A grid-connected stability analysis method for systems containing black-box converters

Abstract

The present invention discloses a grid-connected stability analysis method for a system containing a black-box converter, and belongs to the technical field of power system stability analysis. The present invention first injects multi-frequency voltage disturbances when the "black-box" converter is grid-connected and running, measures the current response to obtain admittance data; then uses a vector fitting algorithm to fit it into a frequency domain transfer function; then constructs a system admittance matrix without the "black-box" converter based on the power system network topology, and adds the transfer function to obtain the admittance matrix of the entire system; finally, the s-domain modal analysis method is used to solve the characteristic roots to determine the stability of the system. If it is unstable, the oscillation frequency, participation factor and component sensitivity are analyzed to determine the resonance suppression strategy. This method does not require internal parameters of the equipment, provides a complete stability analysis process, can accurately locate the resonance source and propose an optimization strategy, and can be used for rapid stability evaluation of various new energy systems.

Description

Technical Field

[0001] The present invention relates to the technical field of power system stability analysis, and in particular to a grid-connected stability analysis method for a black-box converter system. Background Art

[0002] Currently, there are two main methods for analyzing power system resonant stability: S-domain modal analysis and state-space analysis. Compared to the state-space method, S-domain modal analysis is widely used due to its ease of modeling, small matrix dimensions, and adaptability to changes in matrix topology. However, the application of S-domain modal analysis requires a clear understanding of the structure of all system components, which to some extent limits its application in increasingly complex renewable energy power systems.

[0003] Because new energy equipment manufacturers maintain confidentiality about their devices, users lack access to their internal control structures and parameters. Converters, like "black boxes," are thus rendered as "black boxes," further complicating stability analysis of new energy systems. To address this issue, research is shifting its focus to impedance measurement of new energy devices. By directly measuring the impedance data of these "black box" devices, it is possible to directly model the converter's small signals, bypassing their internal structure and control parameters.

[0004] Simply knowing the converter impedance and applying S-domain modal analysis to determine the grid-connected stability of a device is insufficient. The device's impedance / admittance transfer function must be clearly understood. To accurately model the "black box" device, the measured impedance data is fitted using vector fitting techniques to obtain its precise S-domain admittance matrix for converter stability analysis.

[0005] The above-mentioned converter impedance measurement, vector fitting and S-domain modal analysis technologies are relatively mature, but a stability analysis system has not yet been formed. Summary of the Invention

[0006] The purpose of the present invention is to provide a grid-connected stability analysis method for black-box converter systems, provide a complete stability analysis process that does not require internal equipment parameters, accurately locate the resonance source through modal and sensitivity analysis and propose optimization strategies, and realize rapid stability evaluation of multi-scenario new energy systems.

[0007] To achieve the above object, the present invention provides a method for analyzing the grid-connected stability of a system containing a black-box converter, comprising the following steps:

[0008] S1. In a grid-connected operation state of a "black box" converter, inject voltage disturbances at multiple frequency points and measure corresponding current responses to obtain admittance data of the "black box" converter;

[0009] S2. fitting the admittance data into a frequency domain transfer function using a vector fitting algorithm;

[0010] S3. Constructing a system admittance matrix excluding the "black box" converter based on the power system network topology and known parameters, and adding the transfer function obtained in step S2 to the corresponding node of the admittance matrix according to the grid-connected position of the "black box" converter to construct the admittance matrix of the entire system;

[0011] S4. Use the s-domain modal analysis method to solve the characteristic roots of the admittance matrix of the entire system, and judge the system stability based on the real part of the characteristic roots. If there are unstable characteristic roots, analyze their oscillation frequency, participation factor and component sensitivity to determine the resonance suppression strategy.

[0012] Preferably, in step S1, the frequency range of the multi-frequency point voltage disturbance is 10:10:500550:50:3000, including a total of 100 discrete frequency points, and the voltage disturbance is a positive sequence small signal voltage with an amplitude less than 5% of the rated voltage.

[0013] Preferably, in step S2, the transfer function expression of the vector fitting algorithm is specifically as follows:

[0014] ;

[0015] The initial order N increases from 1 until the mean square error between the fitting result and the admittance data is less than a preset threshold; the pole a m and residue r m Determined by iterative optimization using the least squares method; the preset threshold is a mean square error less than 1×10 -4 , and the value range of the rational number terms d and e is -1000, 1000.

[0016] Preferably, in step S3, the construction of the system-wide admittance matrix includes the following steps:

[0017] The basic admittance matrix is ​​established according to the parameters of the generator, transformer and line. The basic admittance matrix is ​​an n×n matrix, where n is the total number of system nodes.

[0018] The transfer function of the "black box" converter is superimposed on the diagonal elements of the admittance matrix corresponding to its grid-connected node;

[0019] The transfer function superposition method is:

[0020] If the kth node is connected to the grid with m “black box” converters, the element in the kth row and kth column of the admittance matrix increases ,in is the transfer function of a single converter.

[0021] Preferably, in step S4, the participation factor is calculated as follows:

[0022] ;

[0023] in, is the left eigenvector of the admittance matrix, is the right eigenvector, and the diagonal elements of the participation factor matrix represent the product of the observability and excitability of the node to the resonant mode.

[0024] Preferably, in step S4, the component sensitivity analysis calculates the partial derivative of the real part of the characteristic root with respect to the component parameter by the following formula:

[0025] ;

[0026] in, are system component parameters, is an unstable characteristic root.

[0027] Preferably, in step S4, the resonance suppression strategy is as follows:

[0028] Increase the parameters of the components that are most sensitive to the suppression of the real part of the characteristic roots;

[0029] Prioritize adjusting the capacitance or inductance parameters of the line directly connected to the node with the largest participation factor.

[0030] Therefore, the present invention adopts a grid-connected stability analysis method for a black-box converter system using the above structure, which has the following beneficial effects:

[0031] (1) For new energy systems with "black box" converter devices, the present invention provides a complete technical chain: impedance measurement → transfer function extraction → stability analysis, which can be used for stability analysis of new energy systems with various topology types and various "black box" converter devices.

[0032] (2) The present invention breaks through the limitations of the "black box" and does not require internal parameters of the device. It achieves high-precision modeling through external measurement and fitting, forming a closed loop from data acquisition to resonance suppression, thereby improving analysis efficiency.

[0033] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 A schematic diagram of vector fitting results of a grid-connected stability analysis method for a black-box converter system according to the present invention;

[0035] Figure 2 A schematic diagram of an IEEE 9-node test system for a grid-connected stability analysis method for a black-box converter system according to the present invention;

[0036] Figure 3Schematic diagram of the results of participation factor analysis for a grid-connected stability analysis method for a black-box converter system according to the present invention;

[0037] Figure 4 The figure is a flow chart of a method for analyzing the grid-connected stability of a system containing a black-box converter according to the present invention. DETAILED DESCRIPTION

[0038] The technical solution of the present invention is further described below with reference to the accompanying drawings and embodiments.

[0039] Unless otherwise defined, the technical or scientific terms used in the present invention shall have the usual meanings understood by persons of ordinary skill in the field to which the present invention belongs. The words "first", "second" and similar terms used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. Words such as "include" or "comprise" mean that the elements or objects preceding the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. Words such as "connect" or "connected" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the object being described changes, the relative positional relationship may also change accordingly.

[0040] Example

[0041] like Figure 4 As shown, the present invention provides a grid-connected stability analysis method for a black-box converter system, which specifically includes the following steps:

[0042] S1. For all "black box" new energy equipment, a series of voltage disturbances at different frequencies are injected into the equipment during grid-connected operation, and then the current responses at the corresponding frequencies are measured to obtain the impedance / admittance amplitude and phase data corresponding to each frequency point.

[0043] Under the condition of ensuring that the “black box” new energy equipment does not lose stability under rated operation, the injection frequency of its grid connection point is f p Positive sequence small signal voltage disturbance V p ,in f p There are 100 frequency points in total, [10:10:500550:50:3000]; and for voltage disturbances of different frequencies, the corresponding current response I p , so the “black box” converter admittance expression is shown in formula (1).

[0044] (1);

[0045] In formula (1), Y p The positive-sequence admittance data of the "black-box" converter corresponds to the admittance at 100 frequency points [10:10:500550:50:3000]. The above scheme is also followed for the admittance data measurement of all "black-box" converters.

[0046] S2. The impedance / admittance frequency points of all “black box” devices are brought into the vector fitting algorithm, and the algorithm automatically generates the frequency domain transfer function expressions of all “black box” devices.

[0047] (2);

[0048] In formula (2): N is the initial order, r m is the residue, a m is the transfer function pole, determined by the least squares method; d and e are both rational numbers. The choice of N is determined by the mean square error of the fitting results and the admittance data. N increases from 1. If the mean square error is less than the required range, the number of N is determined. m To transfer the function poles, the initial value can be chosen arbitrarily, and the result after each iteration is used as the new initial value.

[0049] Finally, after fitting, the transfer function f(s) corresponding to the admittance data is obtained. If there are k converters, k transfer functions will be obtained, namely [f(s)1f(s)2…f(s)k].

[0050] S3. Based on the network topology and known system parameters such as generators, transformers, and lines, construct the system s-domain admittance matrix excluding the "black box" new energy devices. Admittance transfer functions are added to the corresponding nodes on the diagonal of the admittance matrix based on the grid-connected locations of each "black box" new energy device to construct the full system admittance matrix.

[0051] First, the admittance matrix without the “black box” converter device is established according to the system topology and parameters, as shown in Equation (3).

[0052] (3);

[0053] If the system has 9 nodes, n=9, then the matrix is Matrix. Based on the known parameters of the generator, transformer, line, etc., the admittance matrix is ​​established according to the admittance matrix establishment principle.

[0054] After the admittance matrix of the entire system is established, the transfer function obtained by vector fitting in step 2) is added to the corresponding diagonal position of the admittance matrix according to the location of the grid connection points of all "black box" converter devices. For example, when the "black box" device 1 is grid-connected at the system node k, the transfer function obtained by vector fitting is Y P1, then the modified admittance matrix is ​​shown in Equation (4). If other "black box" converters are added, they can be added according to the above rules.

[0055] (4);

[0056] S4. Using S-domain modal analysis, first solve the eigenvalues ​​of the system's admittance matrix. Based on these eigenvalues, analyze system stability. If the system is unstable, analyze the oscillation frequency, participation factor, and component sensitivity of the unstable eigenvalues ​​to identify the primary influencing nodes and primary suppression strategies for the resonance.

[0057] S41. Modal analysis

[0058] Research has shown that the zeros of the determinant of the system's admittance matrix are equal to the system's characteristic roots. Therefore, it is only necessary to solve the zeros of the system's determinant to obtain its characteristic roots. Using a convergence algorithm, we find the roots where det(Y) = 0. The form of the characteristic roots is shown in Equation (5).

[0059] (5);

[0060] Where, and They correspond to the imaginary and real parts of the resonant mode respectively.

[0061] Real part of characteristic root Determines the stability of the system. If the real part of all the characteristic roots of the system is less than 0, the system is stable. On the contrary, if there are one or more characteristic roots with real parts greater than 0, the system resonance is unstable. If the resonance is unstable, the imaginary part of the characteristic root corresponds to the resonant angular frequency, corresponding to the resonant frequency .

[0062] For the unstable characteristic root s k According to the matrix modal analysis theory, the unstable characteristic root is substituted into the admittance matrix Y of the whole system to obtain Y(s k ), according to the characteristics of the admittance matrix, we know that Y is a singular matrix, and the product of all eigenvalues ​​is equal to the value of the matrix determinant. k ))=0, we know that the admittance matrix must have an eigenvalue .

[0063] The admittance matrix Diagonalize ,in 、 are the left and right eigenvectors of the admittance matrix, Represents the eigenvalue diagonal matrix According to Ohm's law, the relationship between circuit voltage and current is:

[0064] (6);

[0065] From formula (6), we can see that, assuming the circuit operates normally, when the current is at a normal value, the voltage will reach a maximum value. Since the eigenvalue of the admittance matrix has a minimum value in this resonant mode, that is, There is a maximum value.

[0066] Defining modal voltages , modal current , simplifying the admittance matrix yields:

[0067] (7);

[0068] For the modal voltage analysis, it is assumed that The current is at its maximum value. Perform analysis:

[0069] (8);

[0070] From formula (8), we can see that the modal current is determined by the row vector corresponding to the right eigenvector of the admittance matrix. The elements in the corresponding row can determine the magnitude of the modal current. Here, the right eigenvector of the admittance matrix is ​​defined as the resonant mode excitability.

[0071] Then we analyze the modal voltage, assuming that There is a maximum value at the point Perform analysis:

[0072] (9);

[0073] From formula (9), we can see that when the modal voltage is There is a maximum value at , and the size of the corresponding actual circuit voltage is mainly determined by the column vector corresponding to the left eigenvector of the admittance matrix, that is, the observability of the voltage is determined by the left eigenvector of the admittance matrix, which is defined here as the node voltage vibration mode, that is, the observability of the resonant mode.

[0074] For a fixed system, its eigenvalue It is determined by the frequency of the system. When the system frequency changes, assuming that at a certain frequency point A minimum value appeared , at this frequency the system will resonate. Here we define the matrix is the participation factor matrix;

[0075] (10);

[0076] As shown in formula (10), the diagonal elements of the participation factor matrix represent the product of the observability and excitability of the same node, reflecting the combination of the observability and excitability of the same node under this resonance mode, which can reflect the degree of association between the node and the resonance.

[0077] S42. Sensitivity analysis

[0078] In order to better suppress resonance, it is necessary to analyze the sensitivity of system components to the real part of the characteristic root. The component that increases the degree of suppression of the real part of the characteristic root is the best for suppressing resonance. ))=0, so its port admittance Y( , p) must also be equal to zero, where p is a parameter of a certain component of the system. The sensitivity can be obtained by solving formula (11).

[0079] (11).

[0080] Assume that a "black box" converter is connected to the grid. In its stable grid-connected state, voltage disturbances at 100 frequency points [10:10:500550:50:3000] are injected to measure its admittance data.

[0081] Importing the above data into the vector fitting algorithm, the admittance transfer function is obtained as:

[0082] Yp=(6325795966585517 / 1099511627776-2372586304889043i / 549755813888) / (s+(490 223295909477 / 549755813888-7983797996467541i / 1099511627776))+(6325795966585 517 / 1099511627776+2372586304889043i / 549755813888) / (s+(490223295909477 / 5497 55813888+7983797996467541i / 1099511627776))+6580437719160887 / (17592186044416 (s-2922150161770687 / 8796093022208))-(281725962369937 / 34359738368-5213363030556581 i / 2199023255552) / (s+(2875092906532567 / 4398046511104-476528260396469i / 549755813888 ))-(281725962369937 / 34359738368+5213363030556581i / 2199023255552) / (s+(287509290653 2567 / 4398046511104+476528260396469i / 549755813888))+4298040067624847 / (1099511627776 (s-223579722490749 / 17179869184))+(4193305671571089 / 1099511627776-4854287769400059i / 1099511627776) / (s+(3233912110818839 / 4398046511104-3539975297141741i / 549755813888))+ (4193305671571089 / 1099511627776+4854287769400059i / 1099511627776) / (s+(32339121108188 39 / 4398046511104+3539975297141741i / 549755813888))+7730711712073617 / (140737488355328 (s-840828776470007 / 17592186044416))+1123879729971641 / 4503599627370496.

[0083] Figure 1 The vector fitting results for the current transformer are shown. The upper half shows the amplitude of the impedance Bode plot, while the lower half shows the phase information. The scattered points in the figure represent the actual input data (impedance measurements at various frequencies), while the curve represents the fitting result, demonstrating high fitting accuracy.

[0084] The method is verified using an IEEE 9-node topology system. Figure 2The IEEE 9-node topology diagram shows that the system consists of three generators, three transformers, and nine busbar nodes. Table 1 shows the system parameters, and Table 2 shows the compliance parameters. First, the system admittance matrix Y without the "black box" converter is established. node9 The above-mentioned “black box” converters are connected in parallel in 3 units at 6 nodes.

[0085] Table 1 IEEE9 node parameters

[0086] ;

[0087] Table 2 Load parameter table

[0088] ;

[0089] Note: The base power is 100MVA

[0090] The characteristic roots obtained within 1-1000Hz are:

[0091] 0.3894+1018.6279i;

[0092] -41.3365+2749.1873i;

[0093] -183.6858+4342.5208i;

[0094] There is a characteristic root greater than 0, the system is unstable and the resonant frequency is approximately 1018.6279 / 2 / pi=162.12Hz. Modal and sensitivity analysis is performed on the characteristic root 0.3894+1018.6279i.

[0095] From the analysis of participation factors Figure 3 It can be seen that node 6 has the greatest impact on resonance, and node 2 has the least impact on resonance. Therefore, the sensitivity analysis mainly analyzes the components related to node 6.

[0096] According to the IEEE 9-node topology, the components connected to node 6 include the line resistance R(4_6), inductance L(4_6), and capacitance C(4_6) between 4 and 6, as well as the line resistance R(6_9), inductance L(6_9), and capacitance C(6_9) between 6 and 9. The sensitivity of the active load parameters R(6_0) and the reactive load parameters R(6_0) is calculated, and the sensitivity analysis results are as follows:

[0097] Sen_R(4_6):-16.0219-22.6406i;

[0098] Sen_L(4_6):73.1861-52.1161i;

[0099] Sen_C(4_6):-0.80707-1510.86i;

[0100] Sen_R(6_9):-9.58476+1.93489i;

[0101] Sen_L(6_9):-6.30601-31.0063i;

[0102] Sen_C(6_9):-134.619-1597.62i;

[0103] Sen_R(6_0):-2.31686-0.256928i;

[0104] Sen_L(6_0):0.807476-7.44351i;

[0105] Since the capacitance between the 6th and 9th nodes is most sensitive to the real part of the characteristic root and has a suppressive effect, increasing the capacitance between the 6th and 9th nodes has the best suppressive effect on resonance.

[0106] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A grid-connected stability analysis method for a system containing a "black box" converter, characterized by: The following steps are involved: S1. In a grid-connected operation state of a "black box" converter, inject voltage disturbances at multiple frequency points and measure corresponding current responses to obtain admittance data of the "black box" converter; S2. fitting the admittance data into a frequency domain transfer function using a vector fitting algorithm; In step S2, the transfer function expression of the vector fitting algorithm is specifically as follows: ； The initial order N increases from 1 until the mean square error between the fitting result and the admittance data is less than a preset threshold; the pole a m and residue r m Determined by iterative optimization using the least squares method; the preset threshold is when the mean square error is less than , and the range of the rational number terms d and e is -1000, 1000; S3. Constructing a system admittance matrix excluding the "black box" converter based on the power system network topology and known parameters, and adding the transfer function obtained in step S2 to the corresponding node of the admittance matrix according to the grid-connected position of the "black box" converter to construct the admittance matrix of the entire system; In step S3, the construction of the system-wide admittance matrix includes the following steps: The basic admittance matrix is ​​established according to the parameters of the generator, transformer and line. The basic admittance matrix is ​​an n×n matrix, where n is the total number of system nodes. The transfer function of the "black box" converter is superimposed on the diagonal elements of the admittance matrix corresponding to its grid-connected node; The transfer function superposition method is: If the kth node is connected to the grid with m "black box" converters, the element in the kth row and kth column of the admittance matrix increases ,in is the transfer function of a single converter; S4. Use the s-domain modal analysis method to solve the characteristic roots of the admittance matrix of the entire system, and judge the system stability based on the real part of the characteristic roots. If there are unstable characteristic roots, analyze their oscillation frequency, participation factor and component sensitivity to determine the resonance suppression strategy.

2. The method for grid-connected stability analysis of a "black box" converter system according to claim 1, characterized in that: In step S1, the frequency range of the multi-frequency point voltage disturbance is 10:10:500550:50:3000, which includes 100 discrete frequency points in total, and the voltage disturbance is a positive sequence small signal voltage with an amplitude less than 5% of the rated voltage.

3. The method for grid-connected stability analysis of a "black box" converter system according to claim 1, characterized in that: In step S4, the participation factor is calculated as follows: ； in, is the left eigenvector of the admittance matrix, is the right eigenvector, and the diagonal elements of the participation factor matrix represent the product of the observability and excitability of the node to the resonant mode.

4. The method for analyzing grid-connected stability of a black-box converter system according to claim 3, characterized in that: In step S4, the component sensitivity analysis calculates the partial derivative of the real part of the characteristic root with respect to the component parameter using the following formula: ； in, are system component parameters, is an unstable characteristic root.

5. The method for analyzing grid-connected stability of a black-box converter system according to claim 1, characterized in that: In step S4, the resonance suppression strategy is as follows: Increase the parameters of the components that are most sensitive to the suppression of the real part of the characteristic roots; Prioritize adjusting the capacitance or inductance parameters of the line directly connected to the node with the largest participation factor.

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