was generated with vectors, and each vector was obtained from the minor part length (L), grounding resistances (Rg₁ and Rg₂), grounding inductances (Lg₁ and Lg₂), three-phase line currents (Ia, Ib, Ic), the voltage harmonic distortion in each phase (HDVa, HDVb, HDVc) and the current harmonic distortion in each phase (HDCa, HDCb, HDCc). The input matrix is shown in Figure 7, and the output matrices are shown in Figure 8.

When the prediction method was trained for MHC prediction, the input matrix and output matrix 1 were used, as shown in Figure 8. When the prediction method was trained for the MV prediction, the input matrix and output matrix 2 were used. When the prediction method was trained for the MC prediction, the input matrix and output matrix 3 were used.

The optimum minor part parameters were primarily determined according to the most suitable predicted MV value. In the MV prediction process, the input matrix and output matrix 2 were used for the training of the prediction methods. After the training process for the prediction methods was completed, the optimum minor part parameters were determined according to the most suitable predicted MV value. Thus, a new input matrix was necessary for the minor part optimization. The new input matrix was called the optimization input matrix, and the generation process of the optimization input matrix is shown in Figure 9.

The input matrix consists of the vectors. When the input matrix vectors were generated, the optimum minor part parameters matrix vectors and the line constant vector were used. In other words, the vectors in the input matrix were formed through the combination of these vectors. When the optimum minor part parameter values were determined, the optimum minor part parameter matrix vectors were updated using the optimization methods. After the input matrix was generated, the MV values of the vectors were predicted according to Figure 10.

2.4. Optimum Minor Part Detection Process for the Suggested Method

The optimum minor parameters were determined using the optimization algorithm shown in Figure 11. In this study, the most suitable MV was determined according to the convergence, and the convergence was calculated with the touch voltage limit and the predicted MV of the vector. The touch voltage limit for a person is 70.71 V (peak) according to the IEC 479-1 standard [40]. The convergence shows a vector quality, and convergence is calculated using Equation (5) in the optimization algorithm. The most suitable predicted MV value provides the minimum convergence.

The convergence = 70.71 V − the predicted MV

(5)

The optimum minor part parameter values were determined with the multi-objective optimization method, and the Pareto optimal method was used to determine the most dominant solution in this study. First, the optimum minor part parameter values were determined using the MV optimization algorithm shown in Figure 11. These optimum minor part parameter values should minimize the MC and MHC values as well. The optimum minor parameter values provide this condition, which is the most dominant solution in the Pareto optimal method. The most dominant solution is determined using the Pareto front, and many optimum minor part parameter values are needed to create the Pareto front. Thus, many optimum minor part parameters were generated according to the most suitable MV values for the Pareto front.

The Pareto points and Pareto fronts are shown in Figure 12. The Pareto points are made of the many optimum minor part parameter values determined with the MV algorithm. In this study, an MHC and an MC value were predicted for each Pareto point. The Pareto points were then ranked According to these predicted MC and MHC values, and Pareto front was formed. The most dominant Pareto points were on the Pareto front. Then, the most dominant one was selected from among these dominant points. The most dominant Pareto point was the point that minimized the MC and MHC values the best.

Before the MC and MHC values were predicted, the prediction method was trained. An input matrix was necessary for predicting the MC and MHC values. This input matrix was the input matrix used for training the MV.

The input matrix and output matrix 1 were used when the prediction method was trained for the prediction of the MHC value. The input matrix and output matrix 3 were used when the prediction method was trained for the prediction of the MC. After the prediction methods were trained for predicting the MC and MHC, the MC and MHC values were predicted for each of the optimum minor part parameter vectors (the Pareto point) determined by the MV algorithm.

A new input matrix was necessary for the prediction of the MC and MHC values. This new input matrix was generated using the many optimum minor part parameter vectors determined with the MV algorithm and the line constant vector. This new input matrix is shown in Figure 13. The prediction processes for the MC and MHC are shown in Figure 14 and Figure 15.

3. Results and Discussion

In this study, different prediction methods were used for the objective function, and different optimization methods were used for the multi objective optimization. Therefore, many Pareto points and Pareto fronts were obtained with the multi objective optimization methods, and the most dominant Pareto points were determined using the Pareto front. Simulations of these dominant Pareto points were performed to determine the most dominant Pareto point. The high-voltage line constants were determined according to working conditions of the real high-voltage cable lines. The length of the high-voltage cable line was 5 km, and the other line constant is shown in

Table 2. Current, voltage and harmonic distortion rates of a high-voltage line.

	Line Current (A)	Line Voltage (kV)	THDI (%)	THDV (%)
L1	485	24.7	3.97	4.20
L2	485	24.7	5.44	5.30
L3	455	24.7	3.18	3.04

.

In the literature, the single-point bonding, solid bonding and cross bonding methods are indicated for use according to IEEE 575-1988 standard [41]. These methods are compared with SSBLR method in

Table 3. Comparison of grounding methods.

The Bonding Method	The Sheath Current	The Sheath Voltage	Harmonic Distortion
Single point bonding	not taken into account	above touch voltage limit	not taken into account
Solid bonding	taken into account	under touch voltage limit	not taken into account
Cross Bonding	taken into account	above touch voltage limit	not taken into account
SSBLR	taken into account	under touch voltage limit	taken into account

.

The most important factor is the MV, and the MV value of solid bonding is less than that of single-point bonding and cross bonding. Thus, the bonding of a high-voltage cable line was performed using solid bonding to compare the suggested optimized SSBLR method. The solid bonding shown in Figure 16 was used for the same high-voltage line, and the result of the solid bonding is shown in

Table 4. The results of the solid bonding method.

The Head of Line Cable Terminations Values				The End of Line Cable Terminations Values
Parameters	Phases			Phases
	L1	L2	L3	L1	L2	L3
MV (V)	798	822	647	786	793	630
MC (A)	181	179	173	176	175	169
MHC (%)	5.87	4.75	3.47	5.89	5.01	3.45

.

In Table 4, the MV, MC and MHC increase significantly at the cable termination points. Therefore, the cable temperature increases significantly according to the data in Table 1. Thus, cable insulation faults and electroshock are observed when solid bonding is used as the bonding method for long high-voltage lines in distributed generation plants.

3.1. Training Process for the Prediction Methods in Optimization of the Suggested Method Subsection

The data that were used in the optimization of the SSBLR method were obtained from PSCAD/EMTDC simulation program v.4.6. Fifty-four different high voltage power cable lines were simulated, and the MC, MV and MHC values of these lines were measured using PSCAD/EMTDC. The scenarios created in high-voltage underground cable simulations were created by using different values of L, Rg1, Rg2, Lg1 and Lg2. According to these scenarios, the Ia, Ib, Ic, HDVa, HDVb, HDVc, HDCa, HDCb, HDCc values were measured. These data were used in the training processes for the prediction methods. The input matrix was a 54 × 14 matrix, and the output matrices were 54 × 1 matrices for MV, MC and MHC. The output matrices were the MV, MC and MHC values measured using PSCAD/EMTDC. The prediction methods were primarily trained for the MV algorithm, and the trained prediction methods with the minimum training errors were used to determine the optimum minor part parameters in the MV algorithm. Three types of prediction methods were used to determine the most suitable prediction method. These methods were artificial neural networks (ANNs), hybrid artificial neural networks (H-ANNs) and regression methods. Feed-forward back propagation (FFBP), the Elman Neural Network (ENN) and Narx were used in the ANN network structure. The training error observed for FFBP was 344.1, the training error observed for ENN was 76.76 and the training error observed for Narx was 265.65.

In H-ANN, the optimization methods were used to update the weights of the ANN. These optimization methods were the genetic algorithm (GA), particle swarm optimization (PSO) and the gravitational search algorithm (GSA). In the H-GA method, the weights of ANN were updated using GA. In the H-PSO method, the weights of ANN were updated using PSO. In the H-GSA method, the weights of ANN were updated using GSA. The H-GA, H-PSO and H-GSA methods have been labelled as hybrid ANN methods, and these methods were used in the prediction processes. The initial population in these hybrid ANN methods was a 54 × 14 matrix. MSE was used for the construction of a fitness function for these methods. This algorithm is shown in Figure 6. The number of iterations for the optimization method was set to 100, and the number of populations was set to 50. For PSO, the c1 coefficient was set to 2, and the c2 coefficient to 2. In the GA method, the crossover rate was 0.7, and the mutation rate was 0.01. The training error observed for H-GA was 1.769, the training error observed for H-PSO was 3.449 and the training error observed for H-GSA was 2.36.

Exponential gaussian regression (EGR), squared exponential gaussian regression (SEGR) and matern 5/2 gaussian regression (MGR) were used for the regression, and the input matrix for the training process was a 54 × 14 matrix. The training error observed for EGR was 6.66, the training error observed for SEGR was 5.05 and the training error observed for MGR was 4.60.

The prediction methods were selected according to minimum training error. ENN was selected as the first prediction method from the ANN group of prediction methods. H-GA was selected as the second prediction method from the H-ANN group of prediction methods, and MGR was selected as the third prediction method from the regression group of prediction methods. In addition, the genetic algorithm (GA), particle swarm optimization (PSO) and gravitational search algorithm methods were used as the optimization methods in the MV algorithm.

3.2. Determination of the Optimum Grounding Parameters with the Pareto Optimal for Different Cases

In this study, nine different cases were evaluated separately to determine the optimum minor part parameter values using the Pareto optimal method. In each case, a different prediction method was used as the objective function, and a different optimization method was used for the optimization process in the MV algorithm. When the MV algorithm was performed once, one the optimum minor part parameter values vector was obtained. Namely, one Pareto point was obtained. Thus, the MV algorithm was performed many times to obtain many Pareto points, and Pareto front was formed of these Pareto points. Then, the dominant Pareto points were obtained separately using the Pareto optimal method for the nine cases. The determined dominant Pareto points were simulated, and the most dominant Pareto point in each of the nine cases was determined according to simulation results. The most dominant Pareto point was accepted as the most optimum minor part parameter value.

-

Case 1

When ENN was used as the objective function, and GA was used as the optimization method in the MV algorithm, the optimum minor part parameter values were determined. Afterwards, the optimum minor part parameter values were determined, the MC and MHC values were predicted for each of the optimum minor part parameter vectors and the Pareto points shown in Figure 14 were observed. Each Pareto point represents an optimum minor part parameter value. The red points shown in Figure 17 present the Pareto front, and the dominant Pareto points on the Pareto front are presented in

Table 5. The optimum minor part parameter values of the dominant Pareto points on the Pareto front for Case 1.

Point	L (m)	Rg1 (ohm)	Rg2 (ohm)	Lg1 (H)	Lg2 (H)
A	198	12.49	9	0.0086	0.0014
B	201	22	4	0.0084	0.0051
C	184	23.16	19	0.0073	0.0048
D	188	6	23.29	0.0071	0.0059
E	209	12.2	4.21	0.00325	0.0014
F	204	25	4	0.0043	0.0038
G	202	10	12	0.0058	0.0051
H	183	11	19	0.0081	0.0082

.

-

Case 2

When ENN was used as the objective function, and PSO was used as the optimization method in the MV algorithm, the optimum minor part parameter values were determined. Afterwards, the optimum minor part parameter values were determined and the MC and MHC values were predicted for each of the optimum minor part parameter vectors. The Pareto points are shown in Figure 18, and the dominant Pareto points on the Pareto front are presented in

Table 6. The optimum minor part parameter values of the dominant Pareto points on the Pareto front for Case 2.

Point	L (m)	Rg1 (ohm)	Rg2 (ohm)	Lg1 (H)	Lg2 (H)
A	234	11.8	9.66	0.0092	0.0062
B	224	7.32	1.66	0.0099	0.0078
C	243	13.46	23.08	0.0091	0.0071
D	218	14.46	3.27	0.0088	0.00751

.

-

Case 3

When ENN was used as the objective function, and GSA was used as the optimization method in the MV algorithm, the optimum minor part parameter values were determined. Afterwards, the optimum minor part parameter values were determined and the MC and MHC values were predicted for each of the optimum minor part parameter vectors. The Pareto points are shown in Figure 19, and the dominant Pareto points on the Pareto front are presented in

Table 7. The optimum minor part parameter values of the dominant Pareto points on the Pareto front for Case 3.

Label	L (m)	Rg1 (ohm)	Rg2 (ohm)	Lg1 (H)	Lg2(H)
A	201	21.5	18.48	0.0088	0.0029
B	206	11.77	3.73	0.007	0.0026
C	202	18.71	15.36	0.0082	0.0052
D	201	11.33	12.29	0.0083	0.0057
E	207	4.31	10.03	0.0059	0.0039
F	182	14.81	9.23	0.011	0.0102
G	200	14.18	12.18	0.0035	0.0018

.

-

Case 4

When MGR was used as the objective function, and GA was used as the optimization method in the MV algorithm, the optimum minor part parameter values were determined. Afterwards, the optimum minor part parameter values were determined and the MC and MHC values were predicted for each of the optimum minor part parameter vectors. The Pareto points are shown in Figure 20, and the dominant Pareto points on the Pareto front are presented in

Table 8. The optimum minor part parameter values of the dominant Pareto points on the Pareto front for Case 4.

Point	L (m)	Rg1 (ohm)	Rg2 (ohm)	Lg1 (H)	Lg2 (H)
A	194	7.25	9.31	0.0059	0.0096
B	211	7.94	12	0.0086	0.0055

.

-

Case 5

When MGR was used as the objective function, and PSO was used as the optimization method in the MV algorithm, the optimum minor part parameter values were determined. Afterwards, the optimum minor part parameter values were determined and the MC and MHC values were predicted for each of the optimum minor part parameter vectors, and Pareto points are shown in Figure 21 and the dominant Pareto points on the Pareto front are presented in

Table 9. The optimum minor part parameter values of dominant the Pareto points on the Pareto front for Case 5.

Point	L (m)	Rg1 (ohm)	Rg2 (ohm)	Lg1 (H)	Lg2 (H)
A	213	3.55	13.36	0.0072	0.0095
B	219	13.62	3.28	0.0048	0.0096

.

-

Case 6

When MGR was used as the objective function, and GSA was used as the optimization method in the MV algorithm, the optimum minor part parameter values were determined. Afterwards, the optimum minor part parameter values were determined and the MC and MHC values were predicted for each of the optimum minor part parameter vectors. The Pareto points are shown in Figure 22 and the dominant Pareto points on Pareto front are presented in

Table 10. The optimum minor part parameter values of the dominant Pareto points on the Pareto front for Case 6.

Label	L (m)	Rg1 (ohm)	Rg2 (ohm)	Lg1 (H)	Lg2 (H)
A	211	10.64	10.10	0.0073	0.0067
B	207	6.43	12.39	0.0046	0.0070
C	202	6.49	2.75	0.0044	0.0016

.

-

Case 7

When H-GA was used as the objective function, and GA was used as the optimization method in the MV algorithm, the optimum minor part parameter values were determined. After, the optimum minor part parameter values were determined, the MC and MHC values were predicted for each of the optimum minor part parameter vectors, and Pareto points were shown in Figure 23, and the dominant Pareto points on Pareto front were presented in

Table 11. The optimum minor part parameter values of the dominant Pareto points on the Pareto front for Case 7.

Point	L (m)	Rg1 (ohm)	Rg2 (ohm)	Lg1 (H)	Lg2 (H)
A	204	2.10959	17.65897	0.00904	0.00720
B	206	10.68774	14	0.00936	0.00816
C	208	21.67438	9.763249	0.00113	0.00708

.

-

Case 8

When H-GA was used as the objective function, and PSO was used as the optimization method in the MV algorithm, the optimum minor part parameter values were determined. Afterwards, the optimum minor part parameter values were determined and the MC and MHC values were predicted for each of the optimum minor part parameter vectors. The Pareto points are shown in Figure 24, and the dominant Pareto points on the Pareto front are presented in

Table 12. The optimum minor part parameter values of dominant Pareto points on the Pareto front for Case 8.

Point	L (m)	Rg1 (ohm)	Rg2 (ohm)	Lg1 (H)	Lg2 (H)
A	212	14.77	8.63	0.0051	0.0033
B	219	23.01	16.03	0.0063	0.0072
C	226	17.05	5.14	0.0015	0.0084
D	236	24.21	13.37	0.0095	0.0025
E	249	21.90	6.23	0.0086	0.0030

.

-

Case 9

When H-GA was used as the objective function, and GSA was used as the optimization method in the MV algorithm, the optimum minor part parameter values were determined. Afterwards, the optimum minor part parameter values were determined and the MC and MHC values were predicted for each of the optimum minor part parameter vectors. The Pareto points are shown in Figure 25, and the dominant Pareto points on the Pareto front are presented in

Table 13. The optimum minor part parameter values of the dominant Pareto points on the Pareto front for Case 9.

Point	L (m)	Rg1 (ohm)	Rg2 (ohm)	Lg1 (H)	Lg2 (H)
A	175	5.12	14.20	0.0093	0.0095
B	185	9.80	10.85	0.0055	0.0038
C	189	9.79	10.85	0.0054	0.0040
D	191	14.29	11.47	0.0039	0.0057
E	192	14.10	11.43	0.0040	0.0058
F	191	11.44	8.17	0.0059	0.0073

.

4. Simulation Results for the Nine Different Cases

The optimum minor part parameters on the Pareto front were simulated in PSCAD/EMTDC, and the MV, MC and MHC values of these vectors were measured to determine the dominant Pareto point for each case.

• Simulation results for Case 1

The simulation results for the Pareto points on the Pareto front are listed in

Table 14. The simulation results for the Pareto front solution in Case 1.

Values	A		B		C		D		E		F		G		H
	HL	EL	HL	EL	HL	EL	HL	EL	HL	EL	HL	EL	HL	EL	HL	EL
MV1 (V)	91	16	68	42	59	40	55	48	74	32	58	51	43	40	36	40
MV2 (V)	96	18	73	44	63	43	57	52	79	34	62	53	45	42	38	42
MV3 (V)	77	10	54	36	49	30	48	36	59	26	44	45	33	29	29	28
MC1 (A)	33	33	25	25	25	26	24	25	69	69	41	41	22	23	14	14
MC2 (A)	32	32	24	24	24	25	23	24	66	67	39	40	21	22	13	13
MC3 (A)	30	30	23	23	24	24	23	23	63	63	38	38	20	21	13	13
MHC1 (%)	2.80	2.87	2.82	2.90	2.88	2.95	2.81	2.89	2.70	2.73	2.77	2.82	2.50	2.61	2.51	2.97
MHCI2 (%)	3.54	3.57	3.46	3.50	3.40	3.44	3.45	3.50	3.84	3.85	3.60	3.63	3.63	3.69	3.46	3.55
MHCI3 (%)	5.27	5.31	5.27	5.33	5.29	5.34	5.23	5.29	5.45	5.47	5.27	5.30	5.01	5.08	4.98	5.08

. The MV, MC and MHC values were measured at the head (HL) and end of line (EL) points in PSCAD/EMTDC, where 1, 2 and 3 present each phase (L1, L2 and L3) in high-voltage cable line. The dominant Pareto point was determined according to the MV, MC and MHC values. First, the MV values of the Pareto points were compared with the touch voltage limit, and the Pareto points whose MV values were lower than the touch voltage limit value were selected. These vectors were determined as the C, D, F, G and H vectors, and then the MC and MHC values of these Pareto points were compared with each other. The MHC values of these vectors are near each other, and the lowest MC value belongs to the H Pareto point. Thus, the dominant Pareto point was determined as the H point in Case 1.

• Simulation results for Case 2

The simulation results for the Pareto points on the Pareto front was listed in

Table 15. The simulation results for the Pareto front solution in Case 2.

Values	A		B		C		D
	HL	EL	HL	EL	HL	EL	HL	EL
MV1 (V)	74	52	74	59	73	59	65	56
MV2 (V)	79	56	80	63	76	65	69	59
MV3 (V)	62	42	58	51	62	47	50	48
MC1 (A)	25	26	23	24	25	25	23	23
MC2 (A)	24	25	22	22	24	24	22	22
MC3 (A)	23	24	21	22	23	24	21	21
MHC1 (%)	2.85	2.94	2.80	2.89	2.81	2.91	2.78	2.87
MHC2 (%)	3.42	3.48	3.40	3.47	3.45	3.50	3.39	3.45
MHC3 (%)	5.38	5.44	5.24	5.32	5.23	5.30	5.15	5.22

. The MV values of the Pareto points were compared with the touch voltage limit, and only the MV value of the D Pareto point was lower than the touch voltage limit value. Thus, the dominant Pareto point is the D vector in Case 2.

• Simulation results for Case 3

The simulation results for the Pareto points on the Pareto front are listed in

Table 16. The simulation results for the Pareto front solution in Case 3.

Values	A		B		C		D		E		F		G
	HL	EL	HL	EL	HL	EL	HL	EL	HL	EL	HL	EL	HL	EL
MV1 (V)	81	28	80	30	66	44	64	45	66	45	52	49	51	27
MV2 (V)	86	31	85	32	70	47	68	49	69	50	55	53	54	29
MV3 (V)	68	21	66	25	55	35	54	36	57	34	42	41	39	19
MC1 (A)	29	29	36	36	25	26	24	24	35	35	15	15	43	44
MC2 (A)	28	28	34	34	24	25	23	23	33	34	12	14	42	42
MC3 (A)	27	27	33	33	23	24	22	23	32	33	14	14	39	39
MHC1 (%)	2.81	2.89	2.79	2.85	2.81	2.89	2.81	2.90	2.78	2.84	2.82	2.94	2.46	2.52
MHC2 (%)	3.50	3.54	3.55	3.59	3.46	3.51	3.45	3.50	3.54	3.58	3.44	3.42	3.88	3.91
MHC3 (%)	5.27	5.32	5.28	5.32	5.24	5.30	5.27	5.33	5.27	5.31	5.20	5.29	5.06	5.10

. First, the MV values of Pareto points were compared with the touch voltage limit, and the Pareto points whose the MV value were lower than the touch voltage limit value were the D, E, F and G Pareto points then the MC and MHC values of these Pareto points were compared among each other. The MHC values of these vectors are near each other, and the lowest MC value belongs to the F Pareto point. Thus, the dominant Pareto point was determined as the F point in Case 3.

• Simulation results for Case 4

The simulation results for the Pareto points on the Pareto front are listed in

Table 17. The simulation results for the Pareto front solution in Case 4.

Values	A		B
	HL	EL	HL	EL
MV1 (V)	40	66	69	46
MV2 (V)	42	71	72	50
MV3 (V)	32	55	59	36
MC1 (A)	21	21	25	26
MC2 (A)	20	20	24	24
MC3 (A)	20	20	23	224
MHC1 (%)	2.8	2.89	2.80	2.88
MHC2 (%)	3.41	3.46	3.43	3.48
MHC3 (%)	5.23	5.30	5.22	5.28

. First, the MV values of Pareto points were compared with the touch voltage limit value, and there were no Pareto points whose MV value was lower than the touch voltage limit value. Thus, there is no suitable = Pareto point in Case4.

• Simulation results for Case 5

The simulation results for the Pareto points on the Pareto front are listed in

Table 18. The simulation results for the Pareto front solution in Case 5.

Values	A		B
	HL	EL	HL	EL
MV1	49	68	41	80
MV2	51	74	44	84
MV3	42	53	28	70
MC1	22	22	25	26
MC2	20	21	24	24
MC3	20	20	23	24
MHC1	2.80	2.89	2.75	2.84
MHC2	3.41	3.46	3.41	3.46
MHC3	5.24	5.31	5.14	5.20

. First, the MV values of Pareto points were compared with the touch voltage limit value, and there were no Pareto points whose MV value was lower than the touch voltage limit value. Thus, there is no suitable Pareto point in Case 5.

• Simulation results for Case 6

The simulation results for the Pareto point on the Pareto front are listed in

Table 19. The simulation results for the Pareto front solution in Case 6.

Values	A		B		D
	HL	EL	HL	EL	HL	EL
MV1 (V)	59	56	44	68	77	28
MV2 (V)	62	60	47	73	82	30
MV3 (V)	48	46	37	55	63	23
MC1 (A)	25	25	29	30	54	54
MC2 (A)	24	24	28	28	52	52
MC3 (A)	23	24	27	27	50	50
MHC1 (%)	2.79	2.87	2.79	2.86	2.73	2.77
MHC2 (%)	3.43	3.48	3.49	3.52	3.71	3.73
MHC3 (%)	5.21	5.27	5.25	5.30	5.30	5.33

. The MV values of the Pareto points were compared with the touch voltage limit, and only the MV value of the D Pareto point was lower than the touch voltage limit value. Thus, the dominant Pareto point is the A vector in Case 6.

• Simulation results for Case 7

The simulation results of the Pareto points on the Pareto front are listed in

Table 20. The simulation results for the Pareto front solution in Case 7.

Values	A		B		C
	HL	EL	HL	EL	HL	EL
MV1 (V)	45	40	44	42	17	94
MV2 (V)	46	43	43	47	19	99
MV3 (V)	38	25	32	33	7	83
MC1 (A)	15	16	14	14	41	42
MC2 (A)	15	15	13	13	40	40
MC3 (A)	14	14	12	13	38	38
MHC1 (%)	2.50	2.67	2.50	2.67	3.06	2.16
MHC2 (%)	3.53	3.62	3.44	3.55	3.77	3.81
MHC3 (%)	5.01	5.11	4.98	5.09	4.52	4.58

. First, the MV values of Pareto points were compared with the touch voltage limit, and the Pareto points whose MV values were lower than the touch voltage limit value were the A, B, and C Pareto points, and then the MC and MHC values of these Pareto points were compared with each other. The lowest MC and MHC value belongs to the B Pareto point. Thus, the dominant Pareto point was determined as the B point in Case 7.

• Simulation results for Case 8

The simulation results for the Pareto points on the Pareto front are listed in

Table 21. The simulation results for the Pareto front solution in Case 8.

Values	A		B		C		D		E
	HL	EL	HL	EL	HL	EL	HL	EL	HL	EL
MV1 (V)	51	34	55	64	21	101	99	27	99	35
MV2 (V)	54	36	59	68	23	106	106	30	105	38
MV3 (V)	38	26	44	54	9	89	84	21	80	29
MC1 (A)	20	30	27	27	37	38	33	33	36	36
MC2 (A)	29	29	26	26	36	36	31	32	34	34
MC3 (A)	27	27	25	25	34	35	30	30	33	33
MHC1 (%)	2.50	2.58	2.07	2.16	2.75	2.81	2.80	2.88	2.79	2.86
MHC2 (%)	3.71	3.76	3.62	3.69	3.55	3.58	3.51	3.55	3.55	3.59
MHC3 (%)	5.00	5.06	4.41	4.51	5.27	5.32	5.22	5.28	5.27	5.32

. First, the MV values of Pareto points were compared with the touch voltage limit, and the Pareto points whose MV values were lower than the touch voltage limit value were the A and B Pareto points, and then the MC and MHC values of these Pareto points were compared with each other. The lowest MC and MHC value belongs to the B Pareto point. Thus, the dominant Pareto point was determined as the B point in Case 8.

• Simulation results for Case 9

The simulation results for the Pareto points on the Pareto front are listed in

Table 22. The simulation results for the Pareto front solution in Case 9.

Values	A		B		C		D		E		F
	HL	EL	HL	EL	HL	EL	HL	EL	HL	EL	HL	EL
MV1 (V)	47	50	58	42	43	34	31	47	42	62	47	58
MV2 (V)	49	55	62	45	45	36	33	49	45	65	49	62
MV3 (V)	40	39	49	33	34	24	22	36	31	52	34	49
MC1 (A)	16	16	33	33	24	25	24	24	33	33	24	25
MC2 (A)	15	15	31	32	23	20	23	23	31	31	23	24
MC3 (A)	15	15	31	31	22	22	22	22	30	30	23	23
MHC1 (%)	2.8	7.2	2.8	2.8	2.5	2.5	2.5	2.6	2.8	2.8	2.8	2.9
MHC2 (%)	3.3	5.3	3.5	3.5	3.6	3.5	3.6	3.7	3.5	3.5	3.4	3.5
MHC3 (%)	5.2	5.8	5.2	5.3	5.0	5.0	5.0	5.1	5.3	5.3	5.2	5.3

. First, the MV values of Pareto points were compared with the touch voltage limit, and the Pareto points whose the MV values were lower than the touch voltage limit value were the A, B, C, D, E and F Pareto points, and then the MC and MHC values of these Pareto points were compared with each other. The lowest MC and MHC value belongs to the B Pareto point. Thus, the dominant Pareto point was determined as the A point in Case 9.

5. Discussion

The dominant Pareto points (DPPs) determined for each case are listed in

Table 23. The dominant Pareto points in each of the cases.

The Case	DPP	PM-OM	L (m)	Rg1 (ohm)	Rg2 (ohm)	Lg1 (H)	Lg2 (H)
The Case 1	H	ENN, GA	183	11	19	0.0081	0.0082
The Case 2	D	ENN, PSO	218	14.46	3.27	0.0088	0.00751
The Case 3	F	ENN, GSA	182	14.81	9.23	0.011	0.0102
The Case 6	A	MGR, GSA	211	10.64	10.10	0.0073	0.0067
The Case 7	B	H-GA, GA	206	10.68774	14	0.00936	0.00816
The Case 8	B	H-GA, PSO	219	23.01	16.03	0.0063	0.0072
The Case 9	A	H-GA, GSA	175	5.12	14.20	0.0093	0.0095

. In Table 23, PM presents the prediction method, and OM presents the optimization method for each case. Additionally, the simulation results for the dominant vectors determined are also shown in

Table 24. The simulation results for the dominant Pareto points.

Values	ENN, GA		ENN, PSO		ENN, GSA		MGR, GSA		H-GA, GA		H-GA, PSO		H-GA, GSA
	HL	EL	HL	EL	HL	EL	HL	EL	HL	EL	HL	EL	HL	EL
MV1 (V)	36	40	65	56	52	49	59	56	44	42	55	64	47	50
MV2 (V)	38	42	69	59	55	53	62	60	43	47	59	68	49	55
MV3 (V)	29	28	50	48	42	41	48	46	32	33	44	54	40	39
MC1 (A)	14	14	23	23	15	15	25	25	14	14	27	27	16	16
MC2 (A)	13	13	22	22	12	14	24	24	13	13	26	26	15	15
MC3 (A)	13	13	21	21	14	14	23	24	12	13	25	25	15	15
MHC1 (%)	2.51	2.97	2.78	2.87	2.82	2.94	2.79	2.87	2.50	2.67	2.07	2.16	2.81	7.17
MHC2 (%)	3.46	3.55	3.39	3.45	3.44	3.42	3.43	3.48	3.44	3.55	3.62	3.69	3.37	5.30
MHC3 (%)	4.98	5.08	5.15	5.22	5.20	5.29	5.21	5.27	4.98	5.09	4.41	4.51	5.22	5.83

.

The simulation results for the dominant Pareto points were compared to determine the most dominant Pareto point. The simulation results for the dominant Pareto points are listed in Table 24. The MV values of all of the dominant Pareto points were lower than the touch voltage limit value. Electrical safety was tested using the SSBLR method on a high-voltage cable.

The endurance temperature of XLPE insulation material is 90 °C. The cable temperature is 74 °C when the sheath current is 20A, as shown in Table 1. In addition, the cable temperature is 119 °C when the sheath current is 30A. If the MC current is lower than 20 A, good results can be obtained. In Table 24, the MC values of (ENN-GA), (ENN-GSA), (H-GA-GA) and (H-GA, GSA) are lower than 20 A. Thus, these methods are more dominant than other methods in terms of the MC.

If the minor part length is longer, the total number of minor parts is lower. Hence, the SSBLR method is an economic method for the cable grounding. When the minor part lengths of (ENN-GA), (ENN-GSA), (H-GA, GA) and (H-GA, GSA) were compared, the minor part length of (H-GA-GA) was longer than that of the other methods. Namely, the most dominant solution was obtained the using (H-GA, GA) method, as is shown in Table 23.

In addition, the oldest and most common cable grounding method is the solid bonding method. With this method, the MV of the high-voltage cable was measured at 630 V, and MC was measured at 173 A in this study. These values are very high. In addition, no precautions were taken to suppress the harmonics in this method.

The other methods used in the literature are the OSSB and MSSB methods. In the literature, the optimization of these grounding methods has been carried out with single-objective optimization methods. In these grounding methods, the sheath voltages were measured at 62.4 V, 66.9 V and 66.67 V [39,42,43]. In this study, the proposed cable grounding method was optimized using the multi-objective optimization method, and the MV value was measured at 47 V. This value is lower than those of the other grounding methods.

6. Conclusions

High-voltage cable insulation faults occur due to high sheath voltages, high harmonic distortion and high sheath currents. The methods in the literature are not sufficient to prevent high-voltage cable faults. Hence, the SSBLR method was optimized using the multi-objective optimization method, and the most dominant solution obtained in the solutions obtained using the Pareto optimal method. The sheath voltage was measured at 47 V, and the sheath current maximum was measured at 14 A. According to these results, the sheath voltage remained below the touch voltage, and the sheath current remained below the current value that would cause a dangerous temperature in the high-voltage cable.

The cost of the SSBLR method is higher than that of other methods. However, if harmonic distortion and unbalanced loads are intense, the values of the zero sequence currents are also large. In this case, the value of the sheath current will increase, and a high-voltage cable fault will occur due to overheating. This high cost is not important in places where energy continuity is important, such as hospitals, industrial facilities, transportation and communication facilities. The SSBLR is a method developed exactly for these types of facilities.