Impedance-based harmonic propagation path identification method for distribution network with flexible load access

Abstract

This invention relates to the field of harmonic propagation path identification technology in distribution networks with flexible load access, and provides an impedance-based method for identifying harmonic propagation paths in distribution networks with flexible load access. The method includes: acquiring aliased harmonic signals and measured impedance data at monitoring nodes; constructing a harmonic equivalent circuit based on the impedance data to obtain impedance characteristics; using the impedance characteristics as separation constraints to perform source separation processing on the aliased harmonic signals, decomposing them into background harmonic components and load harmonic components; determining the background harmonic injection direction based on the background harmonic components; locating the load-side harmonic source nodes based on the load harmonic components; and generating the propagation path of harmonics in the power grid topology based on the injection direction and source node location. This invention can distinguish between background harmonics and load harmonics from a physical mechanism perspective, determine the harmonic injection direction and source node location, generate a complete propagation path, and achieve accurate identification of harmonic sources and diffusion directions.

Description

Technical Field

[0001] This invention relates to the field of harmonic propagation path identification technology for distribution networks with flexible load access, and in particular to an impedance-based method for identifying harmonic propagation paths in distribution networks with flexible load access. Background Technology

[0002] With the accelerated construction of new power systems, the large-scale integration of flexible loads (such as electric vehicle charging stations, distributed energy storage, and interruptible loads) into the distribution network has become a key means to improve the grid's flexible regulation capabilities. However, the widespread integration of these loads has also brought about severe power quality problems, among which harmonic pollution is particularly prominent. Unlike traditional fixed industrial harmonic sources, flexible loads are random, time-varying, and dispersed. The harmonics they generate overlap and highly aliased with the inherent background harmonics of the upstream power grid at the grid connection nodes, seriously threatening the safe operation of power equipment and potentially even triggering grid resonance accidents.

[0003] Current conventional methods for investigating harmonic issues in distribution networks mainly fall into two categories: one is to install filtering devices at specific nodes for post-event mitigation, and the other is to predict harmonic distribution based on idealized simulation models. The common logic of these methods is the assumption that the location of harmonic sources is relatively fixed and the propagation path is singular, thus allowing monitoring or filtering at a few key nodes. However, in actual operation, due to the large-scale integration of flexible loads, harmonics at distribution network nodes exhibit a complex aliasing state—background harmonics transmitted from the upstream grid and harmonics generated by the flexible loads themselves at the node are electrically superimposed. This aliasing phenomenon prevents traditional monitoring methods from effectively separating the two types of harmonics, thus blurring the direction of harmonic propagation.

[0004] Existing technologies for addressing this problem typically rely on empirical threshold judgments or simple power flow analysis. However, due to the time-varying nature of impedance parameters and the lack of on-site measured data, it is difficult to accurately determine the true source and attribution of harmonics. Therefore, with the widespread integration of flexible loads, how to effectively distinguish between harmonic components generated by the load itself and those conducted from the grid side based on on-site measured data, and thus accurately trace the initial location and subsequent propagation direction of harmonics, has become a critical technical problem that urgently needs to be solved. Summary of the Invention

[0005] Therefore, the technical problem to be solved by the present invention is to overcome the shortcomings of the prior art, which is that due to the large-scale access of flexible loads, the background harmonics and load harmonics of the distribution network are highly mixed, conventional monitoring methods cannot effectively separate the two types of harmonic components, it is difficult to accurately define the true source and propagation direction of harmonics, and it is impossible to accurately locate the harmonic source node and depict the diffusion trajectory. The present invention provides an impedance-based method for identifying the harmonic propagation path of the distribution network under flexible load access. It can effectively distinguish the background harmonics and load harmonics from the physical mechanism level by using the measured impedance data on site as the separation constraint, and at the same time determine the harmonic injection direction on the grid side and the location of the harmonic source node on the load side, thereby generating a complete harmonic propagation path and realizing accurate identification of the source and diffusion direction of harmonics.

[0006] To address the aforementioned technical problems, this invention provides a method for identifying harmonic propagation paths in distribution networks based on impedance under flexible load access, comprising the following steps: Acquire aliased harmonic signals at monitoring nodes in the distribution network, as well as measured impedance data of the monitoring nodes in the harmonic frequency band; Based on the measured impedance data, the harmonic equivalent circuits of the grid side and load side at the monitoring node are constructed to obtain the impedance characteristics of the monitoring node. Using impedance characteristics as separation constraints, source separation processing is performed on the aliased harmonic signal to decompose it into background harmonic components and load harmonic components. The direction of background harmonic injection is determined based on the amplitude and phase variation trends of background harmonic components between adjacent nodes. Based on the amplitude and timing characteristics of the load harmonic components and their correlation with the load harmonic components of other nodes, the load-side harmonic source nodes are located. Based on the background harmonic injection direction and the location of the load-side harmonic source node, the propagation path of harmonics in the power grid topology is generated.

[0007] In one embodiment of the present invention, acquiring the aliased harmonic signal at a monitoring node in a distribution network, and the measured impedance data of the monitoring node in the harmonic frequency band, includes: the aliased harmonic voltage amplitude V at the target harmonic order after Fourier transform of the three-phase voltage signal and the three-phase current signal at the monitoring node. mix aliased harmonic current amplitude I mix The measured impedance data includes the equivalent resistance R on the grid side at the monitoring node. grid and grid-side equivalent reactance X grid and the equivalent resistance R on the load side load and load-side equivalent reactance X load Among them, the equivalent impedance Z on the grid side grid =R grid +jX grid Equivalent impedance Z on the load side load =R load +jXload , where j is the imaginary unit.

[0008] In one embodiment of the present invention, impedance characteristics are used as separation constraints to perform source separation processing on the aliased harmonic signal, decomposing it into background harmonic components and load harmonic components, including: The equivalent impedance Z on the grid side in the impedance characteristics grid and the equivalent impedance Z on the load side load As known parameters, the following set of linear mixing equations is established between the aliased harmonic signal and the source signal to be separated: ; Among them, V bg The background harmonic voltage component to be solved is expressed in volts, representing the magnitude of the harmonic voltage transmitted from the upstream power grid to this monitoring node; I load The load harmonic current component to be solved is expressed in amperes, representing the magnitude of the harmonic current generated by the flexible load itself at the monitoring node. Solve the linear hybrid equation to obtain the background harmonic components and the load harmonic components.

[0009] In one embodiment of the present invention, determining the background harmonic injection direction based on the amplitude and phase variation trend of the background harmonic components between adjacent nodes includes: For two adjacent monitoring nodes, let the upstream node be node i and the downstream node be node h. The background harmonic voltage amplitude V of node i is then obtained. bg,i Phase θ bg,i and the background harmonic voltage amplitude V at node h bg,h Phase θ bg,h ; Calculate the amplitude attenuation ratio α=V bg,h / V bg,i and phase difference Δθ=θ bg,h θ bg,i If α < 1 and Δθ < 0, then it is determined that the background harmonics are injected from node i to node h; if α ≥ 1 or Δθ ≥ 0, then it is determined that there is no injection relationship from node i to node h.

[0010] In one embodiment of the present invention, the load-side harmonic source node is located based on the amplitude timing characteristics of the load harmonic components and their correlation with load harmonic components at other nodes, including: Monitoring nodes that meet the criteria for sustained high incidence are selected as candidate nodes; For each candidate node, calculate the correlation coefficient between its load harmonic current amplitude sequence and the load harmonic current amplitude sequence of each other monitoring node in the distribution network; If the absolute value of the correlation coefficient between the candidate node and all other monitoring nodes is lower than the preset threshold, the candidate node is determined to be a load-side harmonic source node. The preset threshold is a dynamic correlation threshold determined based on the normal harmonic coupling degree between distribution network nodes.

[0011] In one embodiment of the present invention, determining that a monitoring node meets the condition of continuous high incidence includes: For each monitoring node, the load harmonic current amplitude sequence I is continuously collected within T time windows. load (t), where t=1,2,...,T is the preset number of time windows, which is an integer greater than or equal to 5; To eliminate the interference of short-term random fluctuations on the judgment criterion, the root mean square value I of the sequence is calculated. rms Considering that the harmonic fluctuation amplitude caused by normal switching of flexible loads is usually within ±30%, a preset amplitude threshold I is set. th 1.5I rms ; Calculate the amplitude of the sequence that is greater than the preset amplitude threshold I. th Number of time windows N high If N high If / T≥0.8, then the monitoring node is determined to meet the condition of continuous high incidence.

[0012] In one embodiment of the present invention, the method for calculating the correlation coefficient and the method for determining the dynamic correlation threshold include: Let the candidate node be node p, and its load harmonic current amplitude sequence be I. p (k), where k = 1, 2, ..., K, and K is the sequence length; let any other monitoring node in the distribution network be node q, and its load harmonic current amplitude sequence be I. q (k); Calculate the correlation coefficient r between node p and node q. pq The formula is as follows: ; in, , are all arithmetic means; r pq The correlation coefficient is dimensionless and its value range is [ [1,1]; The dynamic correlation threshold ε is determined based on the statistical distribution of the correlation coefficients between all monitoring nodes in the distribution network, and is taken as 1.2 times the median of the absolute values ​​of all correlation coefficients; If the absolute value of the correlation coefficient between node p and all other monitoring nodes is less than ε, then node p is determined to meet the low correlation condition, and the candidate node is determined to be the load-side harmonic source node.

[0013] In one embodiment of the present invention, the propagation path of harmonics in the power grid topology is generated based on the background harmonic injection direction and the location of the load-side harmonic source node, including: The direction of background harmonic injection determines the propagation start boundary of harmonics in the power grid, and the location of the harmonic source node on the load side determines the propagation start node of harmonics in the power grid. Starting from the propagation initiation node, the propagation extends outward node by node along the line segment in the power grid topology that is consistent with the direction of background harmonic injection. The background harmonic component and load harmonic component of each node are marked at the corresponding node position according to their amplitude, forming a continuous path from the propagation initiation node to the boundary node, which serves as the propagation path of harmonics in the power grid topology.

[0014] In one embodiment of the present invention, the propagation process extends outward node by node from the propagation initiation node along the line segment in the power grid topology that is consistent with the background harmonic injection direction, specifically including: To obtain the adjacency relationship of the power grid topology, for the current node, traverse its directly connected neighboring nodes; If the direction of an adjacent node relative to the current node is the same as the direction of background harmonic injection, then the adjacent node will be included in the propagation path. Repeat the above traversal process until there are no adjacent nodes that satisfy the direction condition. The resulting sequence of consecutive nodes is the complete harmonic propagation path.

[0015] In one embodiment of the present invention, after generating the propagation path of harmonics in the power grid topology, the method further includes the following steps: The background harmonic voltage components V at each node in the generated propagation path bg and load harmonic current component I load The path map is drawn in the order of the nodes. Different colors or line widths are used to mark the harmonic contribution of each node on the path map. The darker the color or the larger the line width, the higher the harmonic amplitude at the node. The output path map is a visual identification result of the harmonic propagation path.

[0016] The technical solution of the present invention has the following advantages compared with the prior art: The impedance-based harmonic propagation path identification method for distribution networks with flexible load access described in this invention can effectively distinguish between aliased background harmonics and load harmonics in distribution networks with flexible load access from a physical mechanism perspective by using field-measured impedance data as separation constraints. Based on these separated harmonic components, it can accurately identify the injection direction and source node location of harmonics, thereby generating a complete harmonic propagation path. This method can solve the problems of ambiguous harmonic source location and unclear responsibility attribution, and achieve accurate identification of harmonic source attribution and propagation direction. Attached Figure Description

[0017] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings, wherein: Figure 1 This is a flowchart of the steps of the method for identifying harmonic propagation paths in a distribution network based on impedance under flexible load access, as described in this invention. Figure 2 This is a flowchart of the steps in this invention to perform source separation processing on aliased harmonic signals to obtain background harmonic components and load harmonic components. Figure 3 This is a flowchart of the steps for determining the background harmonic injection direction in this invention; Figure 4 This is a flowchart of the steps for locating the load-side harmonic source node in this invention; Figure 5 This is a flowchart illustrating the steps of generating the propagation path of harmonics in the power grid topology according to the present invention. Detailed Implementation

[0018] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0019] Reference Figure 1 As shown, this application proposes an impedance-based method for identifying harmonic propagation paths in distribution networks under flexible load access: First, the aliased harmonic signals at monitoring nodes in the distribution network and the measured impedance data of the node in the harmonic frequency band are acquired. The measured impedance data here are the results of actual field measurements, reflecting the equivalent electrical characteristics of the grid side and the load side at the node under actual operating conditions, providing a physical basis for subsequent signal separation.

[0020] Secondly, based on the measured impedance data, the harmonic equivalent circuits of the grid side and the load side at this node are constructed to obtain the impedance characteristics of the node. This step transforms the abstract impedance measurement value into a circuit model that can describe the physical laws of harmonic propagation, clarifying the equivalent impedance parameters of the grid side and the load side in the harmonic frequency band.

[0021] Based on this, impedance characteristics are used as separation constraints to perform source separation processing on aliased harmonic signals, decomposing them into background harmonic components and load harmonic components. The core principle here is that although background harmonics and load harmonics are aliased together at the grid connection point, they face different equivalent impedances—background harmonics are mainly affected by the grid-side impedance, while load harmonics are mainly affected by the load-side impedance. Measured impedance data can provide the differential information between these two paths. Using this as a constraint for blind source separation of aliased signals can overcome the shortcomings of traditional methods that rely solely on signal statistical characteristics while ignoring physical mechanisms, thus theoretically separating the two types of harmonic components relatively cleanly.

[0022] Subsequently, the injection direction of the background harmonics is determined based on the amplitude and phase variation trends of the background harmonic components between adjacent nodes. Since the background harmonics propagate downstream from the upstream power grid, they exhibit a regular trend of amplitude attenuation and phase lag between adjacent nodes. Analyzing this trend allows for the reverse determination of the harmonic propagation direction. Simultaneously, the load-side harmonic source node is located based on the amplitude timing characteristics of the load harmonic components and their correlation with load harmonic components at other nodes. The principle is that a true load-side harmonic source should exhibit a sustained high harmonic amplitude at that node, and due to differences in electrical distance and impedance between different load harmonic sources, their generated harmonic components should not have a significant linear correlation with each other. Using these two characteristics for joint judgment can effectively eliminate false judgments and accurately pinpoint the initial location of harmonic occurrence.

[0023] Finally, based on the background harmonic injection direction and the location of the harmonic source nodes on the load side, the complete propagation path of the harmonics in the power grid topology is generated. Thus, from separation to orientation, and then to location and trajectory generation, a complete harmonic source tracing chain is formed.

[0024] Based on the above technical solution, this application can achieve the following beneficial effects: First, by introducing on-site measured impedance data as a separation constraint, rather than simply relying on signal statistical characteristics or idealized models, it can effectively distinguish between background harmonics and load harmonics at the physical mechanism level, solving the fundamental problem that traditional monitoring methods cannot separate the two types of harmonics due to harmonic aliasing.

[0025] Second, by analyzing the propagation trend of background harmonics between adjacent nodes and the timing and correlation characteristics of load harmonics respectively, it is possible to simultaneously determine the direction of harmonic injection from the grid side and the location of harmonic source nodes from the load side, overcoming the shortcomings of the existing technology where the direction of harmonic propagation is ambiguous and the source attribution is difficult to define.

[0026] Third, the harmonic propagation path generated based on the above accurate separation and positioning has clear physical basis and measured data support, which can provide precise guidance for harmonic control of distribution networks—for example, clarifying whether to install filter devices upstream or control specific flexible loads downstream, thereby avoiding the dilemma of blind filtering and poor effect of traditional methods.

[0027] In summary, this application, without requiring additional hardware equipment, fully utilizes the measured data from existing monitoring nodes to achieve accurate identification of harmonic propagation paths in distribution networks under flexible load access scenarios.

[0028] In some embodiments described above in this application, a method is proposed to use aliased harmonic signals and measured impedance data at monitoring nodes, and to perform source separation processing on the aliased harmonic signals using impedance characteristics as separation constraints, in order to decompose them into background harmonic components and load harmonic components. However, in practical operation, two problems arise: First, if the acquired signals and data are not clearly defined and quantified, the accuracy of subsequent harmonic equivalent circuit construction and source separation processing may be insufficient, making it difficult to effectively support the identification of harmonic propagation paths. Second, how to concretely transform the abstract impedance characteristics into effective separation constraints and construct a mathematical model that can accurately separate aliased harmonic signals is a challenge. Without a clear mathematical expression and solution mechanism, the source separation process may be ambiguous, making it difficult to guarantee the accuracy and reliability of the decomposition results.

[0029] Therefore, refer to Figure 2 As shown, this application first further clarifies the specific methods for obtaining aliased harmonic signals at monitoring nodes in a distribution network, as well as the measured impedance data of the monitoring nodes in the harmonic frequency band. Specifically, obtaining the aliased harmonic signals includes: performing Fourier transforms on the three-phase voltage and three-phase current signals at the monitoring node to obtain the aliased harmonic voltage amplitude V at the target harmonic order. mix and the amplitude of aliased harmonic current I mix Among them, three-phase voltage and three-phase current signals are the raw electrical data actually measured in the distribution network, usually acquired by high-precision sensors (such as voltage transformers and current transformers). Fourier transform is a mathematical tool that converts time-domain signals into frequency-domain signals. It can decompose complex periodic waveforms into a series of sinusoidal wave components of different frequencies, thereby accurately extracting the amplitude and phase information of specific harmonic orders. The selection of the target harmonic order is usually based on common harmonic pollution types in the distribution network or specific analysis requirements. For example, for distribution networks with a large number of nonlinear loads, it may be necessary to focus on characteristic harmonics such as the 3rd, 5th, and 7th harmonics. The amplitude V of aliased harmonic voltage... mix and the amplitude of aliased harmonic current Imix This represents the total harmonic voltage and current intensity at the monitoring node at a specific harmonic frequency, and these are the basic inputs for subsequent harmonic source separation.

[0030] Meanwhile, the measured impedance data was clarified to include the equivalent resistance R on the grid side at the monitoring node. grid and grid-side equivalent reactance X grid and the equivalent resistance R on the load side load and load-side equivalent reactance X load Equivalent resistance R on the grid side grid and grid-side equivalent reactance X grid This characterizes the equivalent impedance characteristics viewed from the monitoring node towards the upstream power grid. These parameters can be calculated using information such as the distribution network topology, line parameters, transformer parameters, and short-circuit capacity, or obtained by injecting disturbance signals online and measuring the response. Load-side equivalent resistance R load and load-side equivalent reactance X load This characterizes the equivalent impedance characteristics of the flexible load connected to the monitoring node. These parameters can be obtained by measuring and calculating the load's voltage and current, or by modeling the flexible load's operating mode and control strategy. These resistance and reactance values ​​are key parameters for constructing the harmonic equivalent circuit. Based on this, the grid-side equivalent impedance Z... grid Defined as R grid +jX grid Equivalent impedance Z on the load side load Defined as R load +jX load , where j is the imaginary unit. This complex form of impedance representation can fully encompass the amplitude and phase information of the impedance, providing a precise mathematical basis for subsequent harmonic equivalent circuit modeling and source separation.

[0031] Furthermore, this application proposes a step of using impedance characteristics as a separation constraint to perform source separation processing on aliased harmonic signals, decomposing them into background harmonic components and load harmonic components. Specifically, this includes: separating the grid-side equivalent impedance Z from the impedance characteristics. grid and the equivalent impedance Z on the load side load As known parameters, the following set of linear mixing equations is established between the aliased harmonic signal and the source signal to be separated: ; Among them, V bg The background harmonic voltage component to be solved is expressed in volts, representing the magnitude of the harmonic voltage transmitted from the upstream power grid to this monitoring node; I loadThe load harmonic current component to be solved is expressed in amperes, representing the magnitude of the harmonic current generated by the flexible load itself at the monitoring node. Subsequently, the linear hybrid equation is solved to obtain the background harmonic component and the load harmonic component.

[0032] Among them, the equivalent impedance Z on the grid side grid and the equivalent impedance Z on the load side load These are key parameters characterizing the electrical properties of the power grid and loads at the monitoring nodes. Treating them as known parameters means that these impedance values ​​are obtained beforehand through measurement or estimation during harmonic source separation and are directly substituted into the separation model. This approach simplifies the complex harmonic source separation problem into a signal decomposition problem under known system parameters, thereby improving the determinism and operability of the separation process.

[0033] The linear hybrid equations in this embodiment are established based on the harmonic equivalent circuit model at the monitoring node. Wherein, V mix and I mix These are the aliased harmonic voltage amplitude and aliased harmonic current amplitude, which can be directly measured at the monitoring node; they are known input quantities. V bg and I load These are the unknowns to be solved, representing the background harmonic voltage component from the upstream power grid and the load harmonic current component generated by the local load, respectively. The first equation V... mix =Z grid ·I load +V bg This describes the voltage balance relationship at the monitoring node, namely the aliased harmonic voltage V. mix Equal to background harmonic voltage V bg With load harmonic current I load Equivalent impedance Z flowing through the grid side grid The sum of the voltage drops produced. The second equation I mix =I load +V bg / Z load This describes the current balance relationship at the monitoring node, i.e., the aliased harmonic current I. mix Equal to load harmonic current I load With background harmonic voltage V bg Equivalent impedance Z acting on the load side load The sum of the currents generated. These two equations together constitute a complete mathematical model that reflects the harmonic mixing mechanism.

[0034] Once the above system of linear mixed equations is established, it can be solved using standard linear algebra methods. This system of equations contains two complex equations and two complex unknowns (V...). bg and I loadTherefore, it can be solved using various mathematical tools such as matrix inversion, substitution elimination, or Cramer's rule. For example, V can be solved from the second equation. bg =Z load ·(I mix -I load Then substitute it into the first equation to get V. mix =Z grid ·I load +Z load ·(I mix -I load Further refinement yields V. mix -Z load ·I mix =(Z grid -Z load )·I load Therefore, I can be solved. load =(V mix -Z load ·I mix ) / (Z grid -Z load ). After obtaining I load Then, bring it back to V. bg V can be obtained from the expression. bg In this way, the aliased harmonic signal is precisely decomposed into background harmonic components and load harmonic components.

[0035] In some of the embodiments described above in this application, it is necessary to determine the background harmonic injection direction based on the amplitude and phase variation trends of the background harmonic components between adjacent nodes. However, in actual power distribution networks, the propagation of harmonic signals is affected by various factors such as line impedance and topology. Simply observing amplitude or phase changes may not accurately and reliably determine the actual injection direction of harmonics, which can easily lead to misjudgments and thus affect the accurate generation of subsequent harmonic propagation paths.

[0036] Reference Figure 3 As shown, this application further proposes a specific method for determining the background harmonic injection direction, which includes: First, for two adjacent monitoring nodes, let the upstream node be node i and the downstream node be node h, and obtain the background harmonic voltage amplitude V of node i respectively. bg,i Phase θ bg,i and the background harmonic voltage amplitude V at node h bg,h Phase θ bg,hThis step aims to clarify the observation objects and data sources for determining the direction of harmonic injection. In distribution networks, monitoring nodes typically acquire data through harmonic monitoring devices installed in critical locations. The relative positions of upstream node i and downstream node h are predetermined based on the network topology and power flow direction. Background harmonic voltage amplitude V bg,i Phase θ bg,i and V bg,h θ bg,h These are the pure background harmonic components obtained after source separation processing; they represent the behavior of harmonics from the power grid at these nodes. Acquiring this data is the basis for subsequent direction determination.

[0037] Secondly, calculate the amplitude attenuation ratio α=V bg,h / V bg,i and phase difference Δθ=θ bg,h θ bg,i This step is crucial for quantifying the propagation characteristics of harmonics between nodes. The amplitude attenuation ratio α reflects the degree of energy loss of the harmonic voltage as it propagates from node i to node h. In passive lines, the harmonic voltage is typically attenuated due to line impedance, so the value of α is usually less than 1. The phase difference Δθ reflects the phase shift of the harmonic signal during propagation caused by line reactance. In a typical inductive distribution network, the harmonic current flowing through the line impedance will cause a voltage drop, resulting in the voltage phase of downstream nodes lagging behind that of upstream nodes; that is, Δθ is usually negative. By calculating these two parameters, a quantitative basis can be provided for subsequent injection direction determination.

[0038] If α < 1 and Δθ < 0, then the background harmonics are determined to be injected from node i to node h. This condition is the core criterion for determining whether background harmonics are injected from upstream node i to downstream node h. When harmonics propagate from upstream to downstream, the harmonic voltage amplitude attenuates due to the line impedance, resulting in a smaller amplitude at the downstream node than at the upstream node (i.e., α < 1). Simultaneously, due to the inductive characteristics of the line, the phase of the harmonic voltage lags, causing the phase at the downstream node to lag behind that at the upstream node (i.e., Δθ < 0). The simultaneous satisfaction of these two conditions indicates that the harmonic energy and phase changes conform to the physical laws of propagation from upstream to downstream, thus reliably determining the direction of harmonic injection.

[0039] Finally, if α ≥ 1 or Δθ ≥ 0, it is determined that there is no injection relationship from node i to node h. This condition excludes the case where background harmonics are injected from upstream node i to downstream node h. If the amplitude attenuation ratio α is greater than or equal to 1, it means that the harmonic voltage amplitude of the downstream node has not attenuated or even increased, which does not conform to the typical attenuation characteristics of propagation from upstream to downstream. If the phase difference Δθ is greater than or equal to 0, it means that the harmonic voltage phase of the downstream node has not lagged or even led, which also does not conform to the typical propagation characteristics of inductive lines. In these cases, it can be considered that the background harmonics are not simply injected from node i to node h; there may be other complex harmonic sources or propagation paths, or the harmonics may propagate from downstream to upstream. Therefore, it is determined that there is no injection relationship from node i to node h, avoiding misjudgment.

[0040] In some embodiments described above in this application, a method for locating load-side harmonic source nodes is proposed based on the amplitude timing characteristics of load harmonic components and their correlation with harmonic components of other node loads. However, in actual distribution networks, the complexity of harmonic signals, the coupling effect between nodes, and the diversity of flexible load behavior make it difficult to accurately distinguish between the true harmonic source and the nodes affected by harmonics simply based on amplitude or correlation characteristics, which may lead to misjudgment or inaccurate location.

[0041] Reference Figure 4 As shown, this application further proposes a step for locating load-side harmonic source nodes based on the amplitude and timing characteristics of load harmonic components and their correlation with load harmonic components of other nodes. The steps include: selecting monitoring nodes that meet the condition of continuous high occurrence as candidate nodes; for each candidate node, calculating the correlation coefficient between its load harmonic current amplitude sequence and the load harmonic current amplitude sequence of each other monitoring node in the distribution network; if the absolute value of the correlation coefficient between the candidate node and all other monitoring nodes is lower than a preset threshold, then the candidate node is determined as a load-side harmonic source node, wherein: the preset threshold is a dynamic correlation threshold determined based on the normal harmonic coupling degree between nodes in the distribution network.

[0042] Specifically, this step aims to preliminarily screen potential harmonic source nodes when selecting monitoring nodes that meet the sustained high-incidence condition as candidate nodes. A true harmonic source typically generates a consistently high level of harmonic current. By setting the sustained high-incidence condition, nodes that consistently and frequently exhibit high harmonic current levels can be identified, thus distinguishing them from nodes that occasionally exhibit high harmonics due to transient events or harmonic propagation. For example, a time window can be set within which the load harmonic current amplitude of a monitoring node exceeds a certain preset threshold for a specified duration or frequency. If this duration or frequency reaches a certain proportion, the node is considered to meet the sustained high-incidence condition. This screening mechanism helps reduce the complexity of subsequent calculations and improves the accuracy of source identification.

[0043] In this embodiment, a method is proposed to determine whether a monitoring node meets the condition of continuous high incidence, specifically including: for each monitoring node, continuously collecting the load harmonic current amplitude sequence I within T time windows. load (t), where t=1,2,..., T is the preset number of time windows, taking values ​​greater than or equal to 5; to eliminate the interference of short-term random fluctuations on the judgment benchmark, the root mean square value I of the sequence is calculated. rms Considering that the harmonic fluctuation amplitude caused by normal switching of flexible loads is usually within ±30%, a preset amplitude threshold I is set. th 1.5I rms ; Calculate the amplitude of the sequence that is greater than the preset amplitude threshold I. th Number of time windows N high If N high If / T≥0.8, then the monitoring node is determined to meet the condition of continuous high incidence.

[0044] Specifically, the load harmonic current amplitude sequence I is continuously collected within T time windows. load (t) aims to acquire the dynamic behavior of harmonic currents at monitoring nodes over a period of time. By observing data from multiple time windows, the random errors caused by judging based on instantaneous values ​​at a single moment can be avoided, thus providing a more comprehensive reflection of the persistence characteristics of harmonic currents. The preset number of time windows T is set to an integer greater than or equal to 5 to ensure sufficient data samples to assess the persistence of harmonics. For example, it can be set to 10 or 20 time windows, each lasting from several seconds to several minutes, depending on the rate of change of harmonics in the distribution network and the sampling capability of the monitoring system. Root mean square value I rms The root mean square (RMS) value is a commonly used method for measuring the effective value of alternating current (AC). It reflects the average energy level of harmonic current over a period of time. This is achieved by calculating the RMS value of the sequence. rms This effectively smooths out the impact of short-term transient peaks or troughs, providing a relatively stable benchmark for subsequent threshold setting and persistence assessment. This approach makes the assessment of harmonic levels more robust and less susceptible to transient disturbances. Preset amplitude threshold I th The setting of the threshold I is one of the core aspects of this method. Considering that the amplitude of the harmonic current generated by the flexible load during normal operation, such as during switching operations, usually fluctuates within a certain range, this application sets this fluctuation range to within ±30%. Therefore, the threshold I is set... th Set to root mean square value I rms 1.5 times, that is, I th =1.5·I rmsThis is designed to distinguish between normal fluctuations and truly sustained high-frequency harmonics. If the harmonic amplitude consistently exceeds this threshold, it indicates that it has significantly exceeded the normal operating fluctuation range, potentially indicating the presence of sustained harmonic emission. This is determined by statistically analyzing how many time windows within a given T time window have load harmonic current amplitudes greater than a preset amplitude threshold I. th , to obtain N high Then, calculate N. high The ratio of N to T. If this ratio N high If / T is greater than or equal to 0.8 (i.e., 80%), the monitoring node is considered to meet the condition of continuous high harmonic occurrence. This criterion ensures that only nodes whose harmonic amplitude is consistently higher than the normal fluctuation range for the vast majority of observation time are identified as sources of continuous high harmonic occurrence. This effectively excludes cases of instantaneous high amplitude caused by occasional events or short-term disturbances, thereby improving the accuracy and reliability of harmonic source identification.

[0045] This step, calculating the correlation coefficient between the load harmonic current amplitude sequence of each candidate node and the load harmonic current amplitude sequences of every other monitoring node in the distribution network, aims to quantify the statistical correlation of harmonic current emissions between the candidate node and all other monitoring nodes. An independent harmonic source, whose harmonic current generation primarily stems from its own internal characteristics, should exhibit low correlation between its harmonic current amplitude sequence and the harmonic current amplitude sequences of other nodes. Conversely, if a node's harmonic current is mainly propagated from other sources, it will show high correlation with that source node or other nodes along the propagation path. The correlation coefficient can be calculated using standard statistical methods such as the Pearson correlation coefficient, which measures the degree of linear correlation by comparing the synchronous trends of the two time series.

[0046] In this embodiment, a method for calculating the correlation coefficient and a method for determining the dynamic correlation threshold are proposed, specifically including: assuming the candidate node is node p, and its load harmonic current amplitude sequence is I. p (k), where k = 1, 2, ..., K, and K is the sequence length; let any other monitoring node in the distribution network be node q, and its load harmonic current amplitude sequence be I. q (k); Calculate the correlation coefficient r between node p and node q. pq The formula is as follows: ; in, All are arithmetic means; r pq The correlation coefficient is dimensionless and its value range is [ [1,1]. The dynamic correlation threshold ε is determined based on the statistical distribution of the correlation coefficients between all monitoring nodes in the distribution network, and is set to 1.2 times the median of the absolute values ​​of all correlation coefficients. If the absolute value of the correlation coefficient between node p and all other monitoring nodes is less than ε, then node p is deemed to meet the low correlation condition, and the candidate node is identified as a load-side harmonic source node.

[0047] Specifically, the correlation coefficient r pq The calculation formula aims to quantify the amplitude sequences of two load harmonic currents. Ip (k) and I q The formula describes the linear correlation between (k) and the two sequences. It uses the Pearson correlation coefficient to calculate a dimensionless value between -1 and 1 by dividing the product of the covariance of the two sequences by their respective standard deviations. This value directly reflects the consistency or oppositeity in the trends of the two sequences, providing a precise mathematical basis for determining the harmonic coupling relationship between nodes. In practice, this calculation can be implemented using statistical functions in data processing software or programming languages. The sequence length K should be chosen sufficiently to capture the dynamic characteristics of the harmonic current; for example, it can be determined based on the data acquisition frequency and the typical fluctuation period of the harmonic source.

[0048] The method for determining the dynamic correlation threshold ε aims to provide an adaptive criterion. This threshold is not a fixed value, but rather dynamically determined based on the statistical distribution of the correlation coefficients between the load harmonic current amplitude sequences of all monitoring nodes in the distribution network. First, the correlation coefficients r between all monitoring nodes in the distribution network are calculated. pq The absolute values ​​of these values ​​are used to form a dataset. Then, the median of this dataset is calculated. The median, as a robust statistic, effectively reflects the general harmonic coupling level in the distribution network and is not easily affected by extreme values. Finally, this median is multiplied by 1.2 to obtain the dynamic correlation threshold ε. The coefficient 1.2 is an empirical value designed to provide a margin to ensure effective differentiation between strong and weak coupling, while avoiding misclassifying normally coupled nodes as independent harmonic sources. This coefficient can also be adjusted appropriately based on the actual operating characteristics of a specific distribution network.

[0049] Determining that node p meets the low correlation condition is the final logical step in identifying load-side harmonic source nodes. For a node p selected as a candidate node, its load harmonic current amplitude sequence needs to be correlated with the load harmonic current amplitude sequences of all monitoring nodes q in the distribution network except p. If the correlation coefficient r between node p and all other monitoring nodes q is low... pq If the absolute value of each node is less than the preset dynamic correlation threshold ε, then the harmonic behavior of node p is considered to have a low correlation with other nodes, meaning that it is more likely to generate harmonics on its own, and thus it is identified as a load-side harmonic source node.

[0050] After identifying the background harmonic injection direction and the location of the load-side harmonic source node, refer to Figure 5 As shown, this application further proposes a method for generating the propagation path of harmonics in the power grid topology based on the background harmonic injection direction and the location of the load-side harmonic source node. The method includes: determining the propagation starting boundary of harmonics in the power grid based on the background harmonic injection direction, and determining the propagation starting node of harmonics in the power grid based on the location of the load-side harmonic source node; starting from the propagation starting node, extending outward node by node along the line segment in the power grid topology that is consistent with the background harmonic injection direction, and marking the background harmonic component and load harmonic component of each node at the corresponding node position according to their amplitude, forming a continuous path from the propagation starting node to the boundary node, which serves as the propagation path of harmonics in the power grid topology.

[0051] This step aims to clarify the starting point and boundary conditions of harmonic propagation. The background harmonic injection direction refers to the direction of harmonic energy flow determined by analyzing the amplitude and phase variation trends of background harmonic components between adjacent nodes. It defines the macroscopic trend and boundary of harmonics entering from the external power grid or propagating within the grid. For example, if a monitoring node receives background harmonic injection from the upstream power grid, that upstream connection point can be considered the starting boundary of harmonic propagation. The load-side harmonic source node location refers to the specific node where the harmonic source generated by the flexible load itself is located, determined by analyzing the amplitude and timing characteristics of the load harmonic components and their correlation with the load harmonic components of other nodes. These nodes are the specific sources of harmonic generation within the distribution network and are therefore identified as the starting nodes of harmonic propagation. By combining these two types of information, the starting point and range of harmonic propagation can be comprehensively defined.

[0052] This step describes the core process of constructing harmonic propagation paths. The propagation initiation node is the load-side harmonic source node identified in the previous step. Starting from these source nodes, the system explores line segments that align with the direction of background harmonic injection, based on the physical or logical connections of the distribution network (i.e., the "adjacency relationships of the network topology"). This means that if the background harmonics exhibit a trend of flowing from node A to node B on a certain line segment, then the connection from node A to node B will be prioritized when constructing the path. This node-by-node outward expansion ensures that the generated path is based on the actual harmonic flow direction, rather than a simple shortest path or topological connection.

[0053] Specifically, the adjacency relationships in a power grid topology refer to the connections between various nodes (such as buses, substations, and user access points) and between nodes and lines in a distribution network. These relationships can typically be obtained from a Geographic Information System (GIS), Supervisory Control and Data Acquisition (SCADA) system, or a pre-established network model. Adjacency relationships can be represented as an adjacency matrix or adjacency list, recording which nodes are directly connected by lines and the attributes of these lines (such as length and impedance). Obtaining this information is fundamental for network traversal and path identification. After determining the propagation starting node, it is necessary to systematically explore its surrounding connections, starting from that node. For the currently processed node, the algorithm queries its adjacency relationship data to find all other nodes directly connected to it by a line, thus traversing its directly connected neighboring nodes. This process ensures a comprehensive examination of all possible extension directions of the current node and is a crucial step in path construction. When traversing the neighboring nodes of the current node, it is necessary to determine whether each neighboring node meets the conditions for harmonic propagation. Here, "same direction" means that, based on a pre-determined background harmonic injection direction, if the direction of the line segment from the current node to an adjacent node is consistent with the injection direction of the background harmonics, then that adjacent node is considered the next valid node on the harmonic propagation path. For example, if the background harmonics are injected from upstream to downstream, only adjacent nodes downstream of the current node will be included in the propagation path. This judgment mechanism ensures the physical rationality of the constructed path, i.e., that the harmonics propagate along their injection direction. Once an adjacent node is included in the propagation path, it becomes the new current node, and the above traversal and judgment process is repeated to continue expanding outward. This process continues until at a certain node, all its directly connected adjacent nodes no longer satisfy the condition that their direction is the same as the injection direction of the background harmonics. This means that the harmonic propagation has reached the end in that direction or encountered a topological boundary. At this point, the series of consecutive nodes formed from the propagation start node to the current end node constitutes a complete harmonic propagation path.

[0054] This step aims to provide quantified harmonic information for the generated propagation path. During path construction, for each node on the path, the amplitude data of the previously separated background harmonic components and load harmonic components are extracted and associated with that node. This annotation can be data storage, visual markers, or any method that can map harmonic amplitude information to node locations. In this way, users can not only see the harmonic propagation path but also intuitively understand the intensity and source composition of harmonics at each point on the path.

[0055] This step is the final result of the aforementioned expansion process. Through continuous node-by-node expansion until a pre-defined boundary node is encountered (e.g., an external connection point of the power grid, or a point where the harmonic amplitude significantly attenuates and the direction is no longer consistent), a complete and uninterrupted sequence of nodes and connecting segments will be formed from the harmonic source (propagation initiation node) to the edge of its influence range (boundary node). This continuous path is the actual propagation path of the harmonic in the distribution network identified by this method, clearly showing the flow trajectory of harmonic energy.

[0056] In practical applications, after generating the propagation path of harmonics in the power grid topology, the background harmonic voltage components V at each node in the generated propagation path are... bg and load harmonic current component I load The path map is drawn according to the node order, and the harmonic contribution of each node is marked with different colors or line widths on the path map. The darker the color or the larger the line width, the higher the harmonic amplitude at the node. Finally, the path map is output as a visual identification result of the harmonic propagation path.

[0057] Specifically, the background harmonic voltage components V of each node bg and load harmonic current component I load The harmonics are arranged according to their topological order in the propagation path, and their values ​​are mapped onto visual elements of the graph. For example, a two-dimensional graph can be constructed, with one axis representing the sequence of nodes along the path and the other axis representing the amplitude of the harmonic components, thus forming an intuitive curve or bar chart. Alternatively, the path can be directly represented graphically on the power grid topology map, and each node or connecting segment along the path can be visually encoded. To further enhance the intuitiveness of the information, this application uses different colors or line widths to represent the degree of harmonic contribution of each node. For example, a color gradient can be set, gradually transitioning from light colors corresponding to low harmonic amplitudes to dark colors corresponding to high harmonic amplitudes; or, by adjusting the size of the node markers or the thickness of the connecting segments along the path, nodes or segments with higher harmonic amplitudes can be displayed as thicker or larger. This visual encoding method allows users to quickly identify the severity of harmonic pollution and key nodes. Finally, this path graph with rich visual information is output as the identification result of the harmonic propagation path, which can be displayed on a monitoring interface or generated as a report file.

[0058] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A method for identifying harmonic propagation paths in a distribution network based on impedance under flexible load access, characterized in that, Includes the following steps: Acquire aliased harmonic signals at monitoring nodes in the distribution network, as well as measured impedance data of the monitoring nodes in the harmonic frequency band; Based on the measured impedance data, the harmonic equivalent circuits of the grid side and load side at the monitoring node are constructed to obtain the impedance characteristics of the monitoring node. Using impedance characteristics as separation constraints, source separation processing is performed on the aliased harmonic signal to decompose it into background harmonic components and load harmonic components. The direction of background harmonic injection is determined based on the amplitude and phase variation trends of background harmonic components between adjacent nodes. Based on the amplitude and timing characteristics of the load harmonic components and their correlation with the load harmonic components of other nodes, the load-side harmonic source nodes are located. Based on the background harmonic injection direction and the location of the load-side harmonic source node, the propagation path of harmonics in the power grid topology is generated.

2. The method for identifying harmonic propagation paths in distribution networks based on impedance under flexible load access as described in claim 1, characterized in that: Acquire the aliased harmonic signals at monitoring nodes in the distribution network, as well as the measured impedance data of the monitoring nodes in the harmonic frequency band, including: the aliased harmonic voltage amplitude V at the target harmonic order after Fourier transform of the three-phase voltage and three-phase current signals at the monitoring node. mix aliased harmonic current amplitude I mix The measured impedance data includes the equivalent resistance R on the grid side at the monitoring node. grid and grid-side equivalent reactance X grid and the equivalent resistance R on the load side load and load-side equivalent reactance X load Among them, the equivalent impedance Z on the grid side grid =R grid +jX grid Equivalent impedance Z on the load side load =R load +jX load , where j is the imaginary unit.

3. The method for identifying harmonic propagation paths in distribution networks based on impedance under flexible load access as described in claim 2, characterized in that: Using impedance characteristics as a separation constraint, source separation processing is performed on the aliased harmonic signal to decompose it into background harmonic components and load harmonic components, including: The equivalent impedance Z on the grid side in the impedance characteristics grid and the equivalent impedance Z on the load side load As known parameters, the following set of linear mixing equations is established between the aliased harmonic signal and the source signal to be separated: ； Among them, V bg The background harmonic voltage component to be solved is expressed in volts, representing the magnitude of the harmonic voltage transmitted from the upstream power grid to this monitoring node; I load The load harmonic current component to be solved is expressed in amperes, representing the magnitude of the harmonic current generated by the flexible load itself at the monitoring node. Solve the linear mixing equations to obtain the background harmonic components and the load harmonic components.

4. The method for identifying harmonic propagation paths in distribution networks based on impedance under flexible load access as described in claim 1, characterized in that: Based on the amplitude and phase variation trends of background harmonic components between adjacent nodes, the background harmonic injection direction is determined, including: For two adjacent monitoring nodes, let the upstream node be node i and the downstream node be node h. The background harmonic voltage amplitude V of node i is then obtained. bg,i Phase θ bg,i and the background harmonic voltage amplitude V at node h bg,h Phase θ bg,h ; Calculate the amplitude attenuation ratio α=V bg,h / V bg,i and phase difference Δθ=θ bg,h θ bg,i If α < 1 and Δθ < 0, then it is determined that the background harmonics are injected from node i to node h; if α ≥ 1 or Δθ ≥ 0, then it is determined that there is no injection relationship from node i to node h.

5. The method for identifying harmonic propagation paths in distribution networks based on impedance under flexible load access as described in claim 1, characterized in that: Based on the amplitude and timing characteristics of load harmonic components and their correlation with load harmonic components at other nodes, the load-side harmonic source nodes are located, including: Monitoring nodes that meet the criteria for sustained high incidence are selected as candidate nodes; For each candidate node, calculate the correlation coefficient between its load harmonic current amplitude sequence and the load harmonic current amplitude sequence of each other monitoring node in the distribution network; If the absolute value of the correlation coefficient between the candidate node and all other monitoring nodes is lower than the preset threshold, the candidate node is determined to be a load-side harmonic source node. The preset threshold is a dynamic correlation threshold determined based on the normal harmonic coupling degree between distribution network nodes.

6. The method for identifying harmonic propagation paths in a distribution network based on impedance under flexible load access as described in claim 5, characterized in that: The criteria for determining whether a monitoring node meets the conditions for a sustained high incidence include: For each monitoring node, the load harmonic current amplitude sequence I is continuously collected within T time windows. load (t), where t=1,2,...,T is the preset number of time windows, which is an integer greater than or equal to 5; To eliminate the interference of short-term random fluctuations on the judgment criterion, the root mean square value I of the sequence is calculated. rms Considering that the harmonic fluctuation amplitude caused by normal switching of flexible loads is usually within ±30%, a preset amplitude threshold I is set. th 1.5I rms ; Calculate the amplitude of the sequence that is greater than the preset amplitude threshold I. th Number of time windows N high If N high If / T≥0.8, then the monitoring node is determined to meet the condition of continuous high incidence.

7. The method for identifying harmonic propagation paths in a distribution network based on impedance under flexible load access as described in claim 5, characterized in that: The methods for calculating the correlation coefficient and determining the dynamic correlation threshold include: Let the candidate node be node p, and its load harmonic current amplitude sequence be I. p (k), where k = 1, 2, ..., K, and K is the sequence length; let any other monitoring node in the distribution network be node q, and its load harmonic current amplitude sequence be I. q (k); Calculate the correlation coefficient r between node p and node q. pq The formula is as follows: ; in, , are all arithmetic means; r pq The correlation coefficient is dimensionless and its value range is [ [1,1]; The dynamic correlation threshold ε is determined based on the statistical distribution of the correlation coefficients between all monitoring nodes in the distribution network, and is taken as 1.2 times the median of the absolute values ​​of all correlation coefficients; If the absolute value of the correlation coefficient between node p and all other monitoring nodes is less than ε, then node p is determined to meet the low correlation condition, and the candidate node is determined to be the load-side harmonic source node.

8. The method for identifying harmonic propagation paths in distribution networks based on impedance under flexible load access as described in claim 1, characterized in that: Based on the background harmonic injection direction and the location of the load-side harmonic source node, the propagation path of harmonics in the power grid topology is generated, including: The direction of background harmonic injection determines the propagation start boundary of harmonics in the power grid, and the location of the harmonic source node on the load side determines the propagation start node of harmonics in the power grid. Starting from the propagation initiation node, the propagation extends outward node by node along the line segment in the power grid topology that is consistent with the direction of background harmonic injection. The background harmonic component and load harmonic component of each node are marked at the corresponding node position according to their amplitude, forming a continuous path from the propagation initiation node to the boundary node, which serves as the propagation path of harmonics in the power grid topology.

9. The method for identifying harmonic propagation paths in a distribution network based on impedance under flexible load access as described in claim 8, characterized in that: Starting from the propagation initiation node, the propagation extends outward node by node along the line segment in the power grid topology that is consistent with the direction of background harmonic injection, specifically including: To obtain the adjacency relationship of the power grid topology, for the current node, traverse its directly connected neighboring nodes; If the direction of an adjacent node relative to the current node is the same as the direction of background harmonic injection, then the adjacent node will be included in the propagation path. Repeat the above traversal process until there are no adjacent nodes that satisfy the direction condition. The resulting sequence of consecutive nodes is the complete harmonic propagation path.

10. The method for identifying harmonic propagation paths in a distribution network based on impedance under flexible load access as described in claim 1, characterized in that: After generating the propagation path of harmonics in the power grid topology, the following steps are also included: The background harmonic voltage components V at each node in the generated propagation path bg and load harmonic current component I load The path map is drawn in the order of the nodes. Different colors or line widths are used to mark the harmonic contribution of each node on the path map. The darker the color or the larger the line width, the higher the harmonic amplitude at the node. The output path map is a visual identification result of the harmonic propagation path.

Images