Harmonic resonance analysis method, device and equipment of power system and storage medium

Abstract

The invention provides a power system harmonic resonance analysis method and device, equipment and a storage medium. The method comprises the steps of solving a maximum characteristic value of a node impedance matrix by using a power iteration method, reducing the calculation amount and improving the speed. And obtaining a maximum characteristic value set of multiple frequency points through iterative calculation, and constructing modal impedance as an analysis parameter. And determining the resonant frequency and the interval by adopting the dual-frequency step length. Meanwhile, a half-power bandwidth method is introduced to calculate the damping ratio, and an accurate harmonic resonance index is constructed in combination with modal impedance, so that the analysis efficiency and accuracy are improved.

Description

Technical Field

[0001] The present application relates to the field of power grid harmonic resonance analysis, and in particular to a power system harmonic resonance analysis method, device, equipment and storage medium. Background Art

[0002] In recent years, with the widespread access to renewable energy, power electronic equipment and nonlinear loads, the harmonic characteristics of power systems have changed significantly. The randomness and distributed characteristics of these access sources, as well as the continuous expansion of system scale, have jointly posed new challenges to harmonic transmission and resonance analysis. The modal analysis method traditionally relied on, which only evaluates the degree of harmonic resonance based on the modal impedance amplitude, has revealed its limitations: the calculation process is complex and lengthy, inefficient, and difficult to accurately adapt to the complex characteristics of new power systems, and may even mislead the analysis conclusions. Summary of the invention

[0003] The purpose of this application is to overcome the problems existing in the above-mentioned prior art and to provide a method, device, equipment and storage medium for analyzing harmonic resonance in an electric power system.

[0004] The present application provides a method for analyzing harmonic resonance of a power system, comprising:

[0005] Determine the frequency range that needs to be analyzed in the power system;

[0006] Collecting node voltages and node injection currents of the power system, and calculating a node admittance matrix according to the node voltages and node injection currents;

[0007] Determine a starting iteration vector for a first frequency point within the frequency range;

[0008] Performing multiple iterative calculations starting from the starting iterative vector to obtain the maximum eigenvalue of the node admittance matrix, including: taking the ratio of the previous iterative vector to the node admittance matrix as a normalized vector; taking the ratio of the normalized vector to the element with the largest modulus in the normalized vector as the current iterative vector; stopping the iteration when a preset iterative termination condition is triggered during the iteration process, and obtaining the element with the largest modulus in the normalized vector as the maximum eigenvalue;

[0009] Using the maximum eigenvalue as the starting iteration vector of the next frequency point in the frequency range, repeating the previous step, and obtaining a maximum eigenvalue set of multiple frequency points;

[0010] The reciprocal of the maximum eigenvalue in the maximum eigenvalue set is used to form the modal impedance of the power system as an analysis parameter;

[0011] According to the analysis parameters, a resonant frequency is determined within the frequency range with a first frequency step, and a resonant frequency interval centered on the resonant frequency is determined with a second frequency step smaller than the first frequency step.

[0012] Optionally, the reciprocal of the maximum eigenvalue in the maximum eigenvalue set is used to form the modal impedance of the power system as an analysis parameter, including:

[0013] Calculating a damping ratio according to the modal impedance;

[0014] The modal impedance and the damping ratio are used as analysis parameters.

[0015] Optionally, the damping ratio is obtained according to the impedance calculation, and the expression is as follows:

[0016]

[0017] Wherein, f0 is the frequency corresponding to the peak value of the modal impedance curve, and f1 and f2 are the frequencies corresponding to the half-power point of the modal impedance curve, respectively.

[0018] Optionally, according to the analysis parameter, determining the resonant frequency within the frequency range with a first frequency step, and determining the resonant frequency interval centered on the resonant frequency with a second frequency step smaller than the first frequency step, comprises:

[0019] The modal impedance and the damping ratio are normalized to the following expression:

[0020]

[0021] In the formula, x is the input data; y is the output data; x max 、x min is the maximum and minimum value of the input data; y max ,y min are the maximum and minimum values ​​of the normalized range, respectively.

[0022] Optionally, according to the analysis parameter, determining the resonant frequency within the frequency range with a first frequency step, and determining the resonant frequency interval centered on the resonant frequency with a second frequency step smaller than the first frequency step, comprises:

[0023] Calculate the harmonic resonance index R RD :

[0024] R RD =Δ|Z m |-Δξ

[0025] Among them, Δ|Z m | is the change in modal impedance amplitude, and Δξ is the change in damping ratio.

[0026] Optionally, the preset iteration termination condition includes:

[0027] V (k) =||y (k) || ∞ -||y (k-1) || ∞

[0028] α (k) =V (k) -V (k-1)

[0029] When α (k) <δ,V (k) <ε, the iteration terminates;

[0030] Among them, y (k) is a normalized vector, ||y (k) || ∞ Yes (k) The element with the largest modulus in the vector, δ and ε are the set thresholds.

[0031] Optionally, the expression of the starting iteration vector is as follows:

[0032]

[0033] Among them, S(Y f ) is the node admittance matrix Y f The sum of all elements in Y ij is the node admittance matrix Y f One of the elements.

[0034] The present application also provides a power system harmonic resonance analysis device, comprising:

[0035] Selection module for determining the frequency range to be analyzed in the power system;

[0036] A collection module, used to collect node voltages and node injection currents of the power system, and calculate a node admittance matrix according to the node voltages and node injection currents;

[0037] An initial module, used for determining a starting iteration vector of a first frequency point within the frequency range;

[0038] An iteration module is used to perform multiple iteration calculations starting from the starting iteration vector to obtain the maximum eigenvalue of the node admittance matrix, including: taking the ratio of the previous iteration vector to the node admittance matrix as a normalized vector; taking the ratio of the normalized vector to the element with the largest modulus in the normalized vector as the current iteration vector; stopping the iteration when a preset iteration termination condition is triggered during the iteration process, and obtaining the element with the largest modulus in the normalized vector as the maximum eigenvalue;

[0039] A loop module, used for taking the maximum eigenvalue as a starting iteration vector for a next frequency point within the frequency range, repeating the previous step, and obtaining a maximum eigenvalue set for a plurality of frequency points;

[0040] A parameter module, used for forming the modal impedance of the power system from the reciprocal of the maximum eigenvalue in the maximum eigenvalue set as an analysis parameter;

[0041] The analysis module is used to determine the resonant frequency within the frequency range with a first frequency step according to the analysis parameters, and to determine the resonant frequency interval centered on the resonant frequency with a second frequency step smaller than the first frequency step.

[0042] The present application also provides a power system harmonic resonance analysis device, comprising:

[0043] Memory;

[0044] A processor is used to retrieve the computer executable program of the above-mentioned power system harmonic resonance analysis method stored in the memory, and execute: determining the frequency range that needs to be analyzed in the power system; collecting the node voltage and node injection current of the power system, and calculating the node admittance matrix according to the node voltage and node injection current; determining the starting iteration vector of the first frequency point within the frequency range; performing multiple iteration calculations starting from the starting iteration vector to obtain the maximum eigenvalue of the node admittance matrix, including: taking the ratio of the previous iteration vector to the node admittance matrix as a normalized vector; comparing the normalized vector with the normalized vector with the largest modulus. The ratio of the elements is used as the iteration vector for this time; when a preset iteration termination condition is triggered during the iteration process, the iteration is stopped, and the element with the largest modulus in the normalized vector is obtained as the maximum eigenvalue; the maximum eigenvalue is used as the starting iteration vector of the next frequency point in the frequency range, and the previous step is repeated to obtain the maximum eigenvalue set of multiple frequency points; the reciprocal of the maximum eigenvalue in the maximum eigenvalue set is used to form the modal impedance of the power system as an analysis parameter; according to the analysis parameters, the resonant frequency is determined within the frequency range with a first frequency step, and the resonant frequency interval centered on the resonant frequency is determined with a second frequency step that is smaller than the first frequency step.

[0045] The present application also provides a storage medium, comprising: storing a computer executable program, wherein the computer executable program is used to be called by a processor to execute the steps of the above-mentioned power system harmonic resonance analysis method.

[0046] The beneficial effects of this application are:

[0047] The present application provides a method for analyzing harmonic resonance of an electric power system, comprising: determining a frequency range to be analyzed in the electric power system; collecting node voltages and node injection currents of the electric power system, and calculating a node admittance matrix according to the node voltages and node injection currents; determining a starting iteration vector of a first frequency point within the frequency range; performing multiple iteration calculations starting from the starting iteration vector to obtain a maximum eigenvalue of the node admittance matrix, comprising: taking a ratio of a previous iteration vector to the node admittance matrix as a normalized vector; taking a ratio of the normalized vector to an element with the largest modulus in the normalized vector as the current iteration vector; stopping iteration when a preset iteration termination condition is triggered during the iteration process, and obtaining an element with the largest modulus in the normalized vector as the maximum eigenvalue; taking the maximum eigenvalue as a starting iteration vector for a next frequency point within the frequency range, and repeating the previous step to obtain a maximum eigenvalue set of multiple frequency points; forming a modal impedance of the electric power system with the inverse of the maximum eigenvalue in the maximum eigenvalue set as an analysis parameter; and determining a resonant frequency within the frequency range according to the analysis parameter with a first frequency step, and determining a resonant frequency interval centered on the resonant frequency with a second frequency step smaller than the first frequency step. This application uses the power iteration method to solve the maximum eigenvalue of the system node impedance matrix, which significantly reduces the amount of calculation and improves the analysis speed. At the same time, the half-power bandwidth method is introduced to calculate the damping ratio. Combining the modal impedance and the damping ratio, a more accurate harmonic resonance degree index is constructed for the harmonic resonance evaluation of the power system. This innovative method effectively improves the efficiency and accuracy of the analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 It is a schematic diagram of the power system harmonic resonance analysis process in this application;

[0049] Figure 2 It is a schematic diagram of the improved power iteration method in this application;

[0050] Figure 3 It is a schematic diagram of the RLC parallel circuit in this application. DETAILED DESCRIPTION

[0051] The present application is further described below in conjunction with the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present application and implement it.

[0052] Traditional modal analysis is a mathematical method based on characteristic analysis technology, which aims to deeply explore the behavioral characteristics of circuit networks at different frequencies. The core of this method is to calculate all the eigenvalues ​​of the inverse matrix of the admittance matrix of the network at each specific frequency point, thereby revealing the modal characteristics of the system. The following is a detailed and complete description of the steps of this method:

[0053] Step 1: Understand the node voltage equations.

[0054] When the circuit network reaches the parallel resonance state at a certain frequency, the relationship between the node voltage and the injected current can be described by the node voltage equation, which is as follows:

[0055] V f =Y f -1 I f

[0056] Among them, Y f is the network admittance matrix at frequency f; V f ,I f are the node voltage and node injection current vector respectively.

[0057] Step 2: Eigenvalue decomposition.

[0058] Network admittance matrix Y f It can be further analyzed by eigenvalue decomposition, which decomposes it into the product of three matrices:

[0059] Y f =LΛT

[0060] Where L=[L1,L2,...L n ] is the left eigenvector matrix, L n is the nth element in the column of L;

[0061] Λ=diag(λ1,λ2,...λ n ) is Y f The diagonal eigenvalue matrix of n ] is the right eigenvector matrix, and L = T -1 .

[0062] Step 3: Substitute the node voltage equation.

[0063] Substituting the result of eigenvalue decomposition into the original node voltage equation, we get:

[0064] TV f =Λ -1 TI f

[0065] Definition U = TV f is the modal voltage vector, J = TI f is the modal current vector, then U=Λ -1 J can be expressed as:

[0066]

[0067] Step 4: Define the modal impedance.

[0068] In the modal space, each mode is represented by a corresponding eigenvalue, and the reciprocal of the eigenvalue is the impedance in that mode. The modal impedance Z of the system n .

[0069] Step 5: Identification of key modes

[0070] In practical applications, in order to simplify the analysis, we usually only focus on the modes that have the greatest impact on the system behavior. This can be achieved by finding the maximum eigenvalue corresponding to each frequency point, because the maximum eigenvalue often represents the dominant mode of the system at that frequency.

[0071] Traditional modal analysis methods use eigenvalue decomposition technology to decompose complex circuit network behavior into a series of simple modes, and deeply understand the dynamic performance of the system by analyzing the impedance characteristics of these modes.

[0072] Please refer to Figure 1 As shown, the present application provides a method for identifying a broadband oscillation pattern, the steps of which include:

[0073] S101. Determine the frequency range that needs to be analyzed in the power system.

[0074] In the modal analysis or frequency response analysis of the power system, we first need to clarify the frequency range we are interested in or need to analyze. This range may be determined based on a variety of factors, such as the natural frequency of the system, the frequency components of external excitation, the operating frequency range of the equipment, etc. For example, to study the behavior of the power system under specific harmonics, it may be necessary to focus on the integer multiple frequencies of the 50Hz fundamental frequency; while when studying the response of the power system to high-frequency signals, it may be necessary to consider a higher frequency range.

[0075] After determining the frequency range, we can divide this range into several frequency points so that they can be analyzed one by one in the subsequent steps. These frequency points can be equally spaced or unequally spaced according to actual needs.

[0076] S102 , collecting node voltages and node injection currents of the power system, and calculating a node admittance matrix according to the node voltages and node injection currents.

[0077] After determining the analysis frequency range, the next step is to collect node voltage and node injection current data of the power system in normal operation or in a specific state. These data can be obtained through field measurement, simulation or historical data recording.

[0078] Node voltage refers to the voltage value of each node (such as bus) in the power system, which reflects the potential difference at different locations in the system. Node injection current refers to the current value flowing into or out of each node, which describes the power supply and load inside and outside the system and the interaction between them.

[0079] With these basic data, we can use the circuit theory methods (such as Kirchhoff's current law and voltage law) to calculate the node admittance matrix of the system. The node admittance matrix is ​​a complex matrix whose elements represent the linear relationship between the current and voltage between nodes. In AC power systems, this matrix contains the frequency characteristics of the system because it changes with the frequency.

[0080] S103: Determine a starting iteration vector for a first frequency point within the frequency range.

[0081] In the modal analysis or frequency response analysis of the power system, when it is necessary to calculate the corresponding system node admittance matrix starting from the first frequency point in the determined frequency range, it includes calculating the node admittance matrix itself and preparing the starting vector for the subsequent iterative process.

[0082] The node admittance matrix is ​​an important matrix that describes the relationship between current and voltage between nodes in the power system. In an AC power system, since impedance is a function of frequency, the node admittance matrix will also change with the change of frequency. In order to analyze the behavior of the system at a specific frequency, it is first necessary to calculate the node admittance matrix corresponding to the frequency point.

[0083] These parameters include line impedance, transformer ratio and impedance, generator internal impedance, etc. These parameters will vary with frequency.

[0084] Based on the collected system parameters, a mathematical model of the power system is established. This is usually a complex network model containing a large number of nodes and branches.

[0085] Using methods from circuit theory (such as Kirchhoff's current law and voltage law) combined with the mathematical model of the system, the node admittance matrix at a given frequency is calculated.

[0086] When performing eigenvalue analysis (solving the eigenvalues ​​and eigenvectors of the node admittance matrix), it is necessary to select a suitable iterative starting vector. The selection of this starting vector has an important influence on the convergence speed and stability of the iterative process.

[0087] For the first frequency point, a starting iteration vector can be selected based on the characteristics of the node admittance matrix. A common method is to construct the starting vector using some statistic of the node admittance matrix (such as the sum of all elements).

[0088] Calculate the sum of all elements in the node admittance matrix, that is, where Y ij is an element in the matrix, representing the admittance between node i and node j.

[0089] Use this sum to construct a starting iteration vector. A simple approach is to distribute the sum evenly over each element of the vector, but it is more common to use an approach that better reflects the characteristics of the matrix. For example, each element Y can be ij Divide by the sum to get a normalized value, and then use this value (or some transformation of it) as the initial value of the corresponding element in the starting vector. The expression is as follows:

[0090]

[0091] Because Y f is a sparse matrix, and the iteration starting vector x obtained by the above formula is (0) The distribution of elements in the matrix Y f The admittance distribution of each node in the is consistent, that is, from the perspective of the average value, the distribution is relatively uniform, which can make the initial vector x (0) The corresponding eigenvector is far away from the orthogonal state, which can speed up the iterative convergence.

[0092] S104, performing multiple iterative calculations starting from the starting iterative vector to obtain the maximum eigenvalue of the node admittance matrix, including: taking the ratio of the previous iterative vector to the node admittance matrix as a normalized vector; taking the ratio of the normalized vector to the element with the largest modulus in the normalized vector as the current iterative vector; stopping the iteration when a preset iteration termination condition is triggered during the iteration process, and obtaining the element with the largest modulus in the normalized vector as the maximum eigenvalue.

[0093] like Figure 2 As shown in the figure, during the iteration process, as the iteration proceeds, the elements of the vector may gradually become too large or too small, which will lead to instability or loss of precision in numerical calculations. Therefore, it is necessary to normalize the vectors during the iteration process to ensure that the size of its elements is within a controllable range.

[0094] Normalization is achieved by dividing each element of a vector by some norm of the vector (such as modulus). The normalization expression is as follows:

[0095]

[0096] x (k) Normalize and calculate x (k) Normalized vector

[0097] In this step, we need to find the element with the largest modulus (or absolute value) in the normalized vector. This element can be used to further evaluate the "size" of the vector, and can also be used to determine the termination condition of subsequent iterations. The expression is as follows:

[0098]

[0099] Among them, ||y (k) || ∞ Yes (k) The element in the vector with the largest magnitude.

[0100] The iteration termination condition is usually based on two main criteria: one is the convergence speed, and the other is the upper limit of the number of iterations.

[0101] To assess the rate of convergence, some form of residual or error is calculated and compared to a preset threshold.

[0102] Calculate the iteration termination condition V (k) and convergence acceleration α (k) , and let V (k) =||y (k) || ∞ -||y (k-1) || ∞ , α (k) =V (k) -V (k-1) ,in:

[0103] V (k) =||y (k) || ∞ -||y (k-1) || ∞ <ε

[0104] α (k) =V (k) -V (k-1) <δ

[0105] Among them, δ and ε are both set thresholds. When α (k) <δ, it means that the convergence speed is slow; when V (k) <ε, indicating that the iteration limit has been reached.

[0106] Only if α is satisfied (k) <δ、V (k) <ε, the iteration process is terminated.

[0107] When the iteration process is terminated, the maximum eigenvalue of the inverse matrix of the system node admittance matrix at the frequency point and its corresponding eigenvector have been found.

[0108] S105: Use the maximum eigenvalue as the starting iteration vector of the next frequency point in the frequency range, repeat the previous step, and obtain a maximum eigenvalue set of multiple frequency points.

[0109] In power system analysis or frequency response analysis, in order to fully understand the characteristics of the system at different frequencies, it is necessary to calculate the maximum eigenvalues ​​at multiple frequency points.

[0110] Starting from the second frequency point, the maximum eigenvalue vector calculated from the previous frequency point is used as the starting iteration vector. This can speed up the convergence process because the eigenvectors of adjacent frequency points often have a certain similarity.

[0111] Using the selected starting iteration vector, the iterative process described in S103 to S105 (including vector normalization, calculation of the maximum modulus element, checking of the iteration termination condition, etc.) is repeated until the iteration termination condition is met (such as the convergence speed is fast enough or the upper limit of the number of iterations is reached).

[0112] Once the iteration process for the current frequency point is completed and the maximum eigenvalue has been calculated, set the iteration counter (k) to the initial value and move on to the next frequency point. For the new frequency point, repeat the above process, using the maximum eigenvalue vector of the previous frequency point as the starting iteration vector.

[0113] Although the iteration process of each frequency point has its own independent termination condition, in this application, a global termination condition is required to decide whether to continue calculating the eigenvalues ​​of more frequency points. For example, if the predetermined number of frequency points has been reached, or the dynamic characteristics of the system no longer change significantly after a certain frequency, the iteration process can be terminated early.

[0114] S106. The reciprocal of the maximum eigenvalue in the maximum eigenvalue set is used to form the modal impedance of the power system as an analysis parameter.

[0115] In power system analysis, modal impedance is an important parameter that reflects the impedance characteristics of the system at different frequencies.

[0116] Arrange and collect the maximum eigenvalues ​​of all calculated frequency points to form a maximum eigenvalue set.

[0117] Then, the inverse of each maximum eigenvalue is calculated. In matrix analysis, the inverse of the eigenvalue of a matrix corresponds to the eigenvalue of the inverse matrix of the matrix. Therefore, the inverse of the eigenvalue calculated here actually reflects the eigenvalue of the inverse matrix of the system node admittance matrix.

[0118] Finally, these inverse values ​​are arranged in a certain order (usually in the order of corresponding frequencies) to form the modal impedance of the power system. Modal impedance is a frequency-dependent parameter set that describes the impedance characteristics of the system at different frequencies and is of great significance for analyzing the stability and resonance phenomena of the system.

[0119] S107. Determine a resonant frequency within the frequency range with a first frequency step size according to the analysis parameters, and determine a resonant frequency interval centered on the resonant frequency with a second frequency step size that is smaller than the first frequency step size.

[0120] First, the frequency range of the analysis needs to be determined, which is usually based on the characteristics of the system and the purpose of the analysis.

[0121] Select a relatively large frequency step size (first frequency step size) for the initial scan. The choice of this step size should balance the computational efficiency with the rough accuracy of the results. A step size that is too large may miss some important resonance points, while a step size that is too small will significantly increase the amount of computation.

[0122] In the selected frequency range, scan with the first frequency step, analyze the system response (such as modal impedance, transfer function, etc.) at each frequency point to find possible resonant frequencies. The purpose of this step is to quickly locate the frequency band area where resonance may exist.

[0123] Based on the analysis parameters (such as the peak of the modal impedance, the zero or pole of the transfer function, etc.), the approximate resonant frequency is identified from the coarse scan results.

[0124] Centered on the approximate resonant frequency identified in the previous step, a smaller frequency interval is set as the range of the fine scan.

[0125] Select a frequency step size (second frequency step size) smaller than the first frequency step size for fine scanning. This step size should be selected to ensure that subtle changes near the resonant frequency can be captured, so as to more accurately determine the resonant frequency and its characteristics.

[0126] In the set fine scan range, the second frequency step is scanned to analyze the system response at each frequency point in detail. The purpose of this step is to accurately determine the resonant frequency and further analyze the frequency interval near the resonant frequency, such as the resonant bandwidth, quality factor, etc.

[0127] Through the results of fine scanning analysis, the resonant frequency can be accurately determined, and with it as the center, the interval range of the resonant frequency can be determined according to the changes in the system response (such as the rate of decrease of the modal impedance, the phase change of the transfer function, etc.). This interval range is very important for understanding the resonant characteristics of the system, evaluating the stability of the system, and designing measures to suppress resonance.

[0128] The "two-step" analysis method effectively balances computational efficiency and analysis accuracy through a coarse-first-fine strategy. In the preliminary scan, a larger step size is used to quickly locate possible resonance areas; in the fine scan, a smaller step size is used to accurately determine the resonance frequency and the frequency interval around it. This method not only improves the speed of resonant modal analysis, but also ensures the accuracy of the analysis results.

[0129] Furthermore, since damping has a certain ability to suppress the resonance amplitude, the amplitude of the resonance can be significantly reduced near the resonance frequency, so the damping ratio can be used to characterize the attenuation ability of the system after resonance due to harmonic excitation. The existing modal analysis method only judges the degree of harmonic resonance based on the amplitude of the modal impedance, ignoring the influence of the damping ratio, which may lead to erroneous analysis conclusions.

[0130] This application introduces the half-power bandwidth method to further solve the modal analysis results. Taking the parallel resonance of the RLC parallel circuit as an example, the resonance is analyzed based on the half-power bandwidth method.

[0131] like Figure 2 As shown, U represents the voltage across the current source, represents the current source current, R represents the resistance, L and C represent the inductive reactance and capacitive reactance respectively. They represent the current flowing through the resistor, inductive reactance, and capacitive reactance respectively.

[0132] The frequency response function H(jω) of the equivalent impedance at both ends of the current source can be expressed as:

[0133]

[0134] Among them, ω is the frequency variable, ξ is the damping ratio, G0 is the amplification factor, ω n is the resonant frequency without damping, Q is the quality factor of parallel resonance, and ω0 is the resonant frequency with damping.

[0135] Specifically expressed as:

[0136]

[0137] When parallel resonance occurs, the input impedance is maximum.

[0138] Since the output amplitude of the output signal of the circuit is large when it is in the vicinity of the resonance point frequency, the area within 0.707 times of the maximum input impedance is called the resonance band, and the critical point of the resonance band is the half-power point.

[0139] The amplitude-frequency response of the frequency response function at the half-power point satisfies:

[0140]

[0141] According to the above formula, the damping ratio ξ can be expressed as:

[0142]

[0143] Where f0 is the peak value of the modal impedance curve |Z n (f0)|corresponding frequency, f1 and f2 are the half-power points of the modal impedance curve The corresponding frequency.

[0144] The modal impedance amplitude of parallel resonance represents the degree of resonance, while the damping ratio represents the system's ability to attenuate resonance. Therefore, when evaluating the harmonic resonance degree of the current system, the changes in modal impedance and damping ratio caused by changes in control parameters should be considered.

[0145] In order to reduce the dimension difference between the variables and make the modal impedance and damping ratio at different resonant frequencies have the same measurement scale, the data needs to be normalized. The maximum and minimum value normalization method is used to map the modal impedance amplitude and damping ratio of the modal analysis results to [0,1]. After the maximum and minimum value normalization, the output data is dimensionless. The normalization formula is:

[0146]

[0147] Among them, x is the input data, y is the output data, x max 、x min is the maximum and minimum value of the input data, y max ,y min are the maximum and minimum values ​​of the normalized range, respectively.

[0148] After normalizing the modal impedance value and damping ratio, the harmonic resonance index R is calculated. RD :

[0149] R RD =Δ|Z m |-Δξ

[0150] Among them, Δ|Z m | is the change of modal impedance amplitude obtained by improved power iteration method, and Δξ is the change of damping ratio obtained by half-power bandwidth method.

[0151] Through the above steps, the harmonic resonance analysis is realized, the harmonic resonance degree index is calculated, and the harmonic resonance is evaluated and analyzed. The beneficial effects are: it has the advantages of high calculation speed, more accurate result analysis, and is in line with reality. It is more suitable for harmonic resonance analysis of new power systems.

[0152] The present application also provides a power system harmonic resonance analysis device, comprising:

[0153] A selection module is used to determine the frequency range that needs to be analyzed in the power system;

[0154] A collection module, used to collect node voltages and node injection currents of the power system, and calculate a node admittance matrix according to the node voltages and node injection currents;

[0155] An initial module, used for determining a starting iteration vector of a first frequency point within the frequency range;

[0156] An iteration module is used to perform multiple iteration calculations starting from the starting iteration vector to obtain the maximum eigenvalue of the node admittance matrix, including: taking the ratio of the previous iteration vector to the node admittance matrix as a normalized vector; taking the ratio of the normalized vector to the element with the largest modulus in the normalized vector as the current iteration vector; stopping the iteration when a preset iteration termination condition is triggered during the iteration process, and obtaining the element with the largest modulus in the normalized vector as the maximum eigenvalue;

[0157] A loop module, used for taking the maximum eigenvalue as a starting iteration vector for a next frequency point within the frequency range, repeating the previous step, and obtaining a maximum eigenvalue set for a plurality of frequency points;

[0158] A parameter module, used for forming the modal impedance of the power system by the inverse of the maximum eigenvalue in the maximum eigenvalue set as an analysis parameter;

[0159] The analysis module is used to determine the resonant frequency within the frequency range with a first frequency step according to the analysis parameters, and to determine the resonant frequency interval centered on the resonant frequency with a second frequency step smaller than the first frequency step.

[0160] The present application also provides a power system harmonic resonance analysis device, comprising:

[0161] Memory;

[0162] A processor is used to retrieve the computer executable program of the above-mentioned power system harmonic resonance analysis method stored in the memory, and execute: determining the frequency range that needs to be analyzed in the power system; collecting the node voltage and node injection current of the power system, and calculating the node admittance matrix according to the node voltage and node injection current; determining the starting iteration vector of the first frequency point within the frequency range; performing multiple iteration calculations starting from the starting iteration vector to obtain the maximum eigenvalue of the node admittance matrix, including: taking the ratio of the previous iteration vector to the node admittance matrix as a normalized vector; comparing the normalized vector with the normalized vector with the largest modulus. The ratio of the elements is used as the iteration vector for this time; when a preset iteration termination condition is triggered during the iteration process, the iteration is stopped, and the element with the largest modulus in the normalized vector is obtained as the maximum eigenvalue; the maximum eigenvalue is used as the starting iteration vector of the next frequency point in the frequency range, and the previous step is repeated to obtain the maximum eigenvalue set of multiple frequency points; the reciprocal of the maximum eigenvalue in the maximum eigenvalue set is used to form the modal impedance of the power system as an analysis parameter; according to the analysis parameters, the resonant frequency is determined within the frequency range with a first frequency step, and the resonant frequency interval centered on the resonant frequency is determined with a second frequency step that is smaller than the first frequency step.

[0163] The present application also provides a storage medium, comprising: storing a computer executable program, wherein the computer executable program is used to be called by a processor to execute the steps of the above-mentioned power system harmonic resonance analysis method.

[0164] The embodiments and / or implementation methods described above are only used to illustrate the preferred embodiments and / or implementation methods for realizing the technology of the present invention, and are not intended to limit the implementation methods of the technology of the present invention in any form. Any technical personnel in this field may make slight changes or modifications to other equivalent embodiments without departing from the scope of the technical means disclosed in the content of the present invention, but they should still be regarded as technologies or embodiments that are essentially the same as the present invention.

[0165] This article uses specific examples to illustrate the principles and implementation methods of this application. The description of the above embodiments is only used to help understand the method and its core ideas of this application. The above is only the preferred implementation method of this application. It should be pointed out that due to the limitations of textual expression and the objective existence of infinite specific structures, ordinary technicians in this technical field can make some improvements, modifications or changes without departing from the principles of this application, and combine the above technical features in an appropriate manner; the improvements, modifications, changes or combinations, or the direct application of the concept and technical solution of the invention to other occasions without improvement, should be regarded as the scope of protection of this application.

Claims

1. A method for analyzing harmonic resonance in power systems. It is characterized in that include: Determine the frequency range that needs to be analyzed in the power system; Collecting node voltages and node injection currents of the power system, and calculating a node admittance matrix according to the node voltages and node injection currents; Determine a starting iteration vector for a first frequency point within the frequency range; Performing multiple iterative calculations starting from the starting iterative vector to obtain the maximum eigenvalue of the node admittance matrix, including: taking the ratio of the previous iterative vector to the node admittance matrix as a normalized vector; taking the ratio of the normalized vector to the element with the largest modulus in the normalized vector as the current iterative vector; stopping the iteration when a preset iterative termination condition is triggered during the iteration process, and obtaining the element with the largest modulus in the normalized vector as the maximum eigenvalue; Using the maximum eigenvalue as the starting iteration vector of the next frequency point in the frequency range, repeating the previous step, and obtaining a maximum eigenvalue set of multiple frequency points; The reciprocal of the maximum eigenvalue in the maximum eigenvalue set is used to form the modal impedance of the power system as an analysis parameter; According to the analysis parameters, a resonant frequency is determined within the frequency range with a first frequency step, and a resonant frequency interval centered on the resonant frequency is determined with a second frequency step smaller than the first frequency step.

2. According to the power system harmonic resonance analysis method of claim 1, It is characterized in that The modal impedance of the power system is formed by the reciprocal of the maximum eigenvalue in the maximum eigenvalue set as an analysis parameter, including: Calculating a damping ratio according to the modal impedance; The modal impedance and the damping ratio are used as analysis parameters.

3. According to the power system harmonic resonance analysis method of claim 2, It is characterized in that The damping ratio is obtained according to the impedance calculation, and the expression is as follows: Among them, the f 0 is the frequency corresponding to the peak value of the modal impedance curve, f 1 、f 2 are the frequencies corresponding to the half-power points of the modal impedance curve.

4. According to the power system harmonic resonance analysis method of claim 2, It is characterized in that Determining a resonant frequency within the frequency range with a first frequency step according to the analysis parameter, and determining a resonant frequency interval centered on the resonant frequency with a second frequency step smaller than the first frequency step, comprising: The modal impedance and the damping ratio are normalized to the following expression: In the formula, x is the input data; y is the output data; x max 、x min is the maximum and minimum value of the input data; y max ,y min are the maximum and minimum values ​​of the normalized range, respectively.

5. According to the power system harmonic resonance analysis method of claim 4, It is characterized in that According to the analysis parameters, determining the resonant frequency within the frequency range with a first frequency step, and determining the resonant frequency interval centered on the resonant frequency with a second frequency step smaller than the first frequency step, further comprising: Calculate the harmonic resonance index R RD : R RD =ΔZ m |-Dx Among them, Δ|Z m | is the change in modal impedance amplitude, and Δξ is the change in damping ratio.

6. According to the power system harmonic resonance analysis method of claim 1, It is characterized in that The preset iteration termination condition includes: V (k) =||and (k) || ∞ -||and (k-1) || ∞ α (k) =V (k) -V (k-1) When α (k) <δ,V (k) <ε, the iteration terminates; Among them, y (k) is a normalized vector, ||y (k) || ∞ Yes (k) The element with the largest modulus in the vector, δ and ε are the set thresholds.

7. According to the power system harmonic resonance analysis method of claim 1, It is characterized in that The expression of the starting iteration vector is as follows: Among them, S(Y f ) is the node admittance matrix Y f The sum of all elements in Y ij is the node admittance matrix Y f One of the elements.

8. A power system harmonic resonance analysis device, It is characterized in that include: Selection module for determining the frequency range to be analyzed in the power system; A collection module, used to collect node voltages and node injection currents of the power system, and calculate a node admittance matrix according to the node voltages and node injection currents; An initial module, used for determining a starting iteration vector of a first frequency point within the frequency range; An iteration module is used to perform multiple iteration calculations starting from the starting iteration vector to obtain the maximum eigenvalue of the node admittance matrix, including: taking the ratio of the previous iteration vector to the node admittance matrix as a normalized vector; taking the ratio of the normalized vector to the element with the largest modulus in the normalized vector as the current iteration vector; stopping the iteration when a preset iteration termination condition is triggered during the iteration process, and obtaining the element with the largest modulus in the normalized vector as the maximum eigenvalue; A loop module, used for taking the maximum eigenvalue as a starting iteration vector for a next frequency point within the frequency range, repeating the previous step, and obtaining a maximum eigenvalue set for a plurality of frequency points; A parameter module, used for forming the modal impedance of the power system from the reciprocal of the maximum eigenvalue in the maximum eigenvalue set as an analysis parameter; The analysis module is used to determine the resonant frequency within the frequency range with a first frequency step according to the analysis parameters, and to determine the resonant frequency interval centered on the resonant frequency with a second frequency step smaller than the first frequency step.

9. A power system harmonic resonance analysis device, It is characterized in that include: Memory; A processor, for retrieving a computer executable program of a power system harmonic resonance analysis method according to any one of claims 1 to 7 stored in the memory, and executing: determining a frequency range to be analyzed in the power system; collecting node voltages and node injection currents of the power system, and calculating a node admittance matrix according to the node voltages and node injection currents; Determine a starting iteration vector for a first frequency point within the frequency range; Perform multiple iterative calculations starting from the starting iteration vector to obtain the maximum eigenvalue of the node admittance matrix, including: taking the ratio of the previous iteration vector to the node admittance matrix as a normalized vector; taking the ratio of the normalized vector to the element with the largest modulus in the normalized vector as the current iteration vector; stopping the iteration when a preset iteration termination condition is triggered during the iteration process, and obtaining the element with the largest modulus in the normalized vector as the maximum eigenvalue; taking the maximum eigenvalue as the starting iteration vector of the next frequency point in the frequency range, repeating the previous step, and obtaining the maximum eigenvalue set of multiple frequency points; forming the modal impedance of the power system with the inverse of the maximum eigenvalue in the maximum eigenvalue set as an analysis parameter; and determining the resonant frequency within the frequency range with a first frequency step according to the analysis parameter, and determining the resonant frequency interval centered on the resonant frequency with a second frequency step smaller than the first frequency step.

10. A storage medium, It is characterized in that include: A computer executable program is stored, and the computer executable program is used to be called by a processor to execute the steps of a power system harmonic resonance analysis method as described in any one of claims 1 to 7.

Images