Direct current micro-grid single-end fault positioning method and system based on piecewise adaptive regularization least square and nonlinear compensation

Abstract

The application discloses a DC micro-grid single-end fault positioning method based on segmented adaptive regularization least square and nonlinear compensation, first constructs a single-end equivalent circuit model of a DC micro-grid line fault; secondly, introduces an adaptive regularization least square method; then, according to the fault resistance size, the fault data is segmented, the data window length, the filter window length and the regularization coefficient are jointly optimized and searched with the positioning precision as a target function, a current interval-optimization parameter expert database is constructed; finally, a segmented nonlinear compensation mechanism based on a fault position residual error driving is constructed, a polynomial compensation model is established according to the nonlinear mapping relationship between the equivalent fault resistance and the positioning error to correct the positioning result. The application only relies on single-end current measurement information, does not need communication support, the maximum relative positioning error is still less than 4% under a 30dB noise environment, and has the characteristics of high positioning precision, strong noise resistance and low calculation complexity.

Description

Technical Field

[0001] This invention belongs to the field of DC microgrid fault location technology, specifically relating to a single-end fault location method and system for DC microgrids based on piecewise adaptive regularized least squares and nonlinear compensation. Background Technology

[0002] Due to their low line impedance and low system inertia, DC microgrids experience rapid and high-amplitude fault current rises during line faults, which can severely impact power electronic equipment. Therefore, quickly and accurately locating the fault is crucial for rapid system recovery and minimizing power outage time for users.

[0003] Existing fault location methods for DC microgrids are mainly classified into three categories: traveling wave methods, model-based methods, and data-driven methods. Traveling wave methods locate faults by detecting the propagation characteristics of transient traveling waves, but they rely on ultra-high-speed sampling equipment and precise time synchronization mechanisms. Furthermore, the small scale and complex structure of DC microgrids mean that traveling wave signals are easily attenuated significantly in the lines, reducing the reliability of the location results. Model-based fault location methods, such as the least squares method, require real-time construction and solution of overdetermined equations and involve matrix inversion operations. They rely on voltage and current measurements at both ends of the line, placing high demands on communication conditions and data accuracy. While data-driven methods can handle complex nonlinear problems, they generally suffer from insufficient physical interpretability, susceptibility to model overfitting, and a lack of reliable training sample data.

[0004] Existing fault location methods for DC distribution networks based on single-ended current waveforms typically utilize fault current sampling data within a short period after a fault to achieve fault location. However, the low impedance of DC microgrid lines makes the regression matrix prone to severe ill-conditioning, causing the parameter estimation results of traditional least squares methods to be highly sensitive to noise and model errors. Furthermore, single-ended information cannot fully reflect the global system state and cannot uniquely identify the combination of fault distance and fault resistance, resulting in insufficient location accuracy. In addition, the characteristics of fault current differ significantly under different fault resistance conditions, making it difficult for a single model parameter to maintain consistent location accuracy across a wide range of fault resistances. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention proposes a single-ended fault location method for DC microgrids based on piecewise adaptive regularized least squares and nonlinear compensation. First, this invention constructs a single-ended equivalent circuit model of a DC microgrid line fault, transforming the fault location problem into a parameter estimation problem based on local current measurement information. Second, to address the ill-conditioned nature of the regression matrix, an adaptive regularized least squares method is introduced, and the fault data is segmented according to the fault resistance magnitude to construct a current interval-optimized parameter expert database. Finally, a piecewise nonlinear compensation mechanism driven by the fault location residual is constructed to correct the location results, achieving high-precision fault location.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] S1. Construct a single-ended equivalent circuit model of DC microgrid line faults, establish fault voltage loop equations based on Kirchhoff's voltage law, and transform the fault location problem into a parameter estimation problem based on local single-ended current measurement information.

[0008] S2, Based on the single-ended equivalent circuit model, the regression equation for fault parameter identification is established using the least squares method, and Tikhonov regularization is introduced to construct an adaptive regularized least squares objective function with L2 regularization term. The influence of the ill-conditioned regression matrix on parameter estimation is suppressed by parameter weighted regularization.

[0009] S3. Based on the size of the fault resistance, the fault data is segmented. For each fault resistance segment, with the positioning accuracy as the objective function, the data window length, filter window length and regularization coefficient are jointly optimized and searched to construct a current range-optimization parameter expert library.

[0010] S4. Construct a piecewise nonlinear compensation mechanism driven by fault location residuals. Utilize the nonlinear mapping relationship between the equivalent fault resistance and the location error obtained by adaptive regularized least squares solution to establish a polynomial compensation model corresponding to each fault resistance segment.

[0011] S5, during online location, the data window length, filter window length and regularization coefficient parameters are obtained by looking up the table based on the single-ended fault current. The original fault location estimate and equivalent fault resistance are obtained by adaptive regularized least squares solution. The equivalent fault resistance is substituted into the corresponding segmented polynomial compensation model to correct the location result and output the final fault location.

[0012] Furthermore, in step S1, the process of constructing the single-ended equivalent circuit model of the DC microgrid line fault is as follows:

[0013] ;

[0014] in, The voltage across the measuring terminal capacitor is... This represents the faulty line current. The relative distance to the fault location. and These represent the resistance and inductance per unit length of the line, respectively. The equivalent fault resistance, It is the inductance of the current-limiting reactor.

[0015] For inter-electrode short-circuit faults, the equivalent fault resistance is... Multiply by a coefficient of 0.5.

[0016] By rearranging the above equations and moving the known constant terms to the left side of the equation, we obtain the standard linear regression form:

[0017] ;

[0018] By collecting data at multiple time points and solving all the equations simultaneously, an overdetermined system of linear equations is obtained:

[0019] ;

[0020] in, The corrected observation vector, For the regression matrix, Let be the parameter vector to be determined.

[0021] Furthermore, in step S2, the adaptive regularized least squares objective function is:

[0022] ;

[0023] in, The number of sampling points within the data window length. The regularization coefficient is . and For the normalized weighting coefficients, take... , , The corrected observation vector The elements, represented as

[0024] ;

[0025] Let the k-th row of regression matrix A be represented as...

[0026] ;

[0027] superscript Represents the transpose of a matrix or vector; Let be the parameter vector to be determined, denoted as , where is the parameter vector to be determined. The equivalent fault resistance, This represents the relative distance to the fault location.

[0028] Its matrix form is:

[0029] ;

[0030] in, Under this regularization framework constraint, the optimal parameter solution can be obtained directly through analytical form:

[0031] .

[0032] Furthermore, in step S3, the specific method for segmenting the fault data based on the magnitude of the fault resistance is as follows:

[0033] After a fault occurs, based on the fault time and fault type information obtained during the fault diagnosis phase, the initial transient current characteristics of the faulty line are extracted, and the peak value of the current at the measurement terminal is calculated within a 2ms transient window after the fault occurs. The magnitude of the initial current during a DC fault is approximately inversely proportional to the fault resistance. Based on the characteristics of the fault resistance range, a rapid coarse classification is performed, dividing the samples into four segments according to the magnitude of the fault resistance:

[0034] ;

[0035] Where p is the segment number to which the fault sample belongs, I peak The maximum absolute value of the fault line current measured within a 2 ms transient window after the fault occurs; I max I high I mid I low and I min The current threshold is pre-calibrated based on the correspondence between the peak current and the fault resistance of offline fault samples, and satisfies... , among which, I max and I min These are the upper and lower threshold values ​​for the peak current within the preset fault condition range, respectively. high I mid and I lo The current boundary threshold between adjacent fault resistor segments.

[0036] For each fault resistor segment, the optimization objective is to minimize the compensated mean square error in positioning, and the data window length is adjusted accordingly. Filter window length and regularization coefficient Perform joint search optimization:

[0037] ;

[0038] in, For the first The mean square value of the compensated localization error on all training samples within the segment of data. For the first The compensation coefficient corresponding to the segment.

[0039] Furthermore, in step S4, the method for constructing the piecewise nonlinear compensation mechanism is as follows:

[0040] Definition of the first Positioning error of each sample For the actual location Compared with fault location estimates based on adaptive regularized least squares Difference:

[0041] ;

[0042] Assuming error function Comply with respect to equivalent fault resistance The second-order polynomial distribution:

[0043] ;

[0044] Build includes An overdetermined system of equations for a sample:

[0045] ;

[0046] Introducing ridge regularization to solve for coefficients:

[0047] ;

[0048] in, Let be the ridge regularization coefficient, and let its value be . , It is an identity matrix.

[0049] Furthermore, in step S5, the online positioning step is as follows:

[0050] S51, based on the fault occurrence time and type information obtained from fault diagnosis, extract the initial transient current amplitude characteristics of the faulty line, and calculate the peak current at the measuring end within a 2ms transient window after the fault occurs. Determine the predefined segment to which the current fault belongs. ;

[0051] S52, load the optimal curing hyperparameters corresponding to this segment. ;

[0052] S53, after intercepting the fault The raw current data of each sampling point, based on the window length Perform moving average filtering on the current signal to construct a regression matrix. With observation vector ;

[0053] S54, Solve the adaptive regularized least squares problem to obtain the original fault location estimate. and equivalent fault resistance ;

[0054] S55, Substitute the first A piecewise quadratic polynomial model is used to calculate the compensation for systematic deviations:

[0055] ;

[0056] S56, Output the compensated, precise positioning result:

[0057] .

[0058] Furthermore, in step S3, the data window length Optimization is performed after a failure occurs, prior to selection. Each discrete sampling point participates in the calculation, through the candidate set The data window length that minimizes the compensated positioning error is selected through a traversal search.

[0059] .

[0060] Furthermore, in step S3, the filter window length The optimization obtains a smooth current signal by performing a moving average process on the original current sequence. The candidate set for the filter window is ,satisfy Constraints: Select the filter window length that minimizes the compensated positioning error.

[0061] .

[0062] Furthermore, in step S3, the regularization coefficient Optimization in logarithmic space The search is performed within the local area, employing a variable step-size strategy based on local refinement, with the initial optimal solution as the starting point. Construct a symmetric candidate set centered on the logarithmic field:

[0063] ;

[0064] in, Given the current search step size, the optimal center point is updated by evaluating the validation performance of each candidate point one by one. During the iteration process, the step size is gradually reduced to [value missing]. Until the preset convergence accuracy is met, select the regularization coefficient that minimizes the positioning error after compensation:

[0065] .

[0066] Furthermore, in step S3, the current range-optimized parameter expert database includes the optimal data window length corresponding to each fault resistor segment. Filter window length Regularization coefficient and compensation coefficient .

[0067] This invention also provides a single-ended fault location system for DC microgrids based on piecewise adaptive regularized least squares and nonlinear compensation, used to implement the above method, and includes the following modules:

[0068] The equivalent circuit model construction module is used to construct a single-ended equivalent circuit model of DC microgrid line faults. Based on Kirchhoff's voltage law, it establishes the fault voltage loop equation and transforms the fault location problem into a parameter estimation problem based on local single-ended current measurement information.

[0069] An adaptive regularized parameter identification module is used to establish a regression equation for fault parameter identification based on the single-ended equivalent circuit model using a least squares system, and to introduce Tikhonov regularization to construct an adaptive regularized least squares objective function with an L2 regularization term. The parameter weighted regularization suppresses the influence of the ill-conditioned regression matrix on parameter estimation.

[0070] The segmented optimization expert database construction module is used to segment fault data according to the size of the fault resistance. For each fault resistance segment, with the positioning accuracy as the objective function, the module performs joint optimization search on the data window length, filter window length and regularization coefficient to construct the current range-optimization parameter expert database.

[0071] The nonlinear compensation mechanism construction module is used to construct a piecewise nonlinear compensation mechanism driven by the fault location residual. It utilizes the nonlinear mapping relationship between the equivalent fault resistance and the location error obtained by adaptive regularized least squares solution to establish a polynomial compensation model corresponding to each fault resistance segment.

[0072] The online location correction module is used to obtain the data window length, filter window length and regularization coefficient parameters from a table based on the single-ended fault current during online location. It then obtains the original fault location estimate and equivalent fault resistance based on adaptive regularized least squares solution. The equivalent fault resistance is substituted into the corresponding piecewise polynomial compensation model to correct the location result and output the final fault location.

[0073] Compared with the prior art, the present invention has the following beneficial effects:

[0074] First, this invention relies solely on single-ended current measurement information to locate faults, eliminating the need for voltage measurement and communication links. This significantly reduces dependence on communication conditions and multi-ended measurement information, improving the engineering applicability and reliability of the fault location method. The online fault location phase involves only fixed parameters and simple algebraic operations, with both time and space complexity being zero. It meets the stringent requirements of DC microgrid protection for millisecond-level fast response.

[0075] Second, by introducing an adaptive regularization mechanism into the traditional least squares method and adding a weighted regularization term to the objective function, this invention effectively suppresses the ill-conditioned problem of the regression matrix caused by the low impedance characteristics of DC microgrids, and improves the numerical stability and noise resistance of parameter estimation; it can still maintain high positioning accuracy in a 30dB strong noise environment.

[0076] Third, this invention segments the fault data based on the magnitude of the fault resistance and independently optimizes the data window length, filter window length, and regularization coefficient for each segment, overcoming the impact of differences in fault characteristics under different fault resistance conditions on positioning accuracy. The optimal hyperparameters corresponding to each segment constitute an expert database, which only needs to be looked up during online positioning, reducing the complexity of online computation.

[0077] Fourth, this invention constructs a piecewise nonlinear compensation mechanism driven by fault location residuals. By utilizing the nonlinear mapping relationship between the equivalent fault resistance and the positioning error obtained by adaptive regularized least squares solution, the positioning results are corrected twice, effectively eliminating the systematic deviation introduced by the single-ended equivalent model due to neglecting the characteristics of distributed parameters, and controlling the maximum relative positioning error within 4%.

[0078] Fifth, the present invention adopts a “sparse training-dense testing” strategy, which requires only a small number of discrete fault samples to complete model training. It can still maintain stable prediction accuracy under the condition of intermediate fault resistance and fault location that are not involved in training, and has good parameter space generalization ability. Attached Figure Description

[0079] Figure 1 The flowchart of the single-ended fault location method for DC microgrids based on piecewise adaptive regularized least squares and nonlinear compensation is shown in the figure.

[0080] Figure 2 : A schematic diagram of the optimization curve for the data window length K in this invention;

[0081] Figure 3 : A schematic diagram of the optimization curve of the moving average filter window W in this invention;

[0082] Figure 4 : A schematic diagram of the optimization curve for the regularization coefficient λ in this invention;

[0083] Figure 5 : A schematic diagram of the nonlinear mapping and polynomial fitting of the equivalent fault resistance and location error in this invention;

[0084] Figure 6 : A schematic diagram comparing grouping errors under different fault resistors in this invention;

[0085] Figure 7: A schematic diagram comparing the corrected fault location estimate with the true value in this invention. Detailed Implementation

[0086] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0087] This embodiment provides a single-ended fault location method for DC microgrids based on piecewise adaptive regularized least squares and nonlinear compensation, including the following steps:

[0088] S1. Construct a single-ended equivalent circuit model of DC microgrid line faults, establish fault voltage loop equations based on Kirchhoff's voltage law, and transform the fault location problem into a parameter estimation problem based on local single-ended current measurement information.

[0089] S2, Based on the single-ended equivalent circuit model, the regression equation for fault parameter identification is established using the least squares method, and Tikhonov regularization is introduced to construct an adaptive regularized least squares objective function with L2 regularization term. The influence of the ill-conditioned regression matrix on parameter estimation is suppressed by parameter weighted regularization.

[0090] S3. Based on the size of the fault resistance, the fault data is segmented. For each fault resistance segment, with the positioning accuracy as the objective function, the data window length, filter window length and regularization coefficient are jointly optimized and searched to construct a current range-optimization parameter expert library.

[0091] S4. Construct a piecewise nonlinear compensation mechanism driven by fault location residuals. Utilize the nonlinear mapping relationship between the equivalent fault resistance and the location error obtained by adaptive regularized least squares solution to establish a polynomial compensation model corresponding to each fault resistance segment.

[0092] S5, during online location, the data window length, filter window length and regularization coefficient parameters are obtained by looking up the table based on the single-ended fault current. The original fault location estimate and equivalent fault resistance are obtained by adaptive regularized least squares solution. The equivalent fault resistance is substituted into the corresponding segmented polynomial compensation model to correct the location result and output the final fault location.

[0093] like Figure 1is a flowchart of the method of the present invention. The above method includes two parts: an offline training phase and an online positioning phase. The offline training phase sequentially includes: collecting fault current data under different fault types, fault resistances and fault positions; performing fault resistance segmentation on the data; jointly optimizing the data window length K, the filtering window length W and the regularization coefficient λ for each segment; fitting the nonlinear compensation coefficient of each segment; constructing a current interval-optimization parameter expert database. The online positioning phase sequentially includes: collecting real-time fault current signals; determining the fault type and the fault resistance segment; loading the optimal hyperparameters from the expert database; performing adaptive regularized least squares solution; conducting nonlinear compensation; and outputting the final fault position.

[0094] As shown in Figure 2 , it is a schematic diagram of the optimization curve of the data window length K in the present invention. The data window length K determines the range of the fault transient time window involved in the calculation. When the value of K is too small, the transient feature extraction is insufficient, leading to an ill-conditioned matrix structure; when the value of K is too large, unmodeled dynamic processes such as traveling wave reflection, distributed capacitance effect and controller action will be introduced, resulting in model mismatch. With the goal of minimizing the positioning error after compensation, the present invention traverses and searches for the optimal K value in the candidate set.

[0095] As shown in Figure 3 , it is a schematic diagram of the optimization curve of the moving average filtering window W in the present invention. The filtering window W acts directly on the original current sequence and affects the calculation accuracy of the fault current derivative. When the value of W is too large, it will cause phase lag and amplitude attenuation of the current derivative; when the value of W is too small, it is difficult to effectively filter out high-frequency interference. Under the condition that the constraint of W<K is satisfied, the present invention searches for the optimal W value with the goal of minimizing the positioning error after compensation.

[0096] As shown in Figure 4 , it is a schematic diagram of the optimization curve of the regularization coefficient λ in the present invention. The influence of the regularization coefficient λ on the model performance presents the feature of cross-order-of-magnitude variation, and the present invention adopts a variable step size search strategy based on local refinement in the logarithmic space. The objective function with respect to λ presents a unimodal characteristic in the logarithmic domain and has a clear optimal interval.

[0097] As shown in Figure 5 , it is a schematic diagram of the nonlinear mapping and polynomial fitting between the equivalent fault resistance and the positioning error in the present invention. The figure shows the equivalent fault resistance obtained by adaptive regularized least squares solution and the scatter distribution between the positioning error and the second-order polynomial fitting curve. There is little difference in overall accuracy between the second-order polynomial fitting and the third-order polynomial fitting. Considering the additional computational complexity and overfitting risk introduced by the high-order model, the present invention selects the second-order polynomial to achieve a balance between fitting accuracy and computational efficiency.

[0098] As shown in Figure 6The figure shows a comparison of grouped location errors before and after nonlinear compensation under different fault resistance conditions according to the present invention. The horizontal axis represents different fault resistance groups, and each fault resistance group contains multiple test samples at different fault locations. The vertical axis represents the mean square value of the location error within the corresponding group. Each group shows the location error before and after nonlinear compensation. It can be seen that under each fault resistance group, the location error after compensation is significantly lower than the location error before compensation, and the error difference between different fault resistance groups is suppressed. This indicates that the piecewise quadratic polynomial compensation model can effectively correct the systematic location deviation caused by the simplification of the single-ended equivalent model and the nonlinear coupling between the fault location and the fault resistance, improving the consistency and accuracy of the location results under different fault resistance conditions.

[0099] like Figure 7 The figure shows a comparison between the fault location estimate after nonlinear compensation and the actual fault location according to the present invention. The horizontal axis represents the test samples arranged in groups according to fault resistance, with each fault resistance group containing multiple test samples under different actual fault locations. The vertical axis represents the relative distance between the fault locations. The figure plots the actual fault location and the fault location estimate after nonlinear compensation for each test sample. Under different fault resistance and fault location conditions, the compensated fault location estimate basically coincides with the actual fault location, and no significant systematic drift occurs as the fault resistance increases. This indicates that the piecewise nonlinear compensation mechanism can effectively eliminate the systematic deviation in the original location estimate and maintain stable positioning accuracy over a wide fault resistance range.

[0100] The above description is merely one specific embodiment of the present invention. Any equivalent substitutions or modifications made by those skilled in the art to sensor arrangement, data representation, geometric prior forms, spatial feature mapping methods, temporal network structures, output variables, or application objects without departing from the technical concept of the present invention should fall within the protection scope of the present invention.

Claims

1. A method for single-ended fault location in DC microgrids based on piecewise adaptive regularized least squares and nonlinear compensation, characterized in that, Includes the following steps: S1. Construct a single-ended equivalent circuit model of DC microgrid line faults, establish fault voltage loop equations based on Kirchhoff's voltage law, and transform the fault location problem into a parameter estimation problem based on local single-ended current measurement information. S2, Based on the single-ended equivalent circuit model, the regression equation for fault parameter identification is established using the least squares method, and Tikhonov regularization is introduced to construct an adaptive regularized least squares objective function with L2 regularization term. The influence of the ill-conditioned regression matrix on parameter estimation is suppressed by parameter weighted regularization. S3. Based on the size of the fault resistance, the fault data is segmented. For each fault resistance segment, with the positioning accuracy as the objective function, the data window length, filter window length and regularization coefficient are jointly optimized and searched to construct a current range-optimization parameter expert library. S4. Construct a piecewise nonlinear compensation mechanism driven by fault location residuals. Utilize the nonlinear mapping relationship between the equivalent fault resistance and the location error obtained by adaptive regularized least squares solution to establish a polynomial compensation model corresponding to each fault resistance segment. S5, during online location, the data window length, filter window length and regularization coefficient parameters are obtained by looking up the table based on the single-ended fault current. The original fault location estimate and equivalent fault resistance are obtained by adaptive regularized least squares solution. The equivalent fault resistance is substituted into the corresponding segmented polynomial compensation model to correct the location result and output the final fault location.

2. The method for single-ended fault location in DC microgrids based on piecewise adaptive regularized least squares and nonlinear compensation as described in claim 1, characterized in that, The single-ended equivalent circuit model described in step S1 is as follows: For a single-pole ground fault, the voltage loop equation from the measurement terminal to the fault point is: ； in, The voltage across the measuring terminal capacitor is... This represents the faulty line current. The relative distance to the fault location. and These represent the resistance and inductance per unit length of the line, respectively. The equivalent fault resistance, It is the inductance of the current-limiting reactor.

3. The method for single-ended fault location in DC microgrids based on piecewise adaptive regularized least squares and nonlinear compensation according to claim 2, characterized in that, For inter-electrode short-circuit faults, the equivalent fault resistance The value needs to be multiplied by a coefficient of 0.

5.

4. The method for single-ended fault location in DC microgrids based on piecewise adaptive regularized least squares and nonlinear compensation as described in claim 1, characterized in that, The adaptive regularized least squares objective function described in step S2 is: ； in, The number of sampling points within the data window length. The regularization coefficient is . and For the normalized weighting coefficients, take... , , The corrected observation vector The Each element is represented as: ； Let the k-th row of regression matrix A be represented as... ； superscript Represents the transpose of a matrix or vector; Let be the parameter vector to be determined, denoted as , where is the parameter vector to be determined. The equivalent fault resistance, This represents the relative distance to the fault location.

5. The method for single-ended fault location in DC microgrids based on piecewise adaptive regularized least squares and nonlinear compensation according to claim 1, characterized in that, The specific method for segmenting the fault data based on the magnitude of the fault resistance in step S3 is as follows: After a fault occurs, the initial transient current characteristics of the faulty line are extracted, and the peak value of the current at the measurement terminal is calculated within a 2ms transient window after the fault occurs. Taking advantage of the fact that the amplitude of the initial current in a DC fault is approximately inversely proportional to the fault resistance, the sample is divided into four segments according to the magnitude of the fault resistance: ； Where p is the segment number to which the fault sample belongs, I peak The maximum absolute value of the fault line current measured within a 2 ms transient window after the fault occurs; I max I high I mid I low and I min The current threshold is pre-calibrated based on the correspondence between the peak current and the fault resistance of offline fault samples, and satisfies... , among which, I max and I min These are the upper and lower threshold values ​​for the peak current within the preset fault condition range, respectively. high I mid and I low The current boundary threshold between adjacent fault resistor segments.

6. The method for single-ended fault location in DC microgrids based on piecewise adaptive regularized least squares and nonlinear compensation according to claim 1, characterized in that, The current range-optimization parameter expert library mentioned in step S3 contains the optimal data window length corresponding to each fault resistor segment. Filter window length Regularization coefficient and compensation coefficient .

7. The method for single-ended fault location in DC microgrids based on piecewise adaptive regularized least squares and nonlinear compensation according to claim 1, characterized in that, The polynomial compensation model mentioned in step S4 is a second-order polynomial model: ； in, For positioning error, This is the estimated equivalent fault resistance. , , This is the compensation coefficient.

8. The method for single-ended fault location in DC microgrids based on piecewise adaptive regularized least squares and nonlinear compensation according to claim 7, characterized in that, The compensation coefficient is obtained through ridge regularization: ； in, The equivalent fault resistance estimated from each training sample The Vandermonde matrix is ​​composed of zero powers, first powers, and second powers. Let be the ridge regularization coefficient, and let its value be . , It is a third-order identity matrix. The original localization error of each training sample The column vector formed The vector of optimal compensation coefficients, with superscripts Represents the transpose of a matrix or vector.

9. The method for single-ended fault location in DC microgrids based on piecewise adaptive regularized least squares and nonlinear compensation according to claim 1, characterized in that, The online positioning steps in step S5 are as follows: S51, based on the fault occurrence time and type information obtained from fault diagnosis, extract the initial transient current amplitude characteristics of the faulted line and determine the predefined segment to which the current fault belongs; S52, load the fixed optimal hyperparameters corresponding to the predefined segment to which the current fault belongs; S53, extract the sampling points with the optimal data window length after the fault, perform moving average filtering on the current signal based on the optimal filtering window length, and construct the regression matrix and observation vector; S54, solve the adaptive regularized least squares problem to obtain the original fault location estimate and equivalent fault resistance; S55, substitute the equivalent fault resistance into the polynomial compensation model of the corresponding segment to calculate the compensation amount. S56 outputs the accurate positioning result after compensation.

10. A single-ended fault location system for DC microgrids based on piecewise adaptive regularized least squares and nonlinear compensation, used to implement the method described in any one of claims 1 to 9, characterized in that, Includes the following modules: The equivalent circuit model construction module is used to construct a single-ended equivalent circuit model of DC microgrid line faults. Based on Kirchhoff's voltage law, it establishes the fault voltage loop equation and transforms the fault location problem into a parameter estimation problem based on local single-ended current measurement information. An adaptive regularized parameter identification module is used to establish a regression equation for fault parameter identification based on the single-ended equivalent circuit model using a least squares system, and to introduce Tikhonov regularization to construct an adaptive regularized least squares objective function with an L2 regularization term. The parameter weighted regularization suppresses the influence of the ill-conditioned regression matrix on parameter estimation. The segmented optimization expert database construction module is used to segment fault data according to the size of the fault resistance. For each fault resistance segment, with the positioning accuracy as the objective function, the module performs joint optimization search on the data window length, filter window length and regularization coefficient to construct the current range-optimization parameter expert database. The nonlinear compensation mechanism construction module is used to construct a piecewise nonlinear compensation mechanism driven by the fault location residual. It utilizes the nonlinear mapping relationship between the equivalent fault resistance and the location error obtained by adaptive regularized least squares solution to establish a polynomial compensation model corresponding to each fault resistance segment. The online location correction module is used to obtain the data window length, filter window length and regularization coefficient parameters from a table based on the single-ended fault current during online location. It then obtains the original fault location estimate and equivalent fault resistance based on adaptive regularized least squares solution. The equivalent fault resistance is substituted into the corresponding piecewise polynomial compensation model to correct the location result and output the final fault location.

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