A power distribution network harmonic source tracing method based on twice harmonic shunt mechanism

Abstract

This invention discloses a method for tracing harmonic sources in distribution networks based on the mechanism of two harmonic current splitting, belonging to the technical field of harmonic source tracing in distribution networks. This invention acquires measurement data of the effective values ​​of harmonic voltage and current at each node, constructs a tracing model including a network propagation adjacency matrix and a source splitting coefficient matrix, and represents the measured harmonic current vector as the sum of the network propagation distributed component and the harmonic source component. Furthermore, the harmonic source localization problem is constructed as an optimization solution model with sparsity constraints. Based on the solved comprehensive harmonic source current vector, unified identification and tracing of single-source and multi-source scenarios are achieved. This method does not rely on harmonic phase information and system-side harmonic impedance parameters, has strong anti-phase noise capability, good engineering versatility, and combines the interpretability of the mechanism with the practicality of data-driven solutions.

Description

Technical Field

[0001] This invention relates to the field of harmonic source tracing technology in power distribution networks, and in particular to a method for tracing harmonic sources in power distribution networks based on the mechanism of two harmonic current splitting. Background Technology

[0002] Harmonic source tracing in distribution networks is a core aspect of power quality management. Accurately identifying the location and injection intensity of harmonic pollution sources within the power grid is crucial for developing harmonic mitigation measures and ensuring stable grid operation.

[0003] Among existing methods for tracing harmonic sources, the method based on harmonic power flow analysis offers a relatively intuitive and clear approach. This method relies on measured harmonic power flow direction to locate harmonic sources by determining whether harmonics flow from the main power grid line to the load side or vice versa. However, this method has two significant limitations. First, the measured data is significantly affected by noise interference, with harmonic phase deviation being the most prominent. Harmonics are non-fundamental periodic distortion components, making phase measurement benchmarks unstable and measurement accuracy difficult to guarantee. Since harmonic power is calculated jointly from harmonic voltage, harmonic current, and their phase difference, phase errors directly lead to significant deviations in the calculated harmonic power results. Second, in scenarios with multiple harmonic sources, harmonic backflow is prone to occur. Some harmonic sources are affected by their own harmonic impedance and admittance characteristics, and their own harmonic circulation can easily mask the characteristics of their net harmonic injection, making it difficult for this method to accurately identify the actual harmonic flow direction under such complex conditions.

[0004] Another typical approach is the harmonic responsibility allocation method based on equivalent circuit models. This method relies on the system-side harmonic impedance for analysis, with impedance parameters determined by considering line length, wire diameter, material, grid topology, and the distribution of active and reactive power in the network. Using the Thevenin and Norton equivalent circuits, this method equates the grid system side to harmonic voltage sources in series with harmonic impedance, and the user load side to harmonic current sources in parallel with harmonic impedance. By comparing the harmonic impedance values ​​on the system and user sides, the contribution ratio of each side to harmonic distortion at the point of common coupling is quantified, thereby determining the dominant direction of harmonic injection. This approach is essentially a bisection modeling approach, and through iterative deduction layer by layer, it can complete the harmonic power flow responsibility allocation within the entire network topology, demonstrating strong adaptability in laboratory simulation environments. However, there is no unified and universal standard for the value of system-side harmonic impedance; it needs to be calculated and adjusted according to different field conditions, usually relying on field measurements or engineering experience for assignment. Therefore, its universality is greatly limited when applied to actual engineering scenarios, and it has not achieved large-scale promotion and application.

[0005] In summary, existing methods for tracing harmonic sources in distribution networks rely on harmonic power flow-based schemes, which depend on harmonic phase information susceptible to noise interference and struggle to identify multi-source harmonic backflow conditions. Schemes based on equivalent circuit models, on the other hand, depend on the lack of a standardized system-side harmonic impedance, resulting in poor engineering applicability. Therefore, providing a technical solution that can accurately trace harmonic sources solely based on the effective values ​​of harmonic voltage and current without relying on phase information or impedance calculations has become a pressing issue in this field. Summary of the Invention

[0006] This invention proposes a method for tracing the source of harmonics in a distribution network based on the mechanism of two harmonic current splitting. Its purpose is to overcome the dependence of existing harmonic power flow methods on the easily disturbed harmonic phase information, and to overcome the dependence of existing equivalent circuit methods on the system-side harmonic impedance that needs to be measured on-site. It provides a tracing scheme that can achieve accurate location of harmonic sources and quantification of injection intensity by relying only on the effective values ​​of harmonic voltage, the effective values ​​of harmonic current, and the line topology.

[0007] The technical solution of this invention is as follows:

[0008] A method for tracing the source of harmonics in a distribution network based on the second harmonic shunting mechanism includes the following steps:

[0009] Step S1: Acquire measurement data, including the measured harmonic current matrix composed of the voltage and current measured at each measurement node in the line topology. and measured harmonic voltage matrix ; and All dimensions are , To measure the total number of nodes, The measurement time is represented by a row for each measurement node and a column for the measurement data at each time point.

[0010] S2: Construct a source-tracing mathematical model based on the second harmonic shunting mechanism, and construct an optimized solution model based on this source-tracing mathematical model;

[0011] The source tracing mathematical model is as follows: for any given moment... The measured harmonic current vectors of each node It is represented as the sum of the network propagation shared component and the harmonic source component, i.e. , and They are respectively The measured harmonic current vector and measured harmonic voltage vector at each node at time t, corresponding to and The List, for Network propagation adjacency matrix, For the reason The source split coefficient matrix determined by admittance correlation. For the purposes of the investigation The composite harmonic source current vector remains stable within a given time period. The The component represents the first... Each measurement node injects current into the power grid as a harmonic source during the observation period; the optimization solution model uses... and The variable to be solved, and includes the variables to be solved. Sparsity constraints;

[0012] S3: Solve the optimization model to obtain the optimal estimate. ;

[0013] S4: Based on Harmonic source analysis is performed on the values ​​of the corresponding components at each node.

[0014] As a further improvement to the aforementioned method for tracing the source of harmonics in distribution networks based on the second harmonic shunting mechanism, It is a diagonal matrix, with diagonal elements. Calculate using the following formula:

[0015]

[0016] In the above formula, For matrix The Line number Column elements.

[0017] As a further improvement to the distribution network harmonic source tracing method based on the two-harmonic current splitting mechanism: in step S3, the alternating direction multiplier method is used to iteratively solve the optimization solution model.

[0018] As a further improvement to the distribution network harmonic source tracing method based on the second harmonic current splitting mechanism, the augmented Lagrangian function of the optimized solution model is as follows:

[0019]

[0020] In the above formula, As an auxiliary variable; for The 1-norm is used to constrain... The sparsity of vectors; This is the penalty coefficient, used to adjust the balance between sparse constraints and data fitting terms; Let Lagrange multiplier vectors have dimension 1. ; The first two terms are penalty coefficients; the last two terms are non-zero penalty terms before convergence, driving the... Approaching step by step .

[0021] As a further improvement to the distribution network harmonic source tracing method based on the second harmonic shunting mechanism: in step S3, the equivalent admittance is first calculated based on the measurement data. As Initial value: ;

[0022] During initialization, let , , , , , , , , Indicates the first The network propagation adjacency matrix, harmonic source current vector, auxiliary variables, and Lagrange multiplier vector at each iteration.

[0023] As a further improvement to the distribution network harmonic source tracing method based on the two-harmonic current splitting mechanism: In step S3, after initialization, iterative calculation begins, and the... The update steps for this iteration are as follows:

[0024] (1) Fixed , , ,renew ;

[0025] (2) Fixed , , ,renew ;

[0026] (3) Fixed , , ,renew In order to satisfy and Solve under the constraint of a symmetric matrix;

[0027] (4) Fixed , , Update Lagrange multipliers .

[0028] As a further improvement to the distribution network harmonic source tracing method based on the second harmonic shunting mechanism, fixed , , Update Lagrange multipliers The method is as follows:

[0029] .

[0030] As a further improvement to the distribution network harmonic source tracing method based on the two-harmonic current splitting mechanism, in step S3, the iteration stopping condition is: reaching the preset maximum number of iterations, or the update change amplitude of the optimization variable in two adjacent iterations is less than the preset threshold.

[0031] As a further improvement to the distribution network harmonic source tracing method based on the double harmonic current splitting mechanism, the harmonic source tracing analysis in step S4 includes: calculating the obtained harmonic source current vector... The components are sorted from largest to smallest amplitude, and the decrease rate of adjacent amplitudes is calculated. The dividing point where the decrease rate exceeds a preset threshold is taken as the dividing inflection point, and the node to the left of the inflection point is determined as the harmonic source node.

[0032] As a further improvement to the distribution network harmonic source tracing method based on the second harmonic shunting mechanism, in step S4, the harmonic sources are sorted from largest to smallest... The amplitude of each component is denoted as Its rate of decline is calculated using the following formula: .

[0033] Compared with the prior art, the present invention has the following beneficial effects:

[0034] 1. This invention does not rely on harmonic phase measurement information, but only uses the effective values ​​of harmonic voltage and current synchronously collected at each measurement node as input, fundamentally avoiding the problem of harmonic power calculation offset caused by the instability of the harmonic phase reference and phase measurement deviation. In complex working conditions with multiple harmonic sources coexisting and harmonic power flow backflow, traditional power flow methods are prone to misjudgment due to the difficulty in identifying the net injection direction. This invention, however, constructs a mathematical model of the sum of the network propagation shared components and the harmonic source components, transforming the source tracing problem into a sparse estimation problem of the comprehensive harmonic source current vector. Even if there is harmonic circulation between harmonic sources, it can still accurately extract the harmonic characteristics of the net external injection of each node, achieving reliable identification of the real harmonic source.

[0035] 2. This invention eliminates the need to individually calculate and adjust system-side harmonic impedance for each specific operating condition. Instead, it integrates the harmonic propagation and shunting mechanisms in the network into an adjacency matrix and source shunting coefficient matrix driven by measured data. The adjacency matrix is ​​automatically adapted to the current measurement data through optimization, avoiding the limitations of general applicability caused by manual empirical assignment or on-site impedance measurements. This allows the method to be directly deployed in distribution networks with different voltage levels, network structures, and operating modes, demonstrating excellent engineering replicability.

[0036] 3. This invention constructs a source-tracing model based on a two-stage harmonic current shunting mechanism. The first shunting characterizes the linear propagation relationship of harmonic voltage-current between nodes, while the second shunting utilizes admittance correlation to determine the distribution coefficients of harmonic current from each node to other parts of the network, tightly coupling the line topology with measurement information. This mechanism-based modeling approach gives the final estimated composite harmonic source current vector a clear physical meaning, making the results traceable and interpretable, rather than a completely black-box statistical fitting.

[0037] 4. This invention constructs the problem of locating harmonic sources as an optimization problem with sparsity constraints and uses the alternating direction multiplier method for iterative solution. The 1-norm constraint on the integrated harmonic source current vector fits the natural property of the spatially sparse distribution of harmonic sources in actual power grids, with only a few nodes contributing the main harmonic injection. This constraint effectively eliminates the interference of background harmonics and measurement disturbances on the source tracing results while suppressing measurement noise, thus improving estimation accuracy and noise resistance.

[0038] 5. This method automatically separates harmonic source nodes from the noise floor based on the amplitude ranking and descent rate of each component in the solved comprehensive harmonic source current vector. It is applicable to both single-source and multi-source scenarios without the need for manually setting absolute thresholds. Furthermore, the relative intensity of harmonic injection at each node can be assessed based on the relative magnitudes of their amplitudes, providing a quantitative basis for prioritizing remediation efforts. Attached Figure Description

[0039] Figure 1 This is a schematic diagram of a typical line topology. Detailed Implementation

[0040] The technical solution of the present invention will now be described in detail with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0041] Figure 1 This is a schematic diagram of the power distribution network topology to which this invention applies. (Refer to...) Figure 1 Taking a 10kV line as an example, measurement nodes are installed at the outgoing line locations, and measurement nodes are also installed at the incoming lines of each branch line corresponding to dedicated transformer users or public transformer substations. The same measurement node layout is used on the 400V side of the low-voltage substation. The line topology is denoted as... It mainly includes the connection relationships between the main lines and branch lines, without the need for secondary tracing. The harmonic source tracing method of the present invention uses the effective values ​​of harmonic voltage and current, as well as the line topology at the above-mentioned measurement nodes as basic data. By constructing a mechanism model and using data-driven joint solution, the location and intensity quantification of harmonic sources are realized.

[0042] The method for tracing the source of harmonics in a distribution network based on the two-harmonic shunt mechanism includes the following steps.

[0043] Step S1: Acquire measurement data, including the measured harmonic current matrix composed of the voltages and currents measured at each measurement node in the line topology. and measured harmonic voltage matrix .

[0044] in, and All dimensions are , To measure the total number of nodes, The measurement time is represented by a row for each measurement node and a column for the measurement data at each time point.

[0045] Step S2: Construct a source-tracing mathematical model based on the two-harmonic shunting mechanism, and construct an optimized solution model based on the source-tracing mathematical model.

[0046] In the actual operation of a distribution network, harmonics undergo two physical processes of shunting from their source to their propagation throughout the network. For ease of understanding, this is illustrated using nodes as an example. At any moment This will be illustrated using a single harmonic source as an example.

[0047] The first traffic split is an internal traffic split. Node After harmonic currents are generated, these harmonic currents at the nodes The harmonic current is distributed between the branch line it belongs to and the equivalent circuit formed by all external lines. A portion of the harmonic current remains at the node. One portion is injected locally, while the other is injected into the main line. The allocation ratio of this traffic splitting process is determined by the node. The ratio of the sum of the self-admittance and the external mutual admittance is determined by the value of the self-admittance.

[0048] The second current split is the network propagation split. The portion of the harmonic current injected into the main line is distributed along the main line according to the admittance relationships between the branch lines, and then distributed to each node. Harmonic source node. It also participates in this allocation process. It should be noted that the two splits mentioned above are physically completed instantaneously; they are described separately here only for the sake of understanding their mechanism.

[0049] Based on the above two diversion mechanisms, a source-tracing mathematical model is established: at any given moment The harmonic currents in the line topology are represented as:

[0050]

[0051] In the above formula, for Measured harmonic current vectors at each node at any given time (dimensions) ), corresponding to the measured harmonic current matrix The List, for Measured harmonic voltage vectors at each node at any given time (dimensions) ), corresponding to the measured harmonic voltage matrix The List, Propagating the adjacency matrix (dimensions) of the network Its elements reflect the mapping of admittance or impedance information between each line. It is a symmetric matrix with a significant dominance of diagonal elements; for Time-source harmonic current vector (dimension) Only the node where the harmonic source is located has a corresponding non-zero component, while the corresponding components of the other nodes are zero. Source split coefficient matrix (dimensions) ).

[0052] As can be seen from the above formula, the line harmonic current at any given time consists of two parts: the first part... The shared component for network propagation represents the mutual conduction of harmonic currents between nodes based on admittance relationships, with harmonic source nodes also participating in this sharing process; Part Two This is a harmonic source component, and only the node where the harmonic source is located contributes to this component.

[0053] about matrix, It is a diagonal matrix, where all off-diagonal elements are zero, and the diagonal elements are... Calculate using the following formula:

[0054]

[0055] In the above formula, For matrix The Line number Column elements. The essential meaning is: node The sum of external mutual admittances The larger the node The less harmonic current can remain locally, the stronger the ability of the harmonic source node to output harmonics. It is directly related to the first diversion, and it is composed of It is calculated directly based on the above admittance correlation and does not constitute an independent unknown.

[0056] To perform harmonic source analysis, it is necessary to solve for the harmonic source currents from the measurement data to determine which nodes contain harmonic sources and their injection intensity. The analysis assumes that the occurrence pattern of harmonic sources remains stable within the investigated time period, i.e., at different times... Corresponding harmonic source current It is an unknown quantity that remains unchanged. Under this assumption, we can... Unified as harmonic source current vector This represents the combined harmonic source current at multiple moments within that time period. The The component represents the first... The current injected into the power grid by each measurement node as a harmonic source during the observation period. Therefore, the solution form of the model is:

[0057]

[0058] In this model, and For known measurement data (total) (at a certain moment) and The unknown quantity to be solved is... Depend on It is calculated using the aforementioned formula. It should be particularly noted that... It represents the state of harmonic source injection before harmonic backflow, while This refers to the state of the observed data after harmonic backflow, i.e., the result after redistribution by the network admittance relationship. Therefore, this model effectively avoids the interference of harmonic backflow phenomenon on the source tracing results when multiple harmonic sources coexist, from a mechanistic perspective.

[0059] Based on the above equations, the following optimization model is constructed:

[0060]

[0061]

[0062] In the above formula, for The 1-norm is used to constrain... The sparsity of vectors causes most nodes to have components that are close to zero, with only the actual harmonic source nodes having significant non-zero components. This is the penalty coefficient, used to adjust the balance between sparse constraints and data fitting terms. Constraints ( ) requires the propagation matrix Strict diagonal dominance means that the absolute value of an element on the diagonal is greater than the sum of the absolute values ​​of all other elements in the same row. This is consistent with... The physical property that the diagonal elements of a matrix are significantly dominant is consistent.

[0063] because and In the above optimization model, in product form Coupled with the data fitting term, the two influence each other during the optimization process: any set and As long as the product of the two variables remains constant, the same fitting residuals can be obtained, leading to severe fluctuations in the optimization variable during iterations and making convergence difficult. To alleviate this problem, auxiliary variables are introduced. Defined as:

[0064]

[0065] In the original optimization model Replace with and add consistency constraints Thus and The coupling is optimized as a whole.

[0066] Based on the above decoupling form, the augmented Lagrangian function is constructed as follows:

[0067]

[0068] In the above formula, Lagrange multiplier vectors (dimension) ), is the penalty coefficient. The augmented Lagrangian function adds a quadratic penalty term (i.e., the last term in the above formula) regarding the violation of equality constraints to the standard Lagrangian function, in order to enhance the numerical stability of the optimization process.

[0069] The subsequent solution will be based on the augmented Lagrangian function described above, using the alternating direction multiplier method for iterative optimization. It is important to emphasize that during the iterative optimization process... and Since they are not equal, the latter two terms are always non-zero penalty terms before convergence, driving the variables to gradually satisfy the consistency constraints.

[0070] Step S3: Solve using the alternating direction multiplier method to obtain the optimal estimated harmonic source current vector.

[0071] First, the equivalent admittance is calculated based on the measurement data and used as the network propagation adjacency matrix in the optimization solution model. The initial value.

[0072] Specifically, the equivalent admittance is calculated based on the measurement data. Equivalent admittance (also known as composite admittance) is a manifestation of the mixed information of line coupling and harmonic admittance, encompassing... The main characteristic information of the matrix. Utilizing... Based on the measurement data at each time step, construct the following least-squares optimization problem to solve for the equivalent admittance. :

[0073]

[0074] about The solution, with special note: first construct When the diagonal elements are constant 1, the diagonal elements do not participate in the optimization, while the off-diagonal elements participate in the least squares optimization and are constrained to have a magnitude of less than 1. The solution result is used as the initial value in the subsequent ADMM iteration. Due to the existence of the strict diagonal dominance constraint, the logic before and after is compatible.

[0075] This least squares problem has an analytical solution, which can be obtained by direct solution. .Will As the initial value for the iterative optimization of the Alternating Direction Multiplier Method (ADMM), let .

[0076] initialization , , , , , , , , Indicates the first In the next iteration, the network propagation includes the adjacency matrix, harmonic source current vector, auxiliary variables, and Lagrange multiplier vector, and then the iterative calculation begins:

[0077] In any iteration, let be the th iteration. In the next iteration, other variables are fixed in sequence, and a minimum update is performed on a single variable, as follows:

[0078] (1) Fixed , , ,renew At this point, the optimization problem degenerates into a problem about... The univariate optimization problem is a least squares problem with L1 norm regularization, which can be solved by soft-thresholding or the proximal gradient method.

[0079] (2) Fixed , , ,renew This is a simple unconstrained quadratic optimization problem, which can be solved analytically by taking the derivative and setting the derivative to zero.

[0080] (3) Fixed , , ,renew At the same time ensure ( )and The condition that the symmetric matrix holds true always applies. This is a least-squares problem with diagonal dominance constraints, which can be solved using constrained optimization algorithms such as the projective gradient method or the interior-point method.

[0081] (4) Fixed , , Update Lagrange multipliers .

[0082] (5) This completes one iteration. If the convergence condition has been met or the maximum number of iterations has been reached, then end the iteration; otherwise, let... Then, the next iteration begins.

[0083] The alternating direction multiplier method is an iterative optimization algorithm. It allows for a preset maximum number of iterations (e.g., 200), terminating after the specified number of iterations. It can also monitor the change in the optimization variable between adjacent iterations; if the change is less than a set threshold (e.g., ...), the algorithm will terminate the iteration. When the convergence accuracy is reached, the iteration stops.

[0084] After the iteration, the optimally estimated harmonic source current vector is obtained. and propagation matrix .

[0085] Step S4: Perform harmonic source tracing analysis based on the optimally estimated harmonic source current vector.

[0086] Based on the solution Vectors are used to locate harmonic sources and assess their relative intensity within the observation period.

[0087] First, vector The components are sorted by amplitude from largest to smallest, denoted as:

[0088]

[0089] Then calculate the rate of decrease of adjacent amplitudes in descending order:

[0090]

[0091] Pre-defined descent rate threshold The range of values ​​is If there exists a certain Make If the position is determined to be the dividing inflection point, then all nodes to the left of the inflection point (i.e., to The corresponding node is the harmonic source node, and the node to the right of the inflection point is regarded as the noise floor.

[0092] The above methods are uniformly applicable to scenarios where single-harmonic sources and multiple harmonic sources coexist: when the inflection point When, only the first node is a harmonic source; when At the same time, multiple harmonic sources were identified.

[0093] For a set of nodes identified as harmonic source nodes, it can be determined based on their... The relative magnitude of the components assesses the harmonic injection intensity: the larger the amplitude, the higher the relative intensity of harmonic injection at that node; the smaller the amplitude, the lower the intensity. This relative intensity can be used for prioritizing harmonic control.

[0094] In summary, the harmonic source tracing method for distribution networks based on the two-harmonic current splitting mechanism proposed in this embodiment starts from the physical mechanism of harmonic generation and propagation, decomposes the harmonic current into network propagation components and harmonic source components, and solves the model jointly using the ADMM sparse optimization framework. Finally, the location and intensity quantification of the harmonic source are completed based on the solution results. This method only requires the grid topology and the measured effective values ​​of harmonic voltage and current to achieve source tracing and judgment. It does not rely on harmonic phase information that is susceptible to noise interference, and does not require on-site calculation of system-side harmonic impedance. It can still maintain stable and reliable source tracing performance under complex operating conditions with multiple harmonic sources coexisting and harmonic backflow, and has both mechanistic interpretability and engineering practicality.

[0095] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for tracing the source of harmonics in a distribution network based on the second harmonic shunting mechanism, characterized in that, Includes the following steps: Step S1: Acquire measurement data, including the measured harmonic current matrix composed of the voltage and current measured at each measurement node in the line topology. and measured harmonic voltage matrix ; and All dimensions are , To measure the total number of nodes, The measurement time is represented by a row for each measurement node and a column for the measurement data at each time point. S2: Construct a source-tracing mathematical model based on the second harmonic shunting mechanism, and construct an optimized solution model based on this source-tracing mathematical model; The source tracing mathematical model is as follows: for any given moment... The measured harmonic current vectors of each node It is represented as the sum of the network propagation shared component and the harmonic source component, i.e. , and They are respectively The measured harmonic current vector and measured harmonic voltage vector at each node at time t, corresponding to and The List, for Network propagation adjacency matrix, For the reason The source split coefficient matrix determined by admittance correlation. For the purposes of the investigation The composite harmonic source current vector remains stable within a given time period. The The component represents the first... Each measurement node injects current into the power grid as a harmonic source during the observation period; the optimization solution model uses... and The variable to be solved, and includes the variables to be solved. Sparsity constraints; S3: Solve the optimization model to obtain the optimal estimate. ; S4: Based on Harmonic source analysis is performed on the values ​​of the corresponding components at each node.

2. The method for tracing the source of harmonics in a distribution network based on the second harmonic shunting mechanism as described in claim 1, characterized in that, It is a diagonal matrix, with diagonal elements. Calculate using the following formula: ； In the above formula, For matrix The Line number Column elements.

3. The method for tracing the source of harmonics in a distribution network based on the second harmonic shunting mechanism as described in claim 1, characterized in that: In step S3, the optimization solution model is solved iteratively using the alternating direction multiplier method.

4. The method for tracing the source of harmonics in a distribution network based on the second harmonic shunting mechanism as described in claim 1, characterized in that, The augmented Lagrangian function for optimizing the solution model is as follows: ； In the above formula, As an auxiliary variable; for The 1-norm is used to constrain... The sparsity of vectors; This is the penalty coefficient, used to adjust the balance between sparse constraints and data fitting terms; Let Lagrange multiplier vectors have dimension 1. ; The first two terms are penalty coefficients; the last two terms are non-zero penalty terms before convergence, driving the... Approaching step by step .

5. The method for tracing the source of harmonics in a distribution network based on the second harmonic shunting mechanism as described in claim 4, characterized in that: In step S3, the equivalent admittance is first calculated based on the measurement data. As Initial value: ; During initialization, let , , , , , , , , Indicates the first The network propagation adjacency matrix, harmonic source current vector, auxiliary variables, and Lagrange multiplier vector at each iteration.

6. The method for tracing the source of harmonics in a distribution network based on the second harmonic shunting mechanism as described in claim 5, characterized in that: In step S3, after initialization, iterative calculation begins, the... The update steps for this iteration are as follows: (1) Fixed , , ,renew ; (2) Fixed , , ,renew ; (3) Fixed , , ,renew In order to satisfy and Solve under the constraint of a symmetric matrix; (4) Fixed , , Update Lagrange multipliers .

7. The method for tracing the source of harmonics in a distribution network based on the second harmonic shunting mechanism as described in claim 6, characterized in that, fixed , , Update Lagrange multipliers The method is as follows: 。 8. The method for tracing the source of harmonics in a distribution network based on the second harmonic shunting mechanism as described in claim 6, characterized in that, In step S3, the iteration stopping condition is: reaching the preset maximum number of iterations, or the update change of the optimization variable in two adjacent iterations is less than the preset threshold.

9. The method for tracing the source of harmonics in a distribution network based on the second harmonic shunting mechanism as described in claim 1, characterized in that, Step S4, harmonic source analysis, includes: solving the harmonic source current vector. The components are sorted from largest to smallest amplitude, and the decrease rate of adjacent amplitudes is calculated. The dividing point where the decrease rate exceeds a preset threshold is taken as the dividing inflection point, and the node to the left of the inflection point is determined as the harmonic source node.

10. The method for tracing the source of harmonics in a distribution network based on the second harmonic shunting mechanism as described in claim 9, characterized in that, In step S4, the number of rows after sorting from largest to smallest will be... The amplitude of each component is denoted as Its rate of decline is calculated using the following formula: .

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