The Effect of Cable Aging on Surge Arresters Designed by Genetic Algorithm

Abstract

The degradation of communication cable insulators reduces the availability of the train control system and is caused by the degrading of data transmission line parameters. Due to extremely varying environmental conditions in the railway industry, the effect of data transmission line degradation on the critical parameters of the surge arrester that is used in wayside equipment is not known. The surge arrester module is very important in the railway industry, as it enables the protection of sensitive parts of wayside equipment, especially communication interfaces existing in wheel detectors, evaluators, signals, etc. These are critical to the safe and efficient management of railway infrastructure. The process of selecting a surge arrester component for a two-level voltage input to enable the examination of the degradation impact of a cable insulator used in rail signaling equipment on the performance of the surge arrester is presented in this paper based on the standards, as well as practical experience. To achieve this objective, an innovative design of the goal function that can be adapted to the new requirements of various industry sectors is proposed. The use of a two-stage solution verification is a unique feature of this method. The results indicate that the proper selection of the arrester components ensures the effect of degradation of the communication cable has an insignificant influence on the power dissipation of the surge exposures.

1. Introduction

Electromagnetic compatibility (EMC) is one of the most important requirements in the railway environment. It affects the availability and reliability [1] of railway lines for a train passage. Therefore, it is necessary to provide products with high EMC immunity and compact sizes. It follows from the requirement for compliance with standard EN-50121-4 [2] (defining EMC immunity) and the European Rail Traffic Management System (in terms of the described space limitation for wayside equipment).

Because of these constraints, a surge arrester must be designed efficiently and simulated [3,4] before its final testing at an accredited laboratory. The limitations on the space available for the surge arrester, which arise from the design of the device itself as a whole and the associated maintenance of the infrastructure, are among the basic requirements. For the digital interfaces, modern methodology could be used (e.g., a genetic algorithm [5]) to improve robustness, as the interfaces are inherently vulnerable. Surge voltages make it necessary to limit the voltage to a level that is safe for the sensitive CAN (Control Area Network) driver, as the surge arrester must dissipate high power. This situation can be considered in wayside equipment (e.g., wheel detectors) where a CAN bus is used to exchange data about the number of axles that have been passed over the counting point, which are then processed by the evaluator to report a section status as unoccupied or occupied. An unoccupied section state means that the same number of wheels have entered and left the section, and thereby the section is free. This allows the next vehicle to move into the section. Train movement is ongoing in the occupied section, so there is no possibility for the next train to travel through it.

The CAN line architecture is very useful because it offers the possibility of minimizing the length of cables used to create a network (bus topology). This helps to reduce system maintenance and installation costs. However, it also has some disadvantages, as a long network cabling system is affected by the large disturbances present in the railway industry, such as high voltages of up to 25 kV [6], currents of several kA, and the associated electromagnetic field [7]. These phenomena create new constraints that engineers must overcome in order to design a module [8,9,10] that is robust and resistant to exposure to such stresses.

Overvoltage immunity is well described in the associated literature [11,12,13] but mainly in the context of analysis of power supply lines, which are significantly more robust than communication ports. A few papers provide analyses of the communication links [14,15,16,17,18], but these concentrate on test performance rather than an analysis of the limits, which gives more detailed information about the device and creates new advantages during the life of a product (selection of alternatives).

Several artificial algorithms can be used to provide the most optimal solution to the problem at hand, but due to specific circumstances, only one of them was selected. Since simulated annealing is optimized for a single suboptimal solution only, numerous suboptimal solutions could lead to a similar value of the objective function. In consequence, it was rejected. Ant colony optimization was disqualified because it would have easily fallen into the trap of achieving the local optimum. The genetic algorithm (GA) is therefore the most flexible and universal way to find a suboptimal solution for the circuit under analysis.

As a consequence of the evolution of science and technology [19], it is feasible to perform the evaluation of protection modules with the help of a genetic algorithm. It can be applied in various ways to design optimization of circuits. In paper [20], GA is used to improve component location and routing. In addition, paper [21] provides an instance of applying GA for the purpose of thermal analysis, which increases the environmental stability of the module. It is possible to find articles presenting the need to perform device operation simulation before testing [22] in the relevant literature.

A schematic diagram and a preliminary analysis of GA in terms of the development of a surge arrester module in the railway environment are shown in [23], but some modifications are needed. As a result of the new assumptions, the goal functions have been updated with the following components: an additional test case (when a gas discharge tube—GDT is not involved), a part that optimizes the number in the resistor groups, and limiting the total volume of resistance in the surge arrester. The implementation of GA for the new purpose of performing such an analysis is presented below.

Furthermore, the impact of cable insulator degradation [24,25,26] on the critical parameters, maximum voltage values, maximum current values, and average and maximum power of the protection module for the components remains unknown, but this phenomenon is present in the railway environment due to the need to ensure the long life of the equipment and therefore it needs to be examined. The input data representing the model (Figure 1) and the parameters of the degraded cable are described in detail in ref. [27].

The components of the model presented in Figure 1 are described below:

• R_W—resistance of wire;
• L_W—inductance of wire;
• R_S—resistance of shield;
• L_S—inductance of shield;
• C₁₁—capacitance measured between the wires in the first pair at one end;
• C₁₂—capacitance measured between the wires in the second pair on one end;
• C₂₃=C₂ + C₃, (C₂=C₃)—capacitance measured between the first pair and shield;
• C₄₅=C₄ + C₅, (C₄=C₅)—capacitance measured between the second pair and shield;
• C₇₁₀=C₇ + C₈ + C₉ + C₁₀, (C₇=C₈=C₉=C₁₀)—capacitance measured between the first and the second pair (short wires in pairs).

Based on the information presented in the article [27], a function in the form of:

$$f_3\left(t\right)=a+b\left(1-e^{-\frac{t}{\tau }}\right),$$

(1)

Was used to determine the parameters of the degraded cabling on the basis of the study discussed. In Equation (1):

• $a$ stands for the nominal parameters ($n)$ of the cable:

  $$a \in (R_W^n, L_W^n, R_S^n, L_S^n, C_{11}^n, C_{12}^n, C_{23}^n, C_{45}^n,C_{710}^n);$$

  (2)
• $b$ stands for the parameter change value after degradation process;

  $$b\in (\mathsf{\Delta }{R}_W, ∆L_W, ∆R_S, ∆L_S, ∆C_{11 }, ∆C_{12}, ∆C_{23}, ∆C_{45}, ∆C_{710});$$

  (3)
• $\tau$ stands for the time after which the parameter has changed by 63.2%.

A cable model was added to the circuit for simulating a surge arrester response. Based on the data collected in this way, an experiment was proposed to compare the amount of energy dissipated by the components of the protector with the degraded cable and the nominal parameters. This approach, according to the authors, will demonstrate the effect of a degraded cable on the parameters of the surge arrester, extending the knowledge in this area, which thus should increase the accessibility of the railway traffic management system. The purpose of the experiment is shown in Figure 2.

2. Train Detection System and Component Selection Method

Currently, train detection systems involving wheel detectors are most commonly used to control train movements. Such a system generates safe information in an evaluator that defines the status of a section (free or occupied) on the basis of the information transmitted from the individual wheel detectors, which is the basis for the operation of the supervisory systems that manage the train movements in an automatic or manual way. A diagram of a train detection system with wheel detectors using a digital CAN communication interface is shown in Figure 3.

The CAN interface allows for the connection of multiple devices to the bus and thus contributes to lower installation costs. However, it requires an adequate degree of protection against disturbances occurring in the railway environment. In addition, due to the limited space in the trackside area, the surge arrester must have small dimensions, so there is a justified need to design a dedicated method to meet all requirements. The following test environment (Figure 4) was proposed to verify the performance of the surge arrester.

The wheel detector power supply components are also shown in Figure 4 but are not the subject matter of this paper. The shape of the input voltage waveform (surge) 1.2/50 µs is described in ref. [2] and shown in Figure 5.

A detailed discussion of the signal shape in the time domain and the required response time of the analyzed circuit is presented in ref. [23]. Based on this, the time of surge arrester behavior verification was set to 300 µs.

Surge implementation in LT Spice XVII software is presented in ref. [28]. A diagram of the surge arrester under consideration is shown in Figure 6.

The surge module consists of two groups of elements. For reasons of maintenance cost optimization, it is expected that the probability of failure of Group A components (cheaper part of the wheel detector, easily replaceable) is higher than that of Group B components (main unit, high replacement cost). This requirement is implemented in the goal function. The filter module is fixed and will not be subject to the selection process.

The research process used the Matlab R2021A environment:

• For the implementation of the method (method flow);
• For the determination of component parameters (voltages, powers, currents, etc.);
• With respect to the Global Optimization Toolbox module (Matlab environment), an appropriate function (namely GA() function) was used to configure and start the optimization process using the genetic algorithm.

In addition, the LT Spice XVII software was integrated into Matlab to simulate the electrical parameters of the circuit under test. The method flow chart is presented in Figure 7.

It was necessary to modify the method presented in [23] due to the fact that the GDT was responsible for dissipating a significant part of the energy during exposure to an input surge above the spark gap ignition voltage. However, voltages below the ignition voltage threshold also occur in the real railway environment and can damage components, because the GDT is not involved in the power dissipation. Based on the above, two test cases were selected:

• $U_{WE1}=6 \mathrm{k}\mathrm{V}—$GDT is active in energy dissipation, and the surge amplitude value 6 kV was calculated based on EN-50121-4 [2] standard, which required 2 kV. However, based on the experience gained (i.e., harsh railway conditions [13,29,30,31]), the voltage must be doubled or tripled in order to meet high reliability requirements. In our test scenario, we multiplied it by three and it amounted to 6 kV;
• $U_{WE2}=650 \mathrm{V}$(spark gap ignition voltage for SG75 [32])—GDT is inactive, and the disturbance is dissipated to the remaining components).

Therefore, in the method presented below, this test case has been added in order to improve the selection of the components of the surge arrester.

All the above changes also implied the need to update the input vector describing possible specification configurations. This vector will be presented later in the paper.

The penalty factor also changed as a result of the addition of an extra test case ($U_{WE2}=650 \mathrm{V}$) to the method. It was adapted for the two-stage verification of critical parameters and was involved in the optimization of the number of components in GR₉ and GR₁₀. This resulted in the necessity to update the goal function, too. This is presented in the equation in Figure 8.

All the above parameters are described below:

• $M_k^i$—the calculated value (based on simulations) of the i-th parameter for the component k $\left(M_k^i\ge 0,M_k^i\in \mathbb{R}\right)$. The detailed assignment of parameters is shown in Table 1;
• ${\widehat{M}}_k^i$—the maximum value of the i-th parameter for the component k $\left({\widehat{M}}_k^i>0,{\widehat{M}}_k^i\in \mathbb{R}\right)$ np., e.g., voltage, power or current, as specified in the manufacturer’s documentation (Table 1) without design margins (${\beta }_k^i)$;
• ${\beta }_k^i$—a factor that defines the margins of critical parameters for individual components, and is used to manage the risk of damage to components in defined groups;
• $N_p$—number of parameters analyzed per component $\left(N_p>0,N_p\in \mathbb{N}\right)$, e.g., R₉: $N_p$= 3, i.e., average power, peak power and voltage. $i$ = 1, …, $N_p$, i is the index of the parameter being verified;
• $N_e$—number of components analyzed $\left(N_e>0,N_e\in \mathbb{N}\right)$, $N_e=10$ based on Figure 6. The k index takes the values $k$ = 1, 2, …, 10;
• $N_r$—number of test cases $\left(N_r>0,N_r\in \mathbb{N}\right)$, $N_r=2$ (first test case: exposure above the ignition voltage of the GDT-$U_{WE1}=6\mathrm{k}\mathrm{V}$ and second test case: the surge voltage below the ignition voltage of the GDT $U_{WE2}=650\mathrm{V}$);
• $\alpha \prime$—penalty coefficient; it shall have the values: 1 or $N_r·\alpha$, if $M_k^i\le {\widehat{M}}_k^i$ (no exceeding of the defined critical parameters for the components) then $\alpha =1$, otherwise $M_k^i>{\widehat{M}}_k^i$(overrun of the margins) $\alpha =26$;
• $l$—represents the number of resistors in the groups: GR₉ and GR₁₀ $\left(l>1,l\le 8,l\in \mathbb{N}\right)$;
• $j$—specifies the maximum suggested number of resistors in GR₉ and GR₁₀ so that the algorithm did not seek to significantly increase the number of these components $\left(j>1,j\in \mathbb{N}\right)$. The assumption was $j=3$;
• $\gamma$—penalty factor degrading the value of the objective function for the cases when the resistance of the surge arrester exceeds the requirements (total resistance is higher than 18 Ω).

2.1. Components Limitations

The components used in the specification of the surge arrester are defined in [23], together with an analysis of the critical parameters that will be used in the selection procedure of the components, so that the calculated $M_k^i$ parameters enabled the determination of the goal function that evaluates the solutions for the input vectors generated by the proposed method. All the critical parameters and references are presented in Table 1.

Table 1. Parameters and limits of components used in the surge arrester.

Component Number  $\left(\mathit{k}\right)$	Designator	$\mathit{U}$ Voltage [V] $(\mathit{i}=1)$	$\mathit{I}$ Current [A] $(\mathit{i}=2)$	${\mathit{P}}_{\mathit{a}\mathit{v}\mathit{g}}$ Average Power [kW] $(\mathit{i}=3)$	${\mathit{P}}_{\mathit{m}\mathit{a}\mathit{x}}$ Peak Power [kW] $(\mathit{i}=4)$
1	C4	$M_1^1$	$M_1^2$	$M_1^3$	$M_1^4$
		${\widehat{M}}_1^1=U_{max}^C=$ 4500 [33]	${\widehat{M}}_1^2-$Lack of data	${\widehat{M}}_1^3-$Lack of data	${\widehat{M}}_1^4-$Lack of data
2	GDT	$M_2^1$	$M_2^2$	$M_2^3$	$M_2^4$
		${\widehat{M}}_2^1-$Lack of data	${\widehat{M}}_2^2=I_{max}^{GDT}=$ 2 000 [32]	${\widehat{M}}_2^3-$Lack of data	${\widehat{M}}_2^4-$Lack of data
3	R9 *	$M_3^1$	$M_3^2$	$M_3^3$	$M_3^4$
		${\widehat{M}}_3^1=U_{max}^R=$ 500 [34]	${\widehat{M}}_3^2-$Lack of data	${\widehat{M}}_3^3=P_{mean}^R=$1.0 [34]	${\widehat{M}}_3^4=P_{max}^R=$ 5.0 [34]
4	R10 *	$M_4^1$	$M_4^2$	$M_4^3$	$M_4^4$
		${\widehat{M}}_4^1=U_{max}^R=$ 500 [34]	${\widehat{M}}_4^2-$ Lack of data	${\widehat{M}}_4^3=P_{mean}^R=$1.0 [34]	${\widehat{M}}_4^4=P_{max}^R=$ 5.0 [34]
5	D4	$M_5^1$	$M_5^2$	$M_5^3$	$M_5^4$
		${\widehat{M}}_5^1=U_{max}^D$ [35]	${\widehat{M}}_5^2=I_{max}^D$ [35]	${\widehat{M}}_5^3-$Lack of data	${\widehat{M}}_5^4=P_{max}^D=$ 5.0 [35]
6	R5	$M_6^1$	$M_6^2$	$M_6^3$	$M_6^4$
		${\widehat{M}}_6^1=U_{max}^R=$ 500 [34]	${\widehat{M}}_6^2-$ Lack of data	${\widehat{M}}_6^3=P_{mean}^R=$ 1.0 [34]	${\widehat{M}}_6^4=P_{max}^R=$ 5.0 [34]
7	R6	$M_7^1$	$M_7^2$	$M_7^3$	$M_7^4$
		${\widehat{M}}_7^1=U_{max}^R=$ 500 [34]	${\widehat{M}}_7^2-$ Lack of data	${\widehat{M}}_7^3=P_{mean}^R=$ 1.0 [34]	${\widehat{M}}_7^4=P_{max}^R=$ 5.0 [34]
8	D1	$M_8^1$	$M_8^2$	$M_8^3$	$M_8^4$
		${\widehat{M}}_8^1=U_{max}^D=$ 18 [36]	${\widehat{M}}_8^2=I_{max}^D$ [35]	${\widehat{M}}_8^3-$Lack of data	${\widehat{M}}_8^4=P_{max}^D=$ 5.0 [35]
9	D2	$M_9^1$	$M_9^2$	$M_9^3$	$M_9^4$
		${\widehat{M}}_9^1=U_{max}^D=$ 18 [36]	${\widehat{M}}_9^2=I_{max}^D$ [35]	${\widehat{M}}_9^3-$Lack of data	${\widehat{M}}_9^4=P_{max}^D=$ 5.0 [35]
10	D3	$M_{10}^1$	$M_{10}^2$	$M_{10}^3$	$M_{10}^4$
		${\widehat{M}}_{10}^1=U_{max}^D=$ 18 [36]	${\widehat{M}}_{10}^2=I_{max}^D$ [35]	${\widehat{M}}_{10}^3-$Lack of data	${\widehat{M}}_{10}^4=P_{max}^D=$ 5.0 [35]

* Defines the parameters for a single component in a group.

Table 1. Parameters and limits of components used in the surge arrester.

Component Number  $\left(\mathit{k}\right)$	Designator	$\mathit{U}$ Voltage [V] $(\mathit{i}=1)$	$\mathit{I}$ Current [A] $(\mathit{i}=2)$	${\mathit{P}}_{\mathit{a}\mathit{v}\mathit{g}}$ Average Power [kW] $(\mathit{i}=3)$	${\mathit{P}}_{\mathit{m}\mathit{a}\mathit{x}}$ Peak Power [kW] $(\mathit{i}=4)$
1	C4	$M_1^1$	$M_1^2$	$M_1^3$	$M_1^4$
		${\widehat{M}}_1^1=U_{max}^C=$ 4500 [33]	${\widehat{M}}_1^2-$Lack of data	${\widehat{M}}_1^3-$Lack of data	${\widehat{M}}_1^4-$Lack of data
2	GDT	$M_2^1$	$M_2^2$	$M_2^3$	$M_2^4$
		${\widehat{M}}_2^1-$Lack of data	${\widehat{M}}_2^2=I_{max}^{GDT}=$ 2 000 [32]	${\widehat{M}}_2^3-$Lack of data	${\widehat{M}}_2^4-$Lack of data
3	R9 *	$M_3^1$	$M_3^2$	$M_3^3$	$M_3^4$
		${\widehat{M}}_3^1=U_{max}^R=$ 500 [34]	${\widehat{M}}_3^2-$Lack of data	${\widehat{M}}_3^3=P_{mean}^R=$1.0 [34]	${\widehat{M}}_3^4=P_{max}^R=$ 5.0 [34]
4	R10 *	$M_4^1$	$M_4^2$	$M_4^3$	$M_4^4$
		${\widehat{M}}_4^1=U_{max}^R=$ 500 [34]	${\widehat{M}}_4^2-$ Lack of data	${\widehat{M}}_4^3=P_{mean}^R=$1.0 [34]	${\widehat{M}}_4^4=P_{max}^R=$ 5.0 [34]
5	D4	$M_5^1$	$M_5^2$	$M_5^3$	$M_5^4$
		${\widehat{M}}_5^1=U_{max}^D$ [35]	${\widehat{M}}_5^2=I_{max}^D$ [35]	${\widehat{M}}_5^3-$Lack of data	${\widehat{M}}_5^4=P_{max}^D=$ 5.0 [35]
6	R5	$M_6^1$	$M_6^2$	$M_6^3$	$M_6^4$
		${\widehat{M}}_6^1=U_{max}^R=$ 500 [34]	${\widehat{M}}_6^2-$ Lack of data	${\widehat{M}}_6^3=P_{mean}^R=$ 1.0 [34]	${\widehat{M}}_6^4=P_{max}^R=$ 5.0 [34]
7	R6	$M_7^1$	$M_7^2$	$M_7^3$	$M_7^4$
		${\widehat{M}}_7^1=U_{max}^R=$ 500 [34]	${\widehat{M}}_7^2-$ Lack of data	${\widehat{M}}_7^3=P_{mean}^R=$ 1.0 [34]	${\widehat{M}}_7^4=P_{max}^R=$ 5.0 [34]
8	D1	$M_8^1$	$M_8^2$	$M_8^3$	$M_8^4$
		${\widehat{M}}_8^1=U_{max}^D=$ 18 [36]	${\widehat{M}}_8^2=I_{max}^D$ [35]	${\widehat{M}}_8^3-$Lack of data	${\widehat{M}}_8^4=P_{max}^D=$ 5.0 [35]
9	D2	$M_9^1$	$M_9^2$	$M_9^3$	$M_9^4$
		${\widehat{M}}_9^1=U_{max}^D=$ 18 [36]	${\widehat{M}}_9^2=I_{max}^D$ [35]	${\widehat{M}}_9^3-$Lack of data	${\widehat{M}}_9^4=P_{max}^D=$ 5.0 [35]
10	D3	$M_{10}^1$	$M_{10}^2$	$M_{10}^3$	$M_{10}^4$
		${\widehat{M}}_{10}^1=U_{max}^D=$ 18 [36]	${\widehat{M}}_{10}^2=I_{max}^D$ [35]	${\widehat{M}}_{10}^3-$Lack of data	${\widehat{M}}_{10}^4=P_{max}^D=$ 5.0 [35]

* Defines the parameters for a single component in a group.

The above table contains information about the conditions necessary for the proper operation of the surge arrester. These may be modified or expanded as required, but the component limits presented above are sufficient for the surge arrester under analysis.

2.2. Input Vector

Due to changes in the goal function, the input vector (chromosome, X) also had to be updated. A section defining the number of resistors in the groups was added. The new structure of the input vector is presented in

Table 2. Binary input vector structure (X).

Component/Group	Bit Positions in the Input Vector
Group R9 (GR9) and Group R10 (GR10)	1:4
R5 and R6	5:7
D4	8:12
D1	13:17
D2 and D3	18:22
C4	23:25
Number of resistors in the Group R9 and R10	26:28

.

The binary vector architecture presented above allowed for the optimal use of the genetic algorithm for the purpose of finding the suboptimal solution to the issue discussed. The definition and the circuit implementation (in LT Spice) of the example input vector are shown in Figure 9.

Figure 9 and Table 2 illustrate the mapping of the input vector to the individual components used in the surge arrester, whose structure should remain constant. The domain of the components should be chosen according to the engineer’s experience, results from the specific operating conditions of the device, and the availability of components on the market.

The configuration parameters of the genetic algorithm in the Matlab environment are described in ref. [23] and remain unchanged. Due to the previously proposed configuration, it was possible to deliver satisfactory solutions in a short time.

Due to the prediction of the number of resistors in groups GR₉ and GR₁₀ (Figure 8, $n_{GR}$) at an expectation level of 3, the estimated value of the goal function should be within the range from 204 to less than 256 because of the following relationships.

In the case of a predicted number of resistors equal to 3, the penalty factor for this group is 51. The following part of the equation is responsible for this (Figure 8):

$$\left(l-1\right)·\frac{N_r·\alpha -1}{j-1},$$

(4)

Because the following is assumed:

$$l=j=3,$$

(5)

The factor will be:

$$N_r·\alpha -1=2·26-1=51,$$

(6)

There are two groups of elements with this coefficient (GR₉ and GR₁₀, $l>1$); therefore, the minimum value of this part of the goal function equals 102 (for three resistors in a group in one test case).

To factor should be added the above value of the goal function:

$$\sum _{k=1}^{N_e}\sum _{i=1}^{N_p}\left(\frac{M_k^i}{{\beta }_k^i·{\widehat{M}}_k^i}·\alpha \right),$$

(7)

Part:

$$\frac{M_k^i}{{\beta }_k^i·{\widehat{M}}_k^i}$$

(8)

If the requirements are met and the designated critical parameters are not exceeded ($\alpha =1),$ it will have values within the range of:

$$\frac{M_k^i}{{\beta }_k^i·{\widehat{M}}_k^i}\in \left(\mathrm{0,1}\right)$$

(9)

Therefore, the sub-total equals the following:

$$\sum _{k=1}^{N_e}\sum _{i=1}^{N_p}\left(\frac{M_k^i}{{\beta }_k^i·{\widehat{M}}_k^i}·\alpha \right)\in (\mathrm{0,26}),$$

(10)

Taking the penalty factor for the three resistors in the groups and the compliance with the critical parameters for one test case into account:

$$f_{goal1}\in \left(\mathrm{102,128}\right),$$

(11)

There are two test cases, and therefore the expected value of the goal function will fall within the range described below:

$$f_{goal}=f_{goal1}+f_{goal2}\in \left(\mathrm{204,256}\right),$$

(12)

3. Results

The algorithm was terminated after 851 iterations in less than 21 h due to a lack of expected progress in reducing the goal function. The statistics of the genetic algorithm are shown below in Figure 10.

According to the data presented in Figure 10, the value of the goal function for the suboptimal solution amounts to 214.825, which is consistent with the expectations presented in Equation (12). Based on the histogram of the goal function values, it can be concluded that up to the fifth generation, the algorithm did not manage to find a satisfactory solution (goal function values close to 400 indicate solutions where the critical parameters have been exceeded). Only after the fifth generation did the algorithm find a suboptimal input vector so that the solutions met the goal function requirements. This leads to the conclusion that the analyzed problem has many local minima, searching for the spectrum of solutions is purposeful, and only the selection of a specific combination of surge arrester components allowed us to find a suboptimal solution.

3.1. Test Case $U_{WE1}=6 kV$

The results of the algorithm for an input voltage of $U_{WE1}=6 \mathrm{k}\mathrm{V}$ (GDT contribution to energy dissipation) and analyses of the time courses for the individual components are presented below.

Table 3. Parameters for the proposed specification of the surge arrester $U_{WE2}=6 \mathrm{k}\mathrm{V}$.

Designator	Specification	${\mathit{U}}_{\mathit{m}\mathit{a}\mathit{x}}$ [V]	${\mathit{I}}_{\mathit{m}\mathit{a}\mathit{x}}$ [A]	${\mathit{P}}_{\mathit{m}\mathit{e}\mathit{a}\mathit{n}}$ [W]	${\mathit{P}}_{\mathit{m}\mathit{a}\mathit{x}}$ [W]
C4	1nF	697.96	9.54	2.09	1409.5
GDT	SG75	697.96	1334.5	1251	29,102
GR9	2.2R (×3)	329.44	49.92	198.52	16,444
GR10	2.2R (×3)	329.56	49.93	198.51	16,456
D4	SMDJ28CA	38.96	49.83	49.91	1941.2
R5	1R	3.22	3.22	1.34	10.37
R6	1R	3.22	3.22	1.34	10.37
D1	SMDJ5.0CA	7.12	3.22	4.24	22.90
D2	SMDJ6.0CA	6.79	0.06	0.01	0.43
D3	SMDJ6.0CA	6.80	0.08	0.01	0.51
Number of resistors in Groups R9 and R10:					3

shows the suboptimal specification proposal for the exposure $U_{WE1}=6 \mathrm{k}\mathrm{V}.$

The above results clearly indicate that GDT is the key energy-dissipating component during exposure, as it has the ability to dissipate the highest power, and the determined average power is $P_{mean}^{GDT}=1251 \mathrm{W}$ in the presented result for $U_{WE1}=6 \mathrm{k}\mathrm{V}$. It should be noted that the resistors in groups GR₉ and GR₁₀ are equally important components since the sum of the peak powers exceeds even the peak power of the GDT (sum of the peak powers of the resistor groups $P_{max}^{GR9}+P_{max}^{GR10}=32.9 \mathrm{k}\mathrm{W},$ and the peak power of the GDT is $P_{max}^{GDT}=29.1 \mathrm{k}\mathrm{W}$). This means that they are responsible for the power dissipation until the GDT is triggered.

3.2. Test Case $U_{WE2}=650 V$

The results of the analysis of $U_{WE2}=650 \mathrm{V}$ (GDT is inactive) component parameters are shown in

Table 4. Parameters for the proposed specification of the surge arrester $U_{WE2}=650 \mathrm{V}$.

Designator	Specification	${\mathit{U}}_{\mathit{m}\mathit{a}\mathit{x}}$ [V]	${\mathit{I}}_{\mathit{m}\mathit{a}\mathit{x}}$ [A]	${\mathit{P}}_{\mathit{m}\mathit{e}\mathit{a}\mathit{n}}$ [W]	${\mathit{P}}_{\mathit{m}\mathit{a}\mathit{x}}$ [W]
C4	1nF	469.71	0.49	0.43	26.17
GDT	SG75	469.71	0.00	0.00	0.03
GR9	2.2R (×3)	216.62	32.82	360.50	7109.8
GR10	2.2R (×3)	216.60	32.82	360.50	7108.7
D4	SMDJ28CA	36.50	31.89	74.98	1163.9
R5	1R	3.40	3.40	1.80	11.58
R6	1R	3.40	3.40	1.80	11.58
D1	SMDJ5.0CA	7.12	3.40	5.00	24.23
D2	SMDJ6.0CA	4.38	0.02	0.00	0.03
D3	SMDJ6.0CA	5.70	0.02	0.00	0.08
Number of resistors in Groups R9 and R10:					3

.

In this test case, C₄, GR₉, GR₁₀ and D₄ are the crucial components responsible for power dissipation. The sum of the power dissipated by these components (796.41 W) is higher than in the case for the input voltage $U_{WE1}=6 \mathrm{k}V$ (the sum equals: 449 W). This proves the validity of the analysis of the case where the key component of the surge arrester has extremely non-linear characteristics (e.g., in the case of the GDT). Therefore, the situation where these components will not be involved in energy dissipation should be verified. The above conclusions confirm the need to perform an analysis of the surge arrester components for intermediate input voltage values. Moreover, the maximum peak power for all components from Group A amounts to 15408.6 W, but in Group B it reaches only 47.5 W, which is consistent with the expectation that Group A items are more exposed to damage than Group B items.

3.3. Comparison of the Performance of a Surge Arrester with a Degraded Cable and a Nominal One

The surge arrester configuration (Figure 6) compliant with the specification (Table 4) was used to simulate the surge $U_{WE1}=6 \mathrm{k}\mathrm{V}$ 1.2/50 µs through a degraded RE-2Y(ST)Y 2 × 2 × 0.75 mm² (CT1) cable, as this type of cable was most often used for the short-distance connection of wheel detectors. The parameters of the degraded cable model were determined from the results presented in [27]. A summary of the input cable parameters for the simulations is presented in

Table 5. Comparison of CT1 nominal and aged cable parameters.

Cable Status	RW [mΩ] (20 Hz)	Lw [µH] (10 kHz)	RS [mΩ] (20 Hz)	LS [µH] (20 Hz)	C11 [pF] (10 kHz)	C12 [pF] (10 kHz)	C23 [nF] (10 kHz)	C45 [nF] (10 kHz)	C710 [nF] (10 kHz)
Nominal	364.25	14.50	280.00	10.20	490.00	475.00	1.50	1.49	0.80
Degraded	378.23	14.50	329.88	10.75	724.10	713.30	3.18	3.28	2.45
$\mathsf{\delta }$ (%)	3.84%	0.00%	17.81%	5.38%	47.78%	50.17%	111.80%	120.27%	206.23%

.

The $\mathsf{\delta }$ parameter was represented in the equation:

$$\mathsf{\delta }=\frac{x-x_0}{x_0}\times 100\mathrm{\%},$$

where $x_0$ stands for nominal parameters of the cables and $x$ describes the degraded parameters of the cables affected by penetrating water. The biggest changes in $\mathsf{\delta }$ are observed with respect to the capacitive parameters due to the ingress of water between cable parts.

The result of the approximation of the cable degradation process (1) was the source of the verification of the critical parameters, using the criteria presented in Table 1. The analysis of surge arrester parameters is shown in

Table 6. Comparison of the performance of the surge arrester configuration for a degraded and a non-degraded cable $U_{WE1}=6 \mathrm{k}V$.

Test Case	Group	Designator	Component Specification	Parameter
				${\mathit{U}}_{\mathit{m}\mathit{a}\mathit{x}}$ [V]	${\mathit{I}}_{\mathit{m}\mathit{a}\mathit{x}}$ [A]	${\mathit{P}}_{\mathit{m}\mathit{e}\mathit{a}\mathit{n}}$ [W]	${\mathit{P}}_{\mathit{m}\mathit{a}\mathit{x}}$ [W]
Nominal cable	A	C4	1nF	697.96	9.54	2.09	1 409.5
		GDT	SG75	697.96	1 334.5	1 251	29 102
		GR9	2.2R (×3)	329.44	49.92	198.52	16 444
		GR10	2.2R (×3)	329.56	49.93	198.51	16 456
		D4	SMDJ28CA	38.96	49.83	49.91	1 941.2
	B	R5	1R	3.22	3.22	1.34	10.37
		R6	1R	3.22	3.22	1.34	10.37
		D1	SMDJ5.0CA	7.12	3.22	4.24	22.90
		D2	SMDJ6.0CA	6.79	0.06	0.01	0.43
		D3	SMDJ6.0CA	6.80	0.08	0.01	0.51
Aged cable	A	C4	1nF	705.88	8.88	2.10	1426.64
		GDT	SG75	705.88	1326.87	1239.42	29081.59
		GR9	2.2R (×3)	333.38	50.51	186.82	16840.03
		GR10	2.2R (×3)	333.46	50.52	186.81	16847.91
		D4	SMDJ28CA	39.04	50.43	47.64	1968.67
	B	R5	1R	3.20	3.20	1.31	10.25
		R6	1R	3.20	3.20	1.31	10.25
		D1	SMDJ5.0CA	7.12	3.20	4.18	22.77
		D2	SMDJ6.0CA	6.79	0.06	0.01	0.42
		D3	SMDJ6.0CA	6.79	0.07	0.01	0.46
Parameters change	A	C4	1nF	+1.14%	−7.21%	+0.21%	+1.24%
		GDT	SG75	+1.14%	−0.57%	−0.97%	−0.10%
		GR9	2.2R (×3)	+1.21%	+1.21%	−5.90%	2.42%
		GR10	2.2R (×3)	+1.19%	+1.19%	−5.90%	2.40%
		D4	SMDJ28CA	+0.21%	+1.21%	−4.54%	1.42%
	B	R5	1R	−0.59%	−0.59%	−2.54%	−1.17%
		R6	1R	−0.59%	−0.59%	−2.54%	−1.18%
		D1	SMDJ5.0CA	−0.01%	−0.58%	−1.45%	−0.59%
		D2	SMDJ6.0CA	−0.01%	−0.86%	−9.18%	−0.87%
		D3	SMDJ6.0CA	−0.11%	−9.99%	−9.73%	−10.09%

.

In Group A components (Figure 6), the aging effect on power dissipated on resistive components reaches a maximum of +2.42% ($P_{max}^{GR9}$). In Group B, the relative changes amount to a maximum of −10.09% ($P_{max}^{D4}$), but the change in absolute terms amounts to 0.05 W only.

Table 7. Comparison of the performance of the surge arrester configuration for a degraded and a non-degraded cable $U_{WE2}=650 \mathrm{V}$.

Test Case	Group	Designator	Component Specification	Parameter
				${\mathit{U}}_{\mathit{m}\mathit{a}\mathit{x}}$ [V]	${\mathit{I}}_{\mathit{m}\mathit{a}\mathit{x}}$ [A]	${\mathit{P}}_{\mathit{m}\mathit{e}\mathit{a}\mathit{n}}$ [W]	${\mathit{P}}_{\mathit{m}\mathit{a}\mathit{x}}$ [W]
Nominal cable	A	C4	1nF	469.71	0.49	0.43	26.17
		GDT	SG75	469.71	0.00	0.00	0.03
		GR9	2.2R (×3)	216.62	32.82	360.50	7109.82
		GR10	2.2R (×3)	216.60	32.82	360.50	7108.72
		D4	SMDJ28CA	36.50	31.89	74.98	1163.94
	B	R5	1R	3.40	3.40	1.80	11.58
		R6	1R	3.40	3.40	1.80	11.58
		D1	SMDJ5.0CA	7.123	3.402	4.999	24.229
		D2	SMDJ6.0CA	4.384	0.017	0.002	0.027
		D3	SMDJ6.0CA	5.703	0.016	0.002	0.078
Aged cable	A	C4	1nF	469.17	0.51	0.43	26.02
		GDT	SG75	469.17	0.00	0.00	0.03
		GR9	2.2R (×3)	216.35	32.78	359.46	7092.34
		GR10	2.2R (×3)	216.32	32.78	359.46	7090.29
		D4	SMDJ28CA	36.50	31.84	74.86	1162.27
	B	R5	1R	3.40	3.40	1.80	11.58
		R6	1R	3.40	3.40	1.80	11.58
		D1	SMDJ5.0CA	7.123	3.401	4.998	24.226
		D2	SMDJ6.0CA	4.281	0.018	0.001	0.034
		D3	SMDJ6.0CA	5.510	0.016	0.001	0.074
Parameters change	A	C4	1nF	−0.11%	+5.01%	−0.22%	−0.58%
		GDT	SG75	−0.11%	+4.80%	−0.73%	−0.42%
		GR9	2.2R (×3)	−0.12%	−0.12%	−0.29%	−0.25%
		GR10	2.2R (×3)	−0.13%	−0.13%	−0.29%	−0.26%
		D4	SMDJ28CA	−0.02%	−0.13%	−0.16%	−0.14%
	B	R5	1R	−0.01%	−0.01%	−0.04%	−0.02%
		R6	1R	−0.02%	−0.02%	−0.04%	−0.05%
		D1	SMDJ5.0CA	0.00%	−0.01%	−0.01%	−0.01%
		D2	SMDJ6.0CA	−2.35%	+2.56%	−10.84%	+24.37%
		D3	SMDJ6.0CA	−3.39%	−1.88%	−11.28%	−4.79%

presents the effect of cable degradation on the performance of the surge arrester for input voltage $U_{WE2}=650 \mathrm{V}$.

The change of the critical parameters presented in Table 7 with respect to the components in Group A indicates a slight influence of the degradation of the cabling parameters on the performance of the surge arrester (mostly a percentage change below 1%). The greatest changes concern C_{4 Imax} and GDT _Imax, but considering the absolute changes, these values are negligible in relation to other parameters (∆C_{4 Imax} = 24 mA, C_{4 Imax NOMINAL} = 0.49 A against D_{3 Imax NOMINAL} = 31.89 A). Similarly, in Group B, generally the changes in performance are small. If the relative change is large (∆D_{2 Pmax %} = 24.37%), it is connected with small absolute values (∆D_{2 Pmax} = 7 mW).

The above values were then contrasted with the time waveforms. Since the differences in the critical parameters of the surge arrester between the degraded and the nominal cable did not exceed 10.09% (Table 6), the voltage waveform of a component with a large amplitude was chosen as an example to visualize the differences. For this purpose, the voltage at the input of the surge arrester (U_GDT (t) Figure 6) shown in Figure 11 was used.

The voltage value for the degraded cable is +7.92 V (change of +1.14%) higher than the one for a cable with nominal parameters. The voltage waveform for the degraded cable has a similar shape (the rise has shifted) due to the influence of increased capacitance between the cable elements.

The total of the $P_{mean}$ for all the surge arrester’s component used the cable with nominal parameters amounts to 1706.97 W, and compared with the degraded cable sum of 1669.61 W, the relative difference amounts to −2.19% for the $U_{WE2}=6 \mathrm{k}\mathrm{V}$ test case.

The small difference between the dissipated average power for the surge arrester with degraded and nominal cable parameters is most likely due to a small change in cable resistance (Table 5, +3.84%). Even though there is a shift in the rise of the surge at the input of the arrester, it is due to changes in the capacitive parameters of the cabling (Table 5), but in the case of the 10 m cable length, it is insignificant. However, the worst case to be considered in terms of the surge arrester’s performance is a 10 m long connecting cable. Analyses related to the impact of longer cable sections are planned for the future.

4. Conclusions

The results of the analyses evidence that there is no significant impact of cable degradation in the worst-case scenario on the operation of surge arrester components in trackside equipment using the presented CAN bus topology. The two-variant method of selecting surge arrester components presented in this paper may significantly increase the EMC immunity of trackside equipment to hard conditions of the railway environment. Furthermore, the method (and especially the goal function) is flexible, because it can be easily adapted to new requirements. In addition, the analysis of intermediate cases (e.g., $U_{WE3}=1 \mathrm{k}\mathrm{V},U_{WE4}=2 \mathrm{k}\mathrm{V},U_{WE5}=4 \mathrm{k}\mathrm{V}$) makes it possible to identify the most vulnerable components of the surge arrester, which will enable a mitigation of the risks associated with component failure (e.g., by changing the component technology or its supplier, so that the thresholds of critical component parameters could be higher).

Finally, it can be concluded that the main emphasis should be put on the correct design of the surge arrester and the determination of its critical parameters. Therefore, a method based on a genetic algorithm with an extended goal function was proposed in order to select the components. The annualized goal function and test cases are based on standards, as well as practical experience gained in the implementation of trackside equipment in worldwide markets.