Metro traction power supply system direct current fault distance measurement method and system
By constructing a ranging equation based on the first and second frequency difference characteristics of the natural frequency of the double-ended traveling wave, the accuracy and precision of DC fault ranging in the metro traction power supply system are solved, achieving efficient fault point locking. This adapts to the complex structure and dynamic characteristics of the DC traction network, ensuring the safety and efficiency of metro operation.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- JIANGXI MECHANICAL & ELECTRICAL VOCATIONAL & TECH COLLEGE
- Filing Date
- 2026-02-02
- Publication Date
- 2026-05-01
AI Technical Summary
The method for DC fault location in subway traction power supply systems is not yet mature. Existing methods are difficult to accurately identify traveling wave fronts and have low ranging accuracy. They cannot effectively cope with the complex structure and dynamic characteristics of DC traction networks, making it difficult to locate fault points and affecting train operation safety and transportation efficiency.
The method employs dual-terminal voltage traveling wave data acquisition, periodic Hanning window preprocessing, and fast Fourier transform analysis to extract the primary and secondary frequency differences of the natural frequencies of the dual-terminal traveling wave. The fault distance is calculated using the frequency difference ratio, and a distance measurement equation is constructed to eliminate the influence of traveling wave velocity and frequency variation characteristics of line parameters. This method is applicable to both metallic and non-metallic short-circuit faults.
It achieves accurate and stable fault location across the entire length of DC traction network lines, with a location error consistently within 1%. This simplifies engineering implementation, avoids reliance on clock synchronization mechanisms, adapts to different fault types and transition resistances, and improves the speed and accuracy of fault point location.
Smart Images
Figure CN121955607A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of relay protection technology for electric traction power supply systems, specifically to a DC fault location method and system for subway traction power supply systems. Background Technology
[0002] The metro traction power supply system is one of the four core systems of the metro's "mechanical-electrical-operation-rotation" system, and is the sole power source for train operation. The unique complex dynamic operating characteristics of the metro traction power supply system, including the complex multi-conductor transmission line structure and dynamic topology of the DC traction network, the strong impact and fluctuation of train traction loads, and its susceptibility to external interference, can lead to various faults and abnormal operating conditions. In particular, DC short-circuit faults, which have a high incidence rate and severe consequences, seriously threaten train operation safety and metro transportation efficiency.
[0003] DC short-circuit faults are classified into transient and permanent faults. For transient faults, power supply can be restored by reclosing, but the fault point is often a weak point and can easily trigger secondary faults. For permanent faults, if the circuit breaker reclosing fails, the system will stop supplying power. Therefore, how to quickly and accurately locate the fault and eliminate it is an urgent need to ensure the safety and reliability of the subway traction power supply system at this stage.
[0004] Fault location refers to the timely and accurate identification of fault points after a line fault occurs, reducing the workload of maintenance personnel during line patrols, shortening fault troubleshooting time, and maximizing the operational reliability of the power supply system. Currently, DC fault location in subway traction power supply systems is still in the exploratory research stage, and there is no mature fault location device that can be widely applied. Unlike high-voltage direct current transmission lines, DC traction networks have shorter line lengths, typically not exceeding 5km, and lower traction voltage levels, such as DC 750V or DC 1500V. Furthermore, the electrical quantities during the transient fault process are affected by the frequency-varying characteristics of line parameters, making it difficult to directly transplant mature fault location methods from high-voltage direct current transmission networks to DC traction networks. If the time-domain traveling wave method is used for location, there are problems such as severe transient traveling wave reflections and difficulty in identifying the traveling wave front. If the fault analysis method is used for location, there are problems such as fixed line model parameters and low location accuracy. Therefore, we propose a DC fault location method and system for subway traction power supply systems. Summary of the Invention
[0005] The purpose of this invention is to provide a method and system for DC fault location in a subway traction power supply system, which solves the problems mentioned in the background art.
[0006] To achieve the above objectives, the present invention provides the following technical solution: a method for DC fault location in a subway traction power supply system, comprising the following steps: S1. Collect voltage traveling wave data from the traveling wave coupling boxes at both ends of DC traction network line A and B within a 3ms time window after the fault. , ; When a metallic short-circuit fault occurs, the voltage traveling wave undergoes total reflection and no refraction at the fault point. The voltage traveling waves observed at both ends of the line show the reflected waves arriving at the fault point at equal intervals. When a non-metallic short-circuit fault occurs, the voltage traveling wave undergoes reflection and refraction at the fault point, with reflection being the dominant force. The energy refracted to the other end of the line is weaker. The voltage traveling waves observed at both ends of the line show a wave arrival pattern according to a certain time sequence, and the periodicity of the voltage traveling wave waveform is still obvious. S2. Add a periodic Hanning window to the acquired voltage traveling wave data in the time domain and perform zero-padding preprocessing.
[0007] S3. Perform Fast Fourier Transform analysis on the preprocessed voltage traveling wave data to extract the spectral distribution information of the two-terminal voltage traveling wave, identify the position of the spectral peaks and record their corresponding frequency values.
[0008] S4. Match the spectrum obtained from both ends and calculate the first and second frequency difference values of the natural frequencies of the traveling wave at both ends respectively. S5. Calculate the ratio of the frequency difference between the two ends, and use the functional relationship between this ratio and the fault distance to perform distance measurement.
[0009] Preferably, in S1, the traveling wave coupling box is deployed on the DC feeder.
[0010] Preferably, in S2, with For example, the windowing process can be represented as: ; in: For periodic Hanning windows, ; The length of the window function is the number of discrete sampling points.
[0011] Preferably, in step S2, the length of the collected data sequence is... The data length is often not an integer power of 2; it is padded with zeros to make it equal to the specified length. ( h (where is a positive integer), represented as: ; Preferably, in S3, the fault traveling wave spectrum obtained at end A of the DC traction network line satisfies: ; in: and These are the reflection coefficients of the traveling wave at line A and fault point F, respectively; Let F be the time it takes for the traveling wave to propagate from the fault point F to end A of the line. , Let F be the distance from the fault point F to end A of the line. This represents the propagation speed of the traveling wave.
[0012] Using Euler's formula, the above expression can be transformed into exponential form, which can be expressed as: ; We can solve for: ; in: Let be the reflection angle of the traveling wave at end A of the line. ; Let F be the reflection angle of the traveling wave at the fault point F. ; .
[0013] The imaginary part in the above equation corresponds to the angular frequency of the natural frequency. Therefore, the natural frequency formed by the fault traveling wave can be expressed as: ; Preferably, in S4, the fault traveling wave natural frequency extracted from both ends of the DC traction network lines A and B is... The formula for calculating the next frequency is: ; No. The formula for calculating the next frequency is: ; in: and These are the reflection angles of the traveling wave at points A and B of the line, respectively. The traveling wave velocity is almost constant at its natural high frequency and can be considered a fixed value. This is the total length of the line.
[0014] The formula for calculating the difference between adjacent natural frequencies of a two-ended traveling wave is: ; The formula for calculating the first and second frequency differences of the natural frequencies of a two-ended traveling wave is as follows: ; The difference between the primary and secondary natural frequencies of a two-terminal traveling wave can directly reflect the fault distance, without showing the influence of the line terminal boundary conditions.
[0015] Preferably, in step S5, the formula for calculating the ratio of the two-terminal frequency difference values is: ; make: ; The equation for two-way distance measurement is: ; in: It is the ratio of the difference between the first and second natural frequencies of the two-ended traveling wave.
[0016] Preferably, the ratio of the natural frequency difference of the two-terminal traveling wave can also be expressed as: ; The corresponding two-end distance measurement equation is: ; Using the above ranging equation for fault ranging can mathematically eliminate the influence of traveling wave velocity on the ranging results.
[0017] Preferably, the method does not rely on a dual-end clock synchronization mechanism, and the ranging results are not affected by line terminal boundary conditions, parameter frequency variation characteristics, and fault transition resistance.
[0018] Preferably, the method is applicable to both metallic and non-metallic short circuit faults, and the ranging error is stable at about 1% of the total line length.
[0019] A DC fault location system for a subway traction power supply system includes: The data acquisition module is used to acquire and store voltage traveling wave data at both ends of the DC traction network line traveling wave coupling box at high speed. The data time window is within 3ms after the fault occurs. The preprocessing module is used to perform windowing and zero-padding preprocessing on the acquired voltage traveling wave data. The selected window function is the periodic Hanning window, and zero-padding is used to make the data length [missing information]. (h is a positive integer); The spectrum analysis module is used to extract the spectrum distribution of the traveling wave of the two-terminal voltage using FFT and to determine the frequency value corresponding to the position of the spectrum peak. The frequency difference calculation module is used to calculate the first and second frequency differences of the natural frequencies of the double-ended traveling wave, and to calculate the ratio of the two-ended frequency difference values. The fault location module is used to calculate the fault distance using the ratio of the frequency difference of the two-end traveling waves and output the location result.
[0020] This invention provides a method for locating DC faults in a subway traction power supply system. This method for locating DC faults in a subway traction power supply system has the following advantages: This invention is applied to DC fault location in subway traction power supply systems. The method is not affected by the boundary conditions and frequency variation characteristics of DC traction network line terminals, and avoids the location error caused by inaccurate travel wave head identification and calibration deviation. This invention constructs a ranging equation based on the first and second frequency difference characteristics of the natural frequency of a two-terminal traveling wave, which mathematically eliminates the influence of the traveling wave velocity on the ranging result. Moreover, it does not require a two-terminal clock synchronization mechanism (such as GPS / BeiDou time synchronization), making it simple, reliable, and easy to implement in engineering. This invention can achieve accurate and stable fault location within a short time window over the entire length of a DC traction network line. It has high location accuracy, with the location error remaining stable at around 1% of the total line length, and is unaffected by fault type or fault transition resistance. Attached Figure Description
[0021] Figure 1 A flowchart for DC fault location in a subway traction power supply system, showing the first and second frequency differences of the natural frequencies of a double-ended traveling wave. Figure 2 Functional block diagram of DC fault location system; Figure 3 This is a structural diagram of the subway traction power supply system; Figure 4 The traveling wave of the metallic short-circuit fault measurement terminal at 500m and its corresponding spectrum distribution are shown in this invention. Figure 5 This is a diagram showing the traveling wave of the metallic short-circuit fault measurement terminal at 1000m and its corresponding spectral distribution in this invention. Figure 6 This is a diagram showing the traveling wave of the metallic short-circuit fault measurement terminal at 1500m and its corresponding spectral distribution in this invention. Figure 7 This is a diagram showing the traveling wave of the metallic short-circuit fault measurement terminal at 3000m and its corresponding spectral distribution. Detailed Implementation
[0022] To provide a clearer understanding of the technical features, objectives, and effects of the present invention, specific embodiments of the present invention will now be described with reference to the accompanying drawings.
[0023] like Figure 1-7 As shown, the present invention has the following two specific embodiments.
[0024] Example 1
[0025] Considering that after a fault occurs in a DC traction network line, the fault traveling wave (high-frequency electromagnetic transient wave) only propagates back and forth between the two ends of the DC traction network line and the fault point, the inherent frequency spectrum characteristics of the fault traveling wave contain a wealth of fault distance information, which is quite significant. Among them, the amplitude of the primary and secondary inherent frequencies is large, making them easy to identify and extract.
[0026] In view of this, the present invention provides a method and system for DC fault location in a subway traction power supply system.
[0027] like Figure 1 As shown, a method for DC fault location in a subway traction power supply system includes the following steps: S1. Collect voltage traveling wave data from the traveling wave coupling boxes at both ends of DC traction network line A and B within a 3ms time window after the fault. , ; When a metallic short-circuit fault occurs, the voltage traveling wave undergoes total reflection and no refraction at the fault point. The voltage traveling waves observed at both ends of the line show the reflected waves arriving at the fault point at equal intervals. When a non-metallic short-circuit fault occurs, the voltage traveling wave undergoes reflection and refraction at the fault point, with reflection being the dominant force. The energy refracted to the other end of the line is weaker. The voltage traveling waves observed at both ends of the line show a wave arrival pattern according to a certain time sequence, and the periodicity of the voltage traveling wave waveform is still obvious.
[0028] S2. Add a periodic Hanning window to the acquired voltage traveling wave data in the time domain and perform zero-padding preprocessing.
[0029] S3. Perform Fast Fourier Transform analysis on the preprocessed voltage traveling wave data to extract the spectral distribution information of the two-terminal voltage traveling wave, identify the position of the spectral peaks and record their corresponding frequency values.
[0030] S4. Match the spectrum obtained from both ends and calculate the first and second frequency difference values of the natural frequencies of the traveling wave at both ends respectively. S5. Calculate the ratio of the frequency difference between the two ends, and use the functional relationship between this ratio and the fault distance to perform distance measurement.
[0031] In S1, the traveling wave coupling box is deployed on the DC feeder.
[0032] In S2, with For example, the windowing process can be represented as: ; in: For periodic Hanning windows, ; The length of the window function is the number of discrete sampling points.
[0033] In S2, the length of the collected data sequence The data length is often not an integer power of 2; it is padded with zeros to make it equal to the specified length. ( h (where is a positive integer), represented as: ; In S3, the fault traveling wave spectrum obtained at end A of the DC traction network line satisfies: ; in: and These are the reflection coefficients of the traveling wave at line A and fault point F, respectively; Let F be the time it takes for the traveling wave to propagate from the fault point F to end A of the line. , Let F be the distance from the fault point F to end A of the line. This represents the propagation speed of the traveling wave.
[0034] Using Euler's formula, the above expression can be transformed into exponential form, which can be expressed as: ; We can solve for: ; in: Let be the reflection angle of the traveling wave at end A of the line. ; Let F be the reflection angle of the traveling wave at the fault point F. ; .
[0035] The imaginary part in the above equation corresponds to the angular frequency of the natural frequency. Therefore, the natural frequency formed by the fault traveling wave can be expressed as: ; In S4, the natural frequency of the fault traveling wave extracted from both ends A and B of the DC traction network line is... The formula for calculating the next frequency is: ; No. The formula for calculating the next frequency is: ; in: and These are the reflection angles of the traveling wave at points A and B of the line, respectively. The traveling wave velocity is almost constant at its natural high frequency and can be considered a fixed value. This is the total length of the line.
[0036] The formula for calculating the difference between adjacent natural frequencies of a two-ended traveling wave is: ; The formula for calculating the first and second frequency differences of the natural frequencies of a two-ended traveling wave is as follows: ; Therefore, the difference between the primary and secondary natural frequencies of the double-ended traveling wave can directly reflect the fault distance, without showing the influence of the line terminal boundary conditions.
[0037] In S5, the formula for calculating the ratio of the two-terminal frequency difference values is: ; make: ; The equation for two-way distance measurement is: ; in: It is the ratio of the difference between the first and second natural frequencies of the two-ended traveling wave.
[0038] The ratio of the natural frequency difference of a two-terminal traveling wave can also be expressed as: ; The corresponding two-end distance measurement equation is: ; Using the above ranging equation for fault ranging can mathematically eliminate the influence of traveling wave velocity on the ranging results.
[0039] The method does not rely on a dual-end clock synchronization mechanism, and the ranging results are not affected by line terminal boundary conditions, parameter frequency characteristics, and fault transition resistance.
[0040] The method is applicable to both metallic and non-metallic short circuit faults, with the ranging error remaining stable at approximately 1% of the total line length.
[0041] Example 2 like Figure 2 As shown, a DC fault location system for a subway traction power supply system includes: The data acquisition module is used to acquire and store voltage traveling wave data at both ends of the DC traction network line traveling wave coupling box at high speed. The data time window is within 3ms after the fault occurs. The preprocessing module is used to perform windowing and zero-padding preprocessing on the acquired voltage traveling wave data. The selected window function is the periodic Hanning window, and zero-padding is used to make the data length [missing information]. (h is a positive integer); The spectrum analysis module is used to extract the spectrum distribution of the traveling wave of the two-terminal voltage using FFT and to determine the frequency value corresponding to the position of the spectrum peak. The frequency difference calculation module is used to calculate the first and second frequency differences of the natural frequencies of the double-ended traveling wave, and to calculate the ratio of the two-ended frequency difference values. The fault location module is used to calculate the fault distance using the ratio of the frequency difference of the two-end traveling waves and output the location result.
[0042] Build such a platform in PSCAD / EMTDC Figure 3The simulation model of the DC 1500V subway traction power supply system shown is used to simulate actual fault conditions. The traction substation adopts a dual-unit equivalent 24-pulse rectification (traction transformer ratio is 35 / 1.18 / 1.18kV, diode rectification). The DC line adopts an electromagnetic transient model of the DC traction network considering the frequency variation characteristics of parameters. The total line length is set to 5.0km, and the transition resistance of the negative return rail to ground is... The measurement terminals are A and B of the line, the data time window is 3.0ms after the fault, and the sampling frequency is 5MHz.
[0043] A metallic short-circuit fault occurred between the positive and negative poles 500m from terminal A of the line. The fault transition resistance was... The voltage traveling wave waveforms and their corresponding spectral distributions observed at both ends of line A and B within a 3.0 ms time window are as follows: Figure 4 As shown.
[0044] Depend on Figure 4 It can be seen that the voltage traveling wave observed at the measurement end exhibits a good periodicity. The extracted spectrum is the natural frequency and its harmonics that reflect the fault distance. The difference between the first and second natural frequencies of the traveling wave at line A end is 229.797kHz, and the difference between the first and second natural frequencies of the traveling wave at line B end is 28.382kHz. Since the frequency difference at line A end is larger, the fault point is closer to line A end. Substituting the ratio of the frequency difference values at both ends into the ranging equation for calculation, the fault ranging result is 549.657m, which differs from the actual fault distance by 49.657m, and the ranging error is 0.993%.
[0045] The method for calculating the ranging error is as follows: ; In the formula: This is the result of fault location; This represents the actual distance to the fault. This is the total length of the line.
[0046] A metallic short-circuit fault occurred between the positive and negative poles 1000m from terminal A of the line. The fault transition resistance was... The voltage traveling wave waveforms and their corresponding spectral distributions observed at both ends of line A and B within a 3.0 ms time window are as follows: Figure 5 As shown.
[0047] Depend on Figure 5It can be seen that the voltage traveling wave observed at the measurement end exhibits a good periodicity. The extracted spectrum is the natural frequency and its harmonics that reflect the fault distance. The difference between the first and second natural frequencies of the traveling wave at line A end is 120.240kHz, and the difference between the first and second natural frequencies of the traveling wave at line B end is 32.044kHz. Since the frequency difference at line A end is larger, the fault point is closer to line A end. Substituting the ratio of the frequency difference values at both ends into the ranging equation for calculation, the fault ranging result is 1052.113m, which differs from the actual fault distance by 52.113m, and the ranging error is 1.042%.
[0048] A metallic short-circuit fault occurred between the positive and negative poles 1500m from terminal A of the line. The fault transition resistance was... The voltage traveling wave waveforms and their corresponding spectral distributions observed at both ends of line A and B within a 3.0 ms time window are as follows: Figure 6 As shown.
[0049] Depend on Figure 6 It can be seen that the voltage traveling wave observed at the measurement end exhibits a good periodicity. The extracted spectrum is the natural frequency and its harmonics that reflect the fault distance. The difference between the first and second natural frequencies of the traveling wave at line A end is 81.177kHz, and the difference between the first and second natural frequencies of the traveling wave at line B end is 36.010kHz. Since the frequency difference at line A end is larger, the fault point is closer to line A end. Substituting the ratio of the frequency difference values at both ends into the ranging equation for calculation, the fault ranging result is 1536.433m, which differs from the actual fault distance by 36.433m, and the ranging error is 0.729%.
[0050] A metallic short-circuit fault occurred between the positive and negative poles 3000m from terminal A of the line. The fault transition resistance was... The voltage traveling wave waveforms and their corresponding spectral distributions observed at both ends of line A and B within a 3ms time window are as follows: Figure 7 As shown.
[0051] Depend on Figure 7 It can be seen that the voltage traveling wave observed at the measurement end exhibits a good periodicity. The extracted spectrum is the natural frequency and its harmonics that reflect the fault distance. The difference between the first and second natural frequencies of the traveling wave at line A end is 41.809kHz, and the difference between the first and second natural frequencies of the traveling wave at line B end is 61.645kHz. Since the frequency difference at line B end is larger, the fault point is closer to line B end. Substituting the ratio of the frequency difference values at both ends into the distance measurement equation for calculation, the fault distance result is 2979.343m, which differs from the actual fault distance by 20.657m, and the distance measurement error is 0.413%.
[0052] Table 1 presents the fault location results for different fault distances, as shown in Table 1: Table 1. Distance measurement test results at different fault distances
[0053] As can be seen from Table 1, the present invention can achieve accurate and stable fault location within a short time window over the entire length of a DC traction network line, with the location error at different fault distances remaining stable at about 1% of the total line length.
[0054] Furthermore, when a nonmetallic short-circuit fault occurs at different distances from terminal A of the line, the fault transition resistances are respectively... , and .
[0055] Table 2 presents the fault location results under different fault transition resistances, as shown in Table 2: Table 2 Ranging test results under different fault transition resistances
[0056] As can be seen from Table 2, the present invention has good adaptability to different fault transition resistances. The reason for this is that the existence of the transition resistance only affects the amplitude of the reflection coefficient of the traveling wave at the fault point. It is worth noting that for DC traction network lines, the possibility of large fault transition resistances is generally not considered.
[0057] Furthermore, the first frequency of the natural frequency of the fault traveling wave is relatively high, typically on the order of 10. 4 The Hz is much higher than the harmonics generated by the traction power supply system, so the system harmonics will not affect the accuracy and stability of this DC fault location method.
[0058] The specific embodiments described above do not constitute a limitation on the scope of protection of this application. Those skilled in the art should understand that various modifications, combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the scope of protection of this application. In some cases, the actions or steps described in this application can be performed in a different order than that shown in the embodiments and still achieve the desired results. Furthermore, the processes depicted in the accompanying drawings do not necessarily require a specific or sequential order to achieve the desired results. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.
[0059] The above description is merely an illustrative embodiment of the present invention and is not intended to limit the scope of the invention. Any equivalent changes and modifications made by those skilled in the art without departing from the concept and principles of the present invention should fall within the scope of protection of the present invention. Furthermore, it should be noted that the components of the present invention are not limited to the overall application described above. Each technical feature described in the specification can be used individually or in combination as needed. Therefore, the present invention naturally covers other combinations and specific applications related to this case.
[0060] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. The invention extends to any new features or combinations disclosed in this specification, and any modifications, equivalent substitutions, and improvements made within the spirit and principles of the invention should be included within the scope of protection of the invention. It is obvious to those skilled in the art that the invention is not limited to the details of the above exemplary embodiments, and that detailed technical features not disclosed in this embodiment, such as specific structures, are all prior art and can be obtained by those skilled in the art from the prior art. The connection method can be a fixed connection, a detachable connection, or an integral part; it can be a fixed connection, a movable connection, or a hinged connection; it can be a direct connection or an indirect connection through an intermediate medium. Those skilled in the art can understand the specific manner of the above terms in the embodiments of the present invention according to the specific circumstances, and this disclosure does not specifically limit this aspect.
Claims
1. A method for DC fault location in a subway traction power supply system, characterized in that, Includes the following steps: S1. Collect voltage traveling wave data from the traveling wave coupling boxes at both ends of DC traction network line A and B within a 3ms time window after the fault. , ; S2. Apply a periodic Hanning window to the acquired voltage traveling wave data in the time domain and perform zero-padding preprocessing. S3. Perform fast Fourier transform analysis on the preprocessed voltage traveling wave data to extract the spectral distribution information of the double-ended voltage traveling wave, identify the position of the spectral peak and record its corresponding frequency value. S4. Match the spectrum obtained from both ends and calculate the first and second frequency difference values of the natural frequencies of the traveling wave at both ends respectively. S5. Calculate the ratio of the frequency difference between the two ends, and use the functional relationship between this ratio and the fault distance to perform distance measurement.
2. The method for DC fault location in a subway traction power supply system according to claim 1, characterized in that: In S1, the traveling wave coupling box is deployed on the DC feeder.
3. The DC fault location method for a subway traction power supply system according to claim 1, characterized in that: In S2, with For example, the windowing process can be represented as: ； in: For periodic Hanning windows, ; The length of the window function is the number of discrete sampling points.
4. The DC fault location method for a subway traction power supply system according to claim 1, characterized in that: In S2, the length of the collected data sequence The data length is often not an integer power of 2; it is padded with zeros to make it equal to the specified length. ( h (where is a positive integer), represented as: .
5. The DC fault location method for a subway traction power supply system according to claim 1, characterized in that: In S3, the fault traveling wave spectrum obtained at end A of the DC traction network line satisfies: ； in: and These are the reflection coefficients of the traveling wave at line A and fault point F, respectively; Let F be the time it takes for the traveling wave to propagate from the fault point F to end A of the line. , Let F be the distance from the fault point F to end A of the line. The speed of travel wave propagation; Using Euler's formula, the above expression can be transformed into exponential form, which can be expressed as: ； We can solve for: ； in: Let be the reflection angle of the traveling wave at end A of the line. ; Let F be the reflection angle of the traveling wave at the fault point F. ; ; The imaginary part in the above equation corresponds to the angular frequency of the natural frequency. Therefore, the natural frequency formed by the fault traveling wave can be expressed as: 。 6. The method for DC fault location in a subway traction power supply system according to claim 1, characterized in that: In S4, the calculation of the first frequency of the fault traveling wave natural frequency extracted from both ends A and B of the DC traction network line. The formula is: ； No. The formula for calculating the next frequency is: ； in: and These are the reflection angles of the traveling wave at points A and B of the line, respectively. The traveling wave velocity is almost constant at its natural high frequency and can be considered a fixed value. The total length of the line; The formula for calculating the difference between adjacent natural frequencies of a two-ended traveling wave is: ； The formula for calculating the first and second frequency differences of the natural frequencies of a two-ended traveling wave is as follows: 。 7. The DC fault location method for a subway traction power supply system according to claim 1, characterized in that: In S5, the formula for calculating the ratio of the two-terminal frequency difference values is: ； make: ； The equation for two-way distance measurement is: ； in: It is the ratio of the difference between the first and second natural frequencies of the two-ended traveling wave.
8. The DC fault location method for a subway traction power supply system according to claim 7, characterized in that: The ratio of the natural frequency difference of the two-terminal traveling wave can also be expressed as: ； The corresponding two-end distance measurement equation is: 。 9. The method for DC fault location in a subway traction power supply system according to claim 1, characterized in that: The method does not rely on a dual-end clock synchronization mechanism, and the ranging results are not affected by line terminal boundary conditions, parameter frequency variation characteristics, and fault transition resistance.
10. A method for DC fault location in a subway traction power supply system according to claim 1, characterized in that: The method is applicable to both metallic and non-metallic short circuit faults, with the ranging error remaining stable at approximately 1% of the total line length.
11. A DC fault location system for a subway traction power supply system, used to implement the DC fault location method for a subway traction power supply system as described in any one of claims 1 to 10, characterized in that, include: The data acquisition module is used to acquire and store voltage traveling wave data at both ends of the DC traction network line traveling wave coupling box at high speed. The data time window is within 3ms after the fault occurs. The preprocessing module is used to perform windowing and zero-padding preprocessing on the acquired voltage traveling wave data. The selected window function is the periodic Hanning window, and zero-padding is used to make the data length [missing information]. (h is a positive integer); The spectrum analysis module is used to extract the spectrum distribution of the traveling wave of the two-terminal voltage using FFT and to determine the frequency value corresponding to the position of the spectrum peak. The frequency difference calculation module is used to calculate the first and second frequency differences of the natural frequencies of the double-ended traveling wave, and to calculate the ratio of the two-ended frequency difference values. The fault location module is used to calculate the fault distance using the ratio of the frequency difference of the two-end traveling waves and output the location result.