Method, device and system for identifying main cause of harmonic exceeding of nodes of power distribution network and medium

Abstract

The invention provides a power distribution network node harmonic exceeding main cause identification method, device and system and a medium, and the method comprises the steps: building a node admittance matrix based on the node harmonic voltage and branch current monitoring data of a power distribution network, building a related equation of the harmonic voltage and an injection current, and employing a compressed sampling matching pursuit algorithm to identify the harmonic exceeding main cause of the power distribution network; solving a sparse harmonic injection current vector, and calculating a node harmonic voltage distortion rate according to a harmonic current injection value so as to judge a standard exceeding condition; through a modal analysis method, harmonic current threshold comparison and multi-frequency superposition effect analysis, identifying main factors exceeding the standard, including harmonic injection standard exceeding, multi-frequency superposition and resonance phenomena; and quantizing contribution degrees of resonance and harmonic injection, and distinguishing composite causes of harmonic exceeding. According to the method, the problem that the harmonic cause is unknown in the harmonic exceeding scene is solved, and the accuracy of the harmonic exceeding cause is remarkably improved. Through simulation and actual measurement verification, the accuracy of the method provided by the invention is verified.

Description

Technical Field

[0001] This invention belongs to the field of power system power quality analysis and management technology. Specifically, this invention relates to a method, device, system and medium for identifying the main causes of harmonic exceedance at distribution network nodes. It is used to accurately identify the causes of harmonic exceedance at each node in the distribution network, provide technical support for targeted management, and thus effectively improve power quality. Background Technology

[0002] With the increasing number of nonlinear loads in power distribution networks, harmonic issues have become a significant factor affecting power quality. The presence of harmonics not only reduces the efficiency of power equipment but can also cause equipment damage, system overload, and even power equipment failure, severely impacting the normal operation of the power distribution network. Currently, harmonic mitigation technologies in power distribution networks mainly include harmonic source identification and control, filter installation, and system optimization. However, most existing methods only provide general identification of harmonic sources, lacking precise identification of the specific causes of harmonic exceedances. Common influencing factors for harmonic exceedances include current exceedances caused by nonlinear loads, the superposition effect of multiple harmonic currents, and resonance phenomena. These factors are often intertwined, making the diagnosis of harmonic exceedances complex.

[0003] Traditional harmonic mitigation methods typically rely on experience or simple rules for decision-making, lacking effective intelligent analysis tools, resulting in poor mitigation outcomes and often requiring a long time to identify the root cause of the problem. Therefore, accurately identifying the main causes of harmonic exceedances at each node in the distribution network and providing an effective basis for subsequent mitigation has become an important research topic in current power systems.

[0004] To address the aforementioned issues, a method for identifying the root causes of harmonic exceedances at distribution network nodes is proposed. Through precise calculation and multi-factor analysis of harmonic current injection, the fundamental causes of harmonic exceedances can be effectively identified, providing a scientific basis and technical solutions for harmonic mitigation in distribution networks.

[0005] Terminology Explanation:

[0006] Harmonics: In a power system, harmonic distortions in current or voltage waveforms whose frequencies are integer multiples of the fundamental frequency. Harmonics are typically caused by nonlinear loads (such as rectifiers and frequency converters). The presence of harmonics affects the power quality of the distribution network, leading to problems such as power equipment losses, overheating, and malfunctions.

[0007] Harmonic current injection: The injection of high-order harmonic currents caused by nonlinear loads, which leads to distortion of the voltage or current waveforms at certain nodes in the distribution network.

[0008] CoSaMP algorithm: A signal recovery algorithm based on the sparsity assumption, used to recover sparse signals from a small amount of linear measurement data.

[0009] Resonance: In a power distribution network, harmonic currents of certain frequencies resonate with the natural frequency of the grid, causing the harmonic current or voltage to be amplified at that specific frequency, leading to excessive harmonics. Resonance typically occurs when the system's natural frequency is close to the external excitation frequency.

[0010] Modal analysis: a method for identifying resonance phenomena in power distribution networks. By analyzing the eigenvalues ​​and eigenvectors of the admittance matrix of power distribution network nodes, it is possible to determine whether the system is resonating and to identify the frequency and location of the resonance. Summary of the Invention

[0011] This invention provides a method, device, system, and medium for identifying the root causes of harmonic exceedances at distribution network nodes. The aim is to provide a scientific basis for harmonic mitigation by accurately identifying the causes of harmonic exceedances at nodes in the distribution network, thereby effectively improving the power quality of the distribution network. This method can effectively diagnose the fundamental factors causing harmonic exceedances in the distribution network and provide targeted technical solutions for subsequent harmonic mitigation, thus effectively improving power quality, reducing the impact of harmonics on power equipment, and enhancing the operational stability and reliability of the distribution network.

[0012] The technical solution adopted in this invention is as follows:

[0013] A method for identifying the main causes of excessive harmonics at distribution network nodes includes the following steps:

[0014] (1) Data acquisition and preprocessing: Deploy harmonic monitoring devices in the distribution network, collect harmonic voltage and branch harmonic current data of monitoring nodes and adjacent nodes, construct node admittance matrix based on distribution network topology and determine branch current connection relationship matrix;

[0015] (2) Solution of harmonic injection current vector: Based on Kirchhoff's laws, establish the correlation equation between node harmonic voltage and harmonic injection current, construct an underdetermined set of equations by combining the voltage sampling matrix of the monitoring node, and use the compressed sampling matching pursuit CoSaMP algorithm to solve the node injected harmonic current vector. The voltage sampling matrix of the monitoring node is constructed by the node admittance matrix and the known node harmonic voltage information.

[0016] (3) Harmonic exceedance judgment: Calculate the harmonic voltage distortion rate of each node and compare it with the national standard limit to determine whether there is harmonic exceedance;

[0017] (4) Identification of the causes of harmonic exceedance:

[0018] a. Single-factor identification: By comparing the harmonic current injection value with the national standard allowable value, analyzing the superposition effect of multiple harmonics, and using modal analysis to identify resonance phenomena, the cause of exceeding the standard is determined to be excessive harmonic current injection, multi-frequency superposition, or resonance;

[0019] b. Identification of complex causes: Quantify the contribution of resonance and harmonic injection to the excessive harmonic voltage and determine the dominant factor;

[0020] (5) Output the identification results and generate targeted governance solutions.

[0021] Furthermore, step (2) involves using the CoSaMP algorithm to solve for the nodal injected harmonic current vector, including:

[0022] (1) Initialize the harmonic injection current vector and residual;

[0023] (2) Iteratively calculate the relevant vectors and select the candidate index set;

[0024] (3) Merge the index sets and perform signal estimation and pruning;

[0025] (4) Combine voltage and current constraints to perform iterative optimization until the convergence condition is met, and output the finally recovered node injection harmonic current vector.

[0026] Furthermore, the modal analysis method in step (4) specifically includes:

[0027] (1) Calculate the eigenvalues ​​of the nodal admittance matrix. If there are eigenvalues ​​that approach zero, then the system is in resonance.

[0028] (2) Determine the harmonic exceedance dominated by resonance based on the matching degree between the resonant frequency and the monitored harmonic frequency.

[0029] Furthermore, the contribution quantification formula in step (4) is:

[0030] Resonance contribution:

[0031]

[0032] Harmonic injection contribution:

[0033]

[0034] In the formula, For node j at frequency f r Below, the harmonic voltage value caused by resonance.

[0035] Furthermore, the voltage and current constraints are as follows:

[0036]

[0037]

[0038] Where ε v For node voltage threshold, Let ε be the harmonic voltage vector of the monitoring node; where ε i The branch current threshold, To monitor the harmonic current vector of the branch, Ψ is the current correspondence matrix.

[0039] Furthermore, the analysis of the multi-frequency superposition effect specifically includes:

[0040] When the individual harmonic currents are within the acceptable range, but the total harmonic voltage distortion rate exceeds the acceptable range, it is determined that the excessive harmonic distortion is caused by the superposition of multiple harmonics.

[0041] Furthermore, the determination of resonance-dominated harmonic exceedance based on the matching degree between the resonant frequency and the monitored harmonic frequency is specifically determined by the following formula:

[0042]

[0043] In the formula, ∆f is the difference between the monitored harmonic frequency and the resonant frequency; f is the harmonic frequency monitored by the monitoring device; f res,m The frequency at which the distribution network will resonate; ∆f set The set resonant identification frequency threshold.

[0044] The beneficial effects of this invention are:

[0045] 1) This invention proposes a method for identifying the main causes of harmonic exceedance at distribution network nodes. By optimizing and analyzing the harmonic voltage and current at distribution network nodes, this invention can accurately identify the root causes of harmonic exceedance, including current injection exceedance caused by nonlinear loads, superposition effect of multi-frequency harmonic currents, and resonance phenomena, thereby providing a scientific basis for subsequent management.

[0046] 2) This invention utilizes an optimized calculation method for harmonic injection values, combining the relationship between node voltage, current, and admittance matrices, to accurately calculate the harmonic injection values ​​at each node in the distribution network. This method can effectively recover the harmonic currents of non-monitored nodes, improving the accuracy and reliability of harmonic source location.

[0047] 3) The method for identifying single and multiple causes of harmonic exceedance proposed in this invention can distinguish different causes of harmonic exceedance in complex situations and provide differentiated treatment solutions for each cause, ensuring the efficiency and pertinence of the treatment measures. Attached Figure Description

[0048] Figure 1 This is a flowchart of a method for identifying the main causes of harmonic exceedance at distribution network nodes according to an embodiment of the present invention;

[0049] Figure 2 This is a configuration diagram of the power distribution network topology and harmonic monitoring device provided in an embodiment of the present invention;

[0050] Figure 3 The calculated values ​​of node harmonic injection current and the results of harmonic source location error are provided in the embodiments of the present invention.

[0051] Figure 4 The diagram shows the resonant mode impedance curve of the power distribution network provided in the embodiments of the present invention. Detailed Implementation

[0052] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, 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.

[0053] The implementation principle of the method for identifying the main causes of harmonic exceedances at distribution network nodes in this invention is explained in three parts below:

[0054] I. Optimization Calculation of Harmonic Injection Values

[0055] (1) Objective function

[0056] Calculating the harmonic injection values ​​at each node of the distribution network is beneficial for targeted harmonic mitigation, thereby reducing the impact of harmonics on the distribution network.

[0057] For a distribution network with harmonics (N nodes and L branches), the voltage vector of a node is shown in equation (1):

[0058] (1)

[0059] In the formula, Y f U is the N×N dimensional nodal admittance matrix at frequency f; f Let I be the N×1 dimensional nodal harmonic voltage vector at frequency f; f Inject harmonic current vectors into N×1 dimensional nodes at frequency f.

[0060] To clarify the relationship between node harmonic voltage and branch current, I f It is represented as shown in equation (2):

[0061] (2)

[0062] In the formula, T LThis is an N×(LN) dimensional branch current connection matrix in the distribution network; I fL This is a 1-dimensional harmonic current value matrix (LN) for all branches except the harmonic source injection branch.

[0063] Substituting equation (2) into equation (1), equation (1) can be expressed in the following form:

[0064] (3)

[0065] Distribution networks are numerous and widespread, with the number of monitoring devices far less than the number of nodes. According to Kirchhoff's laws, for a node with installed monitoring devices, the harmonic voltage and harmonic current connected to that node (hereinafter referred to as adjacent nodes) can be monitored, denoted as follows: and As shown in the following formula:

[0066] (4)

[0067] (5)

[0068] In the formula, M represents the number of monitoring devices, u m,j The voltage value at node j monitored by monitoring device m, i m,j This refers to the harmonic current value of branch j monitored by monitoring device m. Assuming the total number of nodes (including monitoring nodes and adjacent nodes) is s, and the number of branches connected to the monitoring node is l, then... The dimension is s×1. The dimension is l×1.

[0069] In equation (4), The dimension is lower than U f In other words, the harmonic voltages of some nodes in the distribution network are known, and the node harmonic injection current I is estimated by using the known node harmonic voltages monitored by monitoring devices. f The equations are an underdetermined system of equations.

[0070] Substituting equation (4) into equation (1), it can be expressed in the following form:

[0071] (6)

[0072] In the formula, U f,no For U f The unknowns in the data are the node harmonic voltage vectors of non-monitored nodes and adjacent nodes.

[0073] Construct the voltage sampling matrix C v From the total node harmonic voltage U f Extracting partial node harmonic voltages Equation (6) can be transformed into the following form:

[0074] (7)

[0075] (8)

[0076] In the formula, C v Φ is an s×N dimensional voltage sampling matrix; Φ is a measurement matrix, which is constructed from the admittance matrix Y and the information of known node harmonic voltages, and has a dimension of s×N.

[0077] Therefore, solve I f The objective function is transformed into the form shown in equation (8).

[0078] (2) Constraints

[0079] For the solved nodal injected harmonic current vector I f Voltage and current constraints need to be set to ensure I f The accuracy of each element.

[0080] 1) Voltage constraint conditions

[0081] According to equation (8), the measurement matrix Φ and the solved nodal injected harmonic current vector I f The product of these is the partial nodal harmonic voltage vector obtained by solving for it. The constraints on this voltage vector are set as follows:

[0082] (9)

[0083] In the formula, ε v This refers to the set node voltage threshold.

[0084] 2) Current constraint conditions

[0085] Construct the current sampling matrix C i Injecting harmonic current vector I from all nodes f Extracting partial branch harmonic currents Equation (2) can be transformed into the following form:

[0086] (10)

[0087] (11)

[0088] (12)

[0089] In the formula, Ψ is the vector of harmonic current injected into the node. f and The correspondence matrix has a dimension of l×N.

[0090] The current constraint conditions are set as follows:

[0091] (13)

[0092] In the formula, ε i This refers to the set branch current threshold.

[0093] (3) Solution algorithm

[0094] Because the number of harmonic sources that have a significant impact on the distribution network is small, only a few nodes (such as generator nodes or load nodes) have non-zero harmonic injection currents, while the harmonic injection currents at other nodes are zero or very small. Therefore, the node harmonic injection current I... f This can be represented as a sparse signal, meaning that most of its elements are zero or close to zero. CoSaMP is a reconstruction algorithm based on the sparsity assumption, which can efficiently recover sparse signals from a small number of linear measurements, and is suitable for the recovery of such sparse signals.

[0095] The following are the specific steps for solving the nodal harmonic injection values ​​based on CoSaMP:

[0096] 1) Set the initial nodal harmonic injection current vector I f,0 The residual r0 is as follows:

[0097] (14)

[0098] (15)

[0099] Initial I f,0 The zero vector represents the initially estimated sparse signal; the initial residual r0 represents the voltage value calculated by the measurement matrix Φ after processing the currently estimated harmonic current value, and the node harmonic voltage value. The difference between them. Set the initial number of iterations k=1.

[0100] 2) Calculate the correlation vector c k As shown in the following formula:

[0101] (16)

[0102] In the formula, c k This refers to the N×1-dimensional correlation vector of the current iteration, representing the correlation between the residual and the columns of the measurement matrix.

[0103] 3) Select candidate index set Ω k As shown in the following formula:

[0104] (17)

[0105] In the formula, Ω k The candidate index set contains ck Supp(v,k) returns the indices of the 2s elements with the largest absolute values ​​in vector v; Supp(v,k) returns the set of indices of the k elements with the largest absolute values ​​in vector v.

[0106] 4) Merge index sets, as shown in the following formula:

[0107] (18)

[0108] In the formula, T k The merged index set, including the candidate index set Ω k The estimated node harmonic current vector I at the current iteration number f,k Index of non-zero elements.

[0109] 5) Signal estimation, as shown in the following formula:

[0110] (19)

[0111] In the formula, b k In the merged index set T k Least squares estimate on; A submatrix of the measurement matrix, containing only T k The corresponding column; w is the temporary optimization variable in the least squares estimation step, representing the value in the merged index set T. k Upfit The coefficient vector.

[0112] 6) Signal trimming, as shown in the following formula:

[0113] (20)

[0114] In the formula, I f,k+1 Inject harmonic current vectors into the pruned nodes, retaining b k The function selects the s elements with the largest absolute value from vector v; Turn(v,k) means to keep only the k elements with the largest absolute value from vector v, and set all other elements to 0.

[0115] 7) Calculate the voltage constraints, as shown below:

[0116] (twenty one)

[0117] 8) Calculate the current constraints, as shown below:

[0118] (twenty two)

[0119] In the formula, v k+1 Inject harmonic current residual vectors into nodes.

[0120] 9) Determine whether the set iteration conditions are met, as shown in equations (23)-(25):

[0121] (twenty three)

[0122] (twenty four)

[0123] (25)

[0124] In the formula, ε v With ε i The set node voltage and branch current thresholds are used to determine whether the residual is small enough to decide whether to stop the iteration; K max This is the maximum number of iterations set.

[0125] If the iteration condition is not met, increment the iteration count by 1 and return to step (2) for calculation; if the set condition is met, output I. f,k+1 The harmonic current vector is injected into the node in the final recovered state based on the CoSaMP algorithm.

[0126] II. Identification of Causes of Harmonic Exceedance

[0127] Excessive harmonics in the distribution network are a key cause of power quality issues, and accurate identification of the causes of excessive harmonics is a prerequisite for efficient harmonic mitigation. Based on the characteristics of harmonic sources and the interaction between the system and the network, this invention proposes three main causes: (1) Nonlinear loads cause excessive harmonic current injection at nodes, leading to excessive harmonic voltage at distribution network nodes; (2) Nonlinear loads cause the presence of injected harmonic currents at nodes, and the combined effect of multiple harmonic currents leads to excessive harmonic voltage at a certain node; (3) Resonance phenomena occur due to the operating parameters of the distribution network, causing amplification of harmonic voltage at some nodes. By effectively identifying the main causes of excessive harmonics and designing differentiated mitigation schemes, effective and targeted harmonic mitigation can be achieved.

[0128] (1) Reason for exceeding the standard 1: Harmonic current injection exceeds the standard

[0129] Excessive harmonic current injection refers to the situation where, during operation, a nonlinear load injects high-order harmonic current into the distribution network that exceeds the relevant standard limits. Excessive harmonic current injection is characterized by the concentration of energy in specific harmonic spectra, which is strongly correlated with the load's operating conditions.

[0130] According to GB / T 14549-1993, the node injection current should not exceed the specified allowable value. When the harmonic current injection exceeds the standard, under the action of the load in the distribution network, it will cause some nodes to generate harmonic voltage exceeding the standard, causing power quality problems.

[0131] (2) Reason for exceeding the standard 2: The superposition of multiple frequency harmonic currents leads to the harmonic exceeding the standard.

[0132] While meeting the harmonic current limits, the harmonic voltage values ​​of the distribution network should also not exceed the specified limits. According to Fourier analysis theory, any periodic non-sinusoidal current i(t) can be decomposed into the sum of the fundamental current and multiple harmonic components of integer multiple frequencies:

[0133] (26)

[0134] In the formula, i h The current is the h-th harmonic current; The fundamental angular frequency; Let be the initial phase angle of the h-th harmonic.

[0135] Harmonic current content I H With harmonic voltage content U H The calculation formula is as follows:

[0136] (27)

[0137] (28)

[0138] In the formula, u h The voltage is the h-th harmonic.

[0139] For multi-frequency node harmonic injection currents, the values ​​exceed the allowable values ​​for harmonic current injection into the node at each frequency. Based on equation (1), the corresponding harmonic voltage values ​​at each frequency under the influence of the node harmonic injection current are calculated, and the total harmonic distortion rate of the voltage is calculated, as shown in the following equation:

[0140] (29)

[0141] In the formula, THD u,j The harmonic voltage distortion rate at node j, j={1,2,…,N}; U H,j The harmonic voltage content of node j; U 1,j The fundamental voltage value of node j.

[0142] (3) Reason for exceeding the standard 3: Resonance causes harmonic exceedance.

[0143] In power distribution networks, resonance refers to a situation where the frequency of a high-frequency current injected by a harmonic source approaches the network's inherent resonant frequency, causing a sharp decrease in system impedance, even approaching zero, leading to a significant amplification of harmonic currents or voltages. Harmonic exceedances caused by resonance manifest as a concentration of energy in specific harmonic spectra, exhibiting a strong correlation with load operating conditions. According to circuit theory, the essence of resonance lies in the formation of a resonant mode between the grid's equivalent impedance and the harmonic source impedance at a specific frequency. The impedance characteristic Z of a parallel resonant circuit... p for:

[0144] (30)

[0145] (31)

[0146] When equation (30) satisfies the frequency condition When, as in equation (31), the impedance modulus reaches its maximum, resulting in severe harmonic voltage amplification.

[0147] Modal analysis can identify multi-node resonance phenomena in distribution networks. When resonance occurs in a distribution network, the node voltage becomes very large, and the node admittance matrix Y of the distribution network... f It will gradually lose its reversibility, Y f The smallest eigenvalue converges to zero, and its determinant gradually approaches zero. Therefore, the eigenvalue analysis method is used to calculate Y. f The eigenvalues ​​of the system are used to determine whether the system exhibits resonance by calculating whether their eigenvalues ​​approach zero. The nodal admittance matrix Y... f It can be broken down into:

[0148] (32)

[0149] In the formula, T is a diagonal characteristic matrix, and its diagonal elements are represented by λ. m (m=1,2,...,N) indicates that the remaining elements are 0; P and Q are eigenvector matrices. In the scenario where the asymmetry of the system admittance matrix is ​​not considered, P and Q are orthogonal matrices, and the relationship between P and Q is shown in equation (25).

[0150] (33)

[0151] Substituting equation (32) into equation (1) and transforming it, we can obtain:

[0152] (34)

[0153] (35)

[0154] (36)

[0155] In the formula, U M Defined as a modal voltage vector; I M Defined as the modal current vector. Expanding equation (34) yields:

[0156] (37)

[0157] In equation (37), the eigenvalue λ m The modal admittance is defined as Z, and its reciprocal is defined as the modal impedance, denoted as Z. m, where m is the modal order. When λ i When the modal current approaches zero, even a very small injected modal current will generate a large modal voltage. However, other modal voltages are unaffected because they are not connected to the injected modal current. Therefore, modal analysis can be used to further identify the specific location of harmonic resonances. The set of all resonance scenarios for a specific system is denoted as {f}. res,m}

[0158] (4) Identification of the causes of exceeding the standard

[0159] To address harmonic issues in distribution networks, this section proposes a harmonic exceedance identification model based on the configuration of distribution network monitoring devices. This model extracts information such as harmonic frequencies and voltages from monitoring nodes to identify the causes of harmonic exceedances in the distribution network. The identification model process is as follows:

[0160] Step 1: Harmonic Voltage Compliance Verification

[0161] Based on the harmonic voltage and harmonic current information collected by the monitoring nodes, the harmonic injection value I at the nodes is optimized using a harmonic injection value optimization calculation method. f Calculations are performed, and based on Equation (1), the node harmonic voltages in the corresponding scenarios are calculated.

[0162] If the calculated harmonic voltage distortion rate (THD) u,j If the value is ≤ the specified limit, then the distribution network does not have harmonic exceedance issues; if the calculated harmonic voltage distortion rate (THD) is... u,j If the specified limit is not met, it indicates that there is a problem of excessive harmonic voltage in the distribution network, and the cause of the excessive harmonic voltage needs to be further identified.

[0163] Step 2: Single-cause identification of harmonic exceedance

[0164] (1) Resonance risk band

[0165] Based on the identification of various resonance scenarios in the distribution network, a set of all resonance scenarios under a specific system was obtained, denoted as . Based on the harmonic frequencies extracted from the monitoring nodes, the resonance scenarios are matched. If the monitored harmonic frequency is close to the frequency of the resonance scenario, the system is considered to have experienced resonance, as shown in the following formula:

[0166] (38)

[0167] In the formula, ∆f is the difference between the monitored harmonic frequency and the resonant frequency; f is the harmonic frequency monitored by the monitoring device; f res,m The frequency at which the distribution network will resonate; ∆f set The set resonant identification frequency threshold.

[0168] (2) Harmonic current compliance

[0169] The node harmonic current injection value I is calculated using an optimized calculation method for harmonic injection values. f Whether the allowed value is exceeded is shown in the following formula:

[0170] (39)

[0171] In the formula, ∆I f,j I refers to the difference between the harmonic injection current value at node j at frequency f and the allowable value of the harmonic current injected into that node; f,j The value of the harmonic injection current at node j at frequency f; I thes , f,j This refers to the allowable value of harmonic current injected into node j at frequency f.

[0172] (3) Single-factor identification verification

[0173] The set resonant identification frequency threshold is denoted as ∆f. set By comparing the harmonic current difference ∆I respectively f,j The cause of harmonic exceedance is determined by whether the resonant frequency meets the conditions, as shown in Table 1.

[0174] surface Single-factor identification table for excessive harmonic voltage

[0175]

[0176] Regarding the cause of the excessive harmonic voltage in Case 5 of Table 1, it is necessary to further determine the main cause of the excessive harmonic voltage to provide a theoretical basis for targeted harmonic mitigation; regarding the cause of the harmonics in Case 6, targeted mitigation is required at the same time to prevent the harmonics from developing further and causing serious power quality problems.

[0177] Step 3: Identification of the combined causes of harmonic exceedance

[0178] To address the causes of the excessive harmonic voltage in Case 5 of Table 1, it is necessary to further quantify the impact of node harmonic injection current and resonance on the nodes with excessive harmonic voltage, and to implement targeted remediation.

[0179] Assume the frequency of resonance is f r The harmonic voltage at node j exceeds the limit. The contribution of the harmonic voltage at node j caused by resonance is denoted as G. r,j The contribution of node j-harmonic voltage caused by the superposition of harmonic currents of other frequencies is denoted as G. i,j The calculation formula is as follows:

[0180] (40)

[0181] (41)

[0182] In the formula, For node j at frequency f r Below, the harmonic voltage value caused by resonance.

[0183] In Case 5, if G r,j ≥G i,j If the harmonic voltage exceeds the standard, it is dominated by resonance; if G r,j <G i,j If the harmonic voltage exceeds the standard, it is still dominated by the harmonic injection current.

[0184] Based on the above principles and analysis, such as Figure 1 As shown in the figure, this embodiment of the invention provides a method for identifying the main causes of harmonic exceedances at distribution network nodes, including the following steps:

[0185] Step 1: Data Acquisition and Preprocessing

[0186] (1) Data acquisition: Harmonic monitoring devices are deployed in the power distribution network, such as... Figure 2 As shown, the harmonic voltages of the monitoring node and its adjacent nodes are collected. Branch harmonic current The data covers the fundamental frequency and major harmonic frequency bands.

[0187] (2) Topology parameter extraction: Based on the distribution network topology, the node admittance matrix Y is constructed. f And determine the branch current connection matrix T L .

[0188] Step 2: Solving for the harmonic injection current vector

[0189] (1) Constructing an underdetermined system of equations:

[0190] Based on Kirchhoff's laws, the relationship equation between node harmonic voltage and harmonic injection current is established:

[0191] (42)

[0192] Combined with the voltage sampling matrix C of the monitoring node v (With dimensions s×N), the equation is transformed into a sparse reconstruction problem:

[0193] (43)

[0194] In the formula, Φ is the measurement matrix, which is constructed from the admittance matrix Y and the information of known node harmonic voltages, and has a dimension of s×N.

[0195] (2) Solve using the CoSaMP algorithm:

[0196] (1) Set the initial nodal harmonic injection current vector I f,0 The residual r0 is as follows:

[0197] (44)

[0198] (45)

[0199] Initial I f,0 The zero vector represents the initially estimated sparse signal; the initial residual r0 represents the voltage value calculated by the measurement matrix Φ after processing the currently estimated harmonic current value, and the node harmonic voltage value. The difference between them. Set the initial number of iterations k=1.

[0200] (2) Calculate the correlation vector c k As shown in the following formula:

[0201] (46)

[0202] In the formula, c k This refers to the N×1-dimensional correlation vector of the current iteration, representing the correlation between the residual and the columns of the measurement matrix.

[0203] (3) Select candidate index set Ω k As shown in the following formula:

[0204] (47)

[0205] In the formula, Ω k The candidate index set contains c k Supp(v,k) returns the indices of the 2s elements with the largest absolute values ​​in vector v; Supp(v,k) returns the set of indices of the k elements with the largest absolute values ​​in vector v.

[0206] (4) Merge the index sets, as shown in the following formula:

[0207] (48)

[0208] In the formula, T k The merged index set, including the candidate index set Ω k The estimated node harmonic current vector I at the current iteration number f,k Index of non-zero elements.

[0209] (5) Signal estimation, as shown in the following formula:

[0210] (49)

[0211] In the formula, b k In the merged index set Tk Least squares estimate on; A submatrix of the measurement matrix, containing only T k The corresponding column; w is the temporary optimization variable in the least squares estimation step, representing the value in the merged index set T. k Upfit The coefficient vector.

[0212] (6) Signal trimming, as shown in the following formula:

[0213] (50)

[0214] In the formula, I f,k+1 Inject harmonic current vectors into the pruned nodes, retaining b k The function selects the s elements with the largest absolute value from vector v; Turn(v,k) means to keep only the k elements with the largest absolute value from vector v, and set all other elements to 0.

[0215] (7) Calculate the voltage constraints as follows:

[0216] (51)

[0217] (8) Calculate the current constraints as follows:

[0218] (52)

[0219] In the formula, v k+1 Inject harmonic current residual vectors into nodes.

[0220] (9) Determine whether the set iteration conditions are met, as shown in equations (23)-(25):

[0221] (53)

[0222] (54)

[0223] (55)

[0224] In the formula, ε v With ε i The set node voltage and branch current thresholds are used to determine whether the residual is small enough to decide whether to stop the iteration; K max This is the maximum number of iterations set.

[0225] If the iteration condition is not met, increment the iteration count by 1 and return to step (2) for calculation; if the set condition is met, output I. f,k+1 The harmonic current vector is injected into the node in the final recovered state based on the CoSaMP algorithm.

[0226] The results of nodal harmonic injection current and harmonic source location error are as follows: Figure 3 As shown in the figure, the method proposed in this invention shows a certain increase in both the calculation error of harmonic injection current and the location deviation of harmonic sources as the number of harmonic sources gradually increases. However, the maximum error in the calculation of harmonic injection current does not exceed 5%, and the deviation of the harmonic source location result is not less than 79%. Therefore, the accuracy of the method proposed in this invention in calculating the node harmonic injection current is verified.

[0227] Step 3: Harmonic Exceedance Determination

[0228] (1) Calculate the harmonic voltage distortion rate:

[0229] According to the formula:

[0230] (56)

[0231] In the formula, THD u,j The harmonic voltage distortion rate at node j, j={1,2,…,N}; U H,j The harmonic voltage content of node j; U 1,j The fundamental voltage value of node j.

[0232] (2) Determination of exceeding the standard: If THD u,j If the national standard limit (e.g., 5%) is exceeded, it is determined that node j has a harmonic exceeding the standard.

[0233] Step 4: Identification of the causes of harmonic exceedance

[0234] (1) Single-factor identification:

[0235] 1) Harmonic current injection exceeds the standard:

[0236] Comparison I f,j Compared with the national standard allowable value I thes,f,j , if I f,j > I thes,f,j It was determined that the harmonic current injection exceeded the standard.

[0237] 2) Superposition of multiple harmonics:

[0238] If the individual harmonic currents do not exceed the standard, but the total harmonic voltage distortion rate exceeds the standard, it is determined to be a multi-frequency superposition effect.

[0239] 3) Resonance phenomenon:

[0240] Modal analysis: based on the admittance matrix Y f eigenvalues ​​λ m If |λ i If |≈0, it indicates that the system is in resonance, and the resonant node and resonant frequency are output. Figure 2 The distribution network model shown has the following resonance calculation results: Figure 4 As shown.

[0241] (2) Identification of complex causes:

[0242] 1) Contribution Calculation:

[0243] a. Calculate the resonance contribution

[0244] (57)

[0245] b. Calculate the harmonic injection contribution.

[0246] (58)

[0247] 2) Determination of dominant factors:

[0248] If G r,j ≥G i,j If the resonance is dominant, then harmonic injection is dominant; otherwise, harmonic injection is dominant.

[0249] Step 5: Comparative analysis to verify the effectiveness of the model.

[0250] This embodiment is respectively in Figure 2 In the distribution network model shown, random harmonic currents are injected into randomly selected nodes. The effectiveness of the model is verified by identifying the main causes of harmonic exceedances.

[0251] Harmonic currents of frequency 21.34 and 11, with magnitudes of 1A and 15A, were injected into nodes 21 and 22 respectively. Through the above steps, the harmonic voltage at node 21 was calculated to be 473.1V, with a total harmonic voltage distortion rate of 4.7%, exceeding the requirement of GB / T 14549-1993 that the harmonic voltage distortion rate in a 10kV distribution network should not exceed 4.0%. Therefore, there is a harmonic voltage exceeding the standard. A harmonic current of frequency 21.3 was injected into node 21. Figure 4 As shown, this frequency is the resonance frequency; node 22 injected a harmonic current of frequency 11 and magnitude 3A, which is significantly greater than the requirement in GB / T 14549-1993 that the 11th harmonic current in a 10kV distribution network shall not exceed 9.3A; therefore, the harmonic exceedance here is due to the simultaneous occurrence of excessive harmonic injection current at node 22 and resonance at node 21, which is the reason for Case 6 in Table 1. The harmonic voltage contribution of node 21 is calculated as G. r,21 =98.4%, G i,22 =1.6%, G r,21 >G i,22 Therefore, the excessive harmonic voltage at node 21 is dominated by resonance.

[0252] Another embodiment of the present invention provides a device for identifying the main causes of harmonic exceedance at a distribution network node, comprising the following steps:

[0253] The data acquisition and preprocessing module is used to deploy harmonic monitoring devices in the distribution network, collect harmonic voltage and branch harmonic current data of monitoring nodes and adjacent nodes, construct node admittance matrix based on the distribution network topology, and determine branch current connection relationship matrix.

[0254] The harmonic injection current vector solving module is used to establish the correlation equation between node harmonic voltage and harmonic injection current based on Kirchhoff's laws, construct an underdetermined set of equations by combining the voltage sampling matrix of the monitoring node, and solve the node injected harmonic current vector using the compressed sampling matching pursuit CoSaMP algorithm. The voltage sampling matrix of the monitoring node is constructed from the node admittance matrix and the information of the known node harmonic voltage.

[0255] The harmonic exceedance determination module is used to calculate the harmonic voltage distortion rate of each node and compare it with the national standard limit to determine whether there is harmonic exceedance.

[0256] The harmonic exceedance cause identification module is used for

[0257] a. Single-factor identification: By comparing the harmonic current injection value with the national standard allowable value, analyzing the superposition effect of multiple harmonics, and using modal analysis to identify resonance phenomena, the cause of exceeding the standard is determined to be excessive harmonic current injection, multi-frequency superposition, or resonance;

[0258] b. Identification of complex causes: Quantify the contribution of resonance and harmonic injection to the excessive harmonic voltage and determine the dominant factor;

[0259] The output identification results module is used to generate targeted governance solutions from the identification results.

[0260] Another embodiment of the present invention provides a system for identifying the main causes of harmonic exceedance at distribution network nodes, comprising: a computer-readable storage medium and a processor;

[0261] The computer-readable storage medium is used to store executable instructions;

[0262] The processor is used to read executable instructions stored in the computer-readable storage medium and execute the method for identifying the main causes of harmonic exceedances at distribution network nodes.

[0263] Another embodiment of the present invention provides a non-transitory computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the aforementioned method for identifying the main causes of harmonic exceedances at distribution network nodes.

[0264] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0265] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0266] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0267] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0268] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A method for identifying the main causes of excessive harmonics at distribution network nodes, characterized in that, Includes the following steps: (1) Data acquisition and preprocessing: Deploy harmonic monitoring devices in the distribution network, collect harmonic voltage and branch harmonic current data of monitoring nodes and adjacent nodes, construct node admittance matrix based on distribution network topology and determine branch current connection relationship matrix; (2) Solution of harmonic injection current vector: Based on Kirchhoff's laws, establish the correlation equation between node harmonic voltage and harmonic injection current, construct an underdetermined set of equations by combining the voltage sampling matrix of the monitoring node, and use the compressed sampling matching pursuit CoSaMP algorithm to solve the node injected harmonic current vector. The voltage sampling matrix of the monitoring node is constructed by the node admittance matrix and the known node harmonic voltage information. (3) Harmonic exceedance judgment: Calculate the harmonic voltage distortion rate of each node and compare it with the national standard limit to determine whether there is harmonic exceedance; (4) Identification of the causes of harmonic exceedance: a. Single-factor identification: By comparing the harmonic current injection value with the national standard allowable value, analyzing the superposition effect of multiple harmonics, and using modal analysis to identify resonance phenomena, the cause of exceeding the standard is determined to be excessive harmonic current injection, multi-frequency superposition, or resonance; b. Identification of complex causes: Quantify the contribution of resonance and harmonic injection to the excessive harmonic voltage and determine the dominant factor; (5) Output the identification results and generate targeted governance solutions.

2. The method according to claim 1, characterized in that, The step (2) of solving for the nodal injected harmonic current vector using the CoSaMP algorithm includes: (1) Initialize the harmonic injection current vector and residual; (2) Iteratively calculate the relevant vectors and select the candidate index set; (3) Merge the index sets and perform signal estimation and pruning; (4) Combine voltage and current constraints to perform iterative optimization until the convergence condition is met, and output the finally recovered node injection harmonic current vector.

3. The method according to claim 1, characterized in that, The modal analysis method in step (4) specifically includes: (1) Calculate the eigenvalues ​​of the nodal admittance matrix. If there are eigenvalues ​​that approach zero, then the system is in resonance. (2) Determine the harmonic exceedance dominated by resonance based on the matching degree between the resonant frequency and the monitored harmonic frequency.

4. The method according to claim 1, characterized in that, The contribution quantification formula in step (4) is as follows: Resonance contribution: ； Harmonic injection contribution: ； In the formula, For node j at frequency f r Below, the harmonic voltage value caused by resonance.

5. The method according to claim 1, characterized in that, The voltage and current constraints are as follows: ； ； Where ε v For node voltage threshold, Let ε be the harmonic voltage vector of the monitoring node; where ε i The branch current threshold, To monitor the harmonic current vector of the branch, Ψ is the current correspondence matrix.

6. The method according to claim 1, characterized in that, The analysis of the multi-frequency superposition effect specifically includes: When the individual harmonic currents are within the acceptable range, but the total harmonic voltage distortion rate exceeds the acceptable range, it is determined that the excessive harmonic distortion is caused by the superposition of multiple harmonics.

7. The method according to claim 3, characterized in that, The determination of resonance-dominated harmonic exceedance based on the matching degree between the resonant frequency and the monitored harmonic frequency is specifically based on the following formula: ； In the formula, ∆f is the difference between the monitored harmonic frequency and the resonant frequency; f is the harmonic frequency monitored by the monitoring device; f res,m The frequency at which the distribution network will resonate; ∆f set The set resonant identification frequency threshold.

8. A device for identifying the main causes of excessive harmonics at distribution network nodes, characterized in that, Includes the following steps: The data acquisition and preprocessing module is used to deploy harmonic monitoring devices in the distribution network, collect harmonic voltage and branch harmonic current data of monitoring nodes and adjacent nodes, construct node admittance matrix based on the distribution network topology, and determine branch current connection relationship matrix. The harmonic injection current vector solving module is used to establish the correlation equation between node harmonic voltage and harmonic injection current based on Kirchhoff's laws, construct an underdetermined set of equations by combining the voltage sampling matrix of the monitoring node, and solve the node injected harmonic current vector using the compressed sampling matching pursuit CoSaMP algorithm. The voltage sampling matrix of the monitoring node is constructed from the node admittance matrix and the information of the known node harmonic voltage. The harmonic exceedance determination module is used to calculate the harmonic voltage distortion rate of each node and compare it with the national standard limit to determine whether there is harmonic exceedance. The harmonic exceedance cause identification module is used for a. Single-factor identification: By comparing the harmonic current injection value with the national standard allowable value, analyzing the superposition effect of multiple harmonics, and using modal analysis to identify resonance phenomena, the cause of exceeding the standard is determined to be excessive harmonic current injection, multi-frequency superposition, or resonance; b. Identification of complex causes: Quantify the contribution of resonance and harmonic injection to the excessive harmonic voltage and determine the dominant factor; The output identification results module is used to generate targeted governance solutions from the identification results.

9. A system for identifying the main causes of harmonic exceedances at distribution network nodes, comprising: Computer-readable storage media and processors; The computer-readable storage medium is used to store executable instructions; The processor is used to read executable instructions stored in the computer-readable storage medium and execute the method for identifying the main causes of harmonic exceedances at distribution network nodes as described in any one of claims 1-7.

10. A non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method for identifying the main causes of harmonic exceedances at distribution network nodes according to any one of claims 1-7.

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