A method and device for predicting fault properties of a multi-terminal flexible direct current selective reclosing line

Abstract

This invention relates to a method and device for predicting the nature of faults in multi-terminal flexible DC selective reclosing lines. The method includes: determining whether a fault has occurred in the line; determining the area where the fault occurred; selecting one end from the sending and receiving ends as the injection end based on the area where the fault occurred, and controlling the injection end to inject a mixed voltage wave sequence; calculating the fault-preceding traveling wave of the line-mode voltage at the injection end; constructing an equivalent calculation circuit model for lossless traveling wave calculation to theoretically calculate the fault-free forward traveling wave of the line-mode voltage at the injection end; reconstructing the fault-preceding traveling wave and the fault-free forward traveling wave of the line-mode voltage at the injection end, and calculating the Hausdorff distance between the reconstructed fault-preceding traveling wave and the fault-free forward traveling wave of the line-mode voltage at the injection end, thereby determining the nature of the line fault. This invention completely eliminates the overcurrent risk of DC circuit breakers or MMC converters, significantly improves the safety of primary equipment, and has the advantages of high resistance to transition resistance and dead-zone fault identification capability.

Description

Technical Field

[0001] This invention relates to the field of power grids, and specifically to a method and device for predicting the fault nature of a multi-terminal flexible DC selective reclosing line. Background Technology

[0002] Flexible DC transmission systems have many advantages, such as immunity to commutation failure and power supply to passive systems, making them very suitable for forming flexible DC grids in a flexible form. They utilize increasingly mature advanced power electronic equipment such as MMC to achieve multi-point power transmission and multi-point power reception, supplemented by millisecond-level main protection criteria and DC circuit breakers to ensure ultra-high-speed isolation of faulty lines and ensure uninterrupted operation of the system in N-1 state.

[0003] However, the traditional method of reactivating a faulty line requires attempting to reclose the DC circuit breaker of the faulty line. If a permanent fault occurs, this not only introduces new fault transients and reduces the operational stability of the parallel system, but also subjects the DC circuit breaker to severe impacts from secondary short-circuit currents, reducing its service life and operational reliability. Currently, academia and engineering have proposed many adaptive fault reclosing methods that can predict the nature of the fault before reclosing and only target transient conditions. However, these methods still have the following problems:

[0004] 1) Fault nature prediction method based on the intrinsic morphology of fault components: including methods for predicting fault nature such as equivalent impedance, dominant frequency of fault traveling wave, and fault traveling wave refraction / reflection characteristics in permanent / transient fault scenarios. Its advantage is that no additional signal injection is required, but there is a certain dead zone in some near-end / far-end fault scenarios, and the distinction between high-impedance permanent / transient faults is not ideal.

[0005] 2) Fault nature prediction method based on DC circuit breaker injected signal: This method includes hardware modifications such as introducing auxiliary circuits and parallel capacitors into the DC circuit breaker, and using methods such as injecting high-frequency pulses and controllable frequency sine waves to construct indicators based on the polarity and amplitude of the reflected waves for fault nature prediction. However, this method requires the introduction of auxiliary circuits and parallel capacitors into the DC circuit breaker, which significantly increases the manufacturing cost, size and design difficulty of the equipment.

[0006] 3) Fault nature prediction method based on active control of MMC converter: Its basic principle is similar to 2), the difference is that the injected signal comes from the MMC converter, and it is suitable for multi-terminal DC grids without DC circuit breakers. This method has a wide application prospect in point-to-point flexible DC transmission systems, but when applied to multi-terminal flexible DC transmission networks, it will affect the normal operation of the sound part of the system (it is necessary to control the MMC converter in normal operation). Summary of the Invention

[0007] This invention provides a method and device for predicting the fault nature of a multi-terminal flexible DC selective overclosing line, in order to solve at least one of the above-mentioned technical problems.

[0008] The technical solution of this invention to solve the above-mentioned technical problems is as follows: A method for predicting the fault nature of a multi-terminal flexible DC selective overclosing line, comprising:

[0009] S1, based on the current time, collects the voltage and current of the sending and receiving ends in the first preset time window of the multi-terminal flexible DC line to be selectively overlapped, and performs phase mode transformation on the voltage and current of the sending and receiving ends in the first preset time window respectively to obtain the first matrix of line and zero mode voltage and current of the sending and receiving ends.

[0010] S2, calculate the fault start action quantity of the sending and receiving ends according to the first matrix of the sending and receiving end lines and the zero-mode voltage and current respectively, and use the fault start action quantity of the sending end under the most unfavorable influence to calculate the threshold value of the fault start action quantity, thereby constructing the start criterion to determine whether the line has a fault, and record the time when the start criterion is met as the start time.

[0011] S3, after determining that a line fault has occurred, calculates the cumulative reference value of the mode voltage of the sending and receiving lines according to the first matrix of the sending and receiving line and the zero-mode voltage and current, so as to determine the area where the fault occurred.

[0012] S4. Select one end from the sending and receiving ends as the injection end of the mixed voltage wave sequence according to the area where the fault occurs, and control the DC circuit breaker on the injection end side to inject the mixed voltage wave sequence based on the start time and after a preset deionization time.

[0013] S5, taking the moment when the hybrid voltage wave sequence is first reflected back to the injection end as a reference, the voltage and current of the injection end within the second preset time window are collected, and the voltage and current of the injection end within the second preset time window are transformed to obtain the second matrix of injection end line and zero mode voltage and current;

[0014] S6. Calculate the forward traveling wave of the injection terminal mode voltage fault based on the second matrix of the injection terminal line and zero-mode voltage and current.

[0015] S7 is used to build an equivalent calculation circuit model for lossless traveling wave calculation of a multi-terminal flexible DC line with selective overlap, and to simulate the process of injecting a mixed voltage wave sequence in order to theoretically calculate the fault-free forward traveling wave of the injected line mode voltage.

[0016] S8 uses transient extraction transform based on continuous wavelet transform as a tool to reconstruct the forward traveling wave of the injected line-mode voltage fault and the forward traveling wave of the injected line-mode voltage without fault, and calculates the Hausdorff distance between the reconstructed forward traveling wave of the injected line-mode voltage fault and the forward traveling wave of the injected line-mode voltage without fault, thereby determining the nature of the line fault.

[0017] Based on the above-mentioned method for predicting the fault nature of a multi-terminal flexible DC selective overclosing line, the present invention also provides a device for predicting the fault nature of a multi-terminal flexible DC selective overclosing line.

[0018] A fault nature prediction device for a multi-terminal flexible DC selective overclosing line includes a processor, a memory, and a computer program stored in the memory. When the computer program is executed by the processor, it implements the fault nature prediction method for the multi-terminal flexible DC selective overclosing line as described above.

[0019] The beneficial effects of this invention are as follows: In the fault nature prediction method and device for multi-terminal flexible DC selective reclosing lines of this invention, firstly, there is no need to implement additional control on the MMC converter during fault identification. For multi-terminal DC power grids that have disconnected one DC line and are in the N-1 state, the implementation of this invention does not affect their normal operation. Secondly, this invention only uses the transfer branch of the DC circuit breaker for signal injection, and before fault nature prediction, a strict fault section prediction method is adopted to uniquely determine the time-domain expression of the injected signal, completely eliminating the overcurrent risk of the DC circuit breaker or MMC converter, and significantly improving the safety of primary equipment. Finally, this invention models the multi-terminal DC power grid based on a hypothetical lossless scenario and constructs an equivalent calculation circuit model for its traveling wave calculation. The Hausdorff distance between the faultless theoretical voltage forward traveling wave waveform generated by the equivalent calculation circuit model for traveling wave calculation and the measured voltage forward traveling wave waveform is used as an indicator to measure whether the line is lossless (whether the fault nature is permanent). Compared with the traditional polarity / amplitude method of reflected waves, it has the advantages of high resistance to transition resistance and dead zone fault identification capability. Attached Figure Description

[0020] Figure 1 This is a flowchart of a method for predicting the fault nature of a multi-terminal flexible DC selective overclosing line according to the present invention;

[0021] Figure 2 A schematic diagram of a four-terminal bipolar MMC DC transmission network;

[0022] Figure 3 This is a schematic diagram of the activation criteria in the example;

[0023] Figure 4 This is a schematic diagram of the voltage and current before and after the fault in the example;

[0024] Figure 5 This is a calculation diagram for determining the line area where the fault is located in the example.

[0025] Figure 6 This is a schematic diagram of the traveling wave during a line fault in the example.

[0026] Figure 7This is a schematic diagram of the traveling wave of the line-mode fault voltage in the example.

[0027] Figure 8 This is the equivalent circuit diagram used for lossless traveling wave calculation in the example.

[0028] Figure 9 This is a schematic diagram of the continuous wavelet transform results in the example;

[0029] Figure 10 This is a schematic diagram of the transient extraction transformation results in the example;

[0030] Figure 11 The diagram shows the fault-reconstructed waveform of the injected line-mode voltage and the fault-free reconstructed waveform of the injected line-mode voltage in the example. Detailed Implementation

[0031] The principles and features of the present invention are described below with reference to the accompanying drawings. The examples given are only for explaining the present invention and are not intended to limit the scope of the present invention.

[0032] like Figure 1 As shown, a method for predicting the fault nature of a multi-terminal flexible DC selective overclosing line includes:

[0033] S1, based on the current time, collects the voltage and current of the sending and receiving ends in the first preset time window of the multi-terminal flexible DC line to be selectively overlapped, and performs phase mode transformation on the voltage and current of the sending and receiving ends in the first preset time window respectively to obtain the first matrix of line and zero mode voltage and current of the sending and receiving ends.

[0034] S2, calculate the fault start action quantity of the sending and receiving ends according to the first matrix of the sending and receiving end lines and the zero-mode voltage and current respectively, and use the fault start action quantity of the sending end under the most unfavorable influence to calculate the threshold value of the fault start action quantity, thereby constructing the start criterion to determine whether the line has a fault, and record the time when the start criterion is met as the start time.

[0035] S3, after determining that a line fault has occurred, calculates the cumulative reference value of the mode voltage of the sending and receiving lines according to the first matrix of the sending and receiving line and the zero-mode voltage and current, so as to determine the area where the fault occurred.

[0036] S4. Select one end from the sending and receiving ends as the injection end of the mixed voltage wave sequence according to the area where the fault occurs, and control the DC circuit breaker on the injection end side to inject the mixed voltage wave sequence based on the start time and after a preset deionization time.

[0037] S5, taking the moment when the hybrid voltage wave sequence is first reflected back to the injection end as a reference, the voltage and current of the injection end within the second preset time window are collected, and the voltage and current of the injection end within the second preset time window are transformed to obtain the second matrix of injection end line and zero mode voltage and current;

[0038] S6. Calculate the forward traveling wave of the injection terminal mode voltage fault based on the second matrix of the injection terminal line and zero-mode voltage and current.

[0039] S7 is used to build an equivalent calculation circuit model for lossless traveling wave calculation of a multi-terminal flexible DC line with selective overlap, and to simulate the process of injecting a mixed voltage wave sequence in order to theoretically calculate the fault-free forward traveling wave of the injected line mode voltage.

[0040] S8 uses transient extraction transform based on continuous wavelet transform as a tool to reconstruct the forward traveling wave of the injected line-mode voltage fault and the forward traveling wave of the injected line-mode voltage without fault, and calculates the Hausdorff distance between the reconstructed forward traveling wave of the injected line-mode voltage fault and the forward traveling wave of the injected line-mode voltage without fault, thereby determining the nature of the line fault.

[0041] This embodiment uses, as follows Figure 2 Taking the line MN to be selectively reclosed in the four-terminal bipolar MMC DC transmission network as an example, the two ends of line MN are connected to line MQ and line NP respectively, and the voltage and current signal measurement points of line MN are at the sending end M and the receiving end N. In this embodiment, it is set that... A permanent 300Ω positive ground fault occurs at a position 80% of the distance from the sending end M on line MN.

[0042] The following is an example Figure 2 The power transmission network shown illustrates the specific steps of the present invention.

[0043] S1 specifically includes the following S11~S12:

[0044] S11, based on the current time, collect the positive and negative voltages and currents of the sending and receiving ends in the first preset time window of the multi-terminal flexible DC line to be selectively overlapped, and obtain the first matrix of positive and negative voltages and currents of the sending and receiving ends.

[0045] Specifically, in S11, the voltage and current at the sending end M and receiving end N of line MN are monitored in real time, and the current time is used as the reference value. Based on this, the data from the sending end M and the receiving end N are captured within the first preset time window. The positive voltage, negative voltage, positive current, and negative current within the electrode; among which, In this embodiment, the first preset time period is defined as follows: =1 ms. At sampling rate The positive voltage, negative voltage, positive current, and negative current at the sending end M and the receiving end N are collected and used to construct the first matrix of positive and negative voltage and current at the sending end. and the first matrix of positive and negative terminal voltage and current. ;in, and It will be updated in real time over time; and They are represented as follows:

[0046] (1)

[0047] (2)

[0048] in, , , , These represent the positive voltage vector, negative voltage vector, positive current vector, and negative current vector of the sending end M within the first preset time window, respectively. , , , These represent the current time of the sending end M within the first preset time window. t Positive voltage, negative voltage, positive current, and negative current; , , , These represent the positive voltage vector, negative voltage vector, positive current vector, and negative current vector of the receiving end N within the first preset time window, respectively. , , , These represent the current time of the receiving end N within the first preset time window. t Positive voltage, negative voltage, positive current, and negative current;

[0049] The number of sampling points within the first preset time window, and ; , ... These represent different times within the first preset time window.

[0050] In this example, the sampling rate is set. =500 kHz, first preset time period =1 ms Therefore, in the first preset time window The number of sampling points is 501.

[0051] S12, based on the Kelenberger transformation, perform phase mode transformation on the first matrix of positive and negative voltage and current at the sending and receiving ends respectively to obtain the first matrix of line and zero-mode voltage and current at the sending and receiving ends.

[0052] The formula for phase mode transformation of the first matrix of positive and negative voltage and current at the sending and receiving ends is as follows:

[0053] (3)

[0054] In the formula, or ;when hour, This represents the first matrix of sending line and zero-mode voltage and current. The first matrix represents the positive and negative voltage and current of the sending terminal; when hour, This represents the first matrix of received-end line and zero-mode voltage and current. This represents the first matrix representing the positive and negative voltage and current at the receiving end; Let be the phase transformation matrix, and Represented as:

[0055] (4)

[0056] and They are represented as follows:

[0057] (5)

[0058] (6)

[0059] in, , , , These represent the line-mode voltage vector, zero-mode voltage vector, line-mode current vector, and zero-mode current vector of the sending end M within the first preset time window, respectively. , , , These represent the current time of the sending end M within the first preset time window. t Line-mode voltage, zero-mode voltage, line-mode current, and zero-mode current; , , , These represent the line-mode voltage vector, zero-mode voltage vector, line-mode current vector, and zero-mode current vector of the receiving end N within the first preset time window, respectively. , , , These represent the current time of the receiving end N within the first preset time window. t Line-mode voltage, zero-mode voltage, line-mode current, and zero-mode current.

[0060] S2 specifically includes the following S21~S23:

[0061] S21, based on the line surge impedance, perform matrix transformations on the first matrices of the sending and receiving end lines and zero-mode voltage and current, respectively, to obtain the corresponding sending and receiving end start-up reference matrices; wherein, the transformation formulas for the sending and receiving end start-up reference matrices are:

[0062] (7)

[0063] In the formula, or ;when hour, This represents the sending end start reference matrix. This represents the first matrix of the sending line and zero-mode voltage and current; when hour, This represents the receiving end start reference matrix. This represents the first matrix of the receiving end line and zero-mode voltage and current; B Let be the line wave impedance matrix, and Represented as:

[0064] (8)

[0065] In the formula, This is the line wave impedance. Therefore, and They are represented as follows:

[0066] (9)

[0067] (10)

[0068] According to the calculations in equations (9) and (10), It can be represented as:

[0069] (11)

[0070] In the formula, for The first in 1 element, and =1, 2, ..., a +1.

[0071] S22, calculate the fault start action quantities for the sending and receiving ends respectively based on the corresponding start reference matrices of the sending and receiving ends; wherein, the calculation formulas for the fault start action quantities of the sending and receiving ends are:

[0072] (12)

[0073] In the formula, when hour, ;when hour, ;when hour, Indicates the fault initiation action quantity at the sending end; when hour, This indicates the amount of fault initiation action at the receiving end; express The largest element in the middle, and is The first in One element, express The absolute value; express The first in One element; express The first in Each element.

[0074] S23, calculate the sending and receiving end start criteria based on the fault start action quantity, and determine whether the sending and receiving end start criteria are both invalid. If yes, it is determined that the line has not been faulted, and return to S1. If no, it is determined that the line has been faulted, and the time when the start criteria are met is recorded as the start time, and S3 is executed.

[0075] Specifically, fault identification is performed by calculating the threshold value of the fault initiation action. Taking a 600 Ω single-pole ground fault occurring at 90% of the line distance from the sending end as the most unfavorable influencing factor, the fault initiation action value at the sending end under this condition is calculated. Value multiplied by To adjust .

[0076] (13)

[0077] In the formula, The reliability coefficient is the threshold value for the fault initiation action quantity in this embodiment. =0.85, =560 kV. The start-up criteria for the sending and receiving ends are: ,in, This includes the sending end start criterion. and receiving end start criteria .like and If none of these conditions are met, then it is assumed that line MN is not faulty; if and If one or both of these conditions are met, then line MN is considered to be faulty. However, if only one of these conditions is met... If it is established, it will satisfy The time recorded is the start time; if only If it is established, it will satisfy The time recorded is the startup time; if and If both criteria are met, determine which criterion is met first, and record the moment when the startup criterion is first met as the startup moment.

[0078] The multi-terminal flexible DC transmission system in this embodiment has a rated DC voltage of [voltage value missing]. 500 kV, rated DC current of 3 kA, sampling rate =500 kHz, step size 2 Under these conditions, 501 data points were collected, and then the activation criterion for the receiving end N was calculated. 4400kV The startup criteria are met, and the startup criteria are as follows: Figure 3 As shown.

[0079] Additionally, in terms of sampling rate Under the condition of 500 kHz, 1001 data points were collected to obtain the voltage and current before and after the fault, as shown below. Figure 4 As shown.

[0080] S3 specifically includes the following S31~S35:

[0081] S31, extract the sending and receiving line-mode voltage vectors from the sending and receiving line and the first matrix of zero-mode voltage and current respectively, and perform second and third derivatives on the extracted sending and receiving line-mode voltage vectors respectively to obtain the second reference vector and the third reference vector of the sending and receiving line-mode voltages respectively.

[0082] Specifically, extract from equation (5) In formula (6) The first row corresponds to the sending-end line-mode voltage vector. and the receiving end line-mode voltage vector And respectively represented as:

[0083] (14)

[0084] (15)

[0085] According to the following equation (16), the sending-end line-mode voltage vector and the receiving end line-mode voltage vector By taking the second derivative, we obtain the second reference vector of the sending-end line-mode voltage. and the second reference vector of the receiving end line mode voltage According to the following equation (17), the voltage vector of the sending end line mode is... and the receiving end line-mode voltage vector Taking the third derivative yields the third reference vector of the sending-end line-mode voltage. and the third reference vector of the receiving end line mode voltage .

[0086] (16)

[0087] (17)

[0088] In the formula, Sampling step size ; or ;when hour, This represents the second-order reference vector of the sending-end line-mode voltage. Represents the third reference vector of the sending-end line-mode voltage; when hour This represents the second-order reference vector of the receiving-end line-mode voltage. Represents the third reference vector of the receiving-end line-mode voltage; vector , , , The elements are respectively from It is calculated one by one when taking different values. , , , They are represented as follows:

[0089] (18)

[0090] (19)

[0091] (20)

[0092] .(twenty one)

[0093] S32 performs zero-padding operations on the beginning and end of the third reference vectors of the sending and receiving line-mode voltages respectively, to obtain the corresponding third reference zero-padding vectors of the sending and receiving line-mode voltages.

[0094] The formula for padding the first and last ends of the third reference vector of the line-mode voltage at the sending and receiving ends is as follows:

[0095] ;(twenty two)

[0096] In the formula, or ;when hour, This represents the third reference vector of the sending-end line-mode voltage. Represents the third reference zero-padding vector of the sending-end line-mode voltage; when hour, This represents the third reference vector of the receiving-end line-mode voltage. This represents the third reference zero-padding vector of the received-end line-mode voltage; Let be the zero vector, and represent it as:

[0097] ;(twenty three)

[0098] but and Specifically, it is expressed as follows:

[0099] ;(twenty four)

[0100] (25)

[0101] S33, add the secondary reference vectors of the sending and receiving end line-mode voltages to the cubic reference zero-filling vectors of the sending and receiving end line-mode voltages respectively to obtain the mixed reference vectors of the sending and receiving end line-mode voltages.

[0102] The formula for calculating the mixed reference vector of the sending and receiving line-mode voltages is as follows:

[0103] (26)

[0104] In the formula, or ;when hour, This represents the second-order reference vector of the sending-end line-mode voltage. This represents the third reference zero-padding vector of the sending-end line-mode voltage. Represents the mixed reference vector of the sending-end line-mode voltage; when hour, This represents the second-order reference vector of the receiving-end line-mode voltage. This represents the third reference zero-padding vector of the received-end line-mode voltage. This represents the mixed reference vector of the receiving-end line-mode voltage; It can be represented as :

[0105] (27)

[0106] In the formula, for The first in x 1 element, andx= 1, 2, ..., .

[0107] In the formula, or ;when hour, , express The first in x One element; when hour, , express The first in x Each element.

[0108] S34, accumulate the elements in the mixed reference vector of the sending and receiving end line-mode voltages respectively to obtain the accumulated reference values ​​of the sending and receiving end line-mode voltages;

[0109] The formula for calculating the cumulative reference value of the line-mode voltage at the sending and receiving ends is as follows:

[0110] (28)

[0111] In the formula, or ;when hour, , Indicates the cumulative reference value of the sending-end line-mode voltage; when hour, , This represents the accumulated reference value of the receiving-end line-mode voltage.

[0112] S35. Compare the cumulative reference values ​​of the line-mode voltage at the sending and receiving ends. If the cumulative reference value of the line-mode voltage at the sending end is greater than or equal to the cumulative reference value of the line-mode voltage at the receiving end, the fault is determined to occur in the first half of the region, including the midpoint of the line. If the cumulative reference value of the line-mode voltage at the sending end is less than the cumulative reference value of the line-mode voltage at the receiving end, the fault is determined to occur in the second half of the region, excluding the midpoint of the line.

[0113] The formula for comparing the cumulative reference values ​​of the line-mode voltages at the sending and receiving ends is as follows:

[0114] (29)

[0115] (30)

[0116] If the result of equation (29) If the fault is located in the first half of line MN, then the fault is considered to be located in the first half of line MN. If so, the fault is considered to be located in the latter half of line MN.

[0117] In this embodiment, the sampling rate of line MN 500 kHz, step size 2 Under these conditions, 501 data points were collected, and the following calculations were performed. -173 kV, such as Figure 5 As shown; according to The fault is determined to occur in the latter half of line MN; proceed to S4.

[0118] Specifically, S4 is:

[0119] If the fault occurs in the first half of the line, the receiving end is used as the injection end, and based on the start time, after a preset deionization time, the DC circuit breaker on the receiving end is controlled to inject a mixed voltage wave at preset time intervals within a preset time period determined by the line length. If the fault occurs in the second half of the line, the sending end is used as the injection end, and based on the start time, after a preset deionization time, the DC circuit breaker on the sending end is controlled to inject a mixed voltage wave at preset time intervals within a preset time period determined by the line length.

[0120] Specifically, based on S3, the fault location is determined. If the fault is located in the first half of line MN or exactly at the midpoint, the DC circuit breaker on the receiving end N side will activate within a preset time period. A mixed voltage wave is injected internally; conversely, a mixed voltage wave is injected in the same way by the DC circuit breaker on the sending end M side.

[0121] In this embodiment, the fault occurs in the latter half of line MN, so a mixed voltage wave is injected from the sending end M for a preset time period. = The length of the line MN (in this embodiment) 184 km), The propagation speed of the line wave (in this embodiment) Let the startup time be... Start-up time Afterwards, the DC circuit breakers on both sides of line MN open, and after a preset deionization time (e.g., 500 ms deionization time), the transfer branch is operated through the DC circuit breaker at end M, within a preset time period. Within the same preset time interval Close the circuit three times, injecting an amplitude of [value] into the circuit. A mixed voltage wave of kV. In this embodiment, the preset time period of injection... = Preset time interval = Record the moment when the mixed voltage wave begins to be injected. 500 ms (where 500 ms is the preset deionization time in this embodiment).

[0122] Injection function of mixed voltage waves It can be expressed by the following formula:

[0123] (31)

[0124] In the formula, 0 indicates that the DC circuit breaker is open and no mixed voltage wave is injected, while 1 indicates that the DC circuit breaker is closed and a mixed voltage wave is injected. The sampling rate is used. For time windows The mixed voltage wave within is sampled, and a time window is used. The sampling points within constitute a mixed voltage wave sequence .

[0125] (32)

[0126] In the formula, Injection function for mixed voltage waves In the time window The discrete sequence obtained by internal sampling; where each element is 1 when the DC circuit breaker is closed and 0 when the DC circuit breaker is open; specifically represented as:

[0127] (33)

[0128] In the formula, For time windows The number of sampling points within, and .

[0129] In this embodiment, the line length is 184 km, wave propagation speed in the line 296 The preset time period for injecting the mixed voltage wave. Approximately 0.307 ms, preset time interval The time when the injected mixed voltage wave began was approximately 0.044 ms. .

[0130] Specifically, S5 is:

[0131] When the line is When a fault occurs, the moment when the hybrid voltage wave sequence first reflects back to the injection end, obtained by the following equation (34). As a benchmark, use the sampling rate For the second preset time window The positive and negative voltage and current of the injection terminal are sampled using a second preset time window. The sampling points of the positive and negative voltage and current at the injection terminal constitute the second matrix of positive and negative voltage and current at the injection terminal.

[0132] (34)

[0133] In the formula, This is the fault location coefficient; when there is no fault, In this embodiment =0.8, For the line length, in this embodiment 184 km This refers to the wave propagation speed.

[0134] Since the injection terminal is determined based on the location of the fault, in practical applications, either the sending or receiving end is chosen as the injection terminal. Therefore, the second matrix of positive and negative voltage and current at the injection terminal can be the same as the second matrix of positive and negative voltage and current at the sending end. E 1, or it can be the second matrix of positive and negative terminal voltage and current. E 11 .

[0135] E 1 and E 11 They are represented as follows:

[0136] (35)

[0137] (36)

[0138] In the formula, c The number of sampling points within the second preset time window, and ; These represent the positive voltage vector, negative voltage vector, positive current vector, and negative current vector of the sending end M within the second preset time window, respectively. , , , These represent the times of the sending end M within the second preset time window. Positive voltage, negative voltage, positive current, and negative current; , , , These represent the positive voltage vector, negative voltage vector, positive current vector, and negative current vector of the receiving end N within the second preset time window, respectively. , , , These represent the times of the receiving end N within the second preset time window. Positive voltage, negative voltage, positive current, and negative current.

[0139] In this embodiment, the sampling frequency is set. =1 MHz (sampling interval is 1) ), =1 ms, therefore in the second preset time window The number of sampling points is 4000.

[0140] According to the following formula (37), the second matrix of positive and negative terminal voltage and current is used to determine the sending end. E 1 and the second matrix of positive and negative terminal voltage and current. E 11 Performing phase-mode transformation yields the second matrix of voltage and current at the sending end and zero mode. and receiving end line, zero-mode voltage and current second matrix .

[0141] (37)

[0142] In the formula, A With equation (4) A Maintain consistency; or ;when hour, This represents the second matrix indicating the positive and negative voltage and current at the sending end. This represents the second matrix representing the sending line and zero-mode voltage and current; when hour, This represents the second matrix representing the positive and negative voltage and current at the receiving end. This represents the second matrix of the received-end line and zero-mode voltage and current. and They are represented as follows:

[0143] (38)

[0144] (39)

[0145] In the formula, , , , These represent the line-mode voltage vector, zero-mode voltage vector, line-mode current vector, and zero-mode current vector of the sending end M within the second preset time window, respectively. , , , These represent the times of the sending end M within the second preset time window. Line-mode voltage, zero-mode voltage, line-mode current, and zero-mode current; , , , These represent the line-mode voltage vector, zero-mode voltage vector, line-mode current vector, and zero-mode current vector of the receiving end N within the second preset time window, respectively. , , , These represent the times of the receiving end N within the second preset time window. Line-mode voltage, zero-mode voltage, line-mode current, and zero-mode current.

[0146] In this embodiment, as Figure 6 As shown, Hybrid voltage wave array At the injection moment, Hybrid voltage wave array Return to the injection end (protection installation point of the sending end M) At the moment of ( ), with mixed voltage waves Return to injection time Based on this, a second preset time window is set. By sampling the positive and negative voltage and current at the injection terminal and performing phase-mode transformation, the second matrix of injection terminal line and zero-mode voltage and current can be obtained.

[0147] In this embodiment, the injection terminal is the sending terminal M. Therefore, the injection terminal line and the second matrix of zero-mode voltage and current are specifically the sending terminal line and the second matrix of zero-mode voltage and current. In other embodiments, if the fault occurs in the first half of the line, the second matrix of injected terminal line and zero-mode voltage and current is specifically the second matrix of received terminal line and zero-mode voltage and current. .

[0148] S6 specifically includes:

[0149] S61, extract the injection terminal line mode voltage and current vector from the second matrix of injection terminal line and zero-mode voltage and current, and use a non-overlapping sliding window to calculate the local mean of the extracted injection terminal line mode voltage and current vector to obtain the mean vector of injection terminal line mode voltage and current.

[0150] Specifically, the sending-end line mode voltage vector extracted from the second matrix of sending-end line and zero-mode voltage and current is: The sending-end line mode current vector extracted from the second matrix of sending-end line and zero-mode voltage and current is: The sending-end mode voltage vector extracted from the receiving-end line and the second matrix of zero-mode voltage and current is: The sending-end mode current vector extracted from the receiving-end line and the second matrix of zero-mode voltage and current is: ;

[0151] Use window length =2 non-overlapping sliding windows, using the following formula (40) respectively for , , , Perform local mean calculation to obtain the corresponding result. , , , ;in, , , , These are the average vectors of the sending-end line-mode voltage, the sending-end line-mode current, the receiving-end line-mode voltage, and the receiving-end line-mode current, respectively.

[0152] (40)

[0153] In the formula, They represent , , , ; They represent , , , The first in One element; They represent , , , The elements are respectively composed of , , , Different elements are obtained one by one through local mean calculation; Non-overlapping sliding window ( =1, 2, ..., c ), The length of the non-overlapping sliding window (in this embodiment) =2), For the first The starting sampling points of a non-overlapping sliding window. For the first The end sampling point of a non-overlapping sliding window. , , , They are represented as follows:

[0154] (41)

[0155] (42)

[0156] (43)

[0157] (44)

[0158] In this embodiment, the mean vector of the injection terminal line-mode voltage and current is specifically the mean vector of the sending terminal line-mode voltage. and the mean vector of the current in the sending line In other embodiments, if the fault occurs in the first half of the line, the mean vector of the injected line-mode voltage and current is specifically the mean vector of the received line-mode voltage. and the mean vector of the receiving end line mode current .

[0159] S62, combine the mean vectors of the injection terminal line-mode voltage and current to obtain the mean matrix of the injection terminal line-mode voltage and current.

[0160] Specifically, will and By combining the values, we obtain the mean matrix of the line-mode voltage and current at the sending end. ,Will and By combining the values, we obtain the mean matrix of the receiving-end line-mode voltage and current. ; and They are represented as follows:

[0161] (45)

[0162] (46)

[0163] In this embodiment, the mean voltage and current matrix of the injected end line mode is specifically the mean voltage and current matrix of the sent end line mode. In other embodiments, if the fault occurs in the first half of the line, the mean voltage and current matrix of the injected line mode is specifically the mean voltage and current matrix of the received line mode. .

[0164] S63, based on the line wave impedance, calculate the mean matrix of the line-mode voltage and current at the injection end to obtain the forward traveling wave of the line-mode voltage fault at the injection end.

[0165] Specifically, for and Each column element is calculated according to equation (47) to obtain the first... j Column elements , :

[0166] (47)

[0167] Wherein, matrix T is represented as:

[0168] (48)

[0169] In the formula, This is the line wave impedance. , The new element calculated from each column of elements within the input terminal forms the forward traveling wave of the injection terminal line mode voltage fault. , ; and Represented as:

[0170] (49)

[0171] In this embodiment, the injection end is the sending end M. Therefore, the advancing wave before the line-mode voltage fault at the injection end is specifically the advancing wave before the line-mode voltage fault at the sending end. In other embodiments, if the fault occurs in the first half of the line, the advancing wave of the injected line-mode voltage fault is specifically the advancing wave of the received line-mode voltage fault. .

[0172] In this embodiment, the forward traveling wave of the injected terminal line mode voltage fault is described. like Figure 7 As shown. Let for The time series formed by the sampling points is the forward traveling wave of the injected terminal line-mode voltage fault. It can be represented as In this invention, the forward traveling wave of the injected terminal line mode voltage fault is also referred to as the actual measured wave.

[0173] Specifically, S7 includes the following S71~S74:

[0174] S71, based on the law of mixed wave propagation, the line is equivalent to two independent equivalent circuits at the sending end and the receiving end, and an equivalent calculation circuit model for lossless traveling wave calculation is made when a mixed voltage wave sequence is injected at the injection end protection installation point.

[0175] Specifically, S71 includes the following S711~S714:

[0176] S711, Establish the traveling wave relationship for line MN:

[0177] (50)

[0178] In the formula, Indicates any time. for The voltage at the sending end M of the line at any given time. For line wave impedance, for The current flowing through line MN is in the direction of flowing from the sending end M to the receiving end N. Let be the wave propagation time on line MN. for The voltage at the receiving end N of the line at any given time.

[0179] S712, calculate the ECTF (Equivalent-calculative Circuit for Traveling-wave Feature-generation) of the sending end M and receiving end N in the lossless transmission line MN, and transform it using Equation (50) to obtain the voltage expression for the sending end M:

[0180] (51)

[0181] In the formula, For the sending end M in Equivalent voltage source for lossless transmission lines at any given time.

[0182] Transforming equations (50) and (51), we obtain:

[0183] (52)

[0184] In the formula, for The current flowing through line MN is from the receiving end N to the sending end M. The lossless ECTF of the sending end M is obtained through equations (51) and (52) as a line surge impedance. and an equivalent voltage source . .

[0185] According to the duality principle, the lossless ECTF of the receiving end N can be obtained:

[0186] (53)

[0187] In the formula, for The voltage at terminal N at any given time, For the receiving end N in The transmission line lossless equivalent voltage source at any given moment. for The voltage at terminal M is constantly being transmitted. for The current flowing through line MN is from the sending end M to the receiving end N. The lossless ECTF at the receiving end N, obtained through equation (53), is also a surge impedance. and an equivalent voltage source Series connection.

[0188] S713 performs a time offset on the lossless ECTF of the sending end M to obtain the equivalent voltage source. With the sending end M at Voltage at any moment The relationship between them:

[0189] (54)

[0190] In the formula, For the sending end M in The transmission line lossless equivalent voltage source at time t. According to equation (54), the sending end M at t. The recursive formula for the equivalent voltage source at any given time:

[0191] (55)

[0192] In the formula, For the receiving end N in A lossless equivalent voltage source for transmission lines at any given time.

[0193] Similarly, the recursive formula for the equivalent voltage source at terminal N is obtained:

[0194] (56)

[0195] S714, Provides protection for the sending end M. Injected mixed voltage wave sequence Lossless ECTF.

[0196] To maintain consistency with the mixed voltage wave sequence injected in S4, the injection point (the protection installation location at the sending end M) was determined through mode domain analysis. The expression for the line-mode voltage at point ) is:

[0197] (57)

[0198] In the formula, To inject mixed voltage wave sequence Line-mode voltage, The positive rated voltage of the system (set to [value] in this embodiment) kV), =0, 1, 2, It is a three-pulse rectangular wave. For equivalent internal resistance, The timing of injecting the mixed voltage wave sequence, For injecting current into a mixed voltage wave sequence.

[0199] Through the above steps, we obtain the expressions for line MN at the sending end M and the receiving end N, as well as their equivalent calculation circuits, and obtain the injection point (the protection installation location at the sending end M). Injected mixed voltage wave sequence Lossless ECTF.

[0200] S72, the capacitor element in the circuit The equivalent value is a resistance calculation. and equivalent current source Parallel lossless ECTFs.

[0201] Specifically, S72 includes the following S721~722:

[0202] S721, capacitor element The voltage and the current flowing through them have the following relationship:

[0203] (58)

[0204] In the formula, for The current flows through the capacitor element at all times The current flows from the sending end M to the receiving end N. Capacitor element The capacitance value, and They are respectively Time Capacitor Element The terminal voltages near the sending end M and the receiving end N.

[0205] For equation (58) in the time interval Integrating the above, For time step:

[0206] (59)

[0207] In the formula, and They are respectively Time Capacitor Element The terminal voltages near the sending end M and the receiving end N.

[0208] S722: Equation (59) can be approximately calculated as:

[0209] (60)

[0210] In the formula, for The current flows through the capacitor element at all times The current flows from the sending end M to the receiving end N. According to equations (59) and (60), we obtain... , Current at any moment The relationship between them:

[0211] (61)

[0212] Transform equation (61) to obtain the current. The expression:

[0213] (62)

[0214] According to equation (62), we get Equivalent current source at time t :

[0215] (63)

[0216] According to equations (62) and (63), we get Current at any moment and Equivalent current source at time t The relationship between them:

[0217] (64)

[0218] According to equation (64), we can further derive Equivalent current source at time t With current The relationship between them at this time Current at any moment for:

[0219] (65)

[0220] In the formula, for The equivalent current source at time t. and They are respectively Time Capacitor Element The terminal voltages near the sending end M and the receiving end. Equation (63) is transformed according to equation (65) to obtain... Equivalent current source at time t With capacitors The relationship between the voltage differences at both ends:

[0221] (66)

[0222] In this embodiment, the time step is taken as... Then the capacitor element connected in series in line MN can be obtained. Equivalent resistance calculation :

[0223] (67)

[0224] S73, the inductor in the circuit The equivalent value is a resistance calculated from the equivalent value. and equivalent current source Parallel lossless ECTFs;

[0225] Specifically, S73 includes the following S731~S732:

[0226] S731, inductor element The voltage drop and the current flowing through them have the following relationship:

[0227] (68)

[0228] In the formula, and They are respectively Inductor element The terminal voltages near the sending end M and the receiving end N, for The current flows through the inductor at all times The current flows from the sending end M to the receiving end N.

[0229] For equation (68) in the time interval Integrating the above, For time step:

[0230] (69)

[0231] In the formula, Inductor The inductance value. The current can be obtained according to equation (69). The integral expression:

[0232] (70)

[0233] In the formula, for The current flows through the inductor at all times The current flows from the sending end M to the receiving end N.

[0234] S732, when When it approaches 0, we get , Voltage at time Relationship between pressure drops:

[0235] (71)

[0236] In the formula, and They are respectively Inductor element The terminal voltages near the sending end M and the receiving end N.

[0237] According to equations (70) and (71), we obtain , Current at any moment The relationship between them:

[0238] (72)

[0239] According to equation (72), we get Equivalent current source at time t :

[0240] (73)

[0241] According to equation (73), we can further derive Equivalent current source at time t and Current at any moment The relationship between them at this time Current at any moment for:

[0242] (74)

[0243] According to equation (74), a resistance can be calculated from the equivalent value. With an equivalent current source Parallel lossless ECTFs.

[0244] Further determination Equivalent current source at time t With current The relationship between equations is given by substituting equation (74) into equation (72), resulting in... Current at any moment :

[0245] (75)

[0246] In the formula, for The equivalent current source at time t. Then, according to equation (75), we obtain Equivalent current source at time t With inductor The relationship between the voltage differences at both ends:

[0247] (76)

[0248] Through the above derivation, we can obtain At any time, inductor element The lossless ECTF. Similarly, the inductive element in the circuit. It can also be converted into a lossless ECTF for numerical computation.

[0249] In this embodiment, the time step is taken. Then the inductor element connected in series in line MN can be obtained. Equivalent resistance calculation :

[0250] (77)

[0251] In summary, based on S71~S73 above, the lossless ECTF of line MN can be obtained. This embodiment ignores lines NP, PQ, and QM in a four-terminal bipolar MMC DC transmission network, and constructs the lossless ECTF of line MN to be selectively overlapped in a multi-terminal flexible DC transmission network, as follows. Figure 8 As shown. Among them, To inject mixed voltage wave sequence node voltage, For the sending end M in The equivalent voltage source of a lossless transmission line at any given moment. For the receiving end N in The equivalent voltage source of a lossless transmission line at any given moment. for Inductor element Inductor components Equivalent current source, To inject mixed voltage wave sequence The equivalent power source.

[0252] S74 calculates the voltage of each node in the lossless ECTF of the line, obtains the voltage and current at the injection end protection installation point after injecting the mixed voltage wave sequence, and then calculates the fault-free forward traveling wave of the injection end line mode voltage.

[0253] In this embodiment, the lossless ECTF of line MN is calculated. , , , , The voltage at each node is used to obtain the injected hybrid voltage wave sequence. Rear end M protection installation location and the N-end protection installation location The voltage and current are used to calculate the fault-free, lossless ECTF line-mode voltage traveling wave, i.e., the fault-free line-mode voltage traveling wave at the injection end.

[0254] Specifically, S74 includes the following S741~S744:

[0255] S741, according to equation (78), the admittance matrix is ​​obtained. F :

[0256] (78)

[0257] In the formula, For matrixF the number of rows, For matrix F The number of columns, 5.

[0258] (79)

[0259] In the formula, Let be the equivalent resistance of line MN. , For the equivalent current source and equivalent calculated resistance of the lossless ECTF of the inductive components in converter station A on the sending end M side, , The equivalent current source and equivalent calculated resistor of the lossless ECTF for the capacitor element in converter station A on the sending end M side.

[0260] S742: According to Kirchhoff's current theorem, at any node in the circuit, the algebraic sum of the current flowing into and out of that node is always equal to zero. The current excitation of each node in the lossless ECTF of line MN can be calculated according to equation (80). :

[0261] (80)

[0262] In the formula, Indicates the inflow of the first Equivalent current sources at each node, Indicates the outflow of the first The equivalent current source at each node, according to Figure 8 Write down the current excitation matrix for each node. :

[0263] (81)

[0264] Calculate the equivalent current sources and equivalent voltage sources in the current excitation matrix:

[0265] (82)

[0266] S743, Figure 8 middle All represent node voltages. There are a total of 5 nodes, and the node voltages at each node can be calculated using equation (83):

[0267] (83)

[0268] Based on the propagation time of the wave on the line MN Equation (83) can be further expressed as:

[0269] (84)

[0270] The injected hybrid voltage wave sequence is calculated according to equation (84). Rear end M protection installation location and the N-end protection installation location voltage and current :

[0271] (85)

[0272] In the formula, The M protection installation point is located at the sending end. N-end protection installation location The rated voltage and current.

[0273] S744, based on the lossless transmission line in the lossless ECTF, the fault-free forward traveling wave of the sending-end line-mode voltage of line MN can be obtained respectively. and the fault-free forward traveling wave of the receiving-end line mode voltage :

[0274] (86)

[0275] According to equation (32), a theoretically calculated hybrid voltage wave sequence is injected into the lossless ECTFM terminal. The fault-free forward traveling wave of the sending-end mode voltage under the lossless transmission line is obtained. (i.e., the fault-free forward wave of the injected line mode voltage).

[0276] S745, based on the forward traveling wave of the sending-end line mode voltage fault in S63. Sampling time series If the same sampling time sequence is maintained, and a time sequence is formed to construct the fault-free forward traveling wave of the sending-end line-mode voltage, then the fault-free forward traveling wave of the sending-end line-mode voltage is... It can be represented as .

[0277] In this invention, the fault-free forward traveling wave of the sending-end line mode voltage is also called the theoretical calculation wave.

[0278] S8 specifically includes the following S81~S87:

[0279] S81 normalizes the fault-preceding wave of the injection terminal line-mode voltage and the fault-free forward wave of the injection terminal line-mode voltage, respectively.

[0280] Specifically, the traveling wave before the injection terminal line-mode voltage fault. and the fault-free forward traveling wave of the injection terminal line mode voltage Each value is calculated according to equation (87):

[0281] (87)

[0282] In the formula, and They are respectively The maximum and minimum values ​​in the range. and They are respectively The maximum and minimum values ​​in the range. This is the normalized forward traveling wave of the injection terminal line-mode voltage fault. The normalized injection terminal line-mode voltage is the fault-free traveling wave.

[0283] S82, perform continuous wavelet transform on the normalized injection end line mode voltage fault-preceding traveling wave and the injection end line mode voltage fault-free traveling wave respectively, and obtain the corresponding continuous wavelet transform results of the injection end line mode voltage fault-preceding traveling wave and the injection end line mode voltage fault-free traveling wave.

[0284] The formula for performing a continuous wavelet transform (CWT) on the normalized injection terminal line-mode voltage fault traveling wave is as follows:

[0285] (88)

[0286] In the formula, For scale parameters, For translation parameters, For the mother wavelet function, The conjugate function of the mother wavelet. The wavelet function is after translation and scaling. For the traveling wave before the sending-end line mode voltage fault and the forward traveling wave of the sending-end line mode voltage without fault Sampling time series The elements in The result is a continuous wavelet transform of the traveling wave preceding the injection-end line-mode voltage fault. The time-frequency spectrum of the traveling wave preceding the injection-end line-mode voltage fault is as follows: Figure 9 As shown.

[0287] Similarly, the continuous wavelet transform results of the fault-free forward traveling wave of the injected terminal line-mode voltage can be obtained.

[0288] S83, perform signal correction on the continuous wavelet transform results of the advancing wave of the line-mode voltage at the injection end fault and the advancing wave of the line-mode voltage at the injection end without fault, respectively, and obtain the corresponding continuous wavelet transform correction results of the advancing wave of the line-mode voltage at the injection end fault and the advancing wave of the line-mode voltage at the injection end without fault.

[0289] The signal correction formula for the continuous wavelet transform result of the advancing wave of the injected terminal line-mode voltage fault is as follows:

[0290] (89)

[0291] In the formula, The result of continuous wavelet transform correction for the traveling wave before the injection terminal line-mode voltage fault. As the normalization factor, It is the center frequency of the wavelet fundamental. To correct the operator, It is the imaginary unit.

[0292] Similarly, the continuous wavelet transform correction result of the fault-free forward traveling wave of the injected terminal line mode voltage can be obtained.

[0293] S84, based on the instantaneous frequency group delay, performs transient extraction transformation on the continuous wavelet transform correction results of the injected end line mode voltage fault-preceding wave and the injected end line mode voltage fault-free preceding wave, respectively, to obtain the time spectrum of the energy concentration of the injected end line mode voltage fault-preceding wave and the injected end line mode voltage fault-free preceding wave.

[0294] Specifically, will Convert to frequency domain:

[0295] (90)

[0296] In the formula, Time-domain wavelet kernel Fourier transform, The normalization constant is It is a frequency variable. Time-domain signal Fourier transform, Fourier transform of the mother wavelet function in The value on, It is a frequency shift operator.

[0297] Calculate signal group delay and instantaneous frequency operator :

[0298] (91)

[0299] (92)

[0300] In the formula, For signal to The continuous wavelet transform obtained from the wavelet basis, For group delay operators, The angular frequency variable of the signal; For variables Find the partial differential operator for partial derivatives.

[0301] Signal Transforming to the frequency domain, it can be represented as:

[0302] (93)

[0303] In the formula, For signal The expression in the frequency domain. Using the Dirac function, a transient extraction operator is designed to construct a new time-frequency expression:

[0304] (94)

[0305] (95)

[0306] In the formula, This is a transient selection function. It is a transient extraction operator with the property shown in equation (95). For the signal The result of the transient extraction transform (TET) is the time-frequency spectrum of the energy concentration of the advancing wave of the injected line-mode voltage fault. The time-frequency spectrum of the advancing wave of the injected line-mode voltage fault after the transient extraction transform (TET) is as follows: Figure 10 As shown.

[0307] Similarly, the time spectrum of the energy concentration of the fault-free forward traveling wave of the injected line-mode voltage can be obtained. .

[0308] S85 extracts abrupt change points from the time spectrum and reconstructs the fault-preceding wave of the injected line-mode voltage and the fault-free forward wave of the injected line-mode voltage, respectively, to obtain the fault-reconstructed waveform of the injected line-mode voltage and the fault-free reconstructed waveform of the injected line-mode voltage.

[0309] Specifically, S85 includes the following S851~S854:

[0310] S851 lists the time series and corresponding amplitude series of the normalized injection terminal line mode voltage fault-preceding traveling wave and the injection terminal line mode voltage fault-free traveling wave, respectively.

[0311] Specifically, according to S81, the following is listed: and :

[0312] (96)

[0313] (97)

[0314] In the formula, The number of discrete sampling points after normalization of the fault-free and fault-free forward traveling waves of the injection-end line-mode voltage. ={ , ..., }for The time series of discrete sampling points after normalization processing ={ ( ), ( ), ..., ( )} represents the corresponding amplitude; ={ , ..., }for Time series after normalization ={ ( ), ( ), ..., ( } represents the corresponding amplitude.

[0315] S852 lists the time series of abrupt change points after normalization, continuous wavelet transform, and transient extraction transform of the forward traveling wave of the injected line-mode voltage fault and the forward traveling wave of the injected line-mode voltage without fault.

[0316] Specifically, based on S81, S82, S83, and S84, the time series of abrupt change points of the fault-preceding traveling wave of the injected line-mode voltage and the fault-free traveling wave of the injected line-mode voltage are listed after normalization and CWT and TET transformations. :

[0317] (98)

[0318] (99)

[0319] In the formula, The number of abrupt change points in the fault-preceding traveling wave of the injected line-mode voltage and the fault-free traveling wave of the injected line-mode voltage after normalization and CWT / TET transformation. ={ , ..., }for The time series of mutation points, ={ , ..., }for The time series.

[0320] S853, replace the time series of the normalized injection end line-mode voltage fault-preceding travel wave and the injection end line-mode voltage fault-free traveling wave with the time series of the abrupt change points of the injection end line-mode voltage fault-preceding travel wave and the injection end line-mode voltage fault-free traveling wave, respectively, and combine them with the amplitude series of the normalized injection end line-mode voltage fault-preceding travel wave and the injection end line-mode voltage fault-free traveling wave to obtain the injection end line-mode voltage fault reconstruction wave sequence and the injection end line-mode voltage fault-free reconstruction wave sequence.

[0321] Specifically, by substituting the abrupt change times in equations (98) and (99) into equations (96) and (97) respectively, the reconstructed waveform sequence of the injected terminal line-mode voltage fault is obtained. and the fault-free reconstructed waveform sequence of the injection terminal line mode voltage As shown in equations (100) and (101):

[0322] (100)

[0323] (101)

[0324] S854 connects all points in the injection terminal line-mode voltage fault reconstruction waveform sequence and the injection terminal line-mode voltage fault-free reconstruction waveform sequence to obtain the injection terminal line-mode voltage fault reconstruction waveform and the injection terminal line-mode voltage fault-free reconstruction waveform, respectively.

[0325] Specifically, respectively , Connecting all the points will give you the fault reconstruction waveform of the injection terminal line-mode voltage. Fault-free reconstructed waveform of injection terminal line mode voltage .

[0326] In this embodiment, the sampling rate of the lines to be selectively overlapped in the multi-terminal flexible direct current system is... =1 MHz, step size 1 Under these conditions, 4000 data points were collected, and the reconstructed waveform of the injected terminal line mode voltage fault was obtained. Fault-free reconstructed waveform of injection terminal line mode voltage like Figure 11 As shown.

[0327] S86, calculate the Hausdorff distance between the fault-reconstructed waveform of the injection terminal line-mode voltage and the fault-free reconstructed waveform of the injection terminal line-mode voltage.

[0328] Specifically, Let denoted as the two-dimensional point set of the fault-free forward traveling wave of the injected line-mode voltage. Let the two-dimensional point set of the forward traveling wave of the injection terminal line mode voltage fault be denoted as the two-dimensional point set, which can be represented by equation (102).

[0329] (102)

[0330] In the formula, for The first element, for The second element, for The One element, for The first element, for The second element, for The Each element. Calculate. Each point in the and The Euclidean distance between corresponding points is denoted as a new point set. :

[0331] (103)

[0332] Similarly, we obtain and Euclidean distance point set :

[0333] (104)

[0334] calculate arrive One-way Hausdorff distance :

[0335] (105)

[0336] Similarly, we obtain arrive One-way Hausdorff distance :

[0337] (106)

[0338] Finally obtained The final distance of Hausdorff :

[0339] (107)

[0340] S87. Based on the Hausdorff distance criterion, if the Hausdorff distance is greater than or equal to the detection threshold, the line is determined to have a permanent fault; otherwise, the line is determined to have a non-permanent fault.

[0341] Specifically, fault determination is performed by setting detection thresholds. Taking a 600Ω single-pole ground fault occurring at 90% of the line distance from the sending end as the most unfavorable influencing factor, the final Hausdorff distance detected at the sending end under this condition is determined. Value multiplied by To adjust .

[0342] (108)

[0343] In the formula, In this embodiment, the reliability coefficient is used as the detection threshold. =0.85 is consistent with equation (13). =200.

[0344] (109)

[0345] The Hausdorff distance is calculated to be 451 according to formula (107), indicating that a permanent fault has occurred in the flexible straight line, which is consistent with the case of a permanent 300 Ω positive ground fault set in this embodiment.

[0346] Based on the above-mentioned method for predicting the fault nature of a multi-terminal flexible DC selective overclosing line, the present invention also provides a device for predicting the fault nature of a multi-terminal flexible DC selective overclosing line.

[0347] A fault nature prediction device for a multi-terminal flexible DC selective overclosing line includes a processor, a memory, and a computer program stored in the memory. When the computer program is executed by the processor, it implements the fault nature prediction method for the multi-terminal flexible DC selective overclosing line as described above.

[0348] In summary, this invention can predict the nature of a fault before it coincides with another fault and only applies to transient coincidences. Compared with existing methods, this invention has the following advantages:

[0349] 1) No additional control is required for the MMC converter during fault diagnosis. For a multi-terminal DC grid that has one DC line disconnected and is in the N-1 state, the implementation of this invention does not affect its normal operation.

[0350] 2) Signal injection is performed using only the transfer branch of the DC circuit breaker, and (S1, S2) adopt a strict fault section prediction method before the fault nature is predicted to uniquely determine the time domain expression of the injected signal, completely eliminate the overcurrent risk of the DC circuit breaker or MMC converter, and greatly improve the safety of the primary equipment.

[0351] 3) Based on the hypothetical lossless scenario, a multi-terminal DC power grid is modeled and an equivalent calculation circuit model for its traveling wave calculation is constructed. The Hausdorff distance between the faultless theoretical voltage traveling wave waveform generated by the ECTF and the measured voltage traveling wave waveform is used as an indicator to measure whether the line is lossless (whether the fault is permanent). Compared with the traditional polarity / amplitude method of reflected waves, it has the advantages of high resistance to transition resistance and dead zone fault identification capability.

[0352] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for predicting the fault nature of a multi-terminal flexible DC selective overclosing line, characterized in that, include: S1, based on the current time, collects the voltage and current of the sending and receiving ends in the first preset time window of the multi-terminal flexible DC line to be selectively overlapped, and performs phase mode transformation on the voltage and current of the sending and receiving ends in the first preset time window respectively to obtain the first matrix of line and zero mode voltage and current of the sending and receiving ends. S2, calculate the fault start action quantity of the sending and receiving ends according to the first matrix of the sending and receiving end lines and the zero-mode voltage and current respectively, and use the fault start action quantity of the sending end under the most unfavorable influence to calculate the threshold value of the fault start action quantity, thereby constructing the start criterion to determine whether the line has a fault, and record the time when the start criterion is met as the start time. S3, after determining that a line fault has occurred, calculates the cumulative reference value of the mode voltage of the sending and receiving lines according to the first matrix of the sending and receiving line and the zero-mode voltage and current, so as to determine the area where the fault occurred. S4. Select one end from the sending and receiving ends as the injection end of the mixed voltage wave sequence according to the area where the fault occurs, and control the DC circuit breaker on the injection end side to inject the mixed voltage wave sequence based on the start time and after a preset deionization time. S5, taking the moment when the hybrid voltage wave sequence is first reflected back to the injection end as a reference, the voltage and current of the injection end within the second preset time window are collected, and the voltage and current of the injection end within the second preset time window are transformed to obtain the second matrix of injection end line and zero mode voltage and current; S6. Calculate the forward traveling wave of the injection terminal mode voltage fault based on the second matrix of the injection terminal line and zero-mode voltage and current. S7 is used to build an equivalent calculation circuit model for lossless traveling wave calculation of a multi-terminal flexible DC line with selective overlap, and to simulate the process of injecting a mixed voltage wave sequence in order to theoretically calculate the fault-free forward traveling wave of the injected line mode voltage. S8 uses transient extraction transform based on continuous wavelet transform as a tool to reconstruct the fault-preceding wave of the injected line-mode voltage and the fault-free forward wave of the injected line-mode voltage, respectively, and calculates the Hausdorff distance between the reconstructed fault-preceding wave of the injected line-mode voltage and the fault-free forward wave of the injected line-mode voltage, thereby determining the nature of the line fault.

2. The fault nature prediction method for multi-terminal flexible DC selective overclosing lines according to claim 1, characterized in that, S1 specifically includes: S11, based on the current time, collect the positive and negative voltages and currents of the sending and receiving ends in the first preset time window of the multi-terminal flexible DC line to be selectively overlapped, and obtain the first matrix of positive and negative voltages and currents of the sending and receiving ends accordingly. S12, based on the Kelenberger transformation, perform phase mode transformation on the first matrix of positive and negative voltage and current at the sending and receiving ends respectively to obtain the first matrix of line and zero-mode voltage and current at the sending and receiving ends. The formula for phase mode transformation of the first matrix of positive and negative voltage and current at the sending and receiving ends is as follows: ； In the formula, or ;when hour, This represents the first matrix of sending line and zero-mode voltage and current. The first matrix represents the positive and negative voltage and current of the sending terminal; when hour, This represents the first matrix of received-end line and zero-mode voltage and current. This represents the first matrix representing the positive and negative voltage and current at the receiving end; Let be the phase mode transformation matrix, and Represented as: 。 3. The fault nature prediction method for multi-terminal flexible DC selective overclosing lines according to claim 1, characterized in that, S2 specifically includes: S21, based on the line surge impedance, perform matrix transformations on the first matrices of the sending and receiving end lines and zero-mode voltage and current, respectively, to obtain the corresponding sending and receiving end start-up reference matrices; wherein, the transformation formulas for the sending and receiving end start-up reference matrices are: ； In the formula, or ;when hour, This represents the sending end start reference matrix. This represents the first matrix of the sending line and zero-mode voltage and current; when hour, This represents the receiving end start reference matrix. This represents the first matrix of the receiving end line and zero-mode voltage and current; Let be the line wave impedance matrix, and Represented as: ； In the formula, Line impedance; S22, calculate the fault start action quantities for the sending and receiving ends respectively based on the corresponding start reference matrices of the sending and receiving ends; wherein, the calculation formulas for the fault start action quantities of the sending and receiving ends are: ； In the formula, when hour, ;when hour, ;when hour, Indicates the fault initiation action quantity at the sending end; when hour, This indicates the amount of fault initiation action at the receiving end; express The largest element in the middle, and is The first in One element; express The first in One element; express The first in One element; S23: Calculate the threshold value of the fault start action amount of the sending end under the most unfavorable impact condition, and construct the sending and receiving end start criteria in this way. Determine whether the sending and receiving end start criteria are both invalid. If yes, it is determined that no line fault has occurred, and return to S1. If no, it is determined that a line fault has occurred, and the time when the start criteria are met is recorded as the start time, and S3 is executed.

4. The fault nature prediction method for multi-terminal flexible DC selective overclosing lines according to claim 1, characterized in that, S3 specifically includes: S31, extract the sending and receiving line mode voltage vectors from the sending and receiving line and the first matrix of zero-mode voltage and current respectively, and perform second and third derivatives on the extracted sending and receiving line mode voltage vectors respectively to obtain the second reference vector and the third reference vector of the sending and receiving line mode voltages respectively. S32, perform zero-padding operations on the first and last ends of the third reference vector of the line-mode voltage at the sending and receiving ends respectively, and obtain the third reference zero-padding vector of the line-mode voltage at the sending and receiving ends respectively. S33, add the second-order reference vector of the sending and receiving end line-mode voltage to the third-order reference zero-padding vector of the sending and receiving end line-mode voltage respectively to obtain the mixed reference vector of the sending and receiving end line-mode voltage. S34, accumulate the elements in the mixed reference vector of the sending and receiving end line-mode voltages respectively to obtain the accumulated reference values ​​of the sending and receiving end line-mode voltages; S35. Compare the cumulative reference values ​​of the line-mode voltage at the sending and receiving ends. If the cumulative reference value of the line-mode voltage at the sending end is greater than or equal to the cumulative reference value of the line-mode voltage at the receiving end, the fault is determined to occur in the first half of the region, including the midpoint of the line. If the cumulative reference value of the line-mode voltage at the sending end is less than the cumulative reference value of the line-mode voltage at the receiving end, the fault is determined to occur in the second half of the region, excluding the midpoint of the line.

5. The fault nature prediction method for multi-terminal flexible DC selective overclosing lines according to claim 1, characterized in that, The area where the fault occurred is divided into a first half including the midpoint of the line and a second half excluding the midpoint; S4 specifically refers to: If the fault occurs in the first half of the line, the receiving end is used as the injection end, and based on the start time, after a preset deionization time, the DC circuit breaker on the receiving end is controlled to inject a mixed voltage wave at preset time intervals within a preset time period determined by the line length. If the fault occurs in the second half of the line, the sending end is used as the injection end, and based on the start time, after a preset deionization time, the DC circuit breaker on the sending end is controlled to inject a mixed voltage wave at preset time intervals within a preset time period determined by the line length.

6. The fault nature prediction method for multi-terminal flexible DC selective overclosing lines according to claim 1, characterized in that, S6 specifically includes: S61, extract the injection terminal line mode voltage and current vector from the second matrix of injection terminal line and zero-mode voltage and current, and use a non-overlapping sliding window to calculate the local mean of the extracted injection terminal line mode voltage and current vector to obtain the mean vector of injection terminal line mode voltage and current. S62, combine the mean vectors of the injection terminal line-mode voltage and current to obtain the mean matrix of the injection terminal line-mode voltage and current; S63, based on the line wave impedance, calculate the mean matrix of the line-mode voltage and current at the injection end to obtain the forward traveling wave of the line-mode voltage fault at the injection end.

7. The fault nature prediction method for multi-terminal flexible DC selective overclosing lines according to claim 1, characterized in that, Specifically, S7 includes: S71, based on the law of mixed wave propagation, the line is equivalent to two independent equivalent circuits at the sending end and the receiving end, and an equivalent calculation circuit model for lossless traveling wave calculation is made when a mixed voltage wave sequence is injected at the injection end protection installation point. S72, the capacitor element in the circuit is equivalent to an equivalent calculation circuit model for lossless traveling wave calculation, which is a parallel connection of an equivalent calculated resistor and an equivalent current source. S73, which equates the inductive element in the circuit to an equivalent calculation circuit model for lossless traveling wave calculation by connecting an equivalent calculated resistor and an equivalent current source in parallel; S74, by combining the equivalent calculation circuit model for lossless traveling wave calculation when injecting a mixed voltage wave sequence at the injection terminal protection installation point, the equivalent calculation circuit model for lossless traveling wave calculation of capacitor elements, and the equivalent calculation circuit model for lossless traveling wave calculation of inductor elements, the equivalent calculation circuit model for lossless traveling wave calculation of the line is obtained. The lossless traveling wave calculation of the line is performed by calculating the voltage of each node in the equivalent calculation circuit model. After injecting the mixed voltage wave sequence, the voltage and current at the injection end protection installation point are obtained, and then the fault-free traveling wave of the injection end line mode voltage is calculated.

8. The fault nature prediction method for multi-terminal flexible DC selective overclosing lines according to claim 1, characterized in that, S8 includes: S81, normalizes the fault-preceding wave of the injection terminal line-mode voltage and the fault-free forward wave of the injection terminal line-mode voltage respectively. S82, perform continuous wavelet transform on the normalized injection end line mode voltage fault-preceding wave and the injection end line mode voltage fault-free forward wave respectively, and obtain the corresponding continuous wavelet transform results of the injection end line mode voltage fault-preceding wave and the injection end line mode voltage fault-free forward wave. S83, perform signal correction on the continuous wavelet transform results of the incoming line mode voltage fault-preceding wave and the incoming line mode voltage fault-free wave respectively, and obtain the corresponding continuous wavelet transform correction results of the incoming line mode voltage fault-preceding wave and the incoming line mode voltage fault-free wave. S84, based on the instantaneous frequency group delay, performs transient extraction transformation on the continuous wavelet transform correction results of the injected end line mode voltage fault-preceding wave and the injected end line mode voltage fault-free preceding wave respectively, and obtains the time spectrum of the energy concentration of the injected end line mode voltage fault-preceding wave and the injected end line mode voltage fault-free preceding wave respectively. S85, by extracting abrupt change points from the time spectrum, reconstructs the fault-preceding wave of the injected line-mode voltage and the fault-free forward wave of the injected line-mode voltage respectively, and obtains the fault-reconstructed waveform of the injected line-mode voltage and the fault-free reconstructed waveform of the injected line-mode voltage. S86, calculate the Hausdorff distance between the fault-reconstructed waveform of the injection terminal line-mode voltage and the fault-free reconstructed waveform of the injection terminal line-mode voltage; S87. Based on the Hausdorff distance criterion, if the Hausdorff distance is greater than or equal to the detection threshold, the line is determined to have a permanent fault; otherwise, the line is determined to have a non-permanent fault.

9. The fault nature prediction method for multi-terminal flexible DC selective overclosing lines according to claim 8, characterized in that, Specifically, S85 is: S851 lists the time series and corresponding amplitude series of the normalized injection end line mode voltage fault-preceding wave and the injection end line mode voltage fault-free advancing wave, respectively. S852 lists the time series of abrupt change points after normalization, continuous wavelet transform, and transient extraction transform of the forward wave of the injected line mode voltage fault and the forward wave of the injected line mode voltage without fault. S853, replace the time series of the normalized injection end line mode voltage fault-preceding wave and the injection end line mode voltage fault-free advancing wave with the time series of the abrupt change points of the injection end line mode voltage fault-preceding wave and the injection end line mode voltage fault-free advancing wave, respectively, and combine them with the amplitude sequences of the normalized injection end line mode voltage fault-preceding wave and the injection end line mode voltage fault-free advancing wave to obtain the injection end line mode voltage fault reconstruction wave sequence and the injection end line mode voltage fault-free reconstruction wave sequence. S854 connects all points in the injection terminal line-mode voltage fault reconstruction waveform sequence and the injection terminal line-mode voltage fault-free reconstruction waveform sequence to obtain the injection terminal line-mode voltage fault reconstruction waveform and the injection terminal line-mode voltage fault-free reconstruction waveform, respectively.

10. A fault nature prediction device for a multi-terminal flexible DC selective overclosing line, characterized in that, The system includes a processor, a memory, and a computer program stored in the memory. When the computer program is executed by the processor, it implements the fault nature prediction method for a multi-terminal flexible DC selective overclosing line as described in any one of claims 1 to 9.

Images