A photovoltaic grid-connected circulating current resonance analysis method and system based on second-order mode sensitivity

Abstract

A method and system for analyzing photovoltaic grid-connected circulating current resonance based on second-order modal sensitivity. The method includes: establishing the network node admittance matrix of the photovoltaic grid-connected inverter system; detecting the circulating current resonance frequency; determining the optimal observable node, the optimal excitable node, and the circulating current resonance center point; obtaining and standardizing the first-order modal sensitivity of the eigenvalue amplitude for parallel and series elements in the network; obtaining and standardizing the second-order modal sensitivity of the parallel and series elements based on the standardized first-order modal sensitivity; evaluating the participation of circulating current resonance elements by comparing the standardized first-order and second-order modal sensitivities, and defining a critical factor for the percentage adjustment of element parameters to select key circulating current resonance elements for circulating current resonance suppression based on the adjustment amount of element parameters. This invention can refine the granularity of circulating current resonance analysis, improve the efficiency of circulating current resonance analysis, provide a basis for circulating current resonance suppression, and guide the selection of photovoltaic power plant equipment and topology design.

Description

Technical Field

[0001] This invention belongs to the field of photovoltaic grid-connected system resonance analysis technology, and relates to a photovoltaic grid-connected circulating current resonance analysis method and system based on second-order mode sensitivity. Background Technology

[0002] With the continuous growth of distributed photovoltaic (PV) scale in my country, the situation regarding distributed PV grid connection and localized consumption is becoming increasingly severe. As an important energy conversion unit between PV and the grid, distributed PV grid-connected inverters are often connected to the point of common coupling in parallel with multiple units. When the grid connection parameters of each inverter are not completely the same or the carrier phase is not synchronized, circulating current resonance will occur, posing a challenge to the safe and stable operation of the PV grid-connected system.

[0003] In a multi-unit grid-connected inverter system, due to the asynchronous grid connection parameters of each inverter and the existence of grid impedance, the output current of each grid-connected inverter is not completely fed into the grid. A portion of the current will also circulate between the inverters, potentially causing circulating current resonance that leads to instability in the grid-connected system. Identifying and tracing the key components that trigger circulating current resonance provides guidance for resonance suppression.

[0004] Currently, the resonance analysis of grid-connected photovoltaic (PV) systems mainly employs two methods: impedance frequency scanning and modal analysis. These methods primarily address the resonance problem between the grid-connected inverter and the grid, and the proposed solutions focus on ensuring the stability of the PCC voltage and grid-connected current. However, the circulating current resonance problem between grid-connected inverters is often overlooked. Therefore, for multi-PV inverter grid-connected systems, there is an urgent need to develop an analytical method capable of acquiring inverter circulating current resonance information to better characterize the circulating current resonance features and provide guidance for improving power quality and optimizing PV power plant topology. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a photovoltaic grid-connected circulating current resonance analysis method and system based on second-order mode sensitivity. This method accurately obtains the system's circulating current resonance frequency, the participation level of each node, information on the highest excitable node and the best observable node for circulating current resonance, the sensitivity of each component parameter to circulating current resonance, and how to adjust system component parameters to better suppress circulating current resonance. It refines the granularity of circulating current resonance analysis, improves its efficiency, provides a basis for suppressing circulating current resonance, and guides the selection of photovoltaic power plant equipment and topology design.

[0006] The present invention adopts the following technical solution.

[0007] A photovoltaic grid-connected circulating current resonance analysis method based on second-order mode sensitivity is used to achieve circulating current resonance frequency detection, determination of the optimal observable node, optimal excitation node and circulating current resonance center, evaluation of the participation of circulating current resonance components, and determination of key components for circulating current resonance suppression based on the critical factor of component parameter adjustment percentage. The method includes the following steps:

[0008] Step 1: Based on the parameters of the photovoltaic grid-connected inverter system and the output admittance of each inverter, establish the network node admittance matrix of the photovoltaic grid-connected inverter system;

[0009] Step 2: Decompose the features of the network node admittance matrix to obtain eigenvalues, left and right eigenvectors. Based on the eigenvalues, find the frequency corresponding to the singular matrix of the node admittance matrix within the preset frequency range, which is the circulating resonant frequency, and realize the detection of the circulating resonant frequency.

[0010] Step 3: Determine the best observable node and the best excitable node of the circulating resonance based on the left and right eigenvectors at the circulating resonant frequency, and obtain the circulating resonance participation factor of each node. Determine the circulating resonance center point by comparing the circulating resonance participation factors of each node.

[0011] Step 4: Based on the left and right eigenvectors at the circulating resonant frequency, obtain the eigenvalue amplitude for the first-order mode sensitivity of the circulating resonant for parallel and series elements in the network, and perform standardization processing.

[0012] Step 5: Obtain the second-order modal sensitivities of parallel and series elements based on the standardized first-order modal sensitivities to reflect the changing trend of the first-order modal sensitivities with the element parameters, and standardize the second-order modal sensitivities.

[0013] Step 6: Evaluate the participation of circulating resonant components by comparing the standardized first-order modal sensitivity and second-order modal sensitivity, calculate the critical factor for component parameter adjustment percentage, compare it with the component parameter adjustment amount, and select the component with the best circulating resonance suppression effect as the key component for circulating resonance suppression.

[0014] Preferably, in step 1, the network node admittance matrix Y is constructed based on the output admittance of each inverter and the system parameters. n+1 :

[0015]

[0016] Where n is the number of parallel inverters;

[0017] y eqn Y g y fi Let represent the equivalent output admittance of the nth grid-connected inverter, the equivalent grid admittance, and the equivalent line admittance from inverter i to the grid connection point, respectively.

[0018] Preferably, in step 2, the network node admittance matrix Y is... n+1 Perform eigenvalue decomposition:

[0019] Y n+1 =LΛT

[0020] Among them, Λ=diag(λ1,λ2,…λ m (, ...) denotes the eigenvalue diagonal matrix;

[0021] L = [l1, l2, ..., l m [t1,t2,…,t] and T=[t1,t2,…,t m ,…] T Let L and T be the left and right eigenvector matrices, respectively, and satisfy L = T. -1 The subscript m indicates the m-th circulating resonant mode, and the mode corresponding to the minimum eigenvalue is the critical mode;

[0022] λ m l m t m Representing the nodal admittance matrix Y n+1 The m-th eigenvalue, the left eigenvector of the m-th mode, and the right eigenvector of the m-th mode;

[0023] Define U = TV, J = TI, then we can obtain:

[0024]

[0025] The matrix form is:

[0026] U = Λ -1 J

[0027] In the formula: U and J represent the modal voltage vector and modal current vector, respectively, Λ -1 Indicates modal impedance;

[0028] From the above equation, we can obtain that when λ m When the value is small, the elements in U are prone to have maximum values, which in turn leads to circulating resonance.

[0029] Preferably, in step 2, the modal impedance within a preset frequency range is calculated, and the frequency corresponding to the maximum value of the modal impedance is selected as the circulating resonant frequency.

[0030] Preferably, in step 3, each element of the left eigenvector corresponding to the circulating resonant frequency reflects the observability of each bus for circulating resonance, and each element of the right eigenvector reflects the excitation capability of each node for circulating resonance after current injection.

[0031] For the circulating resonant mode m, the node corresponding to the maximum value of the left eigenvector element is the best observable node, and the node corresponding to the maximum value of the right eigenvector element is the best excitable node.

[0032] Based on the elements in the left and right eigenvector matrices, the index V, composed of the circulation resonance participation factor, is obtained. By comparison, the node with the largest participation factor is identified as the circulation resonance center point.

[0033] Among them, the indicator V is:

[0034]

[0035] diagonal elements l in the index V matrix nm t mn is the participation factor of node n in the circulating resonant mode m;

[0036] l nm t mn I n Let n represent the observability of node n with respect to resonant mode m, the excitability of node n with respect to resonant mode m, and the injected current at node n, respectively.

[0037] Preferably, step 4 specifically includes:

[0038] Step 41: Obtain the eigenvalue λ based on the left and right eigenvectors corresponding to the circulating resonant frequency. m For the admittance matrix Y n+1 element Y ij The sensitivity is:

[0039]

[0040] Among them, t mi This is the i-th element in the m-th row of the right eigenvector matrix;

[0041] l jm The j-th element in the m-th column of the left eigenvector matrix;

[0042] Further obtain the eigenvalue λ m Sensitivity matrix S m ;

[0043] Step 42: Set the sensitivity matrix S m The b-th row and b-th column element S m,bb and eigenvalue λ m We obtain the following by decomposing the real and imaginary parts:

[0044]

[0045] Among them, S r Si Representing the sensitivity matrix S respectively m The b-th row and b-th column element S m,bb The real and imaginary parts;

[0046] λ r , λ i They represent the eigenvalues ​​λ respectively. m The real and imaginary parts;

[0047] Step 43: Based on the decomposition results of step 42, we obtain:

[0048] Eigenvalue magnitude |λ m |For the parallel element y at node b in the network sh The first-order modal sensitivity of G+jB is:

[0049]

[0050] Eigenvalue magnitude |λ m |For the series element z between node i and node j sh The first-order modal sensitivity of =R+jX is:

[0051]

[0052] Wherein, G and B are conductance and susceptance, respectively; R and X are resistance and reactance, respectively.

[0053] Step 44: Standardize the first-order modal sensitivity obtained in step 43 as follows:

[0054]

[0055] Where α represents the network element parameter, which can be any one of G, B, R, and X.

[0056] Preferably, step 5 specifically includes:

[0057] Step 51: Based on the standardized first-order modal sensitivity σ α The partial derivative of the element with respect to the element parameter α defines the second-order modal sensitivity σ' of the element. α :

[0058]

[0059] Where, σ' α The second-order sensitivity of the element mode;

[0060] Step 52: Based on the definition in Step 51, the following calculation is obtained:

[0061] Second-order sensitivity of series reactance mode:

[0062]

[0063] In the formula: Second-order sensitivity of parallel susceptance mode:

[0064]

[0065] Parallel point-guided mode second-order sensitivity:

[0066]

[0067] Wherein, G and B are conductance and susceptance, respectively; R and X are resistance and reactance, respectively.

[0068] S r S i Representing the sensitivity matrix S respectively m The b-th row and b-th column element S m,bb The real and imaginary parts; λ r , λ i They represent the eigenvalues ​​λ respectively. m The real and imaginary parts;

[0069] Step 53: Standardize the second-order modal sensitivity of the element obtained in step 52 as follows:

[0070]

[0071] Where α represents the network element parameter, which can be any one of G, B, R, and X.

[0072] Preferably, in step 6, for elements A and B in the network, in |σ A |>|σ B |and σ A '>σ B '

[0073] In this case, element A is the more sensitive element for circulating resonance, that is, element A is the key element for circulating resonance, and the parameters of this element are adjusted to suppress circulating resonance.

[0074] For elements A and B in the network, if |σ A |>|σ B |When, if σ A '<σ B ', then it means that during the component parameter adjustment process, |σ will appear. A |<|σ B In situations where it's impossible to directly determine which component parameter adjustment will better suppress commutator resonance, a critical factor σ for the percentage adjustment of component parameters is defined. criticalWhen guiding the adjustment of component parameters to be consistent, it determines which component adjustment will better suppress circulating current resonance. The specific process is as follows: determine the component parameter adjustment amount |Δα|, and set σ... critical Compare with |Δα|:

[0075] If |Δα|≤σ critical Component A is the key component for circulating current resonance. The parameters of this component should be adjusted to suppress circulating current resonance.

[0076] If |Δα|>σ critical Component B is the key component for circulating current resonance. The parameters of this component should be adjusted to suppress circulating current resonance.

[0077] Preferably, the critical factor σ for adjusting the component parameters is... critical The calculation formula is:

[0078]

[0079] In the formula:

[0080] λ m For eigenvalues;

[0081] σ A σ B The normalized first-order modal sensitivity of components A and B;

[0082] σ A '、σ B ' is the normalized second-order modal sensitivity of elements A and B.

[0083] A photovoltaic grid-connected circulating current resonance analysis system based on second-order modal sensitivity includes:

[0084] The admittance matrix construction module is used to establish the network node admittance matrix of the photovoltaic grid-connected inverter system based on the parameters of the photovoltaic grid-connected inverter system and the output admittance of each inverter.

[0085] The circulating resonant frequency detection module is used to decompose the features of the admittance matrix of network nodes to obtain eigenvalues, left and right eigenvectors. Based on the eigenvalues, it finds the frequency corresponding to the singular matrix of the node admittance matrix within a preset frequency range, which is the circulating resonant frequency, thus realizing the detection of the circulating resonant frequency.

[0086] The circulating resonance center point determination module is used to determine the best observable node and the best excitable node of the circulating resonance based on the left and right eigenvectors at the circulating resonance frequency, and to obtain the circulating resonance participation factor of each node. The circulating resonance center point is determined by comparing the circulating resonance participation factors of each node.

[0087] The first-order modal sensitivity calculation module is used to obtain the first-order modal sensitivity of the circulating current resonance based on the left and right eigenvectors at the circulating resonant frequency, respectively, for parallel and series elements in the network, and then perform standardization processing.

[0088] The second-order modal sensitivity calculation module is used to obtain the second-order modal sensitivity of parallel and series elements based on the first-order modal sensitivity to reflect the changing trend of the first-order modal sensitivity with the element parameters, and to standardize the second-order modal sensitivity.

[0089] The participation evaluation module for circulating resonant components is used to evaluate the participation of circulating resonant components by comparing the standardized first-order modal sensitivity and second-order modal sensitivity, and to calculate the critical factor for the percentage adjustment of component parameters. This critical factor is then compared with the adjustment amount of the component parameters to select the component with the best circulating resonance suppression effect as the key component for circulating resonance suppression.

[0090] A terminal includes a processor and a storage medium; the storage medium is used to store instructions.

[0091] The processor is configured to operate according to the instructions to execute the steps of the method.

[0092] A computer-readable storage medium having a computer program stored thereon that, when executed by a processor, implements the steps of the method.

[0093] The beneficial effects of this invention are compared with those of the prior art:

[0094] This invention enables the determination of circulating resonant frequency, the determination of the highest excitable node and the best observable node of circulating resonance, the sensitivity of each network element to circulating resonance, the determination of the second-order mode sensitivity of each network element, and the evaluation of the participation of circulating resonant elements.

[0095] Based on the parameters of the photovoltaic grid-connected inverter and the control model, the output admittance of the multi-photovoltaic grid-connected inverter system is derived, and the node admittance matrix of the multi-photovoltaic grid-connected inverter system is constructed. This method is applicable even when the parameters of the multi-inverter system are inconsistent and the control methods are different.

[0096] The constructed node admittance matrix is ​​subjected to eigenvalue decomposition to obtain eigenvalues, left and right eigenvectors. Based on the eigenvalues, the frequency corresponding to the singular matrix of the node admittance matrix within a preset frequency range is found to determine the circulating resonant frequency, thus realizing the detection of the circulating resonant frequency. Based on the left and right eigenvectors under the circulating resonant frequency, the best observable node and the best excitable node of the circulating resonance are determined, and the circulating resonance participation factor of each node is obtained. By comparing the circulating resonance participation factors of each node, the circulating resonance center point is determined. The key inverter node causing the circulating resonance and the influence range of the circulating resonance can be determined.

[0097] The optimal observable node and the optimal excitable node are determined based on the left and right eigenvectors corresponding to the circulating resonant frequency, respectively. The sensitivity of the eigenvalue amplitude to the first-order mode of circulating resonance for parallel and series elements in the network is obtained and standardized. This reflects the degree of participation of each network element in the circulating resonance under the current network parameters. The network elements that play a key role in the circulating resonant mode can be identified, as well as their influence on the circulating resonance amplitude.

[0098] Based on the standardized first-order modal sensitivity, the second-order modal sensitivity of parallel and series components is obtained to reflect the trend of first-order modal sensitivity with component parameters, and the second-order modal sensitivity is standardized to reflect the trend of first-order modal sensitivity with network component parameter adjustments. The participation of circulating current resonant components is evaluated by comparing the standardized first-order and second-order modal sensitivities to select key components for circulating current resonance suppression. A critical factor for network component parameter adjustment is also defined, which can determine which network component can better suppress circulating current resonance under different component parameter adjustments, guiding circulating current resonance suppression and parameter design in multi-inverter systems. This invention can perform comprehensive circulating current resonance analysis on multi-PV inverter grid-connected systems, which can consist of identical inverters or inverters with different parameters and control strategies. It refines the granularity of circulating current resonance analysis, improves its efficiency, provides a basis for circulating current resonance suppression, and guides PV power plant equipment selection and topology design. Attached Figure Description

[0099] Figure 1 This is a flowchart of the method of the present invention;

[0100] Figure 2 This is a diagram showing the main circuit and control structure of a three-phase LCL grid-connected inverter.

[0101] Figure 3 The Norton equivalent network for a three-phase LCL grid-connected inverter;

[0102] Figure 4 Norton equivalent model for multi-photovoltaic grid-connected inverter systems. Detailed Implementation

[0103] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of this invention. The embodiments described in this application are merely some embodiments of this invention, and not all embodiments. Based on the spirit of this invention, other embodiments obtained by those skilled in the art without creative effort are all within the protection scope of this invention.

[0104] like Figure 1As shown, Embodiment 1 of the present invention provides a photovoltaic grid-connected circulating current resonance analysis method based on second-order mode sensitivity, which realizes the detection of circulating current resonance frequency, determination of optimal observable node, optimal excitation node and circulating current resonance center, evaluation of the participation of circulating current resonance components, and determination of key components for circulating current resonance suppression based on the critical factor of component parameter adjustment percentage. The method includes the following steps:

[0105] Step 1: Based on the parameters of the photovoltaic grid-connected inverter system and the output admittance of each inverter, establish the network node admittance matrix of the photovoltaic grid-connected inverter system;

[0106] More preferably, Figure 2 The circuit topology and control structure of a single grid-connected inverter are given, where U dc This represents the DC-side voltage; L1, L2, and C are the inverter-side inductor, grid-side inductor, and filter capacitor, respectively, forming an LCL filter; Z g The equivalent impedance of the power grid; u ga,b,c For three-phase power grid voltage; i Ca,b,c i represents the current of the three-phase filter capacitor. ga,b,c This refers to the three-phase grid-connected current; u PCCa,b,c This is the three-phase PCC voltage.

[0107] The inverter employs a dual closed-loop control method with feedback from capacitor current and grid-connected current in the αβ coordinate system, where: u C K is the voltage across the filter capacitor. PWM H represents the proportional gain of the PWM stage. iC For i C Feedback coefficient; G i (s) is the transfer function of the current regulator, which is a quasi-proportional-resonant (QPR) regulator.

[0108] Figure 3 The method of representing the photovoltaic array, inverter, and LCL filter using Norton equivalents is given. eq and admittance y si (i = 1, 2, ..., n) Norton equivalent network.

[0109] Based on the network parameters and the inverter system control strategy, the equivalent impedance y of the photovoltaic inverter system can be obtained. eqi and equivalent current source i eq The expression is:

[0110]

[0111] in:

[0112] Figure 4This is the Norton equivalent circuit diagram for a multi-PV grid-connected inverter system. It illustrates the connection relationship between the PV inverters and the power grid. Each inverter is connected to the public grid at point PCC via an LCL filter and line impedance, i.e., the PV inverter and LCL filter are connected through the line equivalent impedance y. fi (i = 1, 2, ..., n) are connected to the power grid, and the power grid side is equivalent to the grid electromotive force u. g and equivalent impedance Y g Composition. Each inverter has an independent photovoltaic array at its input terminal, and the signals and parameters of each inverter in the same system may be different. Figure 4 The equivalent circuit shown uses the inverter output admittance and system parameters to construct the network node admittance matrix Y. n+1 , where n is the number of parallel inverters. This is expressed as:

[0113]

[0114] y eqn Y g y fi Let represent the equivalent output admittance of the nth grid-connected inverter, the equivalent grid admittance, and the equivalent line admittance from inverter i to the grid connection point, respectively.

[0115] The equivalent output admittance of each inverter was calculated based on the parameters of the photovoltaic grid-connected inverter system and the inverter control strategy, and the node admittance matrix of the grid-connected system was established on this basis.

[0116] Step 2: Decompose the features of the network node admittance matrix to obtain eigenvalues, left and right eigenvectors. Based on the eigenvalues, find the frequency corresponding to the singular matrix of the node admittance matrix within the preset frequency range, which is the circulating resonant frequency, and realize the detection of the circulating resonant frequency.

[0117] More preferably, the network node admittance matrix Y n+1 Perform eigenvalue decomposition:

[0118] Y n+1 =LΛT

[0119] Among them: Λ=diag(λ1,λ2,…λ m (, ...) denotes the eigenvalue diagonal matrix;

[0120] L = [l1, l2, ..., l m [t1,t2,…,t] and T=[t1,t2,…,t m ,…] T The left and right eigenvector matrices are respectively, satisfying L = T -1 .

[0121] The subscript m indicates the m-th circulating resonant mode, and the mode corresponding to the minimum eigenvalue is the critical mode;

[0122] λ m l m t m Representing the nodal admittance matrix Y n+1 The m-th eigenvalue, the left eigenvector of the m-th mode, and the right eigenvector of the m-th mode;

[0123] Define U = TV, J = TI, then we can obtain:

[0124]

[0125] The matrix form is:

[0126] U = Λ -1 J

[0127] In the formula: U and J represent the modal voltage vector and modal current vector, respectively, Λ -1 Indicates modal impedance;

[0128] From the above equation, we can obtain that when λ m When the value is small, the elements in U are prone to have maximum values, which in turn leads to circulating resonance.

[0129] When circulating resonance occurs, the system admittance matrix exhibits eigenvalues ​​that approach zero, meaning the system admittance matrix is ​​close to singular. The minimum value among the eigenvalues ​​of the admittance matrix represents the critical mode of circulating resonance.

[0130] The frequency range for which resonance analysis is required is preset, and the modal impedance within the preset frequency range is calculated using Δf = 5Hz as the scale. The frequency corresponding to the maximum value of the modal impedance when the circulating resonance occurs is the circulating resonance frequency.

[0131] The system achieves a preset frequency range for circulating current resonance and performs eigenvalue decomposition on the node admittance matrix within this frequency band. Based on the characteristic that the node admittance matrix is ​​approximately singular when circulating current resonance occurs, the system finds the frequency at which the admittance matrix satisfies this approximately singularity; this frequency is the circulating current resonance frequency, thus enabling circulating current resonance frequency detection. Furthermore, the eigenvalue derivative can be defined as the modal impedance, and the modal impedance and spectrum curves at this time can be output.

[0132] Steps 1 and 2 above involve constructing the grid-connected system admittance matrix based on the parameters of the multi-photovoltaic grid-connected inverter system and the inverter control strategy, and performing feature analysis to obtain the eigenvalues ​​and eigenvectors of the admittance matrix at each frequency. Based on the characteristic that the admittance matrix is ​​close to singular when the circulating current resonance occurs, the frequency corresponding to the near-singular matrix within the preset frequency range is found as the circulating current resonance frequency.

[0133] Step 3: Determine the best observable node and the best excitable node of the circulating resonance based on the left and right eigenvectors at the circulating resonant frequency, and obtain the circulating resonance participation factor of each node. Determine the circulating resonance center point by comparing the circulating resonance participation factors of each node.

[0134] Among them, the best observable node of the circulating resonance indicates that the circulating resonance at this node has the best observability at this frequency; the best controllable node of the circulating resonance indicates that the circulating resonance at this node has the best controllability at this frequency; combining the two indicators, the circulating resonance participation factor of each node can be obtained, which reflects the distance that the circulating resonance can propagate at this frequency and is used to determine the influence range of the circulating resonance. The generatrix with the largest participation factor is the circulating resonance center.

[0135] More preferably, the left and right eigenvectors obtained by the eigendecomposition of the admittance matrix corresponding to the circulating resonant frequency can determine the best observable node and the highest excitable node of the circulating resonant. Based on the left and right eigenvectors obtained by the eigendecomposition of the admittance matrix at the circulating resonant frequency, the circulating resonant participation factor of each node is defined to determine the circulating resonant center point.

[0136] For a circulating current resonance at a certain frequency, the elements of the left eigenvector obtained from the eigendecomposition of the admittance matrix at that frequency reflect the observability of each bus for that circulating current resonance; while the elements of the right eigenvector reflect the excitation capability of each node after current injection. For the circulating current resonance mode m, the node corresponding to the maximum value in the left eigenvector is the best observable node, and the node corresponding to the maximum value in the right eigenvector is the best excitation node. Combining these two into a single index, we have:

[0137]

[0138] Among them, the diagonal element l nm t mn PF is the participation factor of node n in the circulating resonant mode m. bm The magnitude of the participation factor at each node can reflect the matrix of the propagation of the circulating resonant energy, and the node with the largest participation factor is the circulating resonant center.

[0139] l nm t mn I n Let n represent the observability of node n with respect to resonant mode m, the excitability of node n with respect to resonant mode m, and the injected current at node n, respectively.

[0140] Step 4: Based on the left and right eigenvectors at the circulating resonant frequency, obtain the eigenvalue amplitude for the first-order mode sensitivity of the circulating resonant for parallel and series elements in the network, and perform standardization processing.

[0141] This step defines the circulating current resonance mode sensitivity of parallel and series components in the network based on the circulating current resonance participation factor of each node, and normalizes them to evaluate the sensitivity of each component to circulating current resonance. Specifically, it includes:

[0142] Step 41: To further determine the impact of electrical components at each node on circulating current resonance, locate the key components of circulating current resonance. Calculate the key eigenvalue λ. m For the admittance matrix Y n+1 element Y ij The sensitivity is:

[0143]

[0144] Where: t mi Let l be the i-th element in the m-th row of the right eigenvector matrix. jm The j-th element in the m-th column of the left eigenvector matrix;

[0145] The key eigenvalue λ can be obtained further. m Sensitivity matrix S m .

[0146] Step 42: Set the sensitivity matrix S m The b-th row and b-th column element S m,bb and modal eigenvalues ​​λ m By decomposing the real and imaginary parts, we can obtain:

[0147]

[0148] Step 43: Therefore, the magnitude of the key eigenvalue |λ m For the parallel element at node b in the network (represented by conductance and susceptance, i.e., y...), sh The first-order modal sensitivity of ( =G+jB) is:

[0149]

[0150] Key eigenvalue amplitude |λ m For the series element between node i and node j (represented by resistance and reactance, i.e., z...), sh =R+jX), and its corresponding first-order modal sensitivity is:

[0151]

[0152] Step 44: First-order modal sensitivity can reflect the response of elements in the network to modal eigenvalues ​​|λ. m The degree of influence. To ensure the comparability of modal sensitivities for each component parameter, the first-order modal sensitivities are standardized:

[0153]

[0154] Here, α represents a network element parameter, which can be any one of G, B, R, and X. Its significance lies in expressing the degree of participation of each element in the circulating resonance when the element parameters are fixed.

[0155] Based on steps 3 and 4 above, it is also possible to define the resonance participation factor of each node in each frequency range, determine the bus with the largest participation factor as the "resonance center" of the circulating resonance, and find the best excitable node and the best observable node of the circulating resonance. At the same time, the participation factor is used to further characterize the propagation range of the circulating resonance.

[0156] Step 5: Obtain the second-order modal sensitivities of parallel and series components based on the standardized first-order modal sensitivities to reflect the changing trend of the first-order modal sensitivities with component parameters, and standardize the second-order modal sensitivities. This step considers that the modal sensitivity of components changes with the adjustment of component parameters, which cannot better illustrate the effect of component adjustment. Therefore, the concept of second-order modal sensitivity of components is proposed, and the second-order modal sensitivities of parallel and series components are defined and normalized for comparison of the second-order modal sensitivities of different components in the following text, specifically including:

[0157] Step 51, due to the component modal sensitivity σ α The value changes with component parameter adjustments and cannot effectively guide circulating current resonance suppression. Define σ. α The partial derivative of the component parameter α with respect to the modal second-order sensitivity index σ' α :

[0158]

[0159] Where: σ' α This is the second-order modal sensitivity of the component; this index reflects σ. α Trends in component parameters.

[0160] Step 52: The second-order sensitivity of the series reactance mode can then be calculated.

[0161]

[0162] In the formula:

[0163] Second-order sensitivity of parallel susceptance mode:

[0164]

[0165] Parallel point-guided mode second-order sensitivity:

[0166]

[0167] Step 53: To make the second-order modal sensitivities of different components comparable, they are standardized using the following formula:

[0168]

[0169] After normalization, the most sensitive element in the network can be located by using the first and second-order modal sensitivities.

[0170] Step 6: Evaluate the participation of circulating resonant components by comparing the standardized first-order modal sensitivity and second-order modal sensitivity, calculate the critical factor for component parameter adjustment percentage, compare it with the component parameter adjustment amount, and select the component with the best circulating resonance suppression effect as the key component for circulating resonance suppression.

[0171] More preferably, a critical factor for component parameter adjustment is defined as a modal sensitivity index to characterize the sensitivity of each electrical parameter of a multi-PV grid-connected inverter system to circulating current resonance, and to evaluate the degree of influence of each component parameter on circulating current resonance. The component parameter adjustment methods for achieving circulating current resonance suppression are analyzed under two different conditions. When the magnitudes of the first-order modal sensitivity and the second-order modal sensitivity of the two components are inconsistent, a critical factor for component parameter adjustment is defined to quantify the suppression effect of adjusting different components on commutator resonance under different component adjustment percentages, guiding the suppression of circulating current resonance in distributed PV grid-connected inverters under weak grid conditions.

[0172] The degree of participation of different components in the distributed photovoltaic circulating current resonance under weak grid conditions is determined by combining the first-order mode sensitivity and the second-order mode sensitivity, as follows.

[0173] 1. For elements A and B in the network, if |σ A |>|σ B |and σ A '>σ B Then, we can discuss the following three cases:

[0174] (1)σ A '>σ B If the component parameter adjustment is increased by σ > 0, the corresponding modal sensitivity |σ| will decrease. A and |σ B |Also increases, and there exists |σ A |Growth Rate|σ B |Rapid growth rate, i.e., |σ A |>|σ B The condition remains true, thus adjusting the parameters of component A can achieve a better effect in suppressing circulating resonance.

[0175] (2)σ A >0>σB If the component parameter adjustment is increased at this point, the corresponding modal sensitivity |σ A Increase, |σ B | Decrease, i.e. |σ A |>|σ B The condition remains true, thus adjusting the parameters of component A can achieve a better effect in suppressing circulating resonance.

[0176] (3) 0 > σ A '>σ B If the component parameter adjustment is increased at this point, the corresponding modal sensitivity |σ A With |σ B |decreases, and|σ A |Reduce speed ratio|σ B The rate of decrease is slow, i.e., |σ| A |>|σ B The condition remains true, thus adjusting the parameters of component A can achieve a better effect in suppressing circulating resonance.

[0177] In summary, in |σ A |>|σ B |and σ A '>σ B At that time, for circulating resonance, element A is a more sensitive element. From the perspective of circulating resonance suppression, if the modal sensitivity and second-order modal sensitivity of a certain element are both large, adjusting the element parameter can better suppress circulating resonance.

[0178] 2. For components A and B in the network, given that |σ A |>|σ B |When, if σ A '<σ B ', then the message indicates that |σ will appear during the component parameter adjustment process. A |<|σ B In this situation, it's impossible to intuitively determine which parameter adjustment will achieve better circulating current resonance suppression. Therefore, the following critical factor σ for adjusting the component parameter percentage is defined. critical When guiding the adjustment of component parameters to be consistent, it determines which component adjustment will better suppress circulating current resonance. The specific process is as follows: The component parameter adjustment amount |Δα| is manually determined as needed, and σ... critical Compare with |Δα:

[0179]

[0180] In the formula:

[0181]

[0182] λ mFor eigenvalues;

[0183] σ A σ B The normalized first-order modal sensitivity of components A and B;

[0184] σ A '、σ B ' is the normalized second-order modal sensitivity of elements A and B.

[0185] If the component parameter adjustment satisfies |Δα|≤σ critical At this point, adjusting element A has a better effect on suppressing circulating current resonance; conversely, if the adjustment of the element parameters satisfies |Δα|>σ critical At this time, the regulating element B has a better effect on suppressing circulating resonance.

[0186] Embodiment 2 of the present invention provides a photovoltaic grid-connected circulating current resonance analysis method and system based on second-order mode sensitivity, comprising:

[0187] The admittance matrix construction module is used to establish the network node admittance matrix of the photovoltaic grid-connected inverter system based on the parameters of the photovoltaic grid-connected inverter system and the output admittance of each inverter.

[0188] The circulating resonant frequency detection module is used to decompose the features of the admittance matrix of network nodes to obtain eigenvalues, left and right eigenvectors. Based on the eigenvalues, it finds the frequency corresponding to the singular matrix of the node admittance matrix within a preset frequency range, which is the circulating resonant frequency, thus realizing the detection of the circulating resonant frequency.

[0189] The circulating resonance center point determination module is used to determine the best observable node and the best excitable node of the circulating resonance based on the left and right eigenvectors at the circulating resonance frequency, and to obtain the circulating resonance participation factor of each node. The circulating resonance center point is determined by comparing the circulating resonance participation factors of each node.

[0190] The first-order modal sensitivity calculation module is used to obtain the first-order modal sensitivity of the circulating current resonance based on the left and right eigenvectors at the circulating resonant frequency, respectively, for parallel and series elements in the network, and then perform standardization processing.

[0191] The second-order modal sensitivity calculation module is used to obtain the second-order modal sensitivity of parallel and series elements based on the first-order modal sensitivity to reflect the changing trend of the first-order modal sensitivity with the element parameters, and to standardize the second-order modal sensitivity.

[0192] The participation evaluation module for circulating resonant components is used to evaluate the participation of circulating resonant components by comparing the standardized first-order modal sensitivity and second-order modal sensitivity, and to calculate the critical factor for the percentage adjustment of component parameters. This critical factor is then compared with the adjustment amount of the component parameters to select the component with the best circulating resonance suppression effect as the key component for circulating resonance suppression.

[0193] A terminal includes a processor and a storage medium; the storage medium is used to store instructions.

[0194] The processor is configured to operate according to the instructions to execute the steps of the method.

[0195] A computer-readable storage medium having a computer program stored thereon that, when executed by a processor, implements the steps of the method.

[0196] The beneficial effects of this invention are that, compared with the prior art, it can achieve the determination of circulating resonant frequency, the determination of the highest excitable node and the best observable node for circulating resonance, the sensitivity of each network element to circulating resonance, the determination of the second-order modal sensitivity of each network element, and the evaluation of the participation degree of circulating resonant elements. Based on the inverter control strategy and parameter information of the photovoltaic grid-connected system, the equivalent output admittance of the inverter is determined; and a multi-PV grid-connected system admittance matrix model is established based on line parameters and system equivalent information; the circulating resonant frequency is determined by eigenvalue decomposition of the admittance matrix; the participation factor of each node to circulating resonance is calculated, the circulating resonance center, the best observable node, and the best excitable node are determined, and the participation degree of each network element to circulating resonance is evaluated under the current network parameters based on the modal sensitivity of each network element to circulating resonance; the second-order modal sensitivity of each network element is calculated, and the trend of its modal sensitivity with network element parameter adjustment is determined to evaluate the ability of adjusting the element to suppress circulating resonance, and a critical factor for network element parameter adjustment is defined to determine which network element can better suppress circulating resonance under different element parameter adjustment amounts. This invention can refine the granularity of circulating resonance analysis, improve the efficiency of circulating resonance analysis, provide a basis for circulating resonance suppression, and guide the selection of photovoltaic power plant equipment and topology design.

[0197] This disclosure can be a system, method, and / or computer program product. A computer program product may include a computer-readable storage medium having computer-readable program instructions loaded thereon for causing a processor to implement various aspects of this disclosure.

[0198] Computer-readable storage media can be tangible devices capable of holding and storing instructions for use by an instruction execution device. Computer-readable storage media can be, for example—but not limited to—electrical storage devices, magnetic storage devices, optical storage devices, electromagnetic storage devices, semiconductor storage devices, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of computer-readable storage media include: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), static random access memory (SRAM), portable compact disc read-only memory (CD-ROM), digital multifunction disc (DVD), memory sticks, floppy disks, mechanical encoding devices, such as punch cards or recessed protrusions storing instructions thereon, and any suitable combination of the foregoing. The computer-readable storage media used herein are not to be construed as transient signals themselves, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through waveguides or other transmission media (e.g., light pulses through fiber optic cables), or electrical signals transmitted through wires.

[0199] The computer-readable program instructions described herein can be downloaded from computer-readable storage media to various computing / processing devices, or downloaded via a network, such as the Internet, local area network, wide area network, and / or wireless network, to an external computer or external storage device. The network may include copper transmission cables, fiber optic transmission, wireless transmission, routers, firewalls, switches, gateway computers, and / or edge servers. A network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards them to the computer-readable storage media in the respective computing / processing device.

[0200] Computer program instructions used to perform the operations of this disclosure may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, status setting data, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Smalltalk, C++, etc., and conventional procedural programming languages ​​such as the "C" language or similar programming languages. The computer-readable program instructions may execute entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving a remote computer, the remote computer may be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or may be connected to an external computer (e.g., via the Internet using an Internet service provider). In some embodiments, electronic circuitry, such as programmable logic circuitry, field-programmable gate arrays (FPGAs), or programmable logic arrays (PLAs), is personalized by utilizing the status information of the computer-readable program instructions to implement various aspects of this disclosure.

[0201] 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 protection scope of the claims of the present invention.

Claims

1. A photovoltaic grid-connected circulating current resonance analysis method based on second-order mode sensitivity, which realizes the detection of circulating current resonance frequency, determination of optimal observable node, optimal excitation node and circulating current resonance center, evaluation of the participation of circulating current resonance components, and determination of key components for circulating current resonance suppression based on the critical factor of component parameter adjustment percentage, characterized in that: The method includes the following steps: Step 1: Based on the parameters of the photovoltaic grid-connected inverter system and the output admittance of each inverter, establish the network node admittance matrix of the photovoltaic grid-connected inverter system; Step 2: Decompose the features of the network node admittance matrix to obtain eigenvalues, left and right eigenvectors. Based on the eigenvalues, find the frequency corresponding to the singular matrix of the network node admittance matrix within the preset frequency range, which is the circulating resonant frequency, and realize the detection of the circulating resonant frequency. Step 3: Determine the best observable node and the best excitable node of the circulating resonance based on the left and right eigenvectors at the circulating resonant frequency, and obtain the circulating resonance participation factor of each network node. Determine the circulating resonance center point by comparing the circulating resonance participation factors of each network node. Step 4: Based on the left and right eigenvectors at the circulating resonant frequency, obtain the eigenvalue amplitude for the first-order mode sensitivity of the circulating resonant for parallel and series elements in the network, and perform standardization processing. Step 5: Obtain the second-order modal sensitivities of parallel and series elements based on the standardized first-order modal sensitivities to reflect the changing trend of the first-order modal sensitivities with the element parameters, and standardize the second-order modal sensitivities. Step 6: Evaluate the participation of circulating resonant components by comparing the standardized first-order modal sensitivity and second-order modal sensitivity, calculate the critical factor for component parameter adjustment percentage, compare it with the component parameter adjustment amount, and select the component with the best circulating resonance suppression effect as the key component for circulating resonance suppression.

2. The photovoltaic grid-connected circulating current resonance analysis method based on second-order mode sensitivity according to claim 1, characterized in that: In step 1, the network node admittance matrix is ​​constructed based on the output admittance of each inverter and the system parameters. Y n+1 : Where n is the number of parallel inverters; , Let represent the equivalent output admittance of the nth grid-connected inverter, the equivalent grid admittance, and the equivalent line admittance from inverter i to the grid connection point, respectively.

3. The photovoltaic grid-connected circulating current resonance analysis method based on second-order mode sensitivity according to claim 1, characterized in that: In step 2, the network node admittance matrix Y is... n+1 Perform eigenvalue decomposition: in, Represents an eigenvalue diagonal matrix; and Let be the left and right eigenvector matrices, respectively, and satisfy . The subscript m indicates the m-th circulating resonant mode, and the mode corresponding to the minimum eigenvalue is the critical mode; , , Y represents the network node admittance matrix respectively. n+1 The m-th eigenvalue, the left eigenvector of the m-th mode, and the right eigenvector of the m-th mode; definition U = TV , J = TI We can obtain: The matrix form is: In the formula: U and J These represent the modal voltage vector and the modal current vector, respectively. Indicates modal impedance; V It is an index composed of circulating resonance participation factors; I Inject current into network nodes; From the above formula, we can obtain that when When the value is small, U Elements in the middle element are prone to maxima, which can lead to circulating resonance phenomena.

4. The photovoltaic grid-connected circulating current resonance analysis method based on second-order modal sensitivity according to claim 3, characterized in that: In step 2, the modal impedance within the preset frequency range is calculated, and the frequency corresponding to the maximum value of the modal impedance is selected as the circulating resonant frequency.

5. The photovoltaic grid-connected circulating current resonance analysis method based on second-order mode sensitivity according to claim 1, characterized in that: In step 3, each element of the left eigenvector corresponding to the circulating resonant frequency reflects the observability of each bus for the circulating resonance, and each element of the right eigenvector reflects the excitation capability of each node for the circulating resonance after the injected current. For the circulating resonant mode m, the node corresponding to the maximum value of the left eigenvector element is the best observable node, and the node corresponding to the maximum value of the right eigenvector element is the best excitable node. Based on the elements in the left and right eigenvector matrices, an index composed of the circulation resonance participation factor is obtained. The node with the largest participation factor is identified as the center point of the circulating resonance by comparison. Among them, indicators for: index diagonal elements in a matrix is the participation factor of network node n in the circulating resonant mode m; , Let n represent the observability of network node n with respect to resonant mode m, the excitability of network node n with respect to resonant mode m, and the injected current of network node n, respectively.

6. The photovoltaic grid-connected circulating current resonance analysis method based on second-order mode sensitivity according to claim 1, characterized in that: Step 4 specifically includes: Step 41: Obtain eigenvalues ​​based on the left and right eigenvectors corresponding to the circulating resonant frequency. For the admittance matrix Y n+1 element Y ij The sensitivity is: in, This is the i-th element in the m-th row of the right eigenvector matrix; The j-th element in the m-th column of the left eigenvector matrix; Further obtain eigenvalues Sensitivity matrix ; Step 42: Sensitivity matrix The element in row b and column b and eigenvalues We obtain the following by decomposing the real and imaginary parts: in, Representing the sensitivity matrix respectively The element in row b and column b The real and imaginary parts; They represent the eigenvalues ​​respectively. The real and imaginary parts; Step 43: Based on the decomposition results of step 42, we obtain: Eigenvalue amplitude For the parallel element at node b in the network The first-order modal sensitivity is: Eigenvalue amplitude For the series element between node i and node j The first-order modal sensitivity is: in, These are conductivity and susceptance, respectively. These are resistance and reactance, respectively. Step 44: Standardize the first-order modal sensitivity obtained in step 43 as follows: in, Represents network element parameters, which can be selected as follows: , Any one of them.

7. The photovoltaic grid-connected circulating current resonance analysis method based on second-order mode sensitivity according to claim 1, characterized in that: Step 5 specifically includes: Step 51: Based on the standardized first-order modal sensitivity Depending on component parameters The changing partial derivatives define the second-order modal sensitivity of the element. : in, The second-order modal sensitivity of the element; Step 52: Based on the definition in Step 51, the following calculation is obtained: Second-order mode sensitivity of series reactance: In the formula: Parallel susceptance second-order mode sensitivity: Parallel point-guided second-order modal sensitivity: in, These are conductivity and susceptance, respectively. These are resistance and reactance, respectively. Representing the sensitivity matrix respectively The element in row b and column b The real and imaginary parts; They represent the eigenvalues ​​respectively. The real and imaginary parts; Step 53: Standardize the second-order modal sensitivity of the element obtained in step 52 as follows: in, Represents network element parameters, which can be selected as follows: , Any one of them.

8. The photovoltaic grid-connected circulating current resonance analysis method based on second-order mode sensitivity according to claim 1, characterized in that: In step 6, for elements A and B in the network, and At this time, for circulating resonance, element A is a more sensitive element, that is, element A is the key element for circulating resonance, and the parameters of this element are adjusted to suppress circulating resonance; For elements A and B in the network, under the condition that... At that time, if This indicates that during the component parameter adjustment process, an error will occur. In situations where it's impossible to directly determine which component parameter adjustment will better suppress circulating current resonance, a critical factor for the percentage adjustment of component parameters is defined. When guiding the adjustment of component parameters to be consistent, determining which component adjustment will better suppress circulating current resonance is as follows: The specific process is to determine the component parameter adjustment amount. ,Will and Comparison: if Component A is the key component for circulating current resonance. The parameters of this component should be adjusted to suppress circulating current resonance. if Component B is the key component for circulating current resonance. The parameters of this component should be adjusted to suppress circulating current resonance. in: The normalized first-order modal sensitivity of components A and B; The normalized second-order modal sensitivity of components A and B.

9. The photovoltaic grid-connected circulating current resonance analysis method based on second-order mode sensitivity according to claim 8, characterized in that: Component parameter adjustment percentage critical factor The calculation formula is: In the formula: ; For eigenvalues; The normalized first-order modal sensitivity of components A and B; The normalized second-order modal sensitivity of components A and B.

10. A photovoltaic grid-connected circulating current resonance analysis system based on second-order modal sensitivity, used to implement the method described in any one of claims 1-9, characterized in that: The circulating resonance analysis system includes: The admittance matrix construction module is used to establish the network node admittance matrix of the photovoltaic grid-connected inverter system based on the parameters of the photovoltaic grid-connected inverter system and the output admittance of each inverter. The circulating resonant frequency detection module is used to decompose the features of the network node admittance matrix to obtain eigenvalues, left and right eigenvectors, and find the frequency corresponding to the singular matrix of the network node admittance matrix within a preset frequency range based on the eigenvalues. This frequency is the circulating resonant frequency, thus realizing the detection of the circulating resonant frequency. The circulating resonance center point determination module is used to determine the best observable node and the best excitable node of the circulating resonance based on the left and right eigenvectors at the circulating resonance frequency, and to obtain the circulating resonance participation factor of each network node. The circulating resonance center point is determined by comparing the circulating resonance participation factors of each network node. The first-order modal sensitivity calculation module is used to obtain the first-order modal sensitivity of the circulating current resonance based on the left and right eigenvectors at the circulating resonant frequency, respectively, for parallel and series elements in the network, and then perform standardization processing. The second-order modal sensitivity calculation module is used to obtain the second-order modal sensitivity of parallel and series elements based on the first-order modal sensitivity to reflect the changing trend of the first-order modal sensitivity with the element parameters, and to standardize the second-order modal sensitivity. The participation evaluation module for circulating resonant components is used to evaluate the participation of circulating resonant components by comparing the standardized first-order modal sensitivity and second-order modal sensitivity, and to calculate the critical factor for the percentage adjustment of component parameters. This critical factor is then compared with the adjustment amount of the component parameters to select the component with the best circulating resonance suppression effect as the key component for circulating resonance suppression.

11. A terminal, comprising a processor and a storage medium; characterized in that: The storage medium is used to store instructions; The processor is configured to operate according to the instructions to perform the steps of the method according to any one of claims 1-9.

12. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the program implements the steps of the method according to any one of claims 1-9.

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