Wave velocity real-time correction method and system based on wave equation single-ended solution

Abstract

The invention discloses a wave velocity real-time correction method and system based on a wave equation single-ended solution, and belongs to the technical field of power systems. The method comprises the following steps: acquiring an electric quantity information sequence of two sides of a power transmission line in a cycle before protection starting; calculating the capacitive reactance and the impedance angle of the line; forming a data set of impedance values by using the impedance setting value, and calculating variables required by wave equation measurement and calculation; within the range of the impedance value data set, measuring and calculating the voltage information of the opposite side by using the wave equation according to the electrical quantity information of the two sides; calculating the mean square error of the measured voltage and the measured voltage of the opposite side, and taking the impedance quantity corresponding to the minimum value of the mean square error as the identification result of the power transmission line parameter; and calculating a wave velocity according to an identification result of the line parameters, and applying the calculated wave velocity to calculation of traveling wave distance measurement. Based on the single-end analytical solution of the wave equation, the influence of transition resistance is eliminated, the online identification of the power transmission line and the calculation of the wave velocity are realized, and the traveling wave distance measurement precision is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of power systems, and more particularly to a real-time wave velocity correction method and system based on a single-ended solution of a wave equation. Background Art

[0002] Transmission lines, the core carrier of power transmission, can cause grid instability or even collapse when faults occur. Traditional impedance ranging methods are significantly affected by factors such as transition resistance and system operating mode, resulting in high errors. Against this backdrop, traveling wave ranging technology has seen further development. Traveling wave ranging uses a simple equation of distance, velocity, and time to calculate fault distance. Its core principle is to accurately capture the traveling wave head and precisely calculate the traveling wave velocity, which directly impacts ranging error and accuracy. In traveling wave ranging, the accuracy of traveling wave velocity is a key parameter determining fault location accuracy. Traditional methods typically use fixed empirical values ​​as baseline values ​​for traveling wave velocity, such as 294 km / ms for overhead lines and 170 km / ms for cross-linked polyethylene cables. However, this assumption has significant limitations in practical applications. The dynamic nature of traveling wave velocity, influenced by a combination of line parameters, frequency characteristics, line structure, cable insulation, and environmental factors, leads to errors in ranging methods, seriously hindering further improvements in traveling wave ranging accuracy.

[0003] Currently, several methods exist for calculating traveling wave velocity, including dual-terminal ranging data fusion, fault event-driven learning, frequency domain feature correlation analysis, and model predictive control. However, in practical applications, dual-terminal ranging data fusion relies on high-precision time synchronization, suffers from weak anti-interference capabilities, and the deployment cost of high-precision timing devices is high. Fault event-driven learning establishes a velocity correction model based on historical fault types, but this method relies on data accumulation, lacks real-time performance, and struggles to adapt to sudden environmental changes. Frequency domain feature correlation analysis is poorly adaptable to cable scenarios, with calculation errors reaching up to 2% under certain operating conditions. Model predictive control predicts velocity by establishing a dynamic model of velocity-environmental parameters. However, this method requires accurate quantification of the mapping between environmental parameters and velocity, which is difficult to implement in practical engineering applications. Furthermore, it consumes significant real-time computing resources and is difficult for embedded devices to implement. To address these issues, a simple, highly accurate, and widely applicable traveling wave velocity calculation method is urgently needed. Summary of the Invention

[0004] In order to address the deficiencies in the prior art, the present invention provides a real-time wave velocity correction method and system based on a single-ended solution of a wave equation. Utilizing the single-ended solution of the wave equation, within a given impedance range, different impedance values ​​and the electrical quantities collected on this side are used to calculate the voltage value on the opposite side. The impedance value with the smallest error between the calculated voltage and the measured voltage on the opposite side is selected as the identification result of the transmission line parameters, and the traveling wave velocity is calculated based on this result for use in traveling wave ranging calculations.

[0005] The present invention adopts the following technical solutions.

[0006] The first aspect of the present invention provides a real-time wave velocity correction method based on a single-ended solution of a wave equation, specifically comprising:

[0007] Collect the electrical quantity information sequence of one cycle on both sides of the transmission line before the protection is activated;

[0008] Solve the line resistance and inductance as well as the line capacitive reactance and capacitance values ​​based on the collected electrical quantity information sequence, and construct the line parameters to be input into the wave equation;

[0009] According to the line parameters to be input into the wave equation, the opposite side positive sequence voltage is calculated using the single-ended data based on the single-ended solution of the wave equation;

[0010] Based on the positive sequence voltage on the opposite side, the mean square error between the calculated voltage and the measured voltage on the opposite side is calculated, and the impedance corresponding to the minimum mean square error is taken as the identification result of the transmission line parameters;

[0011] The wave velocity is corrected in real time according to the identification result of the line parameters to obtain the corrected wave velocity, thereby realizing the real-time correction of the wave velocity based on the single-ended solution of the wave equation.

[0012] Preferably, the collecting of a sequence of electrical quantity information of one cycle on both sides of the transmission line before the protection is activated specifically includes:

[0013] Set the sampling frequency of the device, take the protection start time as the reference time, take the electrical quantity data of one cycle forward, and obtain the electrical quantity information sequence of one cycle before the protection start.

[0014] Preferably, the calculating the capacitive reactance, impedance angle and capacitance of the line based on the measured quantities specifically includes:

[0015] Calculate the capacitive reactance, impedance angle and capacitance of the line based on the measured quantity, and form the N R The data set of impedance values ​​is combined with the impedance angle to calculate the line resistance and inductance. The total line length constant in the device constant is combined with the line resistance and inductance as well as the capacitive reactance and capacitance of the line to construct the line parameters to be input into the wave equation.

[0016] Preferably, the calculating the capacitive reactance, impedance angle and capacitance of the line based on the measured quantities specifically includes:

[0017] Using the voltage phasors on both sides of M and N Sum the voltage to get the total At the same time, the current vector Sum the current to get the total After calculating the ratio of the total voltage to the total current, take the absolute value and multiply it by 1 / 2 to get the capacitive reactance Z of the line. C ;

[0018] Substitute the capacitive reactance into the capacitive reactance formula to obtain the capacitance value C;

[0019] Calculate the voltage difference between the two ends of the circuit The impedance angle is obtained by multiplying the ratio of the current to the total by 2 and taking the phase angle of the result.

[0020] Preferably, the device setting value is formed to include N R The impedance data set includes:

[0021] Set the transmission line impedance value as the line's baseline impedance value, and set the fluctuation range and step size of the line's baseline impedance value;

[0022] Within the fluctuation range of the baseline impedance value of the line, the impedance value is evenly divided according to the product of the step length and the step number fluctuation ratio, and the impedance value after the average division is formed into a matrix containing N R A data set of impedance values, where N R The value of is obtained by multiplying the ratio of the fluctuation range of the reference impedance value of the line to the step size by 2 and then adding 1.

[0023] Preferably, the input line parameters of the wave equation are used to calculate the opposite-side positive sequence voltage using single-ended data based on the single-ended solution of the wave equation, and specifically include:

[0024] Solve the resistance-capacitance ratio using capacitive reactance and resistance;

[0025] The wave velocity is obtained based on the inductance and capacitance, and the propagation time of the wave along the entire length of the line is obtained by dividing the total line length by the ratio of the wave velocity.

[0026] Obtain the positive sequence voltage sampling value and the positive sequence current sampling value of the local side at different times;

[0027] The resistance-capacitance ratio, the transmission time of the wave over the entire length of the line, and the positive sequence voltage sampling values ​​and positive sequence current sampling values ​​on this side at different times are substituted into the wave equation to calculate the voltage measurement value on the opposite side.

[0028] Preferably, the obtaining of the local positive-sequence voltage sampling value and the local positive-sequence current sampling value at different moments is calculated using a linear interpolation method, specifically including:

[0029] Find the nearest integer sampling time before and after the target time and round it up and down to obtain the rounded-up time and rounded-down time of the nearest integer sampling time;

[0030] Calculate the difference between the rounding-up and rounding-down times to obtain the time interval, calculate the difference between the positive-sequence sampling values ​​on the local side corresponding to the rounding-up and rounding-down times, and calculate the rate of change per unit time based on the ratio of the time interval to the difference between the positive-sequence sampling values ​​on the local side.

[0031] Subtract the rounded-down time from the target time to get the time offset ratio, and multiply it by the rate of change per unit time to estimate the value of the non-integer time.

[0032] The positive sequence sampling values ​​of the local side corresponding to the rounded-down moment and the value of the non-integer moment are summed to obtain the positive sequence sampling values ​​of the local side corresponding to different moments calculated by the linear interpolation method.

[0033] Preferably, the step of calculating the mean square error between the calculated voltage and the measured voltage on the opposite side based on the positive sequence voltage on the opposite side, and taking the impedance corresponding to the minimum mean square error as the identification result of the transmission line parameters, specifically includes:

[0034] According to the impedance value data set, there are N R The impedance value is N for the opposite side voltage R After each measurement process, the mean square error of the opposite side measured voltage and the opposite side measured voltage of each sampling point within the length of one cycle data is calculated. R Among the mean square error calculation results, the impedance value with the smallest mean square error is selected as the result of line parameter identification.

[0035] Preferably, the real-time correction of the wave velocity according to the identification result of the line parameters to obtain the corrected wave velocity specifically includes:

[0036] Solve the ratio of the modulus of the sum of the voltages and the modulus of the sum of the currents at both ends of the line,

[0037] Calculate the phase angle difference between the voltage difference and the current sum at both ends of the line, and then convert the phase difference into a proportional factor using a sine function;

[0038] The corrected wave velocity is obtained by multiplying the ratio of the frequency to the absolute value of the line parameter identification result by the proportional factor.

[0039] The second aspect of the present invention provides a real-time wave velocity correction system based on a single-ended solution of a wave equation, which executes the real-time wave velocity correction method based on a single-ended solution of a wave equation described in the first aspect, specifically comprising:

[0040] The data acquisition module is used to collect the electrical quantity information sequence of one cycle on both sides of the transmission line before the protection is activated;

[0041] The line parameter solving module is used to solve the line resistance and inductance as well as the line capacitive reactance and capacitance values ​​based on the collected electrical quantity information sequence, and construct the line parameters to be input into the wave equation;

[0042] The wave equation single-ended solution module is used to calculate the opposite-side positive sequence voltage using the single-ended data based on the input line parameters of the wave equation and the single-ended solution of the wave equation;

[0043] The identification result solving module is used to calculate the mean square error between the calculated voltage and the measured voltage on the opposite side based on the positive sequence voltage on the opposite side, and take the impedance corresponding to the minimum mean square error as the identification result of the transmission line parameters;

[0044] The wave velocity correction module is used to correct the wave velocity in real time according to the identification results of the line parameters to obtain the corrected wave velocity, thereby realizing real-time correction of the wave velocity based on the single-ended solution of the wave equation.

[0045] Compared with existing technologies, the present invention offers at least the following advantages: The wave velocity is calculated using electrical quantity data from the cycle preceding protection activation, which is unaffected by the cable transmission medium and results in a small error between the calculated wave velocity and the actual value; the wave equation is unaffected by transition resistance and offers fast calculation speed. The method provided by the present invention enables accurate and rapid calculation of wave velocity, effectively improving the accuracy and reliability of traveling wave ranging. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 It is a schematic diagram of the method flow in an embodiment of the present invention. DETAILED DESCRIPTION

[0047] To make the objectives, technical solutions, and advantages of the present invention more clear, the technical solutions of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. The described embodiments are only part of the embodiments of the present invention, not all of them. Based on the spirit of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0048] like Figure 1 As shown, embodiment 1 of the present invention proposes a real-time wave velocity correction method based on a single-ended solution of a wave equation, the method comprising the following steps:

[0049] Step 1: Collect the electrical quantity information sequence of one cycle on both sides of the transmission line before the protection is activated, wherein the electrical quantity information sequence includes device set values ​​and measured quantities.

[0050] In a preferred but non-limiting embodiment of the present invention, step 1 comprises:

[0051] Set the sampling frequency of the device, take the protection start time as the reference time, take the electrical quantity data of one cycle (a total of 2000 sampling points) forward, and obtain the electrical quantity information sequence of one cycle before the protection start.

[0052] Further preferably, the device setting includes the transmission line total length setting l and the transmission line impedance setting Z set ; The measured quantity includes the positive sequence voltage measurement value u on both sides of the transmission line MN 1.M (t0) and u 1.N (t0), positive sequence current measurement value i 1.M (t0) and i 1.N (t0) is the measured quantity, expressed as follows:

[0053] D1(t0)=[u 1.M (t0) u 1.N (t0) i 1.M (t0) i 1.N (t0)] (1)

[0054] Where,

[0055] D1(t0) is the measured quantity,

[0056] t0 is the sampling point at different times, expressed as follows:

[0057]

[0058] Where,

[0059] n is the serial number of the sampling point, n∈[0,N],

[0060] N is the total number of sampling points, N = 1999,

[0061] f is the sampling frequency of the device, f = 100kHz,

[0062] T is the protection start time,

[0063] u 1.M (t0) is the measured value of the positive sequence voltage on the M side of the transmission line, u 1.N (t0) is the measured value of the positive sequence voltage on the N side of the transmission line,

[0064] i 1.M (t0) is the measured value of the positive sequence current on the M side of the transmission line, i1.N (t0) is the measured value of the positive sequence current on the N side of the transmission line, which is expressed as follows:

[0065]

[0066] Where,

[0067] U 1.M Indicates the positive sequence voltage amplitude on the M side of the transmission line, U 1.N Indicates the positive sequence voltage amplitude on the N side of the transmission line,

[0068] represents the initial phase angle of the positive sequence voltage on the M side, represents the initial phase angle of the positive sequence voltage on the N side,

[0069] i 1.M Indicates the positive sequence current amplitude on the M side of the transmission line, i 1.N Indicates the positive sequence current amplitude on the N side of the transmission line,

[0070] represents the initial phase angle of the positive sequence current on the M side, Indicates the initial phase angle of the positive sequence current on the N side.

[0071] Step 2: Solve the line resistance and inductance as well as the capacitive reactance and capacitance of the line based on the electrical quantity information sequence collected in step 1, and construct the line parameters to be input into the wave equation.

[0072] In a preferred but non-limiting embodiment of the present invention, step 2 comprises:

[0073] Step 2.1: Calculate the capacitive reactance, impedance angle, and capacitance of the line based on the measured quantities in the electrical quantity information sequence collected in step 1.

[0074] Further preferably, step 2.1 includes:

[0075] Using the voltage phasors on both sides of M and N Sum the voltage to get the total At the same time, the current vector Sum the current to get the total After calculating the ratio of the total voltage to the total current, take the absolute value and multiply it by 1 / 2 to get the capacitive reactance Z of the line. C ;

[0076] Substitute the capacitive reactance into the capacitive reactance formula to obtain the capacitance value C;

[0077] Calculate the voltage difference between the two ends of the circuit The impedance angle θ is obtained by multiplying the ratio of the current to the total current by 2 and taking the phase angle of the result. The specific formula is as follows:

[0078]

[0079] Step 2.2: Based on the device setting values ​​in the electrical quantity information sequence collected in step 1, a data set including N is generated. R A dataset of impedance values.

[0080] Further preferably, step 2.2 specifically includes:

[0081] Set the transmission line impedance value as the line's baseline impedance value, and set the fluctuation range and step size of the line's baseline impedance value;

[0082] Within the fluctuation range of the baseline impedance value of the line, the impedance value is evenly divided according to the product of the step length and the step number fluctuation ratio, and the impedance value after the average division is formed into a matrix containing N R The data set of impedance values ​​is expressed as follows:

[0083] Z x =Z set (1±Step*x) (4)

[0084] Where,

[0085] Z x represents the impedance value in the dataset,

[0086] Z set Indicates the fixed value of transmission line impedance.

[0087] Ref represents the fluctuation range of the reference impedance value of the line.

[0088] Step represents the step length,

[0089] x represents the step fluctuation ratio, and its value range is Indicates the number of steps extending from the reference value in the positive and negative directions.

[0090] N R Indicates the total number of impedance values ​​in the data set, N R =2·(Ref / Step)+1.

[0091] This data set is used as the measurement range of the wave equation, and the impedance value closest to the actual operating parameters of the line is found in it.

[0092] More preferably, the transmission line impedance Z is used as the value set The impedance values ​​are divided evenly within the range of ±30% of the reference value according to the step size of 5%, and the impedance values ​​after the average division form a data set Z containing 13 impedance values. x =Z set(1±5%*x), x∈[0,6], and use this data set as the measurement range of the wave equation to find the impedance value closest to the actual operating parameters of the line.

[0093] Step 2.3: Use the line impedance angle θ calculated in step 2.1 and the impedance value Z in the data set in step 2.2. x , calculate the line resistance and inductance, the specific formula is as follows:

[0094]

[0095] Where,

[0096] R is the resistance,

[0097] Z L For inductive reactance,

[0098] L is the inductance value.

[0099] Step 2.4: Combine the total line length constant l in the electrical quantity information sequence with the line resistance R and inductance L and the line capacitive reactance Z C and capacitance value C, construct the line parameters to be input into the wave equation.

[0100] Step 3: Based on the input line parameters of the wave equation solved in step 2 and the single-ended solution of the wave equation, the opposite-side positive sequence voltage is calculated using the single-ended data.

[0101] In a preferred but non-limiting embodiment of the present invention, step 3 specifically comprises:

[0102] Solve the resistance-capacitance ratio h using the capacitive reactance and resistance;

[0103] The wave velocity is obtained based on the inductance and capacitance, and the wave propagation time τ of the entire line is obtained by dividing the total line length by the ratio of the wave velocity.

[0104] Obtain the positive sequence voltage sampling value and the positive sequence current sampling value of the local side at different times;

[0105] Substitute the resistance-capacitance ratio, the transmission time of the wave over the entire line length, and the positive sequence voltage sampling values ​​and positive sequence current sampling values ​​of the local side at different times into the wave equation to calculate the measured voltage value of the opposite side, as shown in the following formula:

[0106]

[0107] Where,

[0108] h is the resistance-capacitance ratio, h = R / 4Z C ;

[0109] u 1.N.cal(t-τ) is the measured positive sequence voltage on the opposite side;

[0110] t is the current sampling time;

[0111] τ = l / v represents the transmission time of the wave along the entire length of the line, where is the wave speed;

[0112] u 1.M (t-2τ),u 1.M (t-τ),u 1.M (t), i 1.M (t-2τ), i 1.M (t-τ), i 1.M (t) is the positive sequence sampling value of the local side corresponding to different time points, which is calculated using linear interpolation, specifically including:

[0113] Find the nearest integer sampling time before and after the target time and round it up and down to obtain the rounded-up time and rounded-down time of the nearest integer sampling time;

[0114] Calculate the difference between the rounding-up and rounding-down times to obtain the time interval, calculate the difference between the positive-sequence sampling values ​​on the local side corresponding to the rounding-up and rounding-down times, and calculate the rate of change per unit time based on the ratio of the time interval to the difference between the positive-sequence sampling values ​​on the local side.

[0115] Subtract the rounded-down time from the target time to get the time offset ratio, and multiply it by the rate of change per unit time to estimate the value of the non-integer time.

[0116] The positive sequence sampling value on the local side corresponding to the rounded-down moment and the value at the non-integer moment are summed to obtain the positive sequence sampling value on the local side corresponding to different moments calculated by linear interpolation. The calculation formula is as follows:

[0117]

[0118] Where,

[0119] Use Δt to uniformly represent τ and 2τ, is the rounding symbol, is the floor symbol.

[0120] Step 4: Calculate the mean square error between the calculated voltage and the measured voltage on the opposite side based on the positive sequence voltage on the opposite side calculated in step 3, and take the impedance value corresponding to the minimum mean square error as the identification result of the transmission line parameters;

[0121] In a preferred but non-limiting embodiment of the present invention, step 4 specifically comprises:

[0122] There are N impedance value data sets in total R Impedance value Zx , so there will be a total of N R After each measurement process, the mean square error of the opposite side voltage and the opposite side measured voltage at each sampling point within one cycle of data is calculated to characterize the error between the calculated voltage and the measured voltage within one cycle, and N is obtained. R The calculation formula for the mean square error is as follows:

[0123]

[0124] Where,

[0125] represents the mean square error calculation result,

[0126] In N R The calculation results of mean square error In the equation, select the impedance value Z with the smallest mean square error. x,min As a result of line parameter identification, it is assumed that the line impedance of one cycle before the fault occurs is Z x,min .

[0127] Step 5: Correct the wave velocity in real time based on the identification results of the line parameters calculated in step 4, and use the calculated wave velocity for traveling wave ranging, thereby realizing real-time correction of the wave velocity based on the single-ended solution of the wave equation.

[0128] In a preferred but non-limiting embodiment of the present invention, step 5 specifically comprises:

[0129] Solve the ratio of the modulus of the sum of the voltages and the modulus of the sum of the currents at both ends of the line,

[0130] Calculate the phase angle difference between the voltage difference and the current sum at both ends of the line, and then convert the phase difference into a proportional factor using a sine function;

[0131] The corrected wave velocity is obtained by multiplying the ratio of the frequency to the absolute value of the line parameter identification result by the proportional factor. The calculation formula is as follows:

[0132]

[0133] Embodiment 2 of the present invention proposes a real-time wave velocity correction system based on a single-ended solution of a wave equation, and executes the real-time wave velocity correction method based on a single-ended solution of a wave equation proposed in embodiment 1, including:

[0134] The data acquisition module is used to collect the electrical quantity information sequence of one cycle on both sides of the transmission line before the protection is activated;

[0135] The line parameter solving module is used to solve the line resistance and inductance as well as the line capacitive reactance and capacitance values ​​based on the collected electrical quantity information sequence, and construct the line parameters to be input into the wave equation;

[0136] The wave equation single-ended solution module is used to calculate the opposite-side positive sequence voltage using the single-ended data based on the input line parameters of the wave equation and the single-ended solution of the wave equation;

[0137] The identification result solving module is used to calculate the mean square error between the calculated voltage and the measured voltage on the opposite side based on the positive sequence voltage on the opposite side, and take the impedance corresponding to the minimum mean square error as the identification result of the transmission line parameters;

[0138] The wave velocity correction module is used to correct the wave velocity in real time according to the identification results of the line parameters to obtain the corrected wave velocity, thereby realizing real-time correction of the wave velocity based on the single-ended solution of the wave equation.

[0139] The present invention provides at least the following beneficial effects: Calculating wave velocity using electrical quantity data from the cycle preceding protection activation is unaffected by the cable transmission medium, resulting in a small error between the calculated wave velocity and the actual value; and the wave equation is unaffected by transition resistance, resulting in a fast calculation speed. The method provided by the present invention enables accurate and rapid calculation of wave velocity, effectively improving the accuracy and reliability of traveling wave ranging.

[0140] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered by the scope of protection of the claims of the present invention.

Claims

1. A real-time wave velocity correction method based on a single-ended solution of a wave equation, comprising: Collect the electrical quantity information sequence of one cycle on both sides of the transmission line before the protection is activated; Solve the line resistance and inductance as well as the line capacitive reactance and capacitance values ​​based on the collected electrical quantity information sequence, and construct the line parameters to be input into the wave equation; According to the line parameters to be input into the wave equation, the opposite side positive sequence voltage is calculated using the single-ended data based on the single-ended solution of the wave equation; Based on the positive sequence voltage on the opposite side, the mean square error between the calculated voltage and the measured voltage on the opposite side is calculated, and the impedance corresponding to the minimum mean square error is taken as the identification result of the transmission line parameters; The wave velocity is corrected in real time according to the identification result of the line parameters to obtain the corrected wave velocity, thereby realizing the real-time correction of the wave velocity based on the single-ended solution of the wave equation.

2. The real-time wave velocity correction method based on a single-ended solution of a wave equation according to claim 1, characterized in that: The acquisition of a sequence of electrical quantity information of one cycle on both sides of the transmission line before the protection is activated specifically includes: Set the sampling frequency of the device, take the protection start time as the reference time, take the electrical quantity data of one cycle forward, and obtain the electrical quantity information sequence of one cycle before the protection start.

3. The real-time wave velocity correction method based on a single-ended solution of a wave equation according to claim 1, characterized in that: Calculating the capacitive reactance, impedance angle, and capacitance of the line based on the measured quantities specifically includes: Calculate the capacitive reactance, impedance angle and capacitance of the line based on the measured quantity, and form the N R The data set of impedance values ​​is combined with the impedance angle to calculate the line resistance and inductance. The total line length constant in the device constant is combined with the line resistance and inductance as well as the capacitive reactance and capacitance values ​​of the line to construct the line parameters to be input into the wave equation.

4. The method for real-time correction of wave velocity based on a single-ended solution of a wave equation according to claim 3, characterized in that: Calculating the capacitive reactance, impedance angle, and capacitance of the line based on the measured quantities specifically includes: Using the voltage phasors on both sides of M and N Sum the voltage to get the total At the same time, the current vector Sum the current to get the total After calculating the ratio of the total voltage to the total current, take the absolute value and multiply it by 1 / 2 to get the capacitive reactance Z of the line. C ; Substitute the capacitive reactance into the capacitive reactance formula to obtain the capacitance value C; Calculate the voltage difference across the circuit The impedance angle is obtained by multiplying the ratio of the current to the total by 2 and taking the phase angle of the result.

5. The real-time wave velocity correction method based on a single-ended solution of a wave equation according to claim 3, characterized in that: The device setting value forms the N R The impedance data set includes: Set the transmission line impedance value as the line's baseline impedance value, and set the fluctuation range and step size of the line's baseline impedance value; Within the fluctuation range of the baseline impedance value of the line, the impedance value is evenly divided according to the product of the step length and the step number fluctuation ratio, and the impedance value after the average division is formed into a matrix containing N R A data set of impedance values, where N R The value of is obtained by multiplying the ratio of the fluctuation range of the reference impedance value of the line to the step size by 2 and then adding 1.

6. The method for real-time correction of wave velocity based on a single-ended solution of a wave equation according to claim 1, characterized in that: The method of calculating the opposite-side positive sequence voltage using single-ended data based on the line parameters to be input into the wave equation and the single-ended solution of the wave equation specifically includes: Solve the resistance-capacitance ratio using capacitive reactance and resistance; The wave velocity is obtained based on the inductance and capacitance, and the propagation time of the wave along the entire length of the line is obtained by dividing the total line length by the ratio of the wave velocity. Obtain the positive sequence voltage sampling value and the positive sequence current sampling value of the local side at different times; The resistance-capacitance ratio, the transmission time of the wave over the entire length of the line, and the positive sequence voltage sampling values ​​and positive sequence current sampling values ​​on this side at different times are substituted into the wave equation to calculate the voltage measurement value on the opposite side.

7. The real-time wave velocity correction method based on a single-ended solution of a wave equation according to claim 6, characterized in that: The obtaining of the local positive sequence voltage sampling value and the local positive sequence current sampling value at different times is calculated using a linear interpolation method, specifically including: Find the nearest integer sampling time before and after the target time and round it up and down to obtain the rounded-up time and rounded-down time of the nearest integer sampling time; Calculate the difference between the rounding-up and rounding-down times to obtain the time interval, calculate the difference between the positive-sequence sampling values ​​on the local side corresponding to the rounding-up and rounding-down times, and calculate the rate of change per unit time based on the ratio of the time interval to the difference between the positive-sequence sampling values ​​on the local side. Subtract the rounded-down time from the target time to get the time offset ratio, and multiply it by the rate of change per unit time to estimate the value of the non-integer time. The positive sequence sampling values ​​of the local side corresponding to the rounded-down moment and the value of the non-integer moment are summed to obtain the positive sequence sampling values ​​of the local side corresponding to different moments calculated by the linear interpolation method.

8. The real-time wave velocity correction method based on a single-ended solution of a wave equation according to claim 1, characterized in that: The method of calculating the mean square error between the calculated voltage and the measured voltage on the opposite side based on the positive sequence voltage on the opposite side, and taking the impedance corresponding to the minimum mean square error as the identification result of the transmission line parameters, specifically includes: According to the impedance value data set, there are N R The impedance value is N for the opposite side voltage R After each measurement process, the mean square error of the opposite side measured voltage and the opposite side measured voltage of each sampling point within the length of one cycle data is calculated. R Among the mean square error calculation results, the impedance value with the smallest mean square error is selected as the result of line parameter identification.

9. The method for real-time correction of wave velocity based on a single-ended solution of a wave equation according to claim 1, characterized in that: The real-time correction of the wave velocity according to the identification result of the line parameters to obtain the corrected wave velocity specifically includes: Solve the ratio of the modulus of the sum of the voltages and the modulus of the sum of the currents at both ends of the line, Calculate the phase angle difference between the voltage difference and the current sum at both ends of the line, and then convert the phase difference into a proportional factor using a sine function; The corrected wave velocity is obtained by multiplying the ratio of the frequency to the absolute value of the line parameter identification result by the proportional factor.

10. A real-time wave velocity correction system based on a single-ended solution of a wave equation, running a real-time wave velocity correction method based on a single-ended solution of a wave equation according to any one of claims 1 to 9, characterized in that: The data acquisition module is used to collect the electrical quantity information sequence of one cycle on both sides of the transmission line before the protection is activated; The line parameter solving module is used to solve the line resistance and inductance as well as the line capacitive reactance and capacitance values ​​based on the collected electrical quantity information sequence, and construct the line parameters to be input into the wave equation; The wave equation single-ended solution module is used to calculate the opposite-side positive sequence voltage using the single-ended data based on the input line parameters of the wave equation and the single-ended solution of the wave equation; The identification result solving module is used to calculate the mean square error between the calculated voltage and the measured voltage on the opposite side based on the positive sequence voltage on the opposite side, and take the impedance corresponding to the minimum mean square error as the identification result of the transmission line parameters; The wave velocity correction module is used to correct the wave velocity in real time according to the identification results of the line parameters to obtain the corrected wave velocity, thereby realizing real-time correction of the wave velocity based on the single-ended solution of the wave equation.

Images