A flexible direct current power distribution line wave speed measurement method and system

By generating voltage traveling waves through step regulation of the MMC converter and calculating the average wave velocity, the problem of wave velocity measurement error in flexible DC distribution lines is solved, and the accuracy of fault location is improved.

CN116359669BActive Publication Date: 2026-03-24YANGZHOU POWER SUPPLY BRANCH OF STATE GRID JIANGSU ELECTRIC POWER CO LTD +2
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Patent Information

Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2023-03-23
Publication Date
2026-03-24

AI Technical Summary

Technical Problem

In existing technologies, the methods for measuring wave velocity in flexible DC distribution lines contain errors, leading to inaccurate fault location using the traveling wave method and affecting power restoration time.

Method used

The MMC converter is started up, and the DC voltage of the output bus is adjusted in stages to generate a voltage traveling wave. The arrival time of the traveling wave is recorded, and the average value of multiple voltage traveling waves is calculated to obtain the wave velocity.

Benefits of technology

It improves the accuracy of wave velocity measurement in flexible DC distribution lines and enhances the accuracy of fault location using the traveling wave method.

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Abstract

The application provides a flexible direct current power distribution line wave speed measurement method and system, including the following steps: S1, converter starting, generating a voltage traveling wave by step adjustment of the outlet bus DC voltage; S2, recording the time when the traveling wave reaches the measuring point of the outlet bus of the converter and each measuring point along the line; S3, calculating the wave speed between any two measuring points before and after according to the physical interval between the measuring points and the time when the traveling wave reaches each measuring point; S4, calculating the corresponding wave speed by detecting multiple voltage traveling waves, and taking the average value of the multiple calculation results as the final result. The application solves the problem of inaccurate wave speed calculation according to line parameters in the traditional method, realizes the wave speed measurement of the flexible direct current power distribution line online, and improves the wave fault distance measurement accuracy of the wave speed information.
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Description

TECHNICAL FIELD

[0001] The present application relates to the field of flexible DC power distribution, in particular to a flexible DC power distribution line wave speed measurement method and system. BACKGROUND

[0002] With the development of power electronics technology, flexible DC power distribution network is gradually becoming an important choice for future power distribution network form, which has the advantages of good power quality, small line loss, easy control, etc., and can be friendly connected to photovoltaic, wind turbine and energy storage and other distributed power sources. In the power distribution system, the power distribution line bears the important responsibility of transmitting electric energy, so the operation reliability of the line directly affects the power supply reliability of the power system. When the power distribution line fails, accurate fault location needs to be performed using the traveling wave method to quickly find the fault and restore power supply. When using the traveling wave method, the wave speed of the line is the prerequisite for fault location, and the accuracy of the wave speed affects the accuracy of the fault location, and ultimately affects the length of time to restore power supply.

[0003] Currently, for wave speed measurement, the line inductance and capacitance parameters are brought into the wave speed calculation formula to obtain the result by comparing the manufacturer's provided parameter table. In fact, inductance and capacitance are only an approximate equivalent of the line, and this method has certain error. On the other hand, the method of determining the wave speed according to the calculation formula is theoretical, and there will be an error between the actual wave speed of the running line and the theoretical wave speed. Therefore, it is necessary to combine the characteristics of the flexible DC power distribution network to research a method that can accurately measure the actual wave speed of the line in this scenario, and improve the accuracy of the traveling wave method fault location from the source. SUMMARY

[0004] The present application aims to at least solve one of the technical problems existing in the prior art.

[0005] The technical scheme of the present application is: a flexible DC power distribution line wave speed measurement method, comprising the following steps:

[0006] S1, starting the converter, generating a voltage traveling wave by step adjusting the outlet bus DC voltage;

[0007] S2, recording the time when the traveling wave arrives at the outlet bus measurement point of the converter and each measurement point along the line;

[0008] S3, calculating the wave speed between any two adjacent measurement points according to the physical interval between the measurement points and the time when the traveling wave arrives at each measurement point;

[0009] S4, by detecting multiple voltage traveling waves, calculating the corresponding wave speed, and taking the average value of the multiple calculation results as the final result.

[0010] The converter includes three phase units connected in parallel, and each phase unit consists of 2N sub-modules connected in series.

[0011] Among them, N sub-modules form the upper bridge arm and the remaining N sub-modules form the lower bridge arm. The sub-modules include IGBTs that can be controlled to turn on and off, anti-parallel diodes, and sub-module capacitors.

[0012] The DC voltage of the converter output bus is controlled by adjusting the input or output of the submodule capacitors in each phase unit.

[0013] In step S1, during the step adjustment, the same number of submodule capacitors are added multiple times until the DC voltage is adjusted to the rated voltage.

[0014] Step S1 includes:

[0015] S11. Determine the constant m to ensure that m can be controlled by the rated voltage U. dc The sum of the number of submodules in each phase's upper and lower bridge arms is divisible by N;

[0016] m represents the sum of the number of upper and lower bridge arm submodules adjusted during the converter startup process. N represents the number of submodules. c Each adjustment will add N / m new sub-modules, generating an amplitude of U. dc A step voltage traveling wave of / m continues until, after m adjustments, N c =N;

[0017] S12. Before startup, pre-charge all submodules in the converter. After charging is complete, disconnect all submodules, and the number of submodules in operation is 0, i.e., N. c =0, i indicates the adjustment of N c The number of times, set i = 1;

[0018] S13. At startup, adjust N. c , making N c =N c +N / m increases the DC voltage amplitude of the outlet bus by U dc / m, the voltage step wave generated during the startup process is denoted as f(i), i=1,2,...m.

[0019] Step S2 includes:

[0020] S21. Using the converter outlet busbar as the coordinate origin, record the coordinates x1, x2...x of each measurement point on the line. r ;

[0021] S22, Record the i-th adjustment N cAfterwards, the time t0(i) when the step voltage traveling wave f(i) reaches the converter outlet bus and the time t1(i), t2(i),..., t r (i).

[0022] In step S3,

[0023] According to the fact that the converter outlet bus is the coordinate origin x0=0, the coordinates of each measuring point are known, and the time when the traveling wave reaches each measuring point is measured, the wave speed between any two adjacent measuring points p and p+1 on the line is:

[0024]

[0025] In step S4,

[0026] After m times of measurement of the time when the traveling wave reaches, a series of wave speeds v p (1), v p (2),..., v p (m) can be obtained by calculation, and the average value is finally taken as the wave speed of the line between the measuring points p and p+1, as follows:

[0027]

[0028] The physical interval between the measuring points is obtained by field measurement or according to the parameters provided by the manufacturer.

[0029] A flexible DC distribution line wave speed measurement system, comprising:

[0030] An adjusting module for starting the converter to generate a voltage traveling wave by step adjusting the DC voltage of the outlet bus;

[0031] A recording module for recording the time when the traveling wave reaches the measuring point of the outlet bus of the converter and each measuring point along the line;

[0032] A calculation module for calculating the wave speed between any two adjacent measuring points according to the physical interval between the measuring points and the time when the traveling wave reaches each measuring point;

[0033] A measurement module for calculating the corresponding wave speed by detecting multiple voltage traveling waves, and taking the average value of the multiple calculation results as the final result.

[0034] The present application solves the problem of inaccurate wave speed calculation according to line parameters in the traditional method, realizes online wave speed measurement of the flexible DC distribution line, and improves the wave fault distance measurement accuracy of the wave speed information. BRIEF DESCRIPTION OF DRAWINGS

[0035] Figure 1 The flowchart of the present application,

[0036] Figure 2 This is a topology diagram of a flexible DC power distribution system.

[0037] Figure 3 This is a diagram of the internal structure of the converter.

[0038] Figure 4 This is a diagram of the ±10kV flexible DC power distribution system in the embodiment.

[0039] Figure 5 For the example u dc With N c Relationship diagram

[0040] Figure 6 For the example u dc Graph showing the relationship between time t and time t. Detailed Implementation

[0041] The present invention is as follows Figure 1 As shown, a method for measuring wave velocity in a flexible DC distribution line includes the following steps:

[0042] S1. The converter (i.e., MMC converter) starts up, and a voltage traveling wave is generated by step-by-step adjustment of the DC voltage of the output bus.

[0043] S2. Record the arrival time of the traveling wave detected at the converter's outlet bus measurement point and at each measurement point along the line.

[0044] S3. Calculate the wave velocity between any two consecutive measurement points based on the physical interval between the measurement points and the arrival time of the traveling wave at each measurement point.

[0045] S4. By detecting multiple voltage traveling waves, the corresponding wave velocity is calculated, and the average value of the multiple calculation results is taken as the final result.

[0046] The principle of this invention is analyzed as follows:

[0047] 1. Topology of Flexible DC Distribution System

[0048] like Figure 2 As shown, in a flexible DC distribution network, the AC grid is connected to the MMC converter via a converter transformer, and the converter converts the AC power to DC power. For the distribution lines and electrical equipment, the converter is approximated as a DC power source. The area from the converter's output busbar onwards falls within the scope of the flexible DC distribution line. There are a total of r measurement points on the distribution line, and determining the wave velocity of each line segment is the objective of this technical solution.

[0049] 2. DC-side control principle of MMC converter

[0050] The MMC converter consists of a series of submodules. Each submodule contains controllable IGBTs (inverter transistors), anti-parallel diodes, and submodule capacitors. The MMC has three parallel phase units, each composed of 2N submodules connected in series, with N submodules in each of the upper and lower arms. By controlling the connection or disconnection of the capacitors in each submodule, the DC voltage at the converter output can be controlled. The internal structure of the MMC converter is as follows: Figure 3 As shown.

[0051] During normal operation, to maintain a constant DC voltage, the number of submodules in the active state in the three phase units must be equal and constant. Ignoring voltage drops due to resistance and inductance, the sum of the voltages of the upper and lower bridge arm submodules and the DC side voltage U... dc The relationship is

[0052] u pa +u na =u pb +u nb =u pc +u nc =U dc

[0053] The subscript p represents the upper bridge arm, n represents the lower bridge arm, and a, b, and c correspond to the three phase units respectively.

[0054] Assuming that the voltage across the capacitor of each submodule is u under the voltage equalization control strategy c Then the number of submodules deployed in each bridge arm is N. mx The sum of the voltages of the bridge arm submodules, u mx The relationship is:

[0055] u mx =N mx u c

[0056] Subscripts m = p, n correspond to the upper or lower bridge arm; subscripts x = a, b, c correspond to the three phase units.

[0057] Assuming that under the control target of rated DC voltage, the sum of the number of upper and lower bridge arm submodules in each phase unit is N, and the rated DC voltage and the voltage u of a single submodule are... c The relationship is

[0058] U dc =Nu c

[0059] Therefore, the relationship between the number of sub-modules deployed in each bridge arm is as follows:

[0060] N pa +N na =N pb +N nb =Npc +N nc =N

[0061] In summary, as long as the sum of the number of upper and lower bridge arm submodules engaged in each phase unit is equal to a certain constant, the DC voltage can be kept constant. Furthermore, by changing the value of this constant, the magnitude of the output DC voltage can be controlled.

[0062] 3. MMC converter startup

[0063] During the startup process of the MMC converter, the sum of the number of upper and lower bridge arm submodules of each phase unit is used as the control variable, denoted as N. c This ensures that the quantity relationship between the upper and lower bridge arm submodules of each phase unit satisfies...

[0064] N pa +N na =N pb +N nb =N pc +N nc =N c (1)

[0065] Before the converter starts up and establishes DC voltage, all submodules need to be pre-charged, and after charging is complete, all submodules are disconnected. Before startup, the number of submodules in operation is 0, i.e., the initial state is N. c =0

[0066] During the converter startup process, N is increased in m equal increments. c Each time, N / m sub-modules are added, until the final startup ends. c =N, the DC voltage reaches the rated value. Each time N increases... c This means that the total number of submodules put into operation in each phase unit increases. Since the submodule capacitors are pre-charged, the capacitor voltage of the newly put submodules will cause a steep rise in the DC voltage at the converter output, generating a voltage traveling wave. Therefore, each increase in N... c All of these will generate an amplitude of U at the converter outlet. dc The voltage step wave / m is denoted as f(i), i=1,2,...m.

[0067] The measurement point at the converter outlet bus is designated as point 0 and set as the origin of the coordinate system. Assume there are r measurement points along the line, numbered sequentially from 1 to r. The coordinates of the measurement points are x1, x2, ..., xr. r .

[0068] After the voltage step traveling wave f(i) is generated, it propagates along the DC distribution line. The arrival time of the traveling wave is detected at measurement point 0 at the converter outlet bus and recorded as t0(i). The arrival times of the traveling wave are recorded at measurement points 1 to r and recorded as t1(i), t2(i), ..., t r (i).

[0069] Given that the converter outlet bus is the origin x0 = 0, and the coordinates of each measuring point are known, and the arrival times of the traveling wave at each measuring point are also measured, the wave velocity between any two consecutive measuring points p and p+1 on the line is:

[0070]

[0071] The physical intervals between measurement points are obtained through on-site measurements or based on parameters provided by the manufacturer.

[0072] After measuring the arrival time of the traveling wave m times, a series of wave velocities v can be obtained through calculation. p (1),v p (2),...v p (m), and finally take the average value as the wave velocity of the line between the measurement points before and after p and p+1.

[0073]

[0074] In summary, the procedure for measuring wave velocity in flexible DC distribution lines is as follows:

[0075] 1) Determine the constant m to ensure that m can be proportional to the rated voltage U. dc The sum of the number of upper and lower bridge arm submodules for each phase is N, which is divisible by m. m represents the number of upper and lower bridge arm submodules for each phase adjusted during converter startup, which is N. c Each adjustment will add N / m new sub-modules, generating an amplitude of U. dc A step voltage traveling wave of / m continues until, after m adjustments, N c =N;

[0076] 2) Pre-charge all submodules of the MMC converter. After charging is complete, disconnect all submodules, and the number of submodules in operation is 0, i.e., N. c =0, i indicates the adjustment of N c The number of times, set i = 1;

[0077] 3) Adjust N c , making N c =N c +N / m increases the DC voltage amplitude of the outlet bus by U dc / m, and maintain for a certain period of time;

[0078] 4) Using the converter outlet bus as the coordinate origin, record the coordinates x1, x2...x at r measurement points along the line. r ;

[0079] 5) Record the i-th adjustment of N c Afterwards, the time t0(i) for the step voltage traveling wave f(i) to reach the converter outlet bus and the times t1(i), t2(i), ..., t1(i), ..., t2(i), ..., t3(i) for reaching the r measurement points on the line are calculated. r (i);

[0080] 6) Calculate N for the i-th adjustment according to formula (2). c Afterwards, the line wave velocity v between points p and p+1 p (i), p = 0, 1, 2, ..., r-1;

[0081] 7) Determine if the loop condition is met: i < m. If it is met, set i = i + 1 and return to step 4) to continue. If it is not met, it means that m traveling waves have been generated during the converter startup process, the DC voltage has reached the rated value, and the startup ends.

[0082] 8) The line wave velocity between points p and p+1 is finally calculated according to formula (3).

[0083] A flexible DC power distribution line wave velocity measurement system includes:

[0084] The regulating module is used for converter startup and generates a voltage traveling wave by step regulating the DC voltage of the outlet bus.

[0085] The recording module is used to record the arrival time of the traveling wave detected at the measurement points of the converter's outlet bus and at various measurement points along the line.

[0086] The calculation module calculates the wave velocity between any two consecutive measurement points based on the physical interval between the measurement points and the arrival time of the traveling wave at each measurement point.

[0087] The measurement module detects multiple voltage traveling waves, calculates the corresponding wave velocity, and takes the average of the multiple calculation results as the final result.

[0088] In a specific application, this method is illustrated using a ±10kV flexible DC distribution line as an example.

[0089] like Figure 4 As shown, the 35kV AC power grid is connected to the MMC converter via a 35kV / 10kV converter transformer, which converts it into DC power with a rated voltage of ±10kV. The rated voltage U between the two poles of the converter's output bus is... dc =20kV

[0090] A measurement point, numbered 0, is set at the converter outlet bus; there are three measurement points, numbered 1 to 3, on the flexible DC distribution lines downstream of the bus. The objective is to determine the wave velocity of the three lines between the measurement points.

[0091] With the converter outlet busbar as the origin x0 = 0, the coordinates of measurement point 1 are x1, the coordinates of measurement point 2 are x2, and the coordinates of measurement point 3 are x3.

[0092] Each phase unit of the MMC converter has a total of 80 sub-modules in both the upper and lower arms: 40 in the upper arm and 40 in the lower arm. According to the definition in the invention, N = 40. Assuming U at rated voltage... dc Each phase unit has N=40 sub-modules in its upper and lower bridge arms. The rated capacitor voltage u of a single sub-module after charging is... c for

[0093]

[0094] The converter outlet bus voltage is denoted as u. dc N is the sum of the number of upper and lower bridge arm submodules of each phase unit. c relation

[0095] u dc =N c u c

[0096] Let the converter outlet bus voltage be denoted as u. dc u dc With N c Relationship such as Figure 5 As shown;

[0097] When N=40 sub-modules are engaged in each phase unit's upper and lower bridge arms, the DC voltage at the converter output bus reaches the rated value, i.e., u. dc =U dc

[0098] During the start-up process of the converter, the sum N of the number of upper and lower bridge arm submodules of each phase unit is adjusted in four equal increments. c Then m = 4. Each time N is adjusted... c After that, N c Will increase After each adjustment, the converter outlet will generate an amplitude of U. dc / m=5kV step voltage traveling wave.

[0099] Before the converter starts up, all submodules are charged to the rated submodule voltage u. c =0.5kV, and disconnect all submodules. Specify t=0 as the start time of the converter startup process, and adjust N once at intervals Δt. c Each time Nc Increase Under this adjustment method, u dc The relationship with time t is as follows Figure 6 As shown;

[0100] Therefore, during the startup process, N is adjusted once every Δt interval. c , making N c Increase by 10. Increase by N each time. c Afterwards, a step voltage traveling wave with an amplitude of 5kV will be generated, which will propagate from the converter output bus to the distribution line. The i-th adjustment of N... c The step voltage traveling wave generated at the output of the converter is denoted as f(i), where i = 1, 2, 3, 4.

[0101] 1) After a time interval Δt, N is adjusted for the first time. c N c From 0 to 10, u dc The amplitude increases from 0 to 5kV, and the resulting step voltage traveling wave is denoted as f(1). At this time, the arrival time of f(1) is recorded at the converter outlet bus measurement point as t0(1), the arrival time of f(1) is recorded at measurement point 1 on the line as t1(1), the arrival time of f(1) is recorded at measurement point 2 as t2(1), and the arrival time of f(1) is recorded at measurement point 3 as t3(1).

[0102] Substitute the time when f(1) arrives at each measurement point into formula (2) to calculate the line wave velocity v1(1) between measurement point 1 and the converter outlet bus, the line wave velocity v2(1) between measurement point 1 and measurement point 2, and the line wave velocity v3(1) between measurement point 2 and measurement point 3.

[0103]

[0104]

[0105]

[0106] 2) After a time interval Δt, adjust N again. c N c From 10 to 20, u dc The amplitude increases from 5kV to 10kV, and the resulting step voltage traveling wave is denoted as f(2). At this time, the measurement point at the converter outlet bus records the arrival time of f(2) as t0(2), the measurement point 1 on the line records the arrival time of f(2) as t1(2), the measurement point 2 records the arrival time of f(2) as t2(2), and the measurement point 3 records the arrival time of f(2) as t3(2).

[0107] Similarly, by substituting the time when f(2) arrives at each measurement point into formula (2), the line wave velocity v1(2) between measurement point 1 and the converter outlet bus, the line wave velocity v2(2) between measurement point 1 and measurement point 2, and the line wave velocity v3(2) between measurement point 2 and measurement point 3 are obtained.

[0108]

[0109]

[0110]

[0111] 3) Similar to steps 1) and 2), the third adjustment of N occurs at t = 3Δt. c N c From 20 to 30, u dc The amplitude increases from 10kV to 15kV, and the resulting step voltage traveling wave is denoted as f(3). Substituting the arrival times of the traveling waves f(3) recorded at each measurement point into formula (2) yields v1(3), v2(3), and v3(3). The specific process will not be elaborated further. Similarly, at t = 4Δt, the fourth adjustment of N... c N c From 30 to 40, u dc The amplitude increases from 15kV to 20kV, and the resulting step voltage traveling wave is denoted as f(4). Finally, the arrival times of the traveling waves f(4) recorded at each measurement point are substituted into formula (2) to calculate v1(4), v2(4), and v3(4).

[0112] 4) After a time interval of 4Δt, N was adjusted a total of 4 times. c The converter startup process is complete. c =N=40, u dc =U dc =20kV. Substituting the wave velocities of each line segment obtained from the four measurements into formula (3) for calculation, the final wave velocity result is obtained:

[0113]

[0114]

[0115]

[0116] The measurement results are for the line wave velocity between measurement point 0 and measurement point 1 at the converter bus outlet.

[0117] The measurement results are for the line wave velocity between measurement point 1 and measurement point 2.

[0118] The measurement results are for the line wave velocity between measurement point 2 and measurement point 3.

[0119] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for measuring wave velocity in a flexible DC distribution line, characterized in that, Includes the following steps: S1. The converter starts up and generates a voltage traveling wave by adjusting the DC voltage of the output bus in a stepped manner. The converter includes three phase units connected in parallel, and each phase unit consists of 2N sub-modules connected in series. Among them, N sub-modules form the upper bridge arm and the remaining N sub-modules form the lower bridge arm. The sub-modules include IGBTs that can be controlled to turn on and off, anti-parallel diodes, and sub-module capacitors. The DC voltage of the converter output bus is controlled by adjusting the input or output of the capacitors in the sub-modules of each phase unit. During step adjustment, the same number of submodule capacitors are added in multiple stages until the DC voltage is adjusted to the rated voltage. Step S1 includes: S11. Determine the constant m to ensure that m can be controlled by the rated voltage. U dc The sum of the number of submodules in each phase upper and lower bridge arm N Divisible; m represents the sum of the number of upper and lower bridge arm submodules adjusted during the converter startup process. N c The number of times, each adjustment, will involve new input. N / m sub-modules, generating an amplitude of U dc A step voltage traveling wave of / m is generated until it is adjusted m times. N c =N ; S12. Before startup, pre-charge all sub-modules in the converter. After charging is complete, disconnect all sub-modules, reducing the number of sub-modules in operation to 0. N c =0, use i Indicating regulation N c The number of times, set i =1; S13. During startup, adjust N c ,make N c =N c +N / m, causing the DC voltage amplitude of the outlet bus to increase. U dc / m, the voltage step traveling wave generated during the startup process is denoted as f ( i ) ,i =1,2,… m ; S2. Record the arrival time of the traveling wave detected at the converter's outlet bus measurement point and at each measurement point along the line. S3. Calculate the wave velocity between any two consecutive measurement points based on the physical interval between the measurement points and the arrival time of the traveling wave at each measurement point. S4. By detecting multiple voltage traveling waves, the corresponding wave velocity is calculated, and the average value of the multiple calculation results is taken as the final result.

2. The wave velocity measurement method for a flexible DC distribution line according to claim 1, characterized in that, Step S2 includes: S21. Using the converter outlet busbar as the coordinate origin, record the coordinates of each measurement point on the line. x 1, x 2... x r ; S22, Record the first i Sub-adjustment N c Afterwards, the step voltage traveling wave f ( i Time to reach the converter outlet bus t 0 ( i And the time of arrival at r measurement points on the line. t 1 ( i ), t 2 ( i ),…, t r ( i ).

3. The wave velocity measurement method for a flexible DC distribution line according to claim 2, characterized in that, In step S3, Based on the converter outlet bus as the origin of the coordinate system x Given that 0=0, the coordinates of each measurement point are known, and the arrival times of the traveling wave at each measurement point are also measured, then the wave velocity between any two consecutive measurement points p and p+1 on the line is: 。 4. The wave velocity measurement method for a flexible DC distribution line according to claim 3, characterized in that, In step S4, After measuring the arrival time of the traveling wave m times, a series of wave velocities can be obtained through calculation. v p (1), v p (2),… v p (m), and finally take the average value as the wave velocity of the line between the measurement points before and after p and p+1, as shown in the following formula: 。 5. The wave velocity measurement method for a flexible DC distribution line according to claim 1, characterized in that, The physical intervals between measurement points are obtained through on-site measurements or based on parameters provided by the manufacturer.

6. A wave velocity measurement system for flexible DC distribution lines, characterized in that, The wave velocity measurement method for flexible DC distribution lines according to any one of claims 1-5 includes: The regulating module is used for converter startup and generates a voltage traveling wave by step regulating the DC voltage of the outlet bus. The recording module is used to record the arrival time of the traveling wave detected at the measurement points of the converter's outlet bus and at various measurement points along the line. The calculation module calculates the wave velocity between any two consecutive measurement points based on the physical interval between the measurement points and the arrival time of the traveling wave at each measurement point. The measurement module detects multiple voltage traveling waves, calculates the corresponding wave velocity, and takes the average of the multiple calculation results as the final result.

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