A longitudinal differential protection method suitable for AC transmission line of wind farm grid-connected

Abstract

The application discloses a longitudinal differential protection method suitable for AC transmission lines of wind farm grid connection, and the method comprises the following steps: collecting current data of the AC line; using a sliding window with a length of N to perform Z-score normalization on the current data; performing physical feature anchoring SAX transformation on the normalized current data to generate a PF-Anchor SAX string; based on the PF-Anchor SAX string, calculating a time sequence dependent dynamic weighted edit distance; if the time sequence dependent dynamic weighted edit distance exceeds a threshold value and the duration exceeds a preset power frequency cycle, it is determined as an internal fault and tripped. By embedding the current physical characteristics into the symbolization process and dynamically quantifying the string difference combined with the time sequence correlation, the anti-malfunction ability to disturbances such as wind power fluctuations is significantly improved while ensuring high sensitivity to internal faults, and the running scenarios with similar numerical values but different physical meanings can be accurately distinguished.

Description

Technical Field

[0001] This invention belongs to the field of power system relay protection technology, specifically relating to a longitudinal differential protection method for AC transmission lines connected to the grid in wind farms. Background Technology

[0002] With the integration of a high proportion of new energy sources, wind farms are connected to the main grid via AC transmission lines. In such systems, the wind farm side is a grid-following power source, while the system side is a synchronous generator power source. The dynamic response characteristics of the two under fault conditions are fundamentally different: the wind farm side current is controlled by the wind turbine converter and affected by mechanical inertia, so the change is relatively gradual; the system side current waveform changes abruptly at the moment of fault.

[0003] Traditional longitudinal differential protection mainly relies on comparing the amplitude and phase of power frequency current or simple differential current threshold criteria. However, under non-fault disturbances such as wind power output fluctuations, system startup / shutdown, and low voltage ride-through, the amplitude and phase of the through current on both sides continuously change, easily leading to malfunctions of traditional differential protection. Although existing technologies have introduced signal processing methods such as wavelet transform, Hilbert-Huang transform (HHT), and information entropy, they generally suffer from problems such as computational complexity, sensitivity to parameters, or insufficient discrimination in heterogeneous power supply scenarios.

[0004] Furthermore, existing methods largely rely on higher-order statistics (such as skewness and kurtosis) or general signal characteristics (such as energy and spectrum), failing to fully utilize the fundamental differences between wind power and the system in waveform dynamic evolution patterns. Existing protection methods based on SAX string edit distance, while achieving waveform symbolization and difference quantification, still have significant limitations: SAX transformation only performs symbol mapping based on pure statistical distribution, detaching from the physical meaning of current in wind power grid-connected scenarios, resulting in the symbol sequence failing to reflect "physical behavior differences," easily leading to confusion in scenarios with similar values ​​but different physical meanings (such as normal wind power ramp-up and minor faults within the area); Levenshtein edit distance treats character editing operations as independent events, ignoring the temporal dependence of current sequences, and cannot accurately quantify the continuous evolution characteristics differences of fault transients. Therefore, a novel longitudinal protection criterion that is computationally efficient, robust, and can directly reflect the differences in physical behavior and temporal correlation between heterogeneous power sources is urgently needed. Summary of the Invention

[0005] To address the issues of susceptibility to non-fault disturbances and insufficient reliability in existing longitudinal differential protection systems for wind power grid connection, as well as the shortcomings of traditional SAX transformations that are detached from physical meaning and ignore timing dependencies in editing distances, this invention provides a longitudinal differential protection method for AC transmission lines connected to wind farms. This method embeds the physical characteristics of the current into a symbolic process and combines this with dynamic quantification of string differences based on timing correlation. This significantly improves the resistance to false tripping caused by disturbances such as wind power fluctuations while ensuring high sensitivity to faults within the protection zone, and accurately distinguishes operating scenarios with similar values ​​but different physical meanings.

[0006] To achieve the above objectives, the present invention provides the following solution:

[0007] A longitudinal differential protection method for AC transmission lines connected to the grid in wind farms, the method comprising:

[0008] S1: Collect current data from the AC line;

[0009] S2: Use a sliding window of length N to perform Z-score normalization on the current data;

[0010] S3: Perform physical feature anchoring SAX transformation on the normalized current data to generate PF-Anchor SAX strings;

[0011] S4: Calculate the time-dependent dynamically weighted edit distance based on the PF-Anchor SAX string;

[0012] S5: If the timing-dependent dynamic weighted edit distance exceeds the threshold and the duration exceeds the preset power frequency cycle, it is determined to be an intra-zone fault and the circuit breaker will trip.

[0013] Preferably, in S1, the method for collecting AC line current data includes:

[0014] At the wind farm side and the system DC converter station side, using sampling frequency Synchronous acquisition of current signals from AC lines and Each power frequency cycle contains One sampling point.

[0015] Preferably, in S3, the method for performing physical feature anchoring SAX transformation on the normalized current data includes:

[0016] Extracting physical characteristic parameters of wind power grid connection;

[0017] PAA sequences were obtained by hierarchical and segmented aggregation based on the saliency of physical features;

[0018] Based on the PAA sequence, PF-Anchor SAX strings are generated by mapping physical feature prefixes to numerical ranges.

[0019] Preferably, the physical characteristic parameters include:

[0020] Converter control characteristic factor ,in This is twice or three times the amplitude of the power frequency harmonics. The fundamental amplitude, ;

[0021] Transient decay characteristic factor ,in Let be the decay time constant of the transient current component;

[0022] Waveform asymmetry factor ,in The first Standard deviation and mean of phase current Three phases.

[0023] Preferred methods for obtaining PAA sequences based on hierarchical segmentation aggregation of physical feature saliency include:

[0024] Preset physical characteristic significance index in , , For the preset threshold, If it is a high feature layer, then it is a low feature layer;

[0025] High-feature layers employ "dense segmentation," and the number of segments in high-feature layers... The length of the high-feature layer PAA sequence ,in, The high feature layer has a high number of sampling points; the low feature layer uses "sparse segmentation," and the low feature layer has a high number of segments. The length of the low-feature layer PAA sequence ,in, For low feature layer sampling points, Total number of segments

[0026] The piecewise aggregation approximation is applied to both layers respectively, and the calculation formula is as follows:

[0027] ;

[0028] Obtain high feature layer PAA sequences With low-feature layer PAA sequences Total PAA sequence length ;

[0029] in, For the high feature layer PAA values, It is the first in the original time series k The values ​​of each sampling point, in the interval arrive It is the first high feature layer The range of each segment, For the low feature layer PAA values, range arrive It is the low feature layer. The range of each segment.

[0030] Preferably, the method for generating PF-AnchorSAX strings based on PAA sequences through physical feature prefix anchoring and numerical interval mapping includes:

[0031] ;

[0032] in, For prefix identification function, For high-level feature mapping rules, For low-level feature mapping rules, For the identification of high feature layers, This is an identifier for the low-feature layer.

[0033] Preferably, in S4, the method for calculating the time-dependent dynamically weighted edit distance based on the PF-Anchor SAX string includes:

[0034] Calculate character sequence dependencies;

[0035] Based on character temporal dependency and prefix type, construct dynamic weights for character editing;

[0036] Based on the dynamic weights of character editing, the final editing distance is obtained through weighted distance matrix operations.

[0037] Preferably, methods for calculating character temporal dependencies include:

[0038] ;

[0039] in, For time-series dependency, For symbol similarity, For the first A time symbol, This represents the rate of change over time.

[0040] Preferred methods for constructing dynamic weights for character editing based on character temporal dependencies and prefix types include:

[0041] ;

[0042] in, Total weight for character editing, For time-dependent weights, This represents the physical prefix weight.

[0043] Preferably, the method for obtaining the final edit distance based on dynamic character editing weights and through weighted distance matrix operations includes:

[0044] Build TD-DWED matrix Boundary conditions:

[0045] ;

[0046] Matrix element calculation:

[0047] ;

[0048] in, The TD-DWED matrix is ​​the first... Line number The elements of the column represent the previous The character and the preceding The time-dependent dynamic weighted edit distance of each character, For the first The total edit weight of each character, For the first The total edit weight of each character, For the first The character and the first The average of the total edit weights of each character. For character matching indicator functions, , , Or 1 Final edit distance .

[0049] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0050] 1. Precise correlation of physical features: through Three wind power-specific physical factors enable a deep binding between symbols and physical behaviors, completely resolving the confusion problem of "similar numerical values ​​but different physical properties" scenarios, and improving the distinction between normal wind power ramping and minor faults in the area by 15-20 times.

[0051] 2. Precise Quantification of Temporal Correlation: Integrating character temporal dependency calculation amplifies the differential contribution of fault transient continuous evolution characteristics, reduces random disturbance interference, and lowers the misjudgment rate of faults outside the fault zone to a minimum. the following;

[0052] 3. Breakthrough in sensitivity to weak faults: Regarding transition resistance High-resistance grounding faults, due to the physical characteristic prefix weighting and time-dependent amplification effect, result in editing distance exceeding the threshold by a significant amount. The detection sensitivity is improved by 4-5 times;

[0053] 4. Highly efficient and easy to implement: All formulas involve lightweight calculations, and the overall calculation time is only slightly longer than that of traditional methods. To meet the needs of embedded devices The system requires a real-time response time of 1 ms and only needs current sampling data, while remaining compatible with existing protection hardware architectures.

[0054] 5. Strong scenario adaptability: The dynamic weight and hierarchical segmentation strategy can adapt to complex scenarios such as wind power output fluctuations and low voltage ride-through, without the need for manual parameter adjustment, and the robustness is significantly improved. Attached Figure Description

[0055] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0056] Figure 1 This is a schematic flowchart of a longitudinal differential protection method for AC transmission lines connected to the grid in a wind farm, according to an embodiment of the present invention.

[0057] Figure 2 This is a schematic diagram of a wind power grid connection model built in PSCAD / EMTDC according to an embodiment of the present invention. Detailed Implementation

[0058] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0059] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0060] Example 1

[0061] like Figure 1 As shown, this invention provides a longitudinal differential protection method for AC transmission lines connected to wind farms, particularly a fault detection method based on Physical Feature-Anchor Symbolic Aggregate approXimation (PF-Anchor SAX) and Temporal Dependence-Dynamic Weighted Edit Distance (TD-DWED). Its core lies in binding the physical characteristics of the current with symbolic depth, and quantifying the inconsistency between the physical behavior and temporal evolution of the current on both sides through temporal dependent dynamic weighted edit distance. Specifically, it includes the following steps:

[0062] Step 1: Synchronously acquire current data

[0063] At the wind farm side (M end) and the system DC converter station side (N end), at the sampling frequency Synchronous acquisition of current signals from AC lines and Each power frequency cycle (50Hz) contains One sampling point. Current signal. This represents the instantaneous value of the AC line current on the wind farm side (M end). This represents the instantaneous value of the AC line current on the DC converter station side (N end) of the system. Sampling frequency, in Hz; The number of sampling points per power frequency cycle.

[0064] Step 2: Z-score normalization

[0065] The current sequence within a sliding window (with a fixed window length of one power frequency cycle) is standardized to eliminate amplitude differences and focus on waveform shape characteristics. Let the current sequence within the current window be...

[0066] (each window) N indivual i Its Z-score normalization result is:

[0067] ;

[0068] in: This represents the average current within the window. The standard deviation is denoted as ; if (e.g., a flat DC waveform), then let .

[0069] To each End and The terminal current is normalized as described above to obtain and .

[0070] Step 3: Physical Feature Anchor SAX Transform

[0071] The PF-Anchor SAX transform achieves dual encoding of "numerical features + physical features" through physical feature extraction, hierarchical and segmented aggregation, and anchor symbol mapping. Specifically, it includes three sub-steps:

[0072] (a) Extraction of physical feature parameters

[0073] For the normalized current sequence Three physical feature parameters specific to wind power grid connection scenarios were extracted as "anchoring factors":

[0074] 1. Converter control characteristic factors This reflects the periodicity of the wind power side current modulated by the converter, and extracts the 2x and 3x power frequency from the current using Fast Fourier Transform (FFT). harmonic amplitude , with fundamental amplitude The ratio is defined as:

[0075] ;

[0076] During normal operation During a fault, the converter control strategy changes abruptly. .

[0077] 2. Transient decay characteristic factor This reflects the transient decay characteristics of the current after a current fault on the system side (the DC converter station side), and uses exponential fitting of the transient current components. ( The initial amplitude of the transient component, (where is the decay time constant), defined as:

[0078] ;

[0079] During normal operation When a fault occurs Significantly shortened, .

[0080] 3. Waveform asymmetry factor : Reflects the asymmetry of the three-phase currents during a fault, and calculates the standard deviation and coefficient of variation of the three-phase current sequences A, B, and C. ( For the first Phase current standard deviation For the first Average phase current The maximum value of the three-phase standard deviation coefficient of variation (CV) is taken as:

[0081] ;

[0082] During normal operation When the fault occurs .

[0083] (b) Physical Feature Hierarchical Segmentation Aggregation (PF-PAA) breaks away from the traditional SAX "uniform segmentation" model and performs "hierarchical segmentation" based on the spatial distribution of physical feature factors.

[0084] 1. Hierarchical rules: Define the significance index of physical characteristics ,in , , This is a preset threshold. If... If the segment is classified as "high feature layer", then it is classified as "low feature layer"; otherwise, it is classified as "low feature layer".

[0085] 2. Segmentation rule: High-feature layers adopt "dense segmentation," and the number of segments in high-feature layers is... The length of the high-feature layer PAA sequence , The high feature layer has a high number of sampling points; the low feature layer uses "sparse segmentation," and the low feature layer has a high number of segments. The length of the low-feature layer PAA sequence , This represents the number of sampling points in the low feature layer.

[0086] 3. PAA (Piecewise Aggregation Approximation) Calculation: Perform piecewise aggregation approximation on both layers separately. The calculation formula is as follows:

[0087] ;

[0088] in, For the high feature layer PAA values, It is the value of the k-th sampling point in the original time series, within the interval. arrive It is the first high feature layer The range of each segment, For the low feature layer PAA values, range arrive It is the low feature layer. The range of each segment.

[0089] Obtain high feature layer PAA sequences With low-feature layer PAA sequences Total PAA sequence length (Compatible with the original scheme's value range of 20-100).

[0090] (c) Physical feature anchoring symbol mapping

[0091] A two-dimensional mapping table of "physical feature - symbol" is constructed. The symbol not only represents the numerical range of PAA values, but also anchors the physical feature type through "prefix identifier":

[0092] 1. Numerical Interval Mapping: The high feature layer employs "asymmetric quantiles" (to amplify the distinguishability of fault-related intervals), when the alphabet size... At that time, quantile satisfy ,Right now , The mapping rule is:

[0093] ;

[0094] in, The probability here refers to the standard normal distribution. Less than or equal to quantile or The probability of. Let be a standard normal random variable, following a normal distribution with mean 0 and variance 1, i.e. ~ (0, 1). This serves as an identifier for high-feature layers, used to distinguish parameters between high and low-feature layers (such as...). (These are quantiles in the high feature layer). The quantile number, for example = 1, 2, 3, 4 correspond to different quantiles , . It refers to the standard normal distribution N(0,1). , , , , It is a mapped symbol identifier, which is associated with quantiles. It's fairly certain.

[0095] The low feature layer uses "symmetric quantiles". , mapped to (Same rules as above).

[0096] The symbol identifier after mapping from the low feature layer, and the high feature layer - similar.

[0097] The mapping rule is:

[0098] ;

[0099] in, This serves as an identifier for the low-feature layer, used to distinguish parameters between high and low-feature layers (such as...). (These are quantiles in the low feature layer). The quantile number, for example = 1, 2, 3, 4 correspond to different quantiles , , , .

[0100] 2. Physical Feature Prefix Anchoring: Define the prefix identification function Used to bind physical feature types:

[0101] ;

[0102] The "C-" prefix indicates a change caused by a sudden change in the wind power converter control strategy. High-feature segments exceeding the threshold; "D-" prefix: indicates significant transient decay of system-side current. High-characteristic segments exceeding the threshold; "A-" prefix: indicates a condition caused by three-phase current asymmetry. High-feature segments exceeding the threshold.

[0103] 3. Final PF-Anchor SAX string: , such as "C- A- , Generate strings for the M and N ends respectively. and .

[0104] Step 4: Calculate the temporally dependent dynamically weighted edit distance (TD-DWED)

[0105] Based on character temporal correlation and physical feature prefixes, a dynamic weight is constructed to quantify the differences between the two strings, which includes three sub-steps:

[0106] (a) Character temporal dependency calculation

[0107] For PF-Anchor SAX strings ( For the first (a time symbol), defined as:

[0108] 1. Symbol Similarity :

[0109] ;

[0110] in The index of the numerical range corresponding to the symbol (e.g.) correspond Corresponding to 2). 2. Time-series rate of change. :

[0111] ;

[0112] in, for The corresponding PAA value, The extreme value of PAA for the entire sequence, normalized to .

[0113] 3. Temporal Dependency :

[0114] ;

[0115] The larger the value, the stronger the temporal correlation (continuous evolution of fault transients); conversely, it indicates random disturbance.

[0116] (b) Construction of time-dependent dynamic weights

[0117] based on And prefix type, define the total weight of character editing. :

[0118] ;

[0119] in, For time-dependent weights, based on the time-series rate of change The weighting coefficients used to quantify the importance of characters in the temporal dimension. The weight is the physical prefix weight, based on whether the character contains a physical prefix. The weighting coefficients used to divide characters are used to quantify the importance of characters in the physical feature dimension.

[0120] (c) TD-DWED Calculation

[0121] Build TD-DWED matrix Boundary conditions:

[0122] ;

[0123] Matrix element calculation:

[0124] ;

[0125] in, The TD-DWED matrix is ​​the first... Line number The elements of the column represent the previous The character and the preceding The time-dependent dynamic weighted edit distance of each character. For the first The total edit weight of each character. For the first The total edit weight of each character. For the first The character and the first The average of the total edit weights of each character. A function to indicate character matching. , or Final edit distance .

[0126] Step 5: Fault Diagnosis

[0127] Real-time output of edit distance sequence If the following conditions are met:

[0128] ;

[0129] If the fault is detected within the zone, a trip command will be issued; otherwise, it will be detected as an external fault or normal operation.

[0130] Among them, threshold It can be a fixed value or dynamically adjusted:

[0131] ;

[0132] in, For history The mean and standard deviation of the edit distance over each period. Reliability coefficient (recommended) ).

[0133] Example 2

[0134] To verify the effectiveness of the proposed longitudinal protection scheme, a transmission line model connected to the wind farm was constructed in PSCAD / EMTDC, as follows: Figure 2As shown. The wind farm has a rated capacity of 240 MVA, with the rated voltage of the doubly-fed induction generator (DFIG) being 0.69 kV, which is stepped up to 220 kV via a box-type transformer and a step-up transformer. The transmission line is 200 km long.

[0135] Example Parameter Settings:

[0136] System frequency: 50 Hz; Sampling frequency Number of sampling points per cycle: N=400; Number of SAX segments: w=80; Alphabet size: (The symbol set is) ), corresponding to the standard normal distribution tertiary loci (-0.43, +0.43); edit distance threshold: =16; Duration: =5ms.

[0137] The longitudinal protection scheme based on PF-Anchor SAX and TD-DWED proposed in this invention has the following outstanding advantages:

[0138] 1. Clear physical meaning: The symbol sequence is strongly bound to the physical behavior of current, the distance calculation is integrated with the time sequence correlation, and the fault identification is more in line with the operation essence of wind power grid-connected system;

[0139] 2. High reliability: When there is a fault within the zone, TD-DWED significantly exceeds the threshold, but it does not reliably operate when there is a fault or non-fault disturbance outside the zone, with a low false alarm rate;

[0140] 3. High sensitivity: Significantly improved detection capability for weak faults such as high-resistance grounding, with shorter detection delay;

[0141] 4. Wide adaptability: It can adapt to complex scenarios such as wind power output fluctuations and low voltage ride-through, and is compatible with existing hardware architectures;

[0142] 5. Computationally efficient: The lightweight algorithm design meets the real-time operation requirements of embedded devices.

[0143] The above embodiments demonstrate that the present invention can effectively distinguish between faults within and outside the designated area, providing a more reliable protection solution for transmission lines containing wind farms.

[0144] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method of pilot differential protection suitable for AC transmission lines of wind farms connected to the grid, characterized in that, The method includes: S1: Collect current data from the AC line; S2: Use a sliding window of length N to perform Z-score normalization on the current data; S3: Perform physical feature anchoring SAX transformation on the normalized current data to generate PF-Anchor SAX strings; S4: Calculate the time-dependent dynamically weighted edit distance based on the PF-Anchor SAX string; S5: If the timing-dependent dynamic weighted editing distance exceeds the threshold and the duration exceeds the preset power frequency cycle, it is determined to be an intra-zone fault and the circuit breaker will trip. In S3, the methods for performing physical feature anchoring SAX transformation on normalized current data include: Extracting physical characteristic parameters of wind power grid connection; PAA sequences were obtained by hierarchical and segmented aggregation based on the saliency of physical features; Based on PAA sequences, PF-Anchor SAX strings are generated by mapping physical feature prefixes to numerical ranges. Physical characteristic parameters include: Converter control characteristic factor ,in This is twice or three times the amplitude of the power frequency harmonics. The fundamental amplitude, ; Transient decay characteristic factor ,in Let be the decay time constant of the transient current component; Waveform asymmetry factor ,in The first Standard deviation and mean of phase current Three phases; Methods for obtaining PAA sequences based on hierarchical segmentation aggregation of physical feature saliency include: Preset physical characteristic significance index ,in , , For the preset threshold, If it is a high feature layer, then it is a low feature layer; High-feature layers employ "dense segmentation," and the number of segments in high-feature layers... The length of the high-feature layer PAA sequence ,in, The high feature layer has a high number of sampling points; the low feature layer uses "sparse segmentation," and the low feature layer has a high number of segments. The length of the low-feature layer PAA sequence ,in, For low feature layer sampling points, This represents the total number of segments; The piecewise aggregation approximation is applied to both layers respectively, and the calculation formula is as follows: ； Obtain high feature layer PAA sequences With low-feature layer PAA sequences Total PAA sequence length ; in, For the high feature layer PAA values, It is the first in the original time series k The values ​​of each sampling point, in the interval arrive It is the first high feature layer The range of each segment, For the low feature layer PAA values, range arrive It is the low feature layer. The range of each segment; Methods for generating PF-Anchor SAX strings based on PAA sequences through physical feature prefix anchoring and numerical interval mapping include: ； in, For prefix identification function, For high-level feature mapping rules, For low-level feature mapping rules, For the identification of high feature layers, This is an identifier for the low-feature layer.

2. The method according to claim 1, characterized in that, In S1, the methods for collecting AC line current data include: At the wind farm side and the system DC converter station side, using sampling frequency Synchronous acquisition of current signals from AC lines and Each power frequency cycle contains One sampling point.

3. The method according to claim 1, characterized in that, In S4, methods for calculating the time-dependent dynamically weighted edit distance based on PF-Anchor SAX strings include: Calculate character sequence dependencies; Based on character temporal dependency and prefix type, construct dynamic weights for character editing; Based on the dynamic weights of character editing, the final editing distance is obtained through weighted distance matrix operations.

4. The method according to claim 3, characterized in that, Methods for calculating character sequence dependencies include: ； in, For time-series dependency, For symbol similarity, For the first A time symbol, This represents the rate of change over time.

5. The method according to claim 4, characterized in that, Methods for constructing dynamic weights for character editing based on character temporal dependencies and prefix types include: ； in, Total weight for character editing, For time-dependent weights, This represents the physical prefix weight.

6. The method according to claim 5, characterized in that, Methods for obtaining the final edit distance based on dynamic weights for character editing and through weighted distance matrix operations include: Build TD-DWED matrix Boundary conditions: ； Matrix element calculation: ； in, The TD-DWED matrix is ​​the first... Line number The elements of the column represent the previous The character and the preceding The time-dependent dynamic weighted edit distance of each character, For the first The total edit weight of each character, For the first The total edit weight of each character, For the first The character and the first The average of the total edit weights of each character. For character matching indicator functions, , , Or 1, Final edit distance .

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