Conducted electromagnetic noise characteristics of pantograph arc and its regression model

Abstract

With the continuous increase of electric locomotive running speed, pantograph arc occurs more and more frequently. The conducted electromagnetic noise caused by pantograph arc will effect seriously normal operation of on-board equipment. With the self-developed electromagnetic noise experimental system, eighty-six groups of conducted electromagnetic noise experiments under different sliding speed, contact pressure, contact current conditions were carried out with single-factor experimental method. Total harmonic distortion (THD) of contact current was proposed and used to reflect the interference level of the conducted electromagnetic noise. The effect of sliding speed, contact pressure and contact current on THD was analyzed. A regression model of the conducted electromagnetic noise was established by using support vector machine (SVM). The independent variable of the model are sliding speed, contact pressure and contact current. The dependent variable of the model is THD. The model parameters were optimized by using particle swarm optimization algorithm. The effectiveness of the regression model was verified with experimental results. It can be used to further understand and forecast the conducted electromagnetic noise.

Keywords

Pantograph arc electromagnetic noise total harmonic distortion sliding electrical contact SVM

1. Introduction

The pantograph and catenary (pantograph-catenary) are important parts of traction power supply system of electrified railway. The electric locomotive obtains electrical energy by sliding electrical contact between pantograph slide and contact wire. During the process of electric locomotive running, the short separation phenomenon between pantograph slide and contact wire occurs due to contact wire irregularity, catenary vibration and so on. This separation phenomenon is named pantograph-catenary disconnection. The arc discharge caused by the disconnection is called pantograph arc. Pantograph arc will generate transients and distort the current waveform. The DC component and harmonics formed by waveform distortion will propagate within both traction power system and signal system and cause serious electromagnetic interference and even cause accident [1, 2]. For example, several train emergency braking accidents happened due to malfunction of on-board equipment of train control system caused by pantograph arc in Chinese Suining-Chongqing Railway in the year 2010–2013. The harmonics generated by pantograph arc also caused false trigger operation of a 220 kV traction substation in Chinese Taiyuan-Zhongwei-Yinchuan Railway on December 10, 2010. With the rapid development of high-speed railway in China, the speed of many passenger trains has reached 350 km/h. The unavoidable pantograph arc phenomenon occurs more and more frequently at that speed and it’s a serious threat to safe operation of trains. Therefore, it is of great significance to study the conducted electromagnetic noise characteristics of pantograph arc.

Tellini et al. studied experimentally the EMI phenomena of pantograph arc with a section of catenary and a real pantograph. It showed that the conducted EMI components are related to the low-frequency part of the current transient [3]. Midya et al. investigated the relationships between different parameters like traction current, supply voltage, line speed and power factor and pantograph arc. It showed that DC current component from pantograph arc increases with increasing train speed and traction current, and reduces at a lower power factor [4]. Karagöz studied experimentally the effects of pantograph arc and its influence factors such as contact distance, load current and power factor on harmonic content of traction current. It showed that the harmonic content increases with the increase of contact distance and power factor, and reduces with the increase of contact current [2]. Liu et al. studied influence of pantograph-catenary offline time on harmonic content of traction current. While dynamic pantograph arc occurs in the rising section of supply voltage waveform, arc duration is longer and the harmonic content is larger than those in the dropping section [5]. Li et al. studied the harmonic spectrum and current waveform distortion of traction current caused by pantograph arc. It showed that DC component, 3 ${}^{\text{rd}}$ harmonic, 5 ${}^{\text{th}}$ harmonic and 7 ${}^{\text{th}}$ harmonic of pantograph arc current respectively account for about 12%, 38%, 30% and 10% of the fundamental waves [6]. Wang et al. proposed that the equivalent interfering current can be used to evaluate the effect of harmonic current caused by pantograph arc on traction transformer loss [7]. Lin et al. investigated conducted electromagnetic interferences on auto-transformer caused by pantograph arc, which was simulated by a wide-band frequency trapezoidal voltage pulse. It showed that voltage pulse caused by arcs which happen at a short distance from auto-transformer decreases fast and oscillate quickly [8]. Östlund et al. suggested that the DC component in traction current can be used as a feature to on-line monitoring the occurrence of pantograph arc [9]. As for conducted electromagnetic noise of pantograph arc, most of existing research focus on the influence factor, harmonic content analysis and its impact on locomotive equipment and so on. The research on conducted electromagnetic noise and corresponding model of pantograph arc is very limited.

The preliminary research on conducted electromagnetic noise of pantograph arc was also carried out in our previous paper [10, 11]. It verified that DC component, odd harmonic and inter-harmonic component occurs in the contact current because of pantograph arc. It showed that the harmonics generated by pantograph arc is usually lower than 500 Hz and the inter-harmonics mainly distributes from 0 Hz to 100 Hz. In this paper, the conducted electromagnetic noise was studied experimentally in the view of current harmonic. Total harmonic distortion (THD) of contact current was proposed and used to reflect the interference level of the conducted electromagnetic noise. The effect of sliding speed, contact pressure and contact current on THD was discussed. A regression model of THD was established and its effectiveness was verified with experimental results. It can be used to further understand and forecast the conducted electromagnetic noise generated by pantograph arc.

2. Experimental design

2.1 Experimental system

The experiments were carried out in an electromagnetic noise experimental system of pantograph arc. It consists of an anechoic chamber, a pantograph arc generator and a measurement and analysis system [10, 11, 12, 13], as shown in Fig. 1.

Figure 1.

The electromagnetic noise experimental system. (a) Pantograph arc generator and test antennas inside the anechoic chamber; (b) Measurement and analysis system. 1 – pantograph arc generator; 2 – wave absorbing material; 3 – ultralog antenna; 4 – spectrum analyzer; 5 – video monitoring system; 6 – supervisory control and data acquisition system.

Figure 2.

Pantograph arc generator and the disconnection control module. (a) Pantograph arc generator; (b) The disconnection control module. 1 – motor; 2 – rotary disc; 3 – contact wire; 4 – slide; 5 – horizontal moving bench; 6 – vertical moving bench; 7 – cable; 8 – spring; 9 – pull-pressure sensor; 10 – sliding block; 11 – ball screw; 12 – stepping motor; 13 – motor.

The anechoic chamber was built according to IEC 62236-2 standard. It ensures that the measured electromagnetic noise signal isn’t interfered by other electromagnetic noise signals.

The pantograph arc generator was designed by adding a disconnection control module to the existing sliding electrical contact testing device in reference [14], as shown in Fig. 2a. The disconnection control module consists of stepping motor, ball screw, sliding block, pull-pressure sensor, spring and slide, as shown in Fig. 2b. The rotational motion of the stepping motor 12 can be converted into linear motion by the ball screw 11. The vertical moving bench 6 is fixed on the end of the ball screw 11. It can be moved back and forward by controlling the stepping motor 12 to realize the disconnection control of slide 4 and contact wire 3. The deformation of the spring 8 can be changed when the vertical moving bench 6 moves. And the contact pressure between slide 4 and contact wire 3 can be detected with the pull-pressure sensor 9 and then the contact pressure can be adjusted by controlling the stepping motor 12.

The main circuit of the pantograph arc generator shown in Fig. 3 is used to generate a pantograph arc with given current. The control circuit of the pantograph arc generator is used to simulate zigzag running trace between pantograph slide and contact wire of electric locomotive. It can be realized by controlling the movements of rotary disc, horizontal moving bench and vertical moving bench. The drive motors and their control circuits of both rotary and horizontal moving bench are the same with that of the sliding electrical contact testing device in Ref [14]. The vertical moving bench is controlled by the disconnection control module.

The measurement and analysis system of pantograph arc is shown in Fig. 1b. It can automatically detect, store and analyze experimental signals such as contact voltage, contact current, contact pressure, sliding speed, reciprocating speed of slide, electromagnetic noise emission of pantograph arc, arc image and so on.

2.2 Experimental materials

The copper contact wire and immersed copper-carbon slide were used in the experiment. The cross-section of the contact wire is 120 mm ${}^{2}$ . And the length, width and height of the slide are 250 mm, 25 mm and 10 mm respectively. The slide is made by hot pressing method. The performance parameters of the contact wire and slide at 20 ${}^{\circ}$ C are shown in Table 1.

Table 1
The performance parameters of the contact wire and slide (20 ${}^{\circ}$ C)

Parameters	Hardness	Density	Resistivity	Thermal conductivity	Specific heat capacity
	[HBS]	[10 ${}^{3}$ kg/m ${}^{3}$ ]	[ $\mu\Omega$ $\cdot$ m]	[W/(m $\cdot$ K)]	[J/(kg $\cdot$ K)]
Contact wire	96.2	8.9	0.0175	380	380
Slide	56.7	3.4	12.32	15	660.2

Figure 3.

The main circuit of the pantograph arc generator.

2.3 Experimental scheme

Eighty-six groups of conducted electromagnetic noise experiments under different sliding speed, contact pressure, contact current conditions were carried out with single-factor experimental method. The experimental conditions are shown in Table 2.

Table 2
Experimental conditions

Factors	Experimental value
Sliding speed (km/h)	20 25 30 35 70 110
Contact pressure (N)	30 50 70 90
Contact current (A, RMS)	50 100 150 200 250

The output voltage of high-current generator in Fig. 3 is 36 V AC. The power resistances were used to adjust the given contact current. The reciprocating speed of the slide is 0.25 m/s. The testing duration in each group is 10 minutes. The LMZJ1 type hall current transformer and DL PT202D type potential transformer were used respectively to measure loop current and contact voltage between contact wire and slide. The outputs of the transformers were converted by corresponding signal processing circuit and then transmitted to an NI PCI-6251 type data acquisition card installed in a computer. The sample frequency is 10 kHz. A self-developed data processing system based on LABVIEW software installed in the computer was used to observe, store and analyze experimental data such as contact current, contact voltage, contact pressure and so on. The UV R2868 type ultraviolet sensor and corresponding circuit were used to detect pantograph arc. Its output pulse signal was used to trigger an AOS S-PRI Plus type high-speed camera. The camera was used to capture pantograph arc image. Its resolution is 1250 frames per second.

3. Conducted electromagnetic noise characteristics of pantograph arc

3.1 Selection of contact current waveforms in arc or spark current collection state

Figure 4.

Experimental results of contact pressure (static contact pressure is 50 N).

Figure 5.

Phenomena occur in two kinds of current collection state. (a) Waveforms of contact voltage, contact current and output signal of ultraviolet sensor; (b) Arc image captured by high-speed camera; (c) Photos of sliding contact area captured by video monitoring system.

Pantograph arc is a kind of special gas discharge phenomenon. The occurrence of pantograph arc not only depends on minimum arcing voltage and minimum arcing current but also contact pressure and sliding speed [13]. It showed that the contact pressure between contact wire and pantograph slide is a kind of hump-shape and periodic fluctuated dynamic contact pressure, as shown in Fig. 4. The fluctuation range of the dynamic contact pressure increases with the increase of sliding speed. For each experiment, the given experimental conditions such as contact current, static contact pressure and sliding speed are constant. But real contact pressure varies with time because it’s a dynamic contact pressure. It will change real electrical contact state of contact area and have great influence on the occurrence of pantograph arc. Experimental results showed that arc or electric spark occurs more frequently with the decrease of the real contact pressure. Therefore, the occurrence of pantograph arc is intermittent in each experiment. It sometimes appears and sometimes disappears. The moment of arc or electric spark seems to be random. Therefore, in order to better study the conducted electromagnetic noise, it’s necessary to judge current collection state and select the corresponding contact current waveforms in arc or electric spark state.

It showed that there are two kinds of current collection state. One is normal current collection state and the other is arc or spark current collection state. In arc or spark current collection state, the following phenomena occur. First, output voltage signal of the ultraviolet (UV) sensor keeps in high level, as shown in Fig. 5a. Second, the arc or spark image can be captured by high-speed camera or video monitoring system, as shown in Fig. 5b and c. Finally, both contact current and contact voltage waveforms are distorted. The contact current decreases and contact voltage increases, as shown in Fig. 5a. All of the above features can be used to determine whether pantograph arc or spark occurs or not. For example, the circle area is in arc or electric spark collection state and the other area is in normal state. Only the contact current waveforms in arc or electric spark collection state are selected and collected to analyze the conducted electromagnetic noise of pantograph arc.

3.2 Definition of total harmonic distortion

Figure 6a and c shows typical contact current waveforms in normal and arc/spark current collection state. We can see that pantograph arc generates transients and causes different levels of distortion of contact current waveform. Figure 6b and d are the corresponding frequency spectrum characteristics, which were obtained by using Fast Fourier Transform [15]. It shows that the distorted current waveform contains dc component and lots of odd and even harmonics. As mentioned above, these harmonics will propagate within both traction power system and signal system. So it is a kind of conducted electromagnetic noise and will affect seriously safe operation of train.

Figure 6.

Typical contact current waveform and its frequency spectrum characteristic in normal and arc/spark current collection state. (a) Contact current waveform without arc; (b) Frequency spectrum characteristic of Fig. 6a; (c) Contact current waveform with arc; (d) Frequency spectrum characteristic of Fig. 6c.

The intensity of the conducted electromagnetic noise is closely related to the distortion level of contact current waveform. Total harmonic distortion (THD) of contact current was proposed and used to reflect the distortion level. THD is ratio of RMS value of the sum of all the harmonic contents ( $I_{n}$ ) up to a specified order ( $H$ ) to the RMS value of the fundamental component ( $I_{1}$ ) [15, 16], as shown in Eq. (1). In this paper, $H=$ 40.

$\displaystyle\textit{THD}=\frac{1}{I_{1}}\sqrt{\sum\limits_{n=2}^{H}{I_{n}^{2}% }}\times 100\%$ (1)

3.3 Relationships between total harmonic distortion and different experimental conditions

Figure 7 presents relationships between THD and sliding speed, contact pressure and contact current. It shows that the THD increases first sharply then slowly with the increase of sliding speed when contact pressure and contact current keep constant. The THD decreases with the increase of contact pressure when contact current and sliding speed keep constant.

Figure 7.

Relationships between THD and sliding speed, contact current and contact pressure. (a) Contact pressure is 70 N; (b) Contact current is 150 A.

Contact pressure and sliding speed affect the disconnection rate. The smaller the contact pressure, the higher the disconnection rate is. The higher the sliding speed, the more intense fluctuation of contact pressure, then the higher the disconnection rate is. Since pantograph arc or spark usually occurs in the disconnection moment, the occurrence numbers of pantograph arc or spark in the same experimental time will become larger with a higher disconnection rate. Figure 8 shows relationships between the occurrence number and sliding speed, contact current and contact pressure. As shown in Fig. 8 and Table 3, if contact current is 150 A and contact pressure is 70 N, the occurrence number of arc or spark in 10 minutes increases from 150 times to 288 times when sliding speed changes from 20 km/h to 110 km/h. Also if sliding speed is 110 km/h, the occurrence numbers increases from 288 times to 348 times when contact pressure changes from 70 N to 30 N. In that case, the contact current waveform will be distorted more seriously by the frequently occurred pantograph arcs or sparks and THD becomes higher and higher. The statistical results in Table 3 verified that THD indeed increases with the increase of the occurrence numbers of arc or spark in the same experimental time.

Table 3

Statistical results on the relationships between occurrence numbers of arc or spark, THD and contact pressure and sliding speed

Contact current	Contact pressure	Sliding speed	Occurrence numbers of arc or	THD
(A)	(N)	(km/h)	spark in 10 minutes	%
150	70	20	150	35.99
	70	25	225	45.00
	70	30	241	49.65
	70	35	253	53.27
	70	70	278	52.62
	70	110	288	55.07
	30	20	232	44.76
	30	25	285	51.97
	30	30	300	57.26
	30	35	325	59.64
	30	70	343	59.53
	30	110	348	60.56
250	70	30	174	48.69
	70	70	242	50.48
	70	110	250	53.86

Figure 8.

Relationships between occurrence numbers of arc or spark in 10 minutes and sliding speed, contact current and contact pressure. (a) Contact pressure is 70 N; (b) Contact current is 150 A.

Figure 7a also shows that the THD decreases with the increase of contact current when contact pressure and sliding speed keep constant. The difference of THD under different contact current is not obvious when sliding speed is lower than 35 km/h. The arc power increases with the increase of contact current if other experimental conditions remain unchanged. Larger arc power will improve the stability of pantograph arc and decrease the transients caused by extinguish and re-ignition of pantograph arc. So the distortion level of contact current waveform is lightened and THD decreased. For example, if contact pressure is 70 N and sliding speed is 110 km/h, the occurrence number of arc or spark in 10 minutes decreases from 288 times to 250 times when contact current changes from 150 A to 250 A, as shown in Table 3. The average arc duration which was calculated by using captured pantograph arc images is 5.14 ms and 9.37 ms when contact current is 150 A and 250 A. Besides, Ref [2] also has verified that harmonic contents of pantograph arc current decreases with the increase of contact current since the zero current crossing time are smaller for higher arc current.

4. Regression model of THD

4.1 Basic principle

In order to forecast accurately and ultimately suppress the conducted electromagnetic noise generated by pantograph arc, a regression model between THD and sliding speed, contact pressure and contact current was established based on support vector machine (SVM).

The given sample data is $\left\{{x_{i},z_{i}}\right\},i=1,2,...,l$ , where, $x_{i}\in R^{m}$ , $z_{i}\in R$ is the expected value, $l$ is the total number of samples. Use Eq. (2) to estimate the function:

$\displaystyle z=f(x)=\left[{\omega\cdot\Phi(x)}\right]+b$ (2)

The corresponding optimization goal is [17]:

$\displaystyle{\min\limits_{\omega,b,\xi,\xi^{*}}}\frac{1}{2}\omega^{T}\omega+C% \sum\limits_{i=1}^{l}{(\xi_{i}^{*}+\xi_{i})}$ $\displaystyle s.t.\left\{{\begin{array}[]{l}z_{i}-\omega^{T}\Phi(x_{i})-b% \leqslant\varepsilon+\xi_{i}^{*}\\ \omega^{T}\Phi(x_{i})+b-z_{i}\leqslant\varepsilon+\xi_{i}^{*}\\ \xi_{i}^{*}\geqslant 0;\xi_{i}\geqslant 0;i=1,2,...,l\\ \end{array}}\right.$ (3)

Where, $C$ is punishment coefficient. $\xi_{i}$ and $\xi_{i}^{*}$ are slack factors respectively. $\varepsilon$ is loss coefficient.

The kernel function of SVM is divided into four kinds. They are linear kernel function, polynomial kernel function, radial basis kernel function and perceptron kernel function. The radial basis kernel function shown in Eq. (4) was used in this paper.

$\displaystyle K(x,x_{i})=\exp(-\gamma\left\|{x-x_{i}}\right\|^{2}),\gamma>0$ (4)

The following four steps are needed to establish the THD regression model.

Experimental data of THD and sliding speed, contact pressure and contact current were selected and used as training samples. In order to improve convergence speed of the model, the training samples were normalized by using Eq. (5).

$\displaystyle f:x|\to z=\frac{x-x_{\min}}{x_{\max}-x_{\min}}$ (5)

Where, $x,z\in R^{n}$ , $x_{\min}=\min(x)$ , $x_{\max}=\max(x)$ , $z_{i}\in\left[{0,1}\right],i=1,2,...,l$ .

The punishment coefficient $C$ and parameter of radial basis kernel function $\gamma$ were optimized by using particle swarm optimization (PSO) algorithm.

The mathematical regression model of THD was established by using SVM. The detailed realization of the model will be described in Section 4.3.

THD values under different experimental conditions were predicted by using the established regression model. The effectiveness of the model was verified by comparing the predicted values and experimental values.

4.2 Optimization of model parameters

It is very important to select appropriately the model parameters including punishment coefficient $C$ and parameter $\gamma$ . Because these parameters have great effect on complexity and accuracy of the regression model. PSO algorithm was used to optimize these model parameters.

The core concept of PSO algorithm is as follows [18, 19]. Initialize a population containing several particles in an $n$ -dimensional solution space. Each particle in the population represents an $n$ -dimensional feasible solution and has its own velocity $V$ . $V$ is an $n$ -dimensional vector. Construct a population fitness function $F$ . And set minimum value $M$ of the fitness function $F$ and maximum iteration number $T$ of population. Where, $M\geqslant 0$ . $M$ is also used as criterion for the convergence of the fitness function $F$ . The particles in the solution space will adjust their own flight traces according to flight experience and move close to the best point. The optimization flowchart of model parameters based on PSO algorithm is shown in Fig. 9.

Figure 9.

The optimization flowchart of model parameters based on PSO algorithm.

Assuming that the total average error of testing samples is $\psi$ , the fitness function $F$ can be defined as in Eq. (6).

$\displaystyle F_{i}=\psi_{i}$ (6)

The total iteration number is $n$ and total particle number is $i$ . The initial position and speed of each particle is assigned as $x_{i}$ and $v_{i}$ respectively. An iteration process defined in Eqs (7) $\sim$ (9) can be carried out and then $x_{i}$ and $v_{i}$ can be updated.

$\displaystyle V_{i}^{k+1}=\omega_{i}V_{i}^{k}+\beta_{1}\cdot r_{1}\cdot(p_{% \textit{besti}}-X_{i}^{k})+\beta_{2}\cdot r_{2}\cdot(g_{\textit{besti}}-X_{i}^% {k})$ (7) $\displaystyle X_{i}^{k+1}=X_{i}^{k}+V_{i}^{k+1}$ (8) $\displaystyle\omega_{i}=\omega_{1}-\frac{\omega_{1}-\omega_{i-1}}{k},\omega_{0% }=\omega_{1},i=1,...,n$ (9)

Here, $p_{\textit{best}}$ is optimal location of particles. $g_{\textit{best}}$ is optimal location of population. $k$ is iteration number. $i$ is the size of the population. $r_{1}$ and $r_{2}$ are random numbers between 0 and 1. $\beta_{1}$ and $\beta_{2}$ are learning factors. $\omega$ is inertia weight. It determines the convergence ability of PSO algorithm. The larger the inertia weight $\omega$ is, the stronger global convergence ability is. If iteration number $k$ equals to total iteration number $n$ , the algorithm terminates.

4.3 Regression model and its evaluation

4.3.1 Establishment of the SVM-based THD regression model

The regression model was realized by using LIBSVM toolbox with MATLAB v2015b software. The toolbox was developed by Professor Lin Chih-Jen in National Taiwan University and can be obtained from Internet. The toolbox is a special software which includes lots of MATLAB functions on SVM. It has been widely used in the field of SVM pattern recognition and SVM regression.

In this paper, svmtrain function was used to establish and train the regression model. The function would be called as follows: model $=$ svmtrain (train_label, train_matrix,‘options’). Where, model is the trained regression model, train_matrix and train_label is independent variable matrix and dependent variable matrix of training samples respectively, options includes many parameters of the function. For the normalized training samples, sliding speed, contact pressure and contact current are independent variables, and the corresponding THD is dependent variable. Table 4 is setting results of SVM model parameters.

Table 4
Setting results of SVM model parameters

No.	Parameter	Parameter description	Parameter value	Notes
1	s	Used to select SVM type	3	Epsilon-SVM type of SVM was used.
2	t	Used to select kernel function	2	Radial basis kernel function was used, as shown in Eq. (4).
3	g	Same to $\gamma$ in Eq. (4)	Initial value was used firstly then the optimized value was used.	Initial value is 2. Optimized by using PSO algorithm, described in Section 4.2.
4	c	Same to punishment coefficient C	Default value was used firstly then the optimized value was used.	Default value is 1. Optimized by using PSO algorithm, described in Section 4.2.
5	p	Same to loss coefficient $\varepsilon$	0.01

Figure 10.

The fitness curve of the process of searching optimal parameters based on PSO.

The PSO algorithm was realized by using psoSVMcgForRress function provided by PSO toolbox with MATLAB v2015b software. Some key parameters must be set when we use the above-mentioned function. In this paper, these function parameters were set as follows. The total iteration number $n$ is 200, the total particle number $i$ is 20. And learning factor $\beta_{1}$ and $\beta_{2}$ equals to 1.5 and 1.7 respectively.

Seventy-two groups of experimental results of THD under different sliding speed, contact pressure and contact current conditions were used to train and optimize the regression model. Figure 10 presents the fitness curve of the process of searching optimal parameters based on PSO. The fitness is used to reflect the accuracy of the model. Figure 10 shows that the average error decreases gradually and the generalization ability of the model increases with the increase of iteration number. The corresponding optimized value of punishment coefficient $C$ and parameter $\gamma$ is 50.7203 and 0.25 respectively.

In addition, svmpredict function was used to obtain prediction result of the THD regression model. The function would be called as follows: predict $=$ svmpredict (test_matrix, model). Where, model is the trained regression model, test_matrix is independent variable matrix of testing samples, predict is the prediction result of the model.

4.3.2 Evaluation of the regression model

The mean square error (MSE) and correlation coefficient $R$ , defined in Eqs (10) and (11) were used to evaluate the regression model. MSE reflects prediction accuracy of the model. The smaller the MSE is, the higher the prediction accuracy is. Correlation coefficient $R$ reflects the correlation level of two variables $x_{i}$ and ${x}^{\prime}_{i}$ . If $R=0$ , the variable $x_{i}$ and ${x}^{\prime}_{i}$ are irrelevant. And if $R=1$ , the variable $x_{i}$ and ${x}^{\prime}_{i}$ are fully relevant.

$\displaystyle\textit{MSE}=\sum\limits_{i=1}^{n}{({z}^{\prime}_{i}-z_{i})^{2}}/n$ (10) $\displaystyle R=\frac{\sum\limits_{i=1}^{n}{(x_{i}-{x}^{\prime}_{i})}(y_{i}-{y% }^{\prime}_{i})}{\sqrt{\sum\limits_{i=1}^{n}{(x_{i}-{x}^{\prime}_{i})^{2}\cdot% \sum\limits_{i=1}^{n}{(y_{i}-{y}^{\prime}_{i})^{2}}}}}$ (11)

Figure 11 shows the comparison results between predicted value obtained from the regression model and experimental value. The corresponding MSE and $R$ is 0.00214 and 0.96904 respectively. We can see that the difference between the two curves is very small.

Figure 11.

Comparison results of predicted values and experimental values with 72 groups of training samples.

Another 14 groups of experimental results were used as testing samples to calculate prediction accuracy of the regression model. For each testing sample, we predicted three times and three prediction values were obtained by using the above-mentioned svmpredict function. They are respectively labeled as predicted value 1, predicted value 2 and predicted value 3. The calculation results are shown in Table 5. The max prediction error of three times of prediction results is lower than 9%. Therefore, the prediction accuracy of the regression model is satisfied.

Table 5

Prediction error of the regression model calculated with 14 groups of testing samples

Group	Experimental condition			THD (%)				Relative error (%)
number	Contact	Contact	Sliding	Experimental	Predicted	Predicted	Predicted	Mean	Max
	pressure	current	speed	value	value 1	value 2	value 3	value	value
	(N)	(A)	(km/h)
1	30	50	70	23.58	23.33	23.33	23.32	1.06	1.08
2	30	150	30	57.26	57.00	56.86	56.99	0.54	0.70
3	30	200	35	55.92	56.19	57.44	57.06	1.74	2.72
4	30	250	25	50.97	51.04	51.22	51.28	0.38	0.51
5	50	100	35	59.54	59.28	59.28	59.28	0.44	0.44
6	50	150	25	49.62	47.37	47.22	47.04	4.86	5.22
7	50	200	30	52.68	52.80	52.55	52.42	0.33	0.51
8	70	100	70	55.24	55.50	55.50	55.50	0.47	0.48
9	70	150	110	55.07	55.33	55.77	55.84	1.05	1.41
10	70	200	20	38.69	38.44	38.43	38.44	0.66	0.68
11	70	250	35	48.03	51.27	52.17	52.01	7.88	8.62
12	90	100	20	32.12	32.38	32.38	32.37	0.81	0.83
13	90	150	25	37.29	37.55	37.79	37.64	1.00	1.36
14	90	200	25	40.35	37.87	37.51	37.47	6.78	7.15

5. Conclusions

Pantograph arc or spark generated due to pantograph-catenary disconnection will cause the distortion of contact current waveform and form a kind of special conducted electromagnetic noise. The total harmonic distortion (THD) can be used to reflect the interference level of the conducted electromagnetic noise.

When other experimental conditions keep constant, THD of contact current waveform increases with the increase of sliding speed, and it decreases with the increase of contact pressure or contact current.

A kind of regression model of THD was proposed and its effectiveness was verified. The regression model was established based on SVM and the model parameters were optimized by using PSO algorithm. The regression model can predict accurately interference level of the conducted electromagnetic noise. These conclusions can be used to further research on suppression methods of the conducted electromagnetic noise.

Footnotes

Acknowledgments

The research reported in this paper was supported by the National Natural Science Foundation of China (No. 51674136, 51477071) and the Scientific Foundation Project of Education Department of Liaoning Province, P.R China (No. LJYL015).

References

Liu

J.Q.

Yang

Q.L.

and Zheng

T.Q.

, Harmonic analysis of traction networks based on the CRH380 series EMUs accident, in: 2012 IEEE Transportation Electrification Conference and Expo (ITEC), 2012, pp. 1–6.

Karagöz

, Analysis of the pantograph arcing and its effect on the railway vehicle, Middle East Technical University, 2014.

Tellini

Macucci

Giannetti

et al., Conducted and radiated interference measurements in the line-pantograph system, IEEE Transactions on Instrumentation & Measurement 50(6) (2001), 1661–1664.

Midya

Bormann

Schutte

et al., DC component from pantograph arcing in AC traction system: influencing parameters, impact, and mitigation techniques, IEEE Transactions on Electromagnetic Compatibility 53(1) (2011), 18–27.

Liu

W.Z.

Wang

Y.F.

Wang

T.Y.

et al., Influence of offline time on the characteristics of arc between pantograph and catenary, High Voltage Engineering 42(11) (2016), 3524–3532.

T.Z.

G.N.

and Zhou

L.J.

, Pantograph arcing’s impact on locomotive equipments, in: 57th IEEE Holm Conf. on Electrical Contact, 2011, pp. 249–253.

Wang

Yang

Z.P.

Lin

et al., Harmonic loss analysis of the traction transformer of high-speed trains considering pantograph-OCS electrical contact properties, Energies (2013), 5826–5846.

Lin

G.H.

Zhang

Y.R.

and Zhi

Y.J.

, Effects of pantograph arcing on railway systems with auto transformers, Journal of Elecctromagnetic Waves and Applications 27(13) (2013), 1686–1693.

Östlund

Gustafsson

Buhrkall

et al., Condition monitoring of pantograph contact strip, in: 4th IET International Conference on Railway Condition Monitoring, 2008, pp. 1–6.

10.

Wang

B.W.

, Experimental research on conducted electromagnetic noise of pantograph-catenary system, Liaoning Technical University, 2015.

11.

Wang

Z.Y.

Guo

F.Y.

Wang

et al., Experimental research on inter-harmonic characteristics of loop current in pantograph-catenary system, Journal of Liaoning Technical University (Natural Science), 2017: in Press.

12.

Wang

Z.Y.

Guo

F.Y.

Wang

X.L.

et al., Experimental research on radiated electromagnetic noise of pantograph arc, in: 61st IEEE Holm Conf. on Electrical Contact, 2015, pp. 256–261.

13.

Guo

F.Y.

Wang

Z.Y.

Zheng

Z.Q.

et al., Electromagnetic noise of pantograph arc under low current conditons, International Journal of Applied Electromagnetics & Mechanics 53(3) (2017), 397–408.

14.

Wang

Z.Y.

Guo

F.Y.

Chen

Z.H.

et al., Research on current-carrying wear characteristics of friction pair in pantograph catenary system, in: 59th IEEE Holm Conf. on Electrical Contact, 2013, pp. 92–96.

15.

IEC 61000-4-7:2002. Electromagnetic compatibility (EMC), Part 4-7: Testing and measurement techniques – General guide on harmonics and interharmonics measurements and instrumentation, for power supply systems and equipment connected thereto. European Committee for Electrotechnical Standardization, 2002.

16.

Shmilovitz

, On the definition of total harmonic distortion and its effect on measurement interpretation, IEEE Transactions on Power Delivery 20(1) (2005), 526–528.

17.

Barmada

Raugi

Tucci

et al., Arc detection in pantograph-catenary systems by the use of support vector machines-based classification, IET Electrical Systems in Transportation 4(2) (2013), 45–52.

18.

Yang

S.Y.

Yang

et al., Robust oriented particle swarm optimization algorithm applied to inverse problem, International Journal of Applied Electromagnetics & Mechanics 33(3) (2010), 1057–1062.

19.

Wei

Zhao

and Zhao

L.S.

, The identification of axial magnetic bearing system based on LS-PSO algorithm, International Journal of Applied Electromagnetics & Mechanics 49(4) (2015), 463–473.

Conducted electromagnetic noise characteristics of pantograph arc and its regression model

Abstract

Keywords

1. Introduction

2. Experimental design

2.1 Experimental system

Table 1 The performance parameters of the contact wire and slide (20 ∘ C)

Table 2 Experimental conditions

3.1 Selection of contact current waveforms in arc or spark current collection state

4.1 Basic principle

4.3.1 Establishment of the SVM-based THD regression model

Table 4 Setting results of SVM model parameters

Footnotes

Acknowledgments

References

Table 1
The performance parameters of the contact wire and slide (20 ${}^{\circ}$ C)

Table 2
Experimental conditions

Table 4
Setting results of SVM model parameters