Multi-node harmonic responsibility division method and system considering harmonic coupling and system fluctuation

Abstract

The application discloses a multi-node harmonic responsibility division method and system considering harmonic coupling and system fluctuation characteristics, and belongs to the field of power system harmonic analysis and power quality treatment. The method comprises the following steps: a nonlinear load harmonic coupling model is constructed, a cross-frequency harmonic contribution quantification model of a concerned node is established in combination with power distribution network harmonic propagation characteristics; non-stationary measurement data is divided into several steady-state intervals by using data segmentation based on sliding window regression residual analysis; harmonic transfer impedance and nonlinear load harmonic coupling admittance parameters are identified in each interval, the harmonic distortion contribution of different harmonic source nodes and different frequency voltage components to the concerned node is calculated; and the overall observation period is comprehensively divided by combining the local responsibility time weighting of the duration of each interval. The application can finely quantify the harmonic distortion contribution of different harmonic source nodes and different frequency voltage components to the concerned node under the conditions of system fluctuations such as load switching, switch action, network operation state and load working condition change.

Description

Technical Field

[0001] This invention belongs to the field of power system harmonic analysis and power quality management technology, specifically relating to a multi-node harmonic responsibility allocation method and system that considers nonlinear load harmonic coupling and system fluctuation characteristics. Background Technology

[0002] With the widespread integration of power electronic equipment in distribution networks, the number of nonlinear loads in the system is constantly increasing, and harmonic pollution problems are becoming increasingly prominent. Accurately assessing the contribution of different harmonic sources to harmonic distortion at nodes of concern is a crucial foundation for harmonic pollution liability delineation, harmonic mitigation device configuration, and power quality management. Therefore, harmonic liability delineation methods are of great significance in power quality analysis and management of distribution networks.

[0003] Existing harmonic responsibility allocation methods are generally categorized into single-node and multi-node methods based on the number and spatial distribution of harmonic sources. For single-node scenarios, common methods include the power direction method, superposition theorem method, harmonic impedance estimation method, correlation coefficient method, probability assessment method, and independent component analysis method. Since harmonic propagation relationships are relatively simple in single-node scenarios, these methods can achieve harmonic responsibility quantification to a certain extent. However, in actual distribution networks, harmonic pollution is usually caused by the combined effects of multiple distributed nonlinear loads. The superposition and coupling between multiple harmonic sources make harmonic responsibility allocation more complex. Therefore, multi-node harmonic responsibility allocation methods are more suitable for practical engineering applications. For multi-node harmonic responsibility allocation scenarios, existing methods often identify the harmonic transmission impedance between each harmonic source node and the node of interest, and calculate the contribution of each harmonic source's injected current to the harmonic voltage of the node of interest. These methods typically establish a multiple linear regression model based on voltage and current measurement data, and then combine phasor projection and other methods to achieve harmonic responsibility quantification.

[0004] The aforementioned methods provide a basic data-driven analysis framework for multi-node harmonic responsibility allocation, but they typically assume that the system operating state remains relatively stable within the observation period, meaning that the harmonic transmission impedance does not change significantly over time. However, in actual distribution network operation, factors such as load switching, tie switch operation, network reconfiguration, and changes in the operating state of nonlinear loads can all cause changes in the system's harmonic propagation relationship. If uniform parameters are still used for fitting throughout the entire time period, data from different operating states will be mixed in the model, easily causing deviations in the harmonic transmission impedance identification results, thus affecting the accuracy of the harmonic responsibility allocation results. Some existing methods improve the analysis effect by tracking time-varying impedance or removing data affected by changes in operating state, but the former usually relies on the assumption of continuous and smooth impedance changes, while the latter may lose the true responsibility information before and after changes in operating state, making it difficult to fully reflect the dynamic changes in harmonic responsibility throughout the entire observation period.

[0005] In summary, existing methods for allocating harmonic responsibility in multi-node systems have the following main shortcomings: (1) It is not adaptable to changes in the operating status of the distribution network, and it is difficult to accurately identify harmonic propagation parameters under complex operating conditions such as load switching and switching operations.

[0006] (2) Harmonic source modeling usually ignores the cross-frequency harmonic coupling characteristics of nonlinear loads, making it difficult to quantify the contribution of voltage components of different frequencies to the harmonic distortion of the node of interest through the coupling effect of nonlinear loads.

[0007] Therefore, there is an urgent need for a multi-node harmonic responsibility allocation method that can simultaneously consider the changes in the operating state of the distribution network and the nonlinear load harmonic coupling characteristics. Summary of the Invention

[0008] To improve the accuracy of harmonic responsibility allocation for multiple nodes under complex distribution network operating conditions and to address the problem that existing harmonic responsibility allocation methods cannot simultaneously adapt to system fluctuations and the harmonic coupling characteristics of nonlinear loads, this invention provides a multi-node harmonic responsibility allocation method that considers both harmonic coupling and system fluctuations. This method can precisely quantify the contribution of different harmonic source nodes and different frequency voltage components to the harmonic distortion of nodes of interest under system fluctuation conditions such as load switching, tie switch operation, changes in network operating status, and changes in the operating status of nonlinear loads.

[0009] To achieve the above objectives, in a first aspect, the present invention provides a multi-node harmonic responsibility allocation method considering harmonic coupling and system fluctuations, comprising the following steps: Acquire measurement data of the distribution network to determine the nodes of interest, the set of harmonic source nodes, and the set of harmonic orders to be analyzed; Based on the nonlinear load harmonic coupling model and network harmonic propagation characteristics, a quantitative model for the cross-frequency harmonic contribution of the node of interest is established, which decomposes the harmonic voltage of the node of interest into the contributions of different harmonic source nodes, voltage components of different frequencies, and background harmonic components. A data segmentation method based on sliding window regression residual analysis is adopted to adaptively segment the measurement data within the entire observation period, resulting in several steady-state intervals; Within each steady-state range, the harmonic transmission impedance and the harmonic coupling admittance parameters of the nonlinear load are identified respectively. Based on the identified harmonic transmission impedance and harmonic coupling admittance parameters, the local responsibility index of different harmonic source nodes and different frequency voltage components for the harmonic voltage of the node of interest in each steady-state interval is calculated. Then, the weighted summation is performed according to the duration of each steady-state interval to obtain the comprehensive harmonic responsibility division result for the entire observation period.

[0010] Furthermore, the nonlinear load harmonic coupling model is used to characterize the cross-frequency coupling relationship between harmonic voltages and harmonic currents of different frequencies at the nonlinear load node. The relationship between the harmonic current vector and the harmonic voltage vector is expressed as:

[0011] in, I NLL This represents the harmonic currents of various frequencies in a nonlinear load. Represents the harmonic coupling model matrix. This represents the voltage at various frequencies of a nonlinear load. express j Frequency harmonic voltage pair i The influence of frequency harmonic currents H The highest harmonic frequency under consideration is given in the formula.

[0012] Furthermore, based on the nonlinear load harmonic coupling model and network harmonic propagation characteristics, a quantitative model for the cross-frequency harmonic contribution of the node of interest is established, including: For nodes of interest in the distribution network m ,That h The expression for the subharmonic voltage is:

[0013] In the formula, Ω S Represents the set of harmonic source nodes. express m Nodes h Subharmonic voltage Represents a node i For nodes m of h Subharmonic transmission impedance express i Nodes inject into the system h Secondary harmonic current Indicates background harmonic pairs m node h The effect of frequency voltage; According to the nonlinear load harmonic coupling model, any harmonic source node i of h The injected harmonic current is represented by its multi-frequency harmonic voltage and harmonic coupling admittance matrix:

[0014] In the formula, Ω H Represents the set of harmonic frequencies. express i node k Frequency-voltage pair h Coupling admittance of frequency currents, express i Nodes k Subharmonic voltage; Substitute the above relationships into the nodes of interest. h From the expression for the subharmonic voltage, we obtain the expression for the harmonic voltage at the node of interest after considering the cross-frequency harmonic coupling of the nonlinear load:

[0015] Further extended to the following formula:

[0016] In the formula, the first term is the same-frequency self-coupling component, the second term is the cross-frequency self-coupling component, and the third term is the cross-coupling component of the other nodes to this node. If you are interested in nodes m If a node is itself a harmonic source node, then there is a self-coupling relationship between its own harmonic voltage and harmonic current at the same frequency. Further decomposing the harmonic voltage of the node of interest into contribution components from different physical sources, the self-coupling term at the same frequency can be summarized as follows:

[0017] Focus Nodes m of h The subharmonic gain coefficient is:

[0018] Substituting the gain coefficient into the above simplified expression, we obtain the node of interest. m of h Decomposition of subharmonic voltage:

[0019] In the above formula, the first two terms correspond to the voltage components formed by the cross-frequency coupling effect of the node of interest and the coupling effect of other harmonic source nodes, respectively, and the third term is the background harmonic component.

[0020] Furthermore, regarding the nodes of interest m of h The subharmonic voltage, the cross-frequency harmonic contribution quantification model of the node of interest decomposes the harmonic voltage of the node of interest into the cross-frequency coupling contribution component of the node of interest itself, the coupling and transmission contribution component of the external harmonic source node, and the background harmonic contribution component, and defines the corresponding harmonic responsibility index for each. Among them, the cross-frequency coupling contribution component of the node itself is represented as:

[0021] The corresponding responsibility indicators are:

[0022] In the formula: , , respectively, vectors , The phase angle; External harmonic source node i To the node of interest m The coupling propagation contribution component is expressed as:

[0023] The corresponding responsibility indicators are:

[0024] In the formula: , , respectively, vectors , The phase angle; The background harmonic responsibility index is: .

[0025] Furthermore, the data segmentation method based on sliding window regression residual analysis includes: An initial reference data window is constructed, and a multiple linear regression model under the initial running state is established based on the ordinary least squares method to obtain the benchmark regression residuals; Expand the data window. After adding measurement data at each new time point, rebuild the multiple linear regression model based on all data within the current expanded window and calculate the regression residuals for the current window.

[0026] In the formula, and They are respectively t Current and voltage measurement matrix within the time window for t Equivalent impedance estimate within the time window; To construct the residual monitoring statistic, normalize the regression residuals of the current expanded window with the baseline regression residuals to obtain the residual monitoring statistic:

[0027] The regression residuals of the model within the baseline window; Based on whether the residual monitoring statistics exceed the set threshold, it is determined whether the system operating status has fluctuated. When system fluctuation is confirmed, the current steady-state interval is terminated, and the detected change point is used as the new segmentation point. The reference window is reinitialized from the change point, and the window expansion, regression residual calculation and residual monitoring statistics judgment are continued until the measurement data segmentation within the entire observation period is completed.

[0028] Furthermore, when determining whether the system's operating status fluctuates, a continuous discrimination mechanism is introduced: when the residual monitoring statistics are continuous... L c When all sampling points exceed the set threshold γ, it is confirmed that the system operating status has changed, and the detected change points are used as new segmentation points.

[0029] Furthermore, when identifying the harmonic coupling admittance parameters of the nonlinear load in each steady-state interval, the ridge regression method is used for identification, and the regularization parameters are determined by the maximum curvature criterion of the L-curve.

[0030] Secondly, the present invention also provides a multi-node harmonic responsibility allocation system that considers harmonic coupling and system fluctuations, including a data acquisition module, a model building module, a data segmentation module, a parameter identification module, and a responsibility allocation module; The data acquisition module is used to acquire measurement data of the distribution network, determine the nodes of interest, the set of harmonic source nodes, and the set of harmonic orders to be analyzed; The model building module is used to establish a quantitative model of cross-frequency harmonic contribution of the node of interest based on the nonlinear load harmonic coupling model and network harmonic propagation characteristics. It decomposes the harmonic voltage of the node of interest into the contributions of different harmonic source nodes, voltage components of different frequencies, and background harmonic components. The data segmentation module is used to adaptively segment the measurement data within the entire observation period using a data segmentation method based on sliding window regression residual analysis, to obtain several steady-state intervals. The parameter identification module is used to identify the harmonic transmission impedance and the harmonic coupling admittance parameters of the nonlinear load in each steady-state range. The responsibility allocation module is used to calculate the local responsibility index of different harmonic source nodes and different frequency voltage components for the harmonic voltage of the node of interest in each steady-state interval based on the identified harmonic transmission impedance and harmonic coupling admittance parameters. It also performs weighted summation according to the duration of each steady-state interval to obtain the comprehensive harmonic responsibility allocation result for the entire observation period.

[0031] Furthermore, the model building module includes: The network relationship establishment unit is used to establish the network harmonic propagation relationship of the node of interest. The network harmonic propagation relationship characterizes the relationship between the harmonic voltage of the node of interest and the harmonic current injected by each harmonic source node and the background harmonic voltage. The coupling introduction unit is used to introduce the nonlinear load harmonic coupling model into the network harmonic propagation relationship so that the injected harmonic current of each harmonic source node is expressed as the product of the multi-frequency harmonic voltage of that node and the harmonic coupling admittance matrix. The decomposition unit is used to organize the self-coupling terms of the node of interest at the same frequency, and based on the defined gain coefficient, decompose the harmonic voltage of the node of interest into the cross-frequency coupling contribution component of the node of interest itself, the coupling transmission contribution component of the external harmonic source node, and the background harmonic contribution component.

[0032] Furthermore, the data segmentation module includes: An initial window unit is used to construct an initial reference data window and establish an initial multiple linear regression model based on the data within the initial reference data window to obtain the initial regression residuals. The extended residual calculation unit is used to add newly collected measurement data sequentially over time to form an extended data window, and to rebuild the regression model based on all the data in the current extended window to calculate the current regression residual. A statistical construction unit is used to construct residual monitoring statistics based on the current regression residual and the initial regression residual; The segmentation judgment unit is used to determine the fluctuation of the system operating state and identify the segmentation point when the residual monitoring statistics exceed the set threshold. The reference window is reinitialized from the segmentation point and the segmentation process continues until the measurement data in the entire observation period is divided into multiple steady-state intervals. The segmentation judgment unit adopts a continuous discrimination mechanism. When the residual monitoring statistics exceed the set threshold for multiple consecutive sampling points, it is confirmed that the system operating state has changed.

[0033] The parameter identification module uses the ridge regression method to identify the harmonic coupling admittance parameters of the nonlinear load nodes, and uses the maximum curvature criterion of the L-curve to determine the regularization parameters of the ridge regression.

[0034] Thirdly, the present invention proposes a computer device including a processor and a memory, wherein the memory is used to store a computer executable program, and the processor calls and executes the computer executable program in the memory, which can realize the multi-node harmonic responsibility allocation method considering harmonic coupling and system fluctuations as described in the first aspect.

[0035] A computer-readable storage medium is also provided, which stores a computer program that, when executed by a processor, enables the implementation of the multi-node harmonic responsibility allocation method considering harmonic coupling and system fluctuations as described in the first aspect.

[0036] Compared with the prior art, the present invention has at least the following beneficial effects: This invention combines a nonlinear load harmonic coupling model with the harmonic propagation relationship of a distribution network, which can further decompose the harmonic distortion of the node of interest into the contributions of different harmonic source nodes, different frequency voltage components, and background harmonic components, thus realizing a refined division of cross-frequency harmonic responsibility in multi-node scenarios.

[0037] This invention employs a data segmentation method based on sliding window regression residual analysis, which can identify system fluctuations caused by factors such as load switching, tie switch operation, changes in network operating status, and changes in nonlinear load operating status. It also divides non-stationary data within the entire observation period into multiple steady-state intervals, reducing the impact of mixed modeling of different operating states on parameter identification results.

[0038] This invention is applicable to complex scenarios where multiple harmonic sources coexist, nonlinear loads have cross-frequency coupling, and the operating status of the distribution network fluctuates. It can provide more accurate analytical basis for harmonic pollution liability identification, harmonic mitigation device configuration, and power quality management of the distribution network. Attached Figure Description

[0039] Figure 1 This is a schematic diagram of the IEEE 18-node topology.

[0040] Figure 2 This is a flowchart illustrating the overall design of the method described in this invention.

[0041] Figure 3 This is a schematic diagram of the data segmentation method based on sliding window regression residual analysis.

[0042] Figure 4(a) shows the harmonic responsibility diagram of the harmonic source node to the node of interest in different time periods, and Figure 4(b) shows the weighted harmonic responsibility diagram for the whole time period. Detailed Implementation

[0043] 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, not all, of the embodiments of the present invention. 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.

[0044] This embodiment uses an IEEE 18-node distribution network as an example. Figure 1 As shown in the diagram, node 18 is the balancing node, node 17 is the node of interest, and the 5th harmonic voltage at node 17 is used as the primary responsibility allocation object. The contributions of the 5th, 7th, 11th, and 13th harmonic voltage components from the harmonic source node to it are analyzed. Multiple harmonic source nodes are set in the system, with node 1 being the background harmonic source node, and nodes 2, 6, and 14 being distributed harmonic source nodes.

[0045] This embodiment provides a multi-node harmonic responsibility allocation method considering harmonic coupling and system fluctuations. The method is applicable to distribution networks with multiple harmonic source nodes and is used to evaluate the contribution of different harmonic source nodes and different frequency voltage components to the harmonic distortion of nodes of interest. System fluctuations include changes in harmonic propagation or harmonic coupling relationships caused by factors such as load switching, tie switch operation, changes in network operating status, and changes in the operating status of nonlinear loads.

[0046] This embodiment describes a multi-node harmonic responsibility allocation method that considers harmonic coupling and system fluctuations, such as... Figure 2 As shown, it includes the following steps: S1: Obtain broadband voltage and current measurement data of the distribution network, and determine the nodes of interest, the set of harmonic source nodes, the set of nonlinear load nodes, and the set of harmonic orders to be analyzed.

[0047] S2. A nonlinear load harmonic coupling model is constructed to characterize the cross-frequency coupling relationship between harmonic voltages and harmonic currents of different frequencies at the nonlinear load nodes. Based on this, the network harmonic propagation characteristics are analyzed.

[0048] S3. Combining the harmonic propagation characteristics of the distribution network and the nonlinear load harmonic coupling model, a quantitative model of the cross-frequency harmonic contribution of the node of interest is established, which decomposes the harmonic voltage of the node of interest into the contributions of different harmonic source nodes, voltage components of different frequencies, and background harmonic components.

[0049] S4. To address the changes in harmonic propagation and harmonic coupling caused by system fluctuations, a data segmentation method based on sliding window regression residual analysis is adopted to adaptively segment the non-stationary measurement data within the entire observation period, resulting in several steady-state intervals.

[0050] S5. In each steady-state range, identify the harmonic transmission impedance from the harmonic source node to the node of interest, as well as the harmonic coupling admittance parameters of the nonlinear load node.

[0051] S6. Based on the identified harmonic transmission impedance and harmonic coupling admittance parameters, calculate the local responsibility index of different harmonic source nodes and different frequency voltage components for the harmonic voltage of the node of interest in each steady-state interval, and perform weighted summation according to the duration of each steady-state interval to obtain the comprehensive harmonic responsibility division result for the entire observation period.

[0052] The specific implementation process of S1 to S6 will be explained below.

[0053] S11: Determine the set of nodes of interest, harmonic source nodes, nonlinear load nodes, and harmonic orders to be analyzed in the distribution network.

[0054] Specifically, let the node of interest be a node. mThe set of harmonic source nodes is Ω. S The set of harmonic orders to be analyzed is Ω. H Among them, the nodes of interest m The nodes for which harmonic responsibility needs to be assigned; the set of harmonic source nodes Ω S This includes nodes that may inject harmonic currents into the system; the set of harmonic orders Ω. H It can be determined according to the actual power quality analysis requirements, such as including the 5th, 7th, 11th and 13th harmonics.

[0055] S12: Collect broadband voltage and current measurement data throughout the entire observation period.

[0056] Specifically, harmonic voltage and harmonic current data for the entire observation period are acquired using a synchronous measurement device. The broadband measurement data includes data from nodes of interest. m of h Subharmonic voltage Harmonic source nodes i of h Sub-injected harmonic current and harmonic voltage and the corresponding harmonic currents ,in i ∈Ω S , h ∈Ω H , k ∈Ω H .

[0057] S13: Preprocess the collected voltage and current measurement data.

[0058] Specifically, harmonic phasors are extracted from the collected voltage and current waveforms to obtain the harmonic voltage phasors and harmonic current phasors of each node at different sampling times. At the same time, missing data, abnormal data and data with obvious noise interference are removed or corrected to form a broadband measurement dataset for subsequent harmonic coupling modeling, system fluctuation segmentation and harmonic responsibility division.

[0059] The following is a detailed description of the S2 implementation method.

[0060] S21: Construct a harmonic coupling model for a nonlinear load.

[0061] For nonlinear loads, the harmonic voltages of different frequencies on the AC side can jointly influence the harmonic currents of different frequencies through their nonlinear characteristics. Therefore, a harmonic coupling model is used to represent the relationship between the harmonic current vector and the harmonic voltage vector:

[0062] In the formula: I NLLThis represents the harmonic currents of various frequencies in a nonlinear load. Y C Represents the harmonic coupling model matrix. This represents the voltage at various frequencies of a nonlinear load. express j Frequency harmonic voltage pair i The influence of frequency harmonic currents H The highest harmonic frequency under consideration.

[0063] When obtaining the specific parameters of this model, there are generally two technical approaches: theoretical analytical derivation and empirical data fitting. Although analytical derivation can clearly reveal the underlying physical mechanism, in engineering applications, many operating parameters of nonlinear loads are difficult to obtain accurately. Therefore, data fitting is generally used to obtain the harmonic coupling model.

[0064] S22: Analysis of the network harmonic interaction process. Multi-frequency harmonic voltages at the nonlinear load port generate multi-frequency harmonic currents via the harmonic coupling admittance matrix. These harmonic currents are injected into the distribution network and, through the corresponding frequency system harmonic impedance, generate a harmonic voltage response. This harmonic voltage response then acts on the nonlinear load port again, thus forming a closed-loop interaction process between harmonic voltage excitation, harmonic current generation, and network harmonic response. (The above is the first...) n The expression for the nonlinear load harmonic current vector in the next iteration is:

[0065] S23: Distinguish the harmonic response relationship between linear and nonlinear loads.

[0066] For a linear load node, the harmonic responses of different frequencies are independent of each other, and its voltage component is linearly mapped only to the current component of the same frequency. The formula for the same-frequency response of a linear load is:

[0067] In the formula: Represents a linear load node i of h Frequency current, Represents a node i of h Frequency admittance Represents a linear load node i of h Frequency voltage.

[0068] For nonlinear load nodes, there is a coupling relationship between harmonic voltages and harmonic currents of different frequencies. The cross-frequency coupling relationship of the nonlinear load is as follows:

[0069] In the formula: Represents nonlinear load nodes j of h Frequency current, Represents a node j of h Frequency autoadmittance, Represents a node j of k Frequency-voltage pair h Trans-admittance of frequency currents, , Representing nodes respectively j of h and k Frequency voltage.

[0070] As the above analysis shows, the harmonic problem caused by power electronic devices essentially involves two factors: the nonlinear effect of the load itself and the transmission characteristics of the power grid. Specifically, harmonic voltages of different frequencies at the nonlinear load port will induce corresponding harmonic currents through internal coupling relationships, reflecting the cross-frequency coupling characteristics of the harmonic source itself. After the harmonic current is injected into the power grid, it will propagate along the network transmission impedance and form harmonic voltage responses of the same frequency at each node. Therefore, when assigning harmonic responsibility, it is necessary to characterize both the cross-frequency voltage-current coupling relationship inside the nonlinear load and the spatial transmission process of harmonic current in the power grid.

[0071] The following is a detailed description of the S3 implementation method.

[0072] S31: Establish the network harmonic propagation relationship for nodes of interest. For nodes of interest in the distribution network... m ,That h The subharmonic voltage is injected by each harmonic source node. h The subharmonic current is formed by the combined effect of the harmonic transmission impedance of the corresponding frequency, and is also affected by the background harmonic voltage. The expression is:

[0073] In the formula, Ω S Represents the set of harmonic source nodes. express m Nodes h Subharmonic voltage Represents a node i For nodes m of h Subharmonic transmission impedance express i Nodes inject into the system h Second harmonic current Indicates background harmonic pairs m node h The influence of frequency voltage.

[0074] S32: Introducing a nonlinear load harmonic coupling model into the network harmonic propagation relationship. According to the nonlinear load harmonic coupling model, any harmonic source node... i of h The injected harmonic current can be represented by its multi-frequency harmonic voltage and harmonic coupling admittance matrix:

[0075] In the formula, Ω H Represents the set of harmonic frequencies. express i node k Frequency-voltage pair h Coupling admittance of frequency currents, express i Nodes k Subharmonic voltage.

[0076] Substitute the above relationships into the nodes of interest. h From the expression for the subharmonic voltage, we obtain the expression for the harmonic voltage at the node of interest after considering the cross-frequency harmonic coupling of the nonlinear load:

[0077] This formula can be further extended to the following formula:

[0078] In the formula, the first term is the same-frequency self-coupling component, the second term is the cross-frequency self-coupling component, and the third term is the cross-coupling component of the other nodes to this node.

[0079] S33: Organize the self-coupling terms of the node of interest. If the node of interest... m If a node is itself a harmonic source node, then there is a self-coupling relationship between its own harmonic voltage and harmonic current at the same frequency. To further decompose the harmonic voltage of the node of interest into contribution components from different physical sources, the self-coupling term at the same frequency is rearranged, and the expression is as follows:

[0080] Based on this, define the nodes of interest. m of h Subharmonic gain coefficient:

[0081] Substituting this gain coefficient into the simplified expression above, we can obtain the node of interest. m of h Decomposition of subharmonic voltage:

[0082] In the above formula, the first two terms correspond to the voltage components formed by the cross-frequency coupling effect of the node of interest and the coupling effect of other harmonic source nodes, respectively, and the third term is the background harmonic component.

[0083] S34: Based on the nodes of interest m of h The subharmonic voltage decomposition forms define the harmonic contribution components from different sources.

[0084] The cross-frequency coupling contribution component of the node itself is represented as follows:

[0085] The corresponding responsibility indicators are:

[0086] In the formula: , , respectively, vectors , The phase angle.

[0087] External harmonic source node i To the node of interest m The coupling propagation contribution component is expressed as:

[0088] The corresponding responsibility indicators are:

[0089] In the formula: , , respectively, vectors , The phase angle.

[0090] The background harmonic responsibility index is:

[0091] Therefore, focus on nodes m of h The subharmonic voltage can be decomposed into the cross-frequency coupling contribution of the node of interest itself, the coupling transmission contribution of the external harmonic source node, and the background harmonic contribution, which provides a basis for subsequent calculation of harmonic responsibility index based on phasor projection.

[0092] The following is a detailed description of the S4 implementation method.

[0093] S41: Construct the initial reference data window. Select a relatively short initial data window. W 0, and assumes that the distribution network operating state remains unchanged within this initial window. t ∈[1, WWithin the range of 0, a multiple linear regression model is established under the initial operating state based on the ordinary least squares method, as shown in the following equation:

[0094] In the formula, and These are the current and voltage measurement matrices within the initial window, respectively. This represents the estimated equivalent impedance within the initial window. At this point, the regression residuals of the model within the baseline window are... . ( ) H It is the conjugate transpose of the vector.

[0095] S42: Expand the data window and calculate the regression residuals. As time progresses, measurement data at new moments are sequentially added to the current data window to form an expanded window. After adding measurement data at each new time point, a new multiple linear regression model is built based on all data within the current expanded window, and the regression residuals corresponding to the current window are calculated, as shown in the following formula:

[0096] In the formula, and They are respectively t Current and voltage measurement matrix within the time window for t Estimated equivalent impedance within the time window.

[0097] S43: Determine whether the system operating state has fluctuated based on the change in regression residuals. When the distribution network operating state remains unchanged, the newly added measurement data corresponds to the same harmonic propagation relationship as the historical measurement data, and the regression residual in the current extended window remains at a small level. If the distribution network experiences load switching, tie switch operation, changes in network operating state, or changes in the operating state of nonlinear loads, the extended window will simultaneously include measurement data under different operating states. In this case, if a uniform harmonic propagation impedance is still used for fitting, the obtained parameter estimation results will deviate from any true operating state, leading to a significant increase in the regression residual. The parameter estimation relationship under mixed operating states is shown in the following formula:

[0098] In the formula, and These represent the current data matrices before and after the system mutation, respectively.

[0099] S44: Constructing the residual monitoring statistic. To mitigate the impact of differences in dimensions and scales on the judgment results, the regression residuals corresponding to the current expanded window and the regression residuals corresponding to the initial reference window are normalized to obtain the residual monitoring statistic, as shown in the following formula:

[0100] S45: Segment the data based on the residual monitoring statistics. If the residual monitoring statistics... If the value exceeds the set threshold γ, the system's operating state is considered to be fluctuating. To avoid misjudgments caused by transient disturbances or random noise, a continuous discrimination mechanism is introduced, meaning that the system will only be considered if the residual monitoring statistic is continuous. L c The system's operating status is only confirmed to have changed when all sampling points exceed the threshold γ.

[0101] S46: Once system fluctuations are confirmed, the current steady-state interval is terminated, and the detected change point is used as the new segmentation point. Subsequently, the reference window is reinitialized from this change point, and window expansion, regression residual calculation, and residual monitoring statistic judgment are continued until the measurement data segmentation for the entire observation period is completed. Through the above process, the non-stationary broadband measurement data for the entire observation period is divided into several steady-state intervals.

[0102] The following is a detailed description of the S5 implementation method.

[0103] S51: Identify harmonic transmission impedance in each steady-state interval. After data segmentation in S4, the operating state of the distribution network in each steady-state interval remains approximately unchanged. Therefore, the harmonic transmission impedance from the harmonic source node to the node of interest can be identified in each steady-state interval using the complex domain least squares method. Specifically, for the first... s For each steady-state interval, a regression model is established using the harmonic current measurement matrix and harmonic voltage measurement matrix within that interval, and the harmonic transmission impedance matrix within that steady-state interval is obtained.

[0104] S52: Identify the harmonic coupling admittance parameters of the nonlinear load nodes in each steady-state interval. For the first... s Nonlinear load nodes within a steady-state interval i , establish its h The multiple linear regression relationship between the injected harmonic current and the harmonic voltages of different frequencies at the port is shown in the following equation:

[0105] In the formula, , , They represent the first s Nonlinear load nodes within each steady-state data segment i Injected into the systemh Subharmonic current, node i of Subharmonic voltage h The coupling admittance parameters of the subharmonic current, and the nodes i port k Subharmonic voltage.

[0106] S53: Ridge regression is used to identify the harmonic coupling admittance matrix. Since different frequency harmonic voltages at the same nonlinear load node port may be affected by both the equipment topology and operating status, and there is a strong correlation between measured variables, directly using the ordinary least squares method may lead to unstable estimation of the coupling admittance parameters. To improve the robustness of parameter identification, this embodiment uses ridge regression to identify the nonlinear load harmonic coupling admittance matrix, and its objective function is shown in the following equation:

[0107] in:

[0108] In the formula, λ is the regularization coefficient, || ||2 represents a vector L The 2-norm is the geometric length of a vector.

[0109] S54: Obtain the closed-form solution of the ridge regression. Setting the derivative of the ridge regression objective function with respect to the coupling admittance parameter vector to zero, we can obtain the closed-form solution of the coupling admittance parameter vector, as shown in the following equation:

[0110] In the formula, E It is a unit array.

[0111] S55: Determine the optimal regularization parameter. To balance fitting accuracy and parameter stability, this embodiment uses the maximum curvature criterion of the L-curve to determine the regularization parameter λ. First, define the residual norm and the solution norm, as shown in the following equation:

[0112] Construct the L-curve based on the residual norm and solution norm, and calculate the curvature of the curve, as shown in the following formula:

[0113] in, , They are respectively The first and second derivatives, , They are respectively The first and second derivatives.

[0114] By searching within the regularization parameter search range, λ that maximizes the curvature is selected as the optimal regularization parameter within the current steady-state interval, as shown in the following equation:

[0115] S56: Substitute the optimal regularization parameter back into the closed-form solution of the ridge regression to obtain the first... s The harmonic coupling admittance matrix of the nonlinear load node within each steady-state interval can be obtained. This provides a parameter basis for subsequent calculations of harmonic liability indicators.

[0116] The following is a detailed explanation of the specific methods of S6.

[0117] S61: Calculate the harmonic contribution voltage components within the steady-state region. For the first... s In a steady-state interval, the harmonic transmission impedance and harmonic coupling admittance parameters identified in S5 are substituted into the cross-frequency harmonic contribution quantification model of the node of interest established in S3 to obtain the cross-frequency coupling contribution voltage component of the node of interest itself, the external harmonic source node coupling transmission contribution voltage component, and the background harmonic contribution voltage component.

[0118] S62: Time-weighted summation of local harmonic responsibility results for each steady-state interval. Since the duration of different system operating states may vary, to reflect the overall level of harmonic responsibility throughout the entire observation period, the local harmonic responsibility results obtained in each steady-state interval are weighted and averaged according to the corresponding steady-state interval duration to obtain the comprehensive harmonic responsibility allocation result for the entire observation period, as shown in the following formula:

[0119] in, T Indicates the duration of the entire observation period. S Indicates the number of steady-state intervals. T s Indicates the first s The duration of each steady-state interval Indicates the first s Local harmonic responsibility results within a steady-state interval This indicates the result of the comprehensive harmonic responsibility allocation over the entire observation period.

[0120] Through the above S1 to S6, this embodiment can segment the non-stationary broadband measurement data within the entire observation period under system fluctuation conditions, and complete the identification of harmonic transmission impedance and harmonic coupling admittance in each steady-state interval, thereby realizing the full-cycle comprehensive division of multi-node, cross-frequency harmonic responsibility.

[0121] Figure 3This is a schematic diagram of the data segmentation method based on sliding window regression residual analysis in an embodiment of the present invention. As can be seen from the figure, as the sliding window gradually expands, the regression residual is small when the data in the window comes from the same grid, but the regression residual increases significantly when other grid data are mixed into the data window. Therefore, the time of grid change can be identified by the residual jump.

[0122] Figure 4(a) is a time-sharing breakdown diagram of the 5th, 7th, 11th and 13th harmonic voltages of the harmonic source node 6 to the 5th harmonic voltage of the node of interest in an embodiment of the present invention. Figure 4(b) is a weighted harmonic responsibility diagram for the entire time period.

[0123] Based on the technical concept of the above method, the present invention also provides a multi-node harmonic responsibility allocation system that considers harmonic coupling and system fluctuations, including a data acquisition module, a model building module, a data segmentation module, a parameter identification module, and a responsibility allocation module. The data acquisition module is used to acquire measurement data of the distribution network, determine the nodes of interest, the set of harmonic source nodes, and the set of harmonic orders to be analyzed; The model building module is used to establish a quantitative model of cross-frequency harmonic contribution of the node of interest based on the nonlinear load harmonic coupling model and network harmonic propagation characteristics. It decomposes the harmonic voltage of the node of interest into the contributions of different harmonic source nodes, voltage components of different frequencies, and background harmonic components. The data segmentation module is used to adaptively segment the measurement data within the entire observation period using a data segmentation method based on sliding window regression residual analysis, to obtain several steady-state intervals. The parameter identification module is used to identify the harmonic transmission impedance and the harmonic coupling admittance parameters of the nonlinear load in each steady-state range. The responsibility allocation module is used to calculate the local responsibility index of different harmonic source nodes and different frequency voltage components for the harmonic voltage of the node of interest in each steady-state interval based on the identified harmonic transmission impedance and harmonic coupling admittance parameters. It also performs weighted summation according to the duration of each steady-state interval to obtain the comprehensive harmonic responsibility allocation result for the entire observation period.

[0124] The model building module includes: The network relationship establishment unit is used to establish the network harmonic propagation relationship of the node of interest. The network harmonic propagation relationship characterizes the relationship between the harmonic voltage of the node of interest and the harmonic current injected by each harmonic source node and the background harmonic voltage. The coupling introduction unit is used to introduce the nonlinear load harmonic coupling model into the network harmonic propagation relationship so that the injected harmonic current of each harmonic source node is expressed as the product of the multi-frequency harmonic voltage of that node and the harmonic coupling admittance matrix. The decomposition unit is used to organize the self-coupling terms of the node of interest at the same frequency, and based on the defined gain coefficient, decompose the harmonic voltage of the node of interest into the cross-frequency coupling contribution component of the node of interest itself, the coupling transmission contribution component of the external harmonic source node, and the background harmonic contribution component.

[0125] The data segmentation module includes: an initial window unit, used to construct an initial reference data window, and to establish an initial multiple linear regression model based on the data within the initial reference data window to obtain the initial regression residuals; The extended residual calculation unit is used to add newly collected measurement data sequentially over time to form an extended data window, and to rebuild the regression model based on all the data in the current extended window to calculate the current regression residual. A statistical construction unit is used to construct residual monitoring statistics based on the current regression residual and the initial regression residual; The segmentation judgment unit is used to determine the fluctuation of the system operating state and identify the segmentation point when the residual monitoring statistics exceed the set threshold. The reference window is reinitialized from the segmentation point and the segmentation process continues until the measurement data in the entire observation period is divided into multiple steady-state intervals. The segmentation judgment unit adopts a continuous discrimination mechanism. When the residual monitoring statistics exceed the set threshold for multiple consecutive sampling points, it is confirmed that the system operating state has changed.

[0126] The parameter identification module uses the ridge regression method to identify the harmonic coupling admittance parameters of the nonlinear load nodes, and uses the maximum curvature criterion of the L-curve to determine the regularization parameters of the ridge regression.

[0127] In addition, the present invention proposes a computer device including a processor and a memory, wherein the memory is used to store a computer executable program, and the processor calls and executes the computer executable program in the memory, which can realize the multi-node harmonic responsibility allocation method considering harmonic coupling and system fluctuations as described in the first aspect.

[0128] A computer-readable storage medium is also provided, which stores a computer program that, when executed by a processor, enables the implementation of the multi-node harmonic responsibility allocation method considering harmonic coupling and system fluctuations as described in the first aspect.

[0129] The computer device may be a laptop, a desktop computer, or a workstation.

[0130] The processor can be a central processing unit (CPU), a graphics processing unit (GPU), a digital signal processor (DSP), an application-specific integrated circuit (ASIC), or an off-the-shelf programmable gate array (FPGA).

[0131] The memory described in this invention can be an internal storage unit of a laptop, desktop computer, or workstation, such as memory or hard disk; or it can be an external storage unit, such as a portable hard disk or flash memory card.

[0132] Computer-readable storage media can include computer storage media and communication media. Computer storage media includes volatile and non-volatile, removable and non-removable media implemented using any method or technology for storing information such as computer-readable instructions, data structures, program modules, or other data. Computer-readable storage media can include: read-only memory (ROM), random access memory (RAM), solid-state drives (SSDs), or optical discs, etc. Random access memory can include resistive random access memory (ReRAM) and dynamic random access memory (DRAM).

[0133] The above content is only for illustrating the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solution based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.

Claims

1. A multi-node harmonic responsibility allocation method considering harmonic coupling and system fluctuations, characterized in that, Includes the following steps: Acquire measurement data of the distribution network to determine the nodes of interest, the set of harmonic source nodes, and the set of harmonic orders to be analyzed; Based on the nonlinear load harmonic coupling model and network harmonic propagation characteristics, a quantitative model for the cross-frequency harmonic contribution of the node of interest is established, which decomposes the harmonic voltage of the node of interest into the contributions of different harmonic source nodes, voltage components of different frequencies, and background harmonic components. A data segmentation method based on sliding window regression residual analysis is adopted to adaptively segment the measurement data within the entire observation period, resulting in several steady-state intervals; Within each steady-state range, the harmonic transmission impedance and the harmonic coupling admittance parameters of the nonlinear load are identified respectively. Based on the identified harmonic transmission impedance and harmonic coupling admittance parameters, the local responsibility index of different harmonic source nodes and different frequency voltage components for the harmonic voltage of the node of interest in each steady-state interval is calculated. Then, the weighted summation is performed according to the duration of each steady-state interval to obtain the comprehensive harmonic responsibility division result for the entire observation period.

2. The multi-node harmonic responsibility allocation method considering harmonic coupling and system fluctuations according to claim 1, characterized in that, The nonlinear load harmonic coupling model is used to characterize the cross-frequency coupling relationship between harmonic voltages and harmonic currents of different frequencies at the nonlinear load node. The relationship between the harmonic current vector and the harmonic voltage vector is expressed as follows: in, I NLL This represents the harmonic currents of various frequencies in a nonlinear load. Represents the harmonic coupling model matrix. This represents the voltage at various frequencies of a nonlinear load. express j Frequency harmonic voltage pair i The influence of frequency harmonic currents H The highest harmonic frequency under consideration is given in the formula.

3. The multi-node harmonic responsibility allocation method considering harmonic coupling and system fluctuations according to claim 1, characterized in that, Based on the nonlinear load harmonic coupling model and network harmonic propagation characteristics, a quantitative model for the cross-frequency harmonic contribution of nodes of interest is established, including: For nodes of interest in the distribution network m ,That h The expression for the subharmonic voltage is: In the formula, Ω S Represents the set of harmonic source nodes. express m Nodes h Subharmonic voltage Represents a node i For nodes m of h Subharmonic transmission impedance express i Nodes inject into the system h Second harmonic current Indicates background harmonic pairs m node h The effect of frequency voltage; According to the nonlinear load harmonic coupling model, any harmonic source node i of h The injected harmonic current is represented by its multi-frequency harmonic voltage and harmonic coupling admittance matrix: In the formula, Ω H Represents the set of harmonic frequencies. express i node k Frequency-voltage pair h Coupling admittance of frequency currents, express i Nodes k Subharmonic voltage; Substitute the above relationships into the nodes of interest. h From the expression for the subharmonic voltage, we obtain the expression for the harmonic voltage at the node of interest after considering the cross-frequency harmonic coupling of the nonlinear load: Further extended to the following formula: In the formula, the first term is the same-frequency self-coupling component, the second term is the cross-frequency self-coupling component, and the third term is the cross-coupling component of the other nodes to this node. If you are interested in nodes m If a node is itself a harmonic source node, then there is a self-coupling relationship between its own harmonic voltage and harmonic current at the same frequency. Further decomposing the harmonic voltage of the node of interest into contribution components from different physical sources, the self-coupling term at the same frequency can be summarized as follows: Focus Nodes m of h The subharmonic gain coefficient is: Substituting the gain coefficient into the simplified expression above, we obtain the node of interest. m of h Decomposition of subharmonic voltage: In the above formula, the first two terms correspond to the voltage components formed by the cross-frequency coupling effect of the node of interest and the coupling effect of other harmonic source nodes, respectively, and the third term is the background harmonic component.

4. The multi-node harmonic responsibility allocation method considering harmonic coupling and system fluctuations according to claim 3, characterized in that, For the nodes of interest m of h The subharmonic voltage, the cross-frequency harmonic contribution quantification model of the node of interest decomposes the harmonic voltage of the node of interest into the cross-frequency coupling contribution component of the node of interest itself, the coupling and transmission contribution component of the external harmonic source node, and the background harmonic contribution component, and defines the corresponding harmonic responsibility index for each. The cross-frequency coupling contribution component of the node itself is represented as follows: The corresponding responsibility indicators are: In the formula: , , respectively, vectors , The phase angle; External harmonic source node i To the node of interest m The coupling propagation contribution component is expressed as: The corresponding responsibility indicators are: In the formula: , , respectively, vectors , The phase angle; The background harmonic responsibility index is: 。 5. The multi-node harmonic responsibility allocation method considering harmonic coupling and system fluctuations according to claim 1, characterized in that, The data segmentation method based on sliding window regression residual analysis includes: An initial reference data window is constructed, and a multiple linear regression model under the initial running state is established based on the ordinary least squares method to obtain the benchmark regression residuals; Expand the data window. After adding measurement data at each new time point, rebuild the multiple linear regression model based on all data within the current expanded window and calculate the regression residuals for the current window. In the formula, and They are respectively t Current and voltage measurement matrix within the time window for t Equivalent impedance estimate within the time window; To construct the residual monitoring statistic, normalize the regression residuals of the current expanded window with the baseline regression residuals to obtain the residual monitoring statistic: The regression residuals of the model within the baseline window; Based on whether the residual monitoring statistics exceed the set threshold, it is determined whether the system operating status has fluctuated. When system fluctuation is confirmed, the current steady-state interval is terminated, and the detected change point is used as the new segmentation point. The reference window is reinitialized from the change point, and the window expansion, regression residual calculation and residual monitoring statistics judgment are continued until the measurement data segmentation within the entire observation period is completed.

6. The multi-node harmonic responsibility allocation method considering harmonic coupling and system fluctuations according to claim 5, characterized in that, When determining whether the system's operating status fluctuates, a continuous discrimination mechanism is introduced: when the residual monitoring statistics are continuous... L c When all sampling points exceed the set threshold γ, it is confirmed that the system operating status has changed, and the detected change points are used as new segmentation points.

7. The multi-node harmonic responsibility allocation method considering harmonic coupling and system fluctuations according to claim 1, characterized in that, When identifying the harmonic coupling admittance parameters of nonlinear loads in each steady-state range, the ridge regression method is used for identification, and the regularization parameters are determined by the maximum curvature criterion of the L-curve.

8. A multi-node harmonic responsibility allocation system considering harmonic coupling and system fluctuations, characterized in that, It includes a data acquisition module, a model building module, a data segmentation module, a parameter identification module, and a responsibility allocation module; The data acquisition module is used to acquire measurement data of the distribution network, determine the nodes of interest, the set of harmonic source nodes, and the set of harmonic orders to be analyzed; The model building module is used to establish a quantitative model of cross-frequency harmonic contribution of the node of interest based on the nonlinear load harmonic coupling model and network harmonic propagation characteristics. It decomposes the harmonic voltage of the node of interest into the contributions of different harmonic source nodes, voltage components of different frequencies, and background harmonic components. The data segmentation module is used to adaptively segment the measurement data within the entire observation period using a data segmentation method based on sliding window regression residual analysis, to obtain several steady-state intervals. The parameter identification module is used to identify the harmonic transmission impedance and the harmonic coupling admittance parameters of the nonlinear load in each steady-state range. The responsibility allocation module is used to calculate the local responsibility index of different harmonic source nodes and different frequency voltage components for the harmonic voltage of the node of interest in each steady-state interval based on the identified harmonic transmission impedance and harmonic coupling admittance parameters. It also performs weighted summation according to the duration of each steady-state interval to obtain the comprehensive harmonic responsibility allocation result for the entire observation period.

9. A computer device comprising a processor and a memory, characterized in that, The memory is used to store computer-executable programs, and the processor calls and executes the computer-executable programs in the memory to implement the multi-node harmonic responsibility allocation method considering harmonic coupling and system fluctuations as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The storage medium stores a computer program that, when executed by a processor, can implement the multi-node harmonic responsibility allocation method considering harmonic coupling and system fluctuations as described in any one of claims 1 to 7.

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