Harmonic responsibility division method based on sliding window regression residual analysis

Abstract

The invention relates to the technical field of energy quality analysis, and discloses a harmonic wave responsibility division method based on sliding window regression residual analysis, and the method comprises the following steps: synchronously collecting harmonic wave current injection data of a harmonic wave source node and harmonic wave voltage data of an attention node; establishing a local linear regression model by applying a sliding window regression residual analysis method, continuously monitoring the change of a model fitting residual, identifying a time point when the residual suddenly changes as a system grid structure change point, and automatically dividing a time sequence data set into a plurality of steady-state time periods with constant internal parameters; secondly, independently solving system parameters for a steady-state time period and calculating responsibilities of all harmonic sources; and finally, aggregating all segment responsibility results by adopting a weighted average algorithm considering time segment duration and pollution severity to obtain final total harmonic responsibility. The method can adapt to the dynamic change of the system without manual intervention, and improves the accuracy, objectivity and fairness of responsibility division.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of power quality analysis, in particular to a harmonic responsibility division method based on sliding window regression residual analysis. BACKGROUND

[0002] Harmonic pollution is one of the key problems affecting power quality in power systems. In order to effectively manage harmonics and clearly define the responsibilities of each party, it is crucial to accurately divide the pollution contribution of different harmonic sources to a specific node in the power grid. The existing harmonic responsibility division is based on a steady-state power system model, which analyzes the linear relationship between voltage and current at a specific harmonic frequency to trace the harmonic source.

[0003] These methods rely on the assumption that the network topology and operating parameters of the power system remain unchanged throughout the analysis period. However, the actual power system is a dynamic and complex system, and events such as switching operations of transmission and distribution lines, start and stop of large-scale industrial loads, and actions of reactive power compensation devices occur frequently, resulting in different characteristics of the system network structure and equivalent impedance at different time periods. If these long-time series data containing multiple different operating conditions are processed as a whole without distinction, the harmonic transfer impedance and other key parameters solved are essentially the average of all operating conditions, which do not correspond to the real physical network state, and the calculated responsibility division results will inevitably have errors.

[0004] The existing technology has limitations in dealing with dynamic changes in power systems, making it difficult to ensure the accuracy and fairness of the harmonic responsibility division results. A new method is needed that can automatically adapt to changes in system operating conditions, intelligently identify different stable operating intervals, and accurately quantify responsibilities based on these intervals to overcome the shortcomings of traditional methods. Therefore, the present application proposes a harmonic responsibility division method based on sliding window regression residual analysis to overcome the shortcomings of the prior art. SUMMARY

[0005] To overcome the shortcomings of the prior art, the present application provides a harmonic responsibility division method based on sliding window regression residual analysis, which solves the problem of inaccurate harmonic responsibility division due to the inability to adapt to dynamic changes in power systems in the prior art.

[0006] To achieve the above purpose, the present application realizes the following technical scheme: a harmonic responsibility division method based on sliding window regression residual analysis, comprising the following steps: First, synchronously collect harmonic current injection data of each harmonic source node and harmonic voltage data of the concerned node in the power system to form a complete time series data set.

[0007] Subsequently, the aforementioned time series data set is processed by using a sliding window regression residual analysis method, the core of which is to identify the time when the inherent physical law of the data changes by continuously monitoring the fitting residual of the local linear regression model, when the system grid structure is stable, the model fitting residual maintains at a low level; When the grid structure changes, the newly collected data points will no longer follow the original linear relationship, resulting in a non-random mutation of the model fitting residual, by detecting the time points when all the model fitting residuals mutate, the system grid structure change points can be identified, and according to all the identified system grid structure change points, the original time series data set is divided into multiple steady-state periods with constant internal parameters.

[0008] Then, for each data subset of the divided steady-state period, harmonic responsibility calculation is independently performed to obtain the harmonic responsibility of each harmonic source node under the specific grid structure.

[0009] Finally, the harmonic responsibilities calculated for all steady-state periods are time-weighted averaged to obtain the overall harmonic responsibility of each harmonic source node in the entire evaluation period.

[0010] Preferably, the specific operation of the sliding window regression residual analysis method is as follows: an initial data window is selected from the starting part of the time series data set, and a local linear regression model representing the linear physical relationship between the harmonic voltage of the concerned node and the harmonic current injected by each harmonic source is established based on the data in the window; The data window is slid forward point by point along the time axis to include new data points, and the model fitting residual of the new data points is calculated by using the established local linear regression model, the calculated model fitting residual value is compared with the preset residual threshold value, if the model fitting residual value is greater than the preset residual threshold value, the time point corresponding to the new data point that causes the residual to increase is determined as the system grid structure change point.

[0011] Preferably, the local linear regression model is used to specifically represent the linear physical relationship between the harmonic voltage phasor of the concerned node, the harmonic current phasor injected by each harmonic source, the inherent harmonic transfer impedance of the system and the background harmonic voltage phasor, the harmonic transfer impedance and the background harmonic voltage phasor to be solved in the local linear regression model are solved by complex least squares method.

[0012] Preferably, in order to improve the accuracy of identification, a change point confirmation mechanism is introduced when determining a system grid structure change point, when the model fitting residual of data is greater than the preset residual threshold for the first time, the data is determined as a candidate change point, then a short confirmation window starting from the candidate change point is selected, and the total number of data points with model fitting residual greater than the preset residual threshold in the confirmation window is counted, only when the number is greater than the preset confirmation count value, the candidate change point is formally confirmed as a real system grid structure change point, so as to avoid misjudgment caused by measurement noise or transient disturbance.

[0013] Preferably, when the system grid structure change point is confirmed, all data from the last system grid structure change point to the current system grid structure change point before the current system grid structure change point is defined as a complete steady state period, and the current confirmed system grid structure change point is taken as the starting point of new segmentation, and the iteration operation of selecting an initial data window, establishing a local linear regression model and detecting a next system grid structure change point is repeated until the entire time series data set is traversed.

[0014] Preferably, when calculating the harmonic responsibility of the harmonic source node in each independent steady state period, a vector projection method is used for quantification, and the responsibility contribution of the harmonic source is evaluated by calculating the projection size of the harmonic voltage component phase generated by a single harmonic source at the concerned node in the direction of the total harmonic voltage phase at the concerned node, wherein the harmonic voltage component phase is obtained by multiplying the harmonic transfer impedance solved in the steady state period and the harmonic current injection data measured in the same period.

[0015] Preferably, in the weighted average algorithm used for final overall harmonic responsibility aggregation, the weight factor used for weighting is determined by the duration of each steady state period and the average of the harmonic voltage amplitude of the concerned node in the steady state period, and in this way, the steady state period with longer duration and more serious harmonic pollution occupies a higher proportion in the overall responsibility evaluation.

[0016] Preferably, when collecting data, the collected harmonic current injection data and the corresponding harmonic voltage data are complex phasors containing respective amplitudes and phase angles, in order to ensure the unity of the data collected by monitoring devices at different geographical positions in time reference, a time synchronization unit is used to add high-precision synchronous time stamps to all collected data, which is the technical basis for ensuring the physical authenticity of subsequent vector operations.

[0017] The application provides a harmonic responsibility division method based on sliding window regression residual analysis, and has the following beneficial effects: 1. The sliding window regression residual analysis method can automatically identify the system grid structure change point caused by line switching, load change and other events. The entire time series data set is dynamically divided into multiple steady-state periods with consistent internal physical characteristics, and each period is independently modeled and calculated, ensuring that each responsibility analysis is based on parameters matching the current system real state, avoiding calculation errors caused by using averaged and distorted parameters.

[0018] 2. The identification of system grid structure change points is based on the analysis of the internal rules of harmonic voltage and current data. The judgment is made by monitoring whether the local regression model fitting residual is mutated. The entire process does not require external information such as power grid dispatching log, and does not require manual intervention and prior knowledge, which eliminates the influence of subjective factors, making the division process repeatable and verifiable, and providing a technical basis for harmonic responsibility judgment.

[0019] 3. The invention does not use simple arithmetic mean when aggregating the segmented calculation results into overall responsibility, but introduces a weighted average algorithm considering the differences of each period. The weight factor of the weighted average algorithm considers the duration of each steady-state period and the severity of harmonic pollution in the period, which ensures that the periods with longer duration or more serious harmonic voltage exceeding standard are given higher importance in the final evaluation, making the final overall responsibility division result more just reflect its influence in the key period, and the evaluation result more convincing. BRIEF DESCRIPTION OF DRAWINGS

[0020] Figure 1 is the overall flowchart of the invention; Figure 2 is a schematic diagram of harmonic voltage superposition of the invention; Figure 3 is a schematic diagram of the data segmentation method of the invention; Figure 4 is a schematic diagram of the node system of the invention; Figure 5 is a schematic diagram of multiple harmonic source injection of the invention; Figure 6 is a sliding window regression residual change trend diagram of the invention; Figure 7 is a harmonic responsibility division result diagram of each steady-state period in the example analysis of the invention; Figure 8 is a total harmonic responsibility division result diagram of the entire period in the example analysis of the invention. DETAILED DESCRIPTION

[0021] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] See attached document Figure 1 This invention provides a method for harmonic responsibility allocation based on sliding window regression residual analysis, which includes the following steps: Data Acquisition: Harmonic current injection data from multiple harmonic source nodes and harmonic voltage data from at least one node of interest in the power system are acquired synchronously to form a time-series dataset. Both harmonic current injection data and harmonic voltage data are complex phasors containing amplitude and phase angle. The acquisition process is performed continuously at preset sampling intervals to obtain a harmonic current phasor sequence and a harmonic voltage phasor sequence.

[0023] Dynamic data segmentation: Based on sliding window regression residual analysis, dynamic data segmentation divides the obtained harmonic current phasor sequences and harmonic voltage phasor sequences into multiple steady-state time periods corresponding to different system network structures. Specifically, these include: Reference Figure 3 A local linear regression model is established: an initial data window is set, containing continuous data points from the beginning of the time series dataset. Based on the data within the initial data window, a linear regression model is established between the harmonic voltage of the node of interest and the injected current from each harmonic source. This model is based on the following physical relationship: ; in, To focus on nodes Measured at Total voltage phasor of subharmonics; This refers to the number of harmonic sources that are independently monitored in the system. For the first When each harmonic source acts independently, at the node of interest produced at the place Phasor of subharmonic voltage components; In addition to the above In addition to the individually monitored harmonic sources, the harmonics at the node of interest are affected by the combined effects of all other unmonitored harmonic sources in the system. produced at the place Sub-background harmonic voltage phasors.

[0024] The above model can be written in matrix form: ; in, a column vector composed of harmonic source currents of corresponding time points, an observation matrix composed of each harmonic source current and constant term 1, a column vector containing each transfer impedance and background harmonic voltage to be solved.

[0025] Solving local model parameters and calculating residuals: solving the linear regression model by using the complex least squares method to obtain the estimated value of the to-be-solved column vector : ; wherein the superscript represents conjugate transpose, and based on the solved parameters, the model fitting residuals of all data points in the data window are calculated.

[0026] Detecting the grid structure change point: sliding the data window along the time axis by one data point, including a new data point, and repeatedly establishing a local linear regression model and solving local model parameters and calculating residuals, continuously generating a fitting residual sequence, comparing the residual value in the fitting residual sequence with a preset residual threshold, when the fitting residual value is greater than the residual threshold, the time point corresponding to the new data point causing the increased residual is determined as the grid structure change point.

[0027] Completing data segmentation: re-detecting the grid structure change point operation until traversing the entire time series data set, identifying all grid structure change points, and dividing the harmonic current phasor sequence and the harmonic voltage phasor sequence into multiple data subsets of steady-state periods according to all identified grid structure change points.

[0028] Segmented harmonic responsibility calculation: for each data subset of the divided steady-state period, the following operations are independently performed: first, the transfer impedance and the background harmonic voltage corresponding to the steady-state period are solved, then based on the solved parameters, the th harmonic voltage component of the th harmonic source at the concerned node is calculated, and finally, the th harmonic responsibility of the th harmonic source to the concerned node is calculated according to the following formula: ; wherein: represents the amplitude of the phasor, is the phase angle of the total harmonic voltage of the concerned node, and ​Phase angle of harmonic voltage component .

[0029] Overall harmonic responsibility aggregation: the harmonic responsibilities calculated for all steady-state periods are weighted averaged to obtain the overall harmonic responsibility of each harmonic source in the whole evaluation period, wherein the weight comprehensively considers the duration of each period and the severity of harmonic pollution.

[0030] Referring to the accompanying Figure 4 , the data required for the implementation of the method is derived from power quality monitoring devices deployed at multiple nodes in the power system network. The power quality monitoring devices are deployed at pre-selected key nodes, including but not limited to: the point of common coupling (PCC) where nonlinear loads are connected to the grid, the bus of a substation with multiple users, the grid connection point of large-scale new energy generation (such as photovoltaic and wind power), and the concerned node itself that needs to be evaluated for harmonic responsibility. Such monitoring devices are deployed at node 1, node 2, node 6, node 14, and concerned node 17 where harmonic sources are located.

[0031] Each power quality monitoring device includes a sensing unit, a data acquisition unit, a data processing unit, and a time synchronization unit. The sensing unit is composed of high-precision voltage and current transformers for obtaining real-time analog voltage and current waveforms of the grid line at the node. The data acquisition unit includes an analog-to-digital converter (ADC) that samples and quantizes the analog waveforms at a fixed sampling frequency that satisfies the Nyquist sampling theorem and meets the harmonic analysis standard (for example, for a 50Hz power system, the sampling rate is 12.8kHz), converting them into digital waveform sequences.

[0032] The data processing unit is built-in with a processor configured to execute a pre-set harmonic analysis algorithm. In one embodiment, the harmonic analysis algorithm is the Fast Fourier Transform (FFT). The data processing unit divides the collected digital waveform sequences into frames with a fixed time window (for example, 10 power frequency cycles), and performs FFT operation on each frame of data, thereby calculating voltage and current phasors of pre-set harmonic orders (for example, 5th harmonic). Each phasor data includes amplitude and phase angle components.

[0033] To ensure that the data collected from monitoring devices at different geographical locations have a unified time reference, the time synchronization unit is used to receive a standard time signal. In one embodiment, the standard time signal is the second pulse signal provided by the Global Positioning System (GPS). Each monitoring device uses the second pulse signal to calibrate its internal clock and attach a high-precision time stamp to each calculated harmonic phasor data. This synchronization mechanism ensures that the phase angle relationship between voltage and current phasors of different nodes in subsequent calculations is physically real, which is a technical prerequisite for vector projection calculation.

[0034] See attached document Figure 5 The data processed by this method consists of two basic types: harmonic current injection data from harmonic source nodes and harmonic voltage data from nodes of interest. Both data are specific to pre-selected harmonic orders. (For example, the 5th harmonic) is analyzed.

[0035] The harmonic current injection data used in this method is specifically from each identified harmonic source node. ( At point ), the amount injected into the power grid was measured. The phasor sequence of subharmonic currents. Each harmonic current... Both consist of the real and imaginary parts, or equivalently, the effective value (RMS) of the current amplitude. and current phase angle Composition, current phase angle The calculation is based on a system-level synchronous reference phasor, for example, using the fundamental voltage phasor of the system's equilibrium node as the zero-degree reference.

[0036] The harmonic voltage data used in this method are specifically at the preset nodes of interest. Measured at The sequence of subharmonic voltage phasors. Each voltage phasor Similarly, the effective value (RMS) voltage amplitude and voltage phase angle Composition, voltage phase angle A synchronous reference phasor base, the same as that used for harmonic current phasors, is adopted to ensure the consistency and validity of phasor data measured at different physical locations in subsequent vector operations.

[0037] After data collection and preprocessing, for each synchronized timestamp (in From 1 to , (Total number of sampling points). This method obtains data records, each containing the harmonic voltage phasor of a node of interest. The set of harmonic current phasors of each harmonic source node is represented as follows: ,Depend on A sequence of such data records constitutes a complete time series dataset.

[0038] See attached document Figure 2 In this method, the definition of harmonic liability is based on the principle of circuit superposition. Under any given system grid structure, the power network exhibits linear time-invariant characteristics with respect to a specific harmonic frequency. Based on this principle, at the nodes of interest... Measured at Subharmonic total voltage phasor It is all within the system The vector sum of the harmonic voltage components generated at this point by the subharmonic source.

[0039] Appendix Figure 1 The vector superposition relationship described by the formula is illustrated on the complex plane, which is composed of the real part axis and the imaginary part axis. In the figure, multiple harmonic voltage component vectors are geometrically added by connecting them end to end. The final result of adding all component vectors forms the total harmonic voltage vector of the node of interest. Each voltage vector has its own voltage amplitude and voltage phase angle.

[0040] The quantification of harmonic responsibility in this method is achieved by calculating the projection of the harmonic voltage component phasor generated by each harmonic source onto the direction of the total harmonic voltage phasor of the node of interest.

[0041] In segmented harmonic liability calculation The term that determines the projection direction and magnitude is the voltage component phasor. With total voltage phasor The cosine of the angle between them, the geometric meaning of this calculation lies in converting the voltage component phasor... Projected onto total voltage phasor First, obtain a projection component, then calculate the length of this projection component and its relationship to the total voltage vector. The ratio of lengths.

[0042] The results of this quantification method It has a clear physical meaning: when When it is positive, it indicates the first... The voltage component generated by a harmonic source is in phase or nearly in phase with the total voltage, and the harmonic source has the effect of increasing the total harmonic voltage amplitude of the node of interest.

[0043] when When it is negative, it indicates that the first... The voltage component generated by a harmonic source is out of phase or nearly out of phase with the total voltage. This harmonic source has the effect of reducing the total harmonic voltage amplitude at the node of interest.

[0044] when When it is zero, it indicates the first... The voltage component generated by the harmonic source is orthogonal to the total voltage, and the harmonic source does not directly increase or decrease the total harmonic voltage amplitude at the node of interest.

[0045] See attached document Figure 4 To calculate harmonic liability, it is necessary to first determine the phasor of the voltage components generated by each harmonic source at the node of interest. This method achieves this goal by constructing a harmonic source tracing model based on the physical characteristics of the system.

[0046] For a fixed power grid topology, at a specific harmonic frequency, the power grid can be considered a linear time-invariant (LTI) system. Therefore, the... The amplitude of the current injected by each harmonic source Instead of focusing on nodes Harmonic voltage component phasor generated at the location There exists a linear relationship between them, determined by the system network parameters, which is transmitted through harmonic impedance. To describe it, it is from the first Focus on node number Focus on nodes Subharmonic transfer function.

[0047] Based on this principle, and by combining the superposition principle with the aforementioned transmission impedance relationship, the harmonic voltage of the node of interest can be established. With the amplitude of the injected current from all harmonic sources A mathematical model was constructed to identify the sources of harmonics, and a multiple linear regression model was established. In this model, the amplitude of the injected current from each harmonic source was measured at multiple time points using a power quality monitoring device. The input (independent variable) of the model is the total harmonic voltage of the node of interest measured at the same time point. The output (dependent variable) of the model is the model's output, and the parameters to be solved for in the model are all transmission impedances. and background harmonic voltage Once these parameters are determined, the known harmonic source current amplitude can be used. Calculate the phasor of the harmonic voltage components at any given time. This enables harmonic source tracing. This method uses the complex field least squares method to solve the constructed linear regression model. This method utilizes a set of... The optimal estimate of the parameter to be solved is obtained by using observation data from multiple synchronous time sampling points.

[0048] First, will contain Substituting the observation data from each time sampling point into the formula, an overdetermined system of equations is formed. This system of equations is organized into the following matrix form: ; The specific structure of each matrix is ​​as follows: ; ; ; in: It is a dimension The column vector, whose The element is the first The harmonic voltage phasor of the node of interest measured at each sampling time.

[0049] is an observation matrix with dimension , whose first columns are respectively the harmonic current phasor sequences injected by harmonic sources at sampling time instants, and the last column with all elements equal to 1 is used to match and solve the background harmonic voltage .

[0050] is a parameter column vector to be solved with dimension .

[0051] Secondly, define the loss function , which is used to quantify the error between the model prediction and the actual observation, and the loss function is defined as the square of the Euclidean norm of the error vector, as shown in the formula: ; where the superscript denotes the conjugate transpose, and finally, the parameter column vector is solved by minimizing the loss function , according to the optimization theory, the minimum point of the loss function appears at the position where its gradient is zero, and the partial derivative of the loss function with respect to is zero, as shown: ; After rearranging the formula, the analytical solution of can be obtained, as shown below: ; The condition for the existence of this analytical solution is that the matrix is a non-singular matrix, i.e., its inverse matrix exists, in practical applications, this requires that there is no complete linear correlation between the injected current sequences of each harmonic source, by calculation, the numerical estimates of all transfer impedances and harmonic voltages within the given data set can be obtained.

[0052] Referring to Table 1, the accuracy of the solution of the complex least squares method depends on a basic premise: the parameter column vector to be solved remains constant within the time period corresponding to the entire data set used for regression calculation (i.e., data containing synchronous time sampling points). This means that the transfer impedances from each harmonic source node to the node of interest and the background harmonic voltage are constant within this time period.

[0053] In actual operating power systems, this premise holds true only for short periods when the system topology and operating mode remain unchanged. However, over longer timescales (e.g., a 24-hour monitoring cycle), the operating state of the power system can change due to a variety of predetermined and unpredictable events. These events include: switching operations of transmission and distribution lines, adjustments to transformer taps, the start-up and shutdown of large-scale industrial loads or load groups, the switching of reactive power compensation devices such as capacitors or reactors, and significant changes in the output of grid-connected generating units.

[0054] The occurrence of any of the above events will alter the equivalent circuit topology or parameters of the power system network, directly causing changes in the propagation path or path impedance of harmonic currents from their source to the node of interest. The direct mathematical consequence is an change in the harmonic transmission impedance matrix. One or more element values ​​will change abruptly. Therefore, throughout the entire monitoring period, It is not a constant matrix, but a matrix that changes piecewise over time.

[0055] If a mixed dataset spanning 24 hours, containing multiple different network structure states, is directly substituted into the calculation as a whole, the result will be a single average value across all the different states. The estimated, averaged harmonic propagation impedance matrix does not correspond to any actual physical network state. Using such an inaccurate impedance matrix to calculate the harmonic voltage component phasors is problematic. This will inevitably introduce significant calculation errors, ultimately causing the resulting harmonic responsibility allocation to lose its accuracy and physical meaning.

[0056] Therefore, to ensure the accuracy and reliability of harmonic responsibility allocation, the collected complete time series dataset must be preprocessed before performing complex domain least squares regression. The core of this preprocessing is to identify the time point when the system network structure changes each time, and use this as the boundary to divide the entire time series data into several continuous steady-state periods with a constant internal network structure. Only by independently applying the least squares method within each such steady-state period can an accurate estimate of the harmonic transmission impedance corresponding to the actual physical state of that period be obtained, thus providing a technical basis for accurate harmonic responsibility allocation.

[0057] Table 1. System network structure and load changes See attached document Figure 3 The core technical principle of dynamic data segmentation in this method is to use the fitting residuals of the local linear regression model to determine whether the data points follow the same physical law.

[0058] In a power system network structure where the physical state remains constant, all the harmonic voltage and current data points collected in this state follow a linear relationship uniquely determined by the network structure. The specific parameters of this linear relationship, i.e. the harmonic transfer impedance matrix When this set of homogeneous data is fitted using a local linear regression model, the model can accurately represent the intrinsic linear physical law of the data, and thus the predicted harmonic voltage values calculated by the model will highly agree with the actual measured harmonic voltage values. The difference between them, i.e. the fitting residual, will maintain at a low level, and its fluctuation will only show random changes caused by measurement noise.

[0059] When an event occurs in the system that causes the network structure to change (e.g. line switching), the physical parameters of the system change, resulting in a step change in the harmonic transfer impedance matrix After this event occurs, any new data points collected will follow a different linear relationship determined by the new network structure.

[0060] If the local linear regression model established based on the old network structure data is applied to this new data point, the mathematical structure of the model will not match the physical law followed by the new data point. This mismatch will result in a significant deviation between the predicted harmonic voltage value calculated by the model and the actual measured voltage value of the new data point, which is directly reflected in the model's fitting residual, causing its amplitude to increase sharply and continuously.

[0061] Therefore, by continuously monitoring the amplitude changes of the fitting residual of the local linear regression model, the time point when the system's physical law changes can be accurately identified. The stable low level interval of the residual amplitude corresponds to a steady state period where the system's network structure has not changed, and the point where the residual amplitude increases significantly and non-randomly directly indicates the time when the system's network structure changes. This method uses this principle to use the residual as an indicator of system state consistency, thereby achieving accurate dynamic segmentation of continuous time series data.

[0062] This method realizes dynamic segmentation of time series data through a systematic process including initialization, window expansion, residual calculation, change point detection and confirmation, and segmentation iteration. The specific steps of the process are as follows: Initialize the local regression model: start from the starting point of the time series data set ( ), select the initial data window, which contains continuous data points from to , where is the pre-set initial window size, The value is set to be greater than the number of parameters to be solved. To ensure the matrix Based on the data within the initial window, the reversibility of the parameters is determined by applying the least squares method in the complex domain to calculate the initial local harmonic propagation impedance parameter vector. .

[0063] Window forward expansion and residual calculation: from the first data point immediately following the initial window ( Begin with a point-by-point forward expansion detection. For the time index of the current data point to be detected... ( ), using its corresponding harmonic current measurement values ​​(i.e., observation matrix) The (and) use the local parameter vector established in the previous steady-state period (initially...) ), calculate the predicted harmonic voltage value at this point. Then, the prediction residual at that point is calculated. : ; in, It is the time index of the data point. The actual measured harmonic voltage at the location, It is the time index of the data point. The observed row vector of harmonic current at the location. It is the local parameter vector for the current steady-state period.

[0064] Residual mutation detection: Calculate the residual amplitude With a preset residual threshold Compare them.

[0065] like Then determine the time index. The data point at this point is consistent with the data in the current steady-state period. Incorporate this data point into the current steady-state period and continue indexing the next time period. The data points at each location undergo continuous monitoring and data analysis processes to keep abreast of the structure's health status.

[0066] like Then determine the time index. If a data point is suspected to be a point of change in the network structure, then pause the forward expansion of the window and initiate the next confirmation mechanism.

[0067] The confirmation mechanism for modified points has been changed: To avoid misjudgments caused by measurement noise or transient disturbances, suspected time indexes are... Execute confirmation for the data points at that location, select from... The beginning of a containing a confirmation window of consecutive data points, for each data point within the confirmation window, repeating the operation of monitoring and data analysis process, calculating its predicted residual relative to the previous steady-state period model the number of data points whose residual amplitude exceeds the threshold value within the statistical confirmation window If the number is greater than a preset confirmation count value (where ), the data point at time index is formally confirmed as a real grid structure change point. Otherwise, the suspected point is considered as an abnormal point, and the monitoring and data analysis process continues to be executed.

[0068] Iterative segmentation: once a grid structure change point is confirmed at the data point at time index , all data points from the last confirmed change point (or the start point of the data set) to the data point at time index are defined as a complete steady-state period, and then the data point at time index is taken as the starting point of the new segment, and the new initial window is selected from the data point at time index to , the local parameter vector representing the new grid structure is calculated , and then based on the new model, the next grid structure change point is searched backward, and this iterative process continues until the entire time series data set is traversed, and finally the data set is divided into steady-state periods with constant internal parameters.

[0069] After successfully dividing the entire time series data set into independent steady-state periods, the method will independently perform a complete harmonic responsibility calculation for each steady-state period. Hereinafter, taking any one of the steady-state periods (labeled as the period, where ) as an example, the detailed calculation process is described.

[0070] First, the harmonic voltage and current data subset corresponding to the steady-state period is extracted. Using this data subset, the observation matrix and the harmonic voltage column vector of this period are constructed.

[0071] Second, the above matrices are substituted into the complex least squares method to solve the harmonic transfer impedance parameter vector effective only in the steady-state period, which contains the specific transfer impedance from each harmonic source node to the node of interest ​and background harmonic voltage .

[0072] Then, for each time sampling point within the th steady state period, the harmonic voltage component generated by the th harmonic source at the concerned node at this time is calculated using the transfer impedance of this period and the harmonic current measured at this sampling point.

[0073] Then, the calculated harmonic voltage component and the total harmonic voltage actually measured at this sampling point are substituted into the harmonic responsibility quantification formula, and through this calculation, the instantaneous harmonic responsibility value of the th harmonic source at time sampling point is obtained.

[0074] Finally, to obtain the comprehensive harmonic responsibility of the th harmonic source within the entire th steady state period, the instantaneous harmonic responsibility values of all sampling points within this period are arithmetically averaged. The calculation result is the harmonic responsibility of the th harmonic source under the specific network structure, and by repeating this calculation for all harmonic sources, the responsibility division results of all harmonic sources within the th period can be obtained.

[0075] After obtaining the harmonic responsibility of each harmonic source within each independent steady state period, these segmented and discrete results need to be integrated into a final evaluation index that can represent the overall impact of each harmonic source within the entire monitoring period (e.g., 24 hours).

[0076] Directly arithmetically averaging all segmented harmonic responsibility values is inappropriate, as this method incorrectly assumes that each steady state period is equally important, whereas in reality, a system operating state that lasts for several hours has a significantly greater impact than a transient state that lasts only a few minutes. Similarly, a period that results in a serious over-standard harmonic voltage at the concerned node is more critical in terms of responsibility attribution than a period with completely normal harmonic voltage levels.

[0077] To solve this problem, this method uses a weighted average algorithm that takes into account the duration of each period and the severity of harmonic pollution to calculate the overall harmonic responsibility of each harmonic source within the entire period. Specifically, a weight factor is defined for the th steady state period, as shown in the formula: ; in, For the first The duration of a steady-state period can be represented by the number of data points contained in that period. For the first During a steady-state period, focus on the nodes of The arithmetic mean of the total voltage amplitude of the subharmonics quantifies the severity of harmonic pollution during that period.

[0078] Weighting factors The physical significance of this is that it integrates the two dimensions of time and hazard. The longer a steady-state period lasts and the higher the harmonic voltage within that period, the greater the weight of that period, and the greater the proportion of the corresponding harmonic responsibility allocation result in the final comprehensive assessment.

[0079] Based on this weighting factor, the first Overall harmonic responsibility of each harmonic source throughout the entire time period The calculation is performed using the following formula: ; in, This represents the total number of steady-state periods.

[0080] The calculation yields a single, comprehensive percentage value that fairly reflects the overall contribution of each harmonic source to the harmonic voltage problem of the node of concern throughout the entire dynamic assessment period. This provides a reliable and quantifiable technical basis for subsequent harmonic mitigation and liability determination.

[0081] To verify the effectiveness and accuracy of the method proposed in this invention, this embodiment uses simulation analysis based on the IEEE 18-node standard test system.

[0082] See attached document Figure 4 In the power system, nodes 6, 18 and 33 are selected as the main harmonic source access points and are labeled as harmonic source 1, harmonic source 2 and background harmonic source, respectively. The common coupling point (PCC) of the system, i.e. node 0, is selected as the node of concern for harmonic responsibility allocation. This example focuses on the responsibility allocation of the 5th harmonic, which has the most common impact on the system.

[0083] Referring to Table 1, to simulate the dynamic characteristics of the power system in actual operation, this example sets a simulation cycle of up to 24 hours, collecting 720 consecutive harmonic voltage and current data samples at fixed time intervals. Within this cycle, two system topology change events are artificially set: At the 241st data sampling point, the tie switch between the 16th node and the 8th node is closed, which changes the network structure and power flow distribution of the system.

[0084] At the 481st data sampling point, all the loads on three randomly selected nodes in the system are cut off, simulating a large-scale load shedding event. Through the above settings, the entire 24-hour data set is artificially divided into three real steady-state periods, each corresponding to a determined but different physical network structure.

[0085] Referring to the accompanying drawings Figure 6 The complete time series data composed of 720 data points collected is taken as the input of the method. By executing the dynamic data segmentation algorithm based on sliding window regression residual analysis, the algorithm successfully detects the obvious mutation of the residual at data point 241 and data point 481 and identifies them as network structure change points. The result is completely consistent with the preset time of the system event in this example, proving that the method can accurately and automatically identify the time when the system topology structure changes and divide the data into three steady-state periods consistent with the physical reality.

[0086] Referring to the accompanying drawings Figure 7 Subsequently, the method independently performs harmonic responsibility calculation for the three identified steady-state periods (period one: 1-240, period two: 241-480, period three: 481-720), and obtains the responsibility of each harmonic source in each period.

[0087] Referring to the accompanying drawings Figure 8 After obtaining the segmented responsibility, the overall harmonic responsibility of each harmonic source in the 24-hour period is calculated according to the weighted average algorithm considering the length of each period and the severity of harmonic pollution.

[0088] As a comparison, we use the traditional method without data segmentation to calculate, that is, the least square regression is performed on all 720 data points as a whole. The calculation result shows that the traditional method has a huge deviation from the actual situation of each period because it uses the averaged harmonic transfer impedance that does not represent any real physical state, and even incorrectly determines the background harmonic source as the main responsible party. Through accurate dynamic segmentation, the present application ensures that each responsibility calculation is based on an accurate system model that matches the current physical state, and the final overall responsibility evaluation result can fairly and reasonably reflect the comprehensive contribution of each harmonic source in the entire dynamic process. This example fully proves the necessity, advancement and reliability of the present application in dealing with dynamic changing systems.

Claims

1. A harmonic responsibility division method based on sliding window regression residual analysis, characterized in that, The method comprises the following steps: S1, synchronously collecting harmonic current injection data of a harmonic source node and harmonic voltage data of a concerned node in a power system to form a time series data set; S2, applying a sliding window regression residual analysis method to identify system grid structure change points by detecting mutations of model fitting residuals, and dividing the time series data set into multiple steady-state periods according to all identified system grid structure change points; S3, independently calculating the harmonic responsibility of the harmonic source node for each divided steady-state period; S4, time-weighted averaging the harmonic responsibilities calculated for all steady-state periods to obtain the overall harmonic responsibility of the harmonic source node in the entire evaluation period.

2. The method of claim 1, wherein, In the S2 step, the operation of applying the sliding window regression residual analysis method comprises: Setting an initial data window, and establishing a local linear regression model between the harmonic voltage of the concerned node and the harmonic current injection based on the data in the initial data window; Sliding the data window forward along the time axis to include new data, calculating the model fitting residual of the new data by using the established local linear regression model, and comparing the value of the model fitting residual with a preset residual threshold value; when the value of the model fitting residual is greater than the preset residual threshold value, the time point corresponding to the new data that causes the model fitting residual to increase is determined as a system grid structure change point.

3. The method of claim 2, wherein, The established local linear regression model is used to represent the linear relationship between the harmonic total voltage phasor of the concerned node, the harmonic current phasor injected by each harmonic source, the harmonic transfer impedance, and the background harmonic voltage phasor.

4. The method of claim 3, wherein, The harmonic transfer impedance and the background harmonic voltage phasor in the local linear regression model are solved by complex least squares method.

5. The method of claim 2, wherein, In the S2 step, before determining the data as a system grid structure change point, it further comprises: When the model fitting residual of the data is greater than the preset residual threshold value, determining that the data point is a candidate change point; Selecting a confirmation window starting from the candidate change point, and counting the number of data points in the confirmation window whose model fitting residual is greater than the preset residual threshold value; If the number of data points is greater than a preset confirmation count value, the candidate change point is formally confirmed as a real system grid structure change point.

6. The method of claim 1, wherein, In the S3 step, the harmonic responsibility of the harmonic source node is quantified by using a vector projection method, which is realized by calculating the projection of the harmonic voltage component phasor generated by the harmonic source in the direction of the total harmonic voltage phasor of the concerned node.

7. The method of claim 6, wherein, The harmonic voltage component phasor is obtained by multiplying the harmonic transfer impedance solved in the corresponding steady-state period and the harmonic current injection data measured in the corresponding steady-state period.

8. The method of claim 1, wherein, In the S4 step, the weight factor used for the time-weighted averaging is determined by the duration of each steady-state period and the average value of the harmonic voltage amplitude of the concerned node in the corresponding steady-state period.

9. The method of claim 1, wherein, In the S1 step, the harmonic current injection data include complex quantities of current amplitude and current phase angle, and the harmonic voltage data include complex quantities of voltage amplitude and voltage phase angle, and the harmonic current injection data and the harmonic voltage data are time-synchronized by a time synchronization unit to add high-precision time stamps to the data collected by the monitoring devices distributed at different nodes.

10. The method of claim 2, wherein, After the system network structure change point is determined, the data from the previous system network structure change point to the current system network structure change point are defined as a steady-state period, and the current system network structure change point is taken as the starting point of a new segment, and the operations of establishing a local linear regression model and detecting a system network structure change point are repeated until the entire time series data set is traversed.

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