Statistical Study on the Time Characteristics of the Transient EMD Excitation Current from the Pantograph–Catenary Arcing Discharge
Abstract
:1. Introduction
2. Experimental Setup and Measured Time Characteristics
- Peak amplitudes (A+ and A−), the positive and negative peak amplitudes of a single current pulse;
- Rise time (tr), the time interval between the instants at which the instantaneous current value first reaches 0.1 A+ and then 0.9 A−;
- Pulse width (tw), i.e., halfwave duration, the period between the instants at which the instantaneous value reaches 50% of its peak amplitude;
- Pulse repetition interval (tin), the time interval between two successive pulses in a pulse train.
3. Experimental Results and Analysis
3.1. Statistical Distribution of Transient Current Waveform Parameters
3.2. Statistical Analysis on the Peak Amplitudes of Transient Current Pulses
3.3. Statistical Analysis on the Pulse Repetition Intervals
3.4. Statistical Study of Transient Current Pulse Rise Time and Pulse Width
4. Deviation of the Stochastic Model of Arcing Currents
5. Conclusions
- The statistical distribution of pulse peak amplitude, rise time, pulse width at half maximum, and pulse interval time follows a specific reference distribution determined by the distribution fitting method. The chosen reference distribution model was validated through a Kolmogorov–Smirnov hypothesis test.
- Statistical analysis demonstrates that the distribution parameters of each fitted model vary with the applied voltage and the gap spacing distance between the electrodes. The fitting relation between the waveform parameters and the experimental conditions is established using a maximum likelihood estimation approach. This allows for the determination of statistically typical current waveform parameters representing different EMD severities and parameters in the later deduced current function.
- A new bipolar MDEF is introduced to describe the amplitude of the PC arcing current as a function of time, and is used to model the ratio between the positive and negative peak amplitudes, which increases with a larger gap spacing. The mathematical parameters of the bipolar MDEF are calculated from the waveform parameters generated by a pseudo-random number generation algorithm, based on the known time characteristics’ statistical distributions. The measured and calculated waveforms show a correlation coefficient of approximately 0.956, confirming the validity of the proposed generation method for a single pulse.
- The PC discharge current pulse train is characterized as the superposition of separated single current pulses generated by the stochastic model. The simulated pulse train closely matches the measured one, indicating that the stochastic model of the discharge waveform is effective in describing the statistical distribution of the waveform.
Author Contributions
Funding
Conflicts of Interest
References
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Parameter | Reference Distribution | ML Estimation | R2 | RMSE |
---|---|---|---|---|
A+ | Burr | α = 9.519, c = 6.259, k = 0.983 | 0.894 | 0.018 |
Birnbaum–Saunders | β = 9.593, γ = 0.277 | 0.873 | 0.020 | |
Gamma | a = 13.424, b = 0.742 | 0.856 | 0.021 | |
tr | t Location–Scale | μ = 19.017, σ = 1.243, ν = 2.024 | 0.967 | 0.016 |
Burr | α = 17.518, c = 228.853, k = 0.037 | 0.932 | 0.023 | |
Lognormal | μ = 2.981, σ = 0.117 | 0.743 | 0.044 | |
tw | Birnbaum–Saunders | β = 40.949, γ = 0.041 | 0.943 | 0.019 |
Burr | α = 40.416, c = 50.860, k = 0.696 | 0.942 | 0.021 | |
Log-Logistic | μ = 3.710, σ = 0.022 | 0.920 | 0.025 | |
tin | Extreme Value | μ = 0.911, σ = 0.025 | 0.934 | 0.012 |
Rician | s = 0.896, σ = 0.029 | 0.894 | 0.020 | |
Burr | α = 0.945, c = 40.489, k = 5.229 | 0.923 | 0.015 |
Parameter | Distribution Law | Dn |
---|---|---|
A+ | Burr | 0.047 |
tr | t Location–Scale | 0.023 |
tw | Birnbaum–Saunders | 0.031 |
tin | Extreme Value | 0.034 |
Significance level: | ||
Critical value: |
Cumulative Probability | Peak Amplitude (A) | Rise Time (ns) | Pulse Width (ns) | Repetition Interval (ms) |
---|---|---|---|---|
5% | 5.96 | 15.41 | 38.27 | 0.835 |
50% | 9.55 | 19.01 | 40.95 | 0.902 |
80% | 11.94 | 20.33 | 42.39 | 0.923 |
95% | 15.36 | 22.61 | 43.81 | 0.939 |
Experimental Condition | Mean Value (ms) | Standard Deviation (ms) | CV (%) |
---|---|---|---|
U = 20 kV, d = 5 mm | 0.905 | 0.310 | 34.3 |
U = 25 kV, d = 5 mm | 0.453 | 0.157 | 34.7 |
U = 30 kV, d = 5 mm | 0.243 | 0.083 | 34.1 |
U = 35 kV, d = 5 mm | 0.185 | 0.064 | 34.8 |
U = 35 kV, d = 10 mm | 0.312 | 0.109 | 35.1 |
U = 35 kV, d = 15 mm | 0.571 | 0.196 | 34.4 |
Experimental Condition | |||
---|---|---|---|
U = 20 kV, d = 5 mm | 19.017 | 1.243 | 2.024 |
U = 25 kV, d = 5 mm | 18.681 | 1.229 | 2.019 |
U = 30 kV, d = 5 mm | 19.118 | 1.235 | 2.014 |
U = 35 kV, d = 5 mm | 18.731 | 1.143 | 2.023 |
U = 35 kV, d = 10 mm | 20.032 | 1.361 | 2.026 |
U = 35 kV, d = 15 mm | 20.889 | 1.585 | 2.024 |
Experimental Condition | Scale Parameter β | Shape Parameter γ |
---|---|---|
U = 20 kV, d = 5 mm | 40. 949 | 0.041 |
U = 25 kV, d = 5 mm | 39.681 | 0.038 |
U = 30 kV, d = 5 mm | 39.562 | 0.041 |
U = 35 kV, d = 5 mm | 38.169 | 0.039 |
U = 35 kV, d = 10 mm | 37.124 | 0.038 |
U = 35 kV, d = 15 mm | 38.758 | 0.039 |
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Jin, M.; Wang, S.; Liu, S.; Fang, Q.; Liu, W. Statistical Study on the Time Characteristics of the Transient EMD Excitation Current from the Pantograph–Catenary Arcing Discharge. Electronics 2023, 12, 1262. https://doi.org/10.3390/electronics12051262
Jin M, Wang S, Liu S, Fang Q, Liu W. Statistical Study on the Time Characteristics of the Transient EMD Excitation Current from the Pantograph–Catenary Arcing Discharge. Electronics. 2023; 12(5):1262. https://doi.org/10.3390/electronics12051262
Chicago/Turabian StyleJin, Mengzhe, Shaoqian Wang, Shanghe Liu, Qingyuan Fang, and Weidong Liu. 2023. "Statistical Study on the Time Characteristics of the Transient EMD Excitation Current from the Pantograph–Catenary Arcing Discharge" Electronics 12, no. 5: 1262. https://doi.org/10.3390/electronics12051262
APA StyleJin, M., Wang, S., Liu, S., Fang, Q., & Liu, W. (2023). Statistical Study on the Time Characteristics of the Transient EMD Excitation Current from the Pantograph–Catenary Arcing Discharge. Electronics, 12(5), 1262. https://doi.org/10.3390/electronics12051262