Distributed power system characteristic value calculation method and system

Abstract

The invention discloses a distributed power system characteristic value calculation method and system, and the method comprises the steps: enabling a distributed power system to locally calculate a characteristic value and a right characteristic vector of a local region, and carrying out the transformation of an input matrix and an output matrix of a linear state-space equation based on the right characteristic vector; transmitting the characteristic value of the region and the transformed input matrix and output matrix to a characteristic value calculation center; respectively obtaining a diagonal eigenvalue matrix, a block diagonal conversion input matrix and a block diagonal conversion output matrix; constructing a network differential equation containing terminal voltage and output current of each region to obtain a network impedance matrix and a network inductance matrix; constructing an equivalent state matrix; and calculating the eigenvalue of the equivalent state matrix, namely the eigenvalue of the distributed power system. The calculation process does not need the original matrix information of the state space equation of each region, and the confidentiality of the core information of each region can be effectively ensured.

Description

Technical Field

[0001] The present invention relates to the technical field of power system eigenvalue calculation, and particularly to a method and system for calculating distributed power system eigenvalues. Background Art

[0002] The statements in this part only provide background technical information related to the present invention and do not necessarily constitute prior art.

[0003] With the access of a high proportion of renewable energy and the response requirements of user-side flexible resources, the power system is accelerating its evolution from the traditional centralized "large power grid" mode to a distributed structure, showing a development trend of more flexible structure, stronger resilience, and higher inclusiveness. Distributed power sources have become its most important feature.

[0004] In a distributed power system, each region adopts a partition management mode to improve local response efficiency and flexibility. Due to differences in management systems, market competition mechanisms, and data privacy protection requirements, the core data of each region is in a non-shared state, and it is difficult to achieve complete transparent sharing of the whole network data, which brings challenges to the stability analysis of the power system.

[0005] Under this background, traditional online security analysis usually performs equivalence on other regions and simplifies other regions into equivalent models to reduce the calculation complexity. However, this method may lead to the loss of key modal information and cannot effectively identify potential instability risks of the system. For example, dynamic interactions between regional units may generate inter-area oscillations. If equivalence is performed on other regions, their dynamic characteristics cannot be accurately reflected by the simplified model, and significant deviations will occur in the eigenvalue calculation results. In addition, when modeling the connection lines between regions, traditional eigenvalue calculation methods usually ignore the dynamic process of the lines and use network algebraic equations to reflect the system topology structure, which will also lead to the loss of oscillation modes. Therefore, it is of great practical significance to retain the dynamic characteristics of each link, avoid equivalence errors, accurately calculate each mode, and at the same time protect the core information of each region.

[0006] In response to the distributed eigenvalue calculation requirements for both accuracy and confidentiality, the prior art proposes a distributed eigenvalue calculation method based on the traditional self-excitation method. This method only requires a small amount of information exchange between the boundary regions of each region and uses the principle of the self-excitation method to iteratively solve the distributed eigenvalues. The results are consistent with the traditional method and have good accuracy. However, this method has obvious limitations. This method can only calculate the key eigenvalues related to the electromechanical oscillation mode and is only applicable to the low-frequency oscillation scenario of the power system, and cannot analyze the broadband oscillation phenomenon in the new power system in the frequency range from sub-synchronous to super-synchronous. Summary of the Invention

[0007] To solve the above problems, the present invention proposes a method and system for calculating the eigenvalues of a distributed power system. Each region of the distributed power system provides the locally transformed input matrix and output matrix, as well as the eigenvalues of this region, to the eigenvalue calculation center. The eigenvalue calculation center constructs an equivalent state matrix that does not contain the information of the original state space equation matrix of each region based on the information transmitted by each region, in combination with the network inductance matrix and the network impedance matrix, and then obtains the eigenvalues of the distributed power system, achieving accurate calculation of the eigenvalues of the distributed power system on the premise of keeping the core information of each region confidential and not losing oscillation modes.

[0008] In some embodiments, the following technical solutions are adopted:

[0009] A method for calculating the eigenvalues of a distributed power system includes:

[0010] Based on the linearized state space equation of each region of the distributed power system, calculate the eigenvalues and right eigenvectors of this region locally respectively, transform the input matrix and output matrix of the linearized state space equation based on the right eigenvectors, and transmit the eigenvalues of this region and the transformed input matrix and output matrix to the eigenvalue calculation center;

[0011] Arrange the eigenvalues transmitted by each region and the transformed input matrix and output matrix diagonally respectively to obtain a diagonal eigenvalue matrix, a block diagonal transformed input matrix, and a block diagonal transformed output matrix;

[0012] Construct a network differential equation including the terminal voltage and output current of each region to obtain a network impedance matrix and a network inductance matrix;

[0013] Based on the diagonal eigenvalue matrix, the block diagonal transformed input matrix, the block diagonal transformed output matrix, the network impedance matrix, and the network inductance matrix, construct an equivalent state matrix;

[0014] Calculate the eigenvalues of the equivalent state matrix, which are the eigenvalues of the distributed power system.

[0015] As a further solution, the linearized state space equation includes a state equation and an output equation. The input variables of the state equation and the output equation are both column vectors composed of the terminal voltages of this region in the d-q rotating coordinate system, and the output variables are both column vectors composed of the output currents of this region in the d-q rotating coordinate system.

[0016] As a further solution, the calculation of the right eigenvector of this region is specifically:

[0017] Taking the kth region as an example, the characteristic equation of this region regarding the right eigenvector is:

[0018] Α kv j = λ j v j ;

[0019] where A k is the state matrix of this area; λ j is the j-th eigenvalue, each eigenvalue corresponds to a mode, the real eigenvalue corresponds to a non-oscillating mode, the complex eigenvalue corresponds to an oscillating mode, its real part represents damping, and its imaginary part represents the oscillation frequency; v j is the right eigenvector corresponding to the j-th eigenvalue.

[0020] As a further solution, based on the right eigenvector, the input matrix and output matrix of the linearized state space equation are transformed. Specifically:

[0021] The right eigenvectors of each area of the distributed power system are arranged in columns to form a right eigenvector matrix, and this right eigenvector matrix is used as the transformation matrix;

[0022] The input matrix in the state space equation is left-multiplied by the inverse matrix of the transformation matrix to obtain the transformed input matrix;

[0023] The output matrix in the state space equation is right-multiplied by the transformation matrix to obtain the transformed output matrix.

[0024] As a further solution, the diagonal eigenvalue matrix Λ, the block diagonal transformed input matrix B t and the block diagonal transformed output matrix C t are respectively:

[0025]

[0026] where diag represents a block diagonal matrix composed of the matrix in its square brackets; assuming that the distributed power system has m areas, Λ k is the diagonal matrix composed of the eigenvalues of the k-th area; B t,k is the transformed input matrix of the k-th area; C t,k is the transformed output matrix of the k-th area; k = 1, 2,..., m.

[0027] As a further solution, a network differential equation including the terminal voltage and output current of each area is constructed. Specifically:

[0028]

[0029] where U is the column vector composed of the terminal voltages of all distributed power sources; I is the column vector composed of the output currents of all distributed power sources; U gm is the column vector composed of m AC grid voltages; L is the network inductance matrix, which consists of m 2A block matrix composed of 2×2 matrices, with diagonal element L ww is the sum of the line inductance matrices connecting the w-th distributed power source to the AC power grid, and the off-diagonal element L wv is the sum of the inductance matrices of the common parts of the lines connecting the w-th distributed power source and the v-th distributed power source to the AC power grid; Z is the network impedance matrix, which is a block matrix composed of m 2 2×2 matrices, with diagonal element Z ww being the sum of the line impedance matrices connecting the w-th distributed power source to the AC power grid, and the off-diagonal element Z wv being the sum of the impedance matrices of the common parts of the lines connecting the w-th distributed power source and the v-th distributed power source to the AC power grid.

[0030] As a further solution, the equivalent state matrix is specifically:

[0031] A s,eq = Λ + B t (E 2m - LC t B t ) -1 (LC t Λ + ZC t );

[0032] wherein, A s,eq is the equivalent state matrix; E 2m is the identity matrix, Λ, B t and C t are the diagonal eigenvalue matrix, the block diagonal transformed input matrix and the block diagonal transformed output matrix respectively, Z is the network impedance matrix, and L is the network inductance matrix.

[0033] In some other embodiments, the following technical solution is adopted:

[0034] A calculation system for eigenvalues of a distributed power system, comprising:

[0035] A regional local calculation module, which is used to calculate the eigenvalues and right eigenvectors of each region locally based on the linearized state space equations of each region in the distributed power system, transform the input matrix and output matrix of the linearized state space equations based on the right eigenvectors, and transmit the eigenvalues of this region and the transformed input matrix and output matrix to the eigenvalue calculation center;

[0036] A matrix reconstruction module, which is used to arrange the eigenvalues and the transformed input matrix and output matrix transmitted from each region diagonally respectively to obtain a diagonal eigenvalue matrix, a block diagonal transformed input matrix and a block diagonal transformed output matrix;

[0037] A network matrix construction module, which is used to construct a network differential equation containing the terminal voltages and output currents of each region, and obtain a network impedance matrix and a network inductance matrix;

[0038] An equivalent state matrix construction module, which is used to construct an equivalent state matrix based on the diagonal eigenvalue matrix, the block diagonal transformed input matrix, the block diagonal transformed output matrix, the network impedance matrix and the network inductance matrix;

[0039] An eigenvalue calculation module, which is used to calculate the eigenvalues of the equivalent state matrix, which are the eigenvalues of the distributed power system.

[0040] In some other embodiments, the following technical solutions are adopted:

[0041] A terminal device, which includes a processor and a memory. The processor is used to implement instructions; the memory is used to store multiple instructions, and the instructions are suitable for being loaded and executed by the processor to perform the above-mentioned calculation method for the eigenvalues of the distributed power system.

[0042] In some other embodiments, the following technical solutions are adopted:

[0043] A computer-readable storage medium, in which multiple instructions are stored, and the instructions are suitable for being loaded and executed by the processor of the terminal device to perform the above-mentioned calculation method for the eigenvalues of the distributed power system.

[0044] Compared with the prior art, the beneficial effects of the present invention are:

[0045] (1) In the present invention, linear transformations are performed on the input matrix and the output matrix locally in each region, and the processed transformed input matrix, transformed output matrix and the eigenvalues of this region are transmitted to the eigenvalue calculation center. The eigenvalue calculation center combines the network inductance matrix and the network impedance matrix to construct an equivalent state matrix of the distributed power system and calculate the eigenvalues. This calculation process does not require the original matrix information of the state space equations of each region, and can effectively ensure the confidentiality of the core information of each region.

[0046] (2) The present invention writes differential equations for the connection lines between regions, takes into account the current differential terms dynamically introduced by the line inductance, and further derives a network differential equation for system eigenvalue calculation, avoiding the risks of inaccurate network modeling and loss of certain oscillation modes caused by traditional network algebraic equations ignoring differential terms, and ensuring that all oscillation modes can be accurately calculated.

[0047] (3) The present invention makes full use of the regional eigenvalue, input matrix, output matrix, and the network topology between regions to obtain the equivalent state matrix of the distributed power system. This matrix is essentially a similarity transformation of the state matrix of the distributed power system. Therefore, the eigenvalues obtained from the equivalent state matrix are the accurate eigenvalues of the distributed system rather than approximate values, ensuring the accuracy of eigenvalue calculation.

[0048] Other features and advantages of the present invention will be partially given in the following description, partially become apparent from the following description, or be understood through the practice of this aspect. Brief Description of the Drawings

[0049] Figure 1 It is a flowchart of the method for calculating the eigenvalues of the distributed power system in the embodiment of the present invention;

[0050] Figure 2 It is a topology diagram of the grid-connected system with distributed power sources in the embodiment of the present invention;

[0051] Figure 3 It is a schematic diagram of the information transmission process in the embodiment of the present invention;

[0052] Figure 4 It is a schematic diagram of the eigenvalue distribution in the embodiment of the present invention. Detailed Embodiments

[0053] It should be noted that the following detailed description is illustrative and is intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used in the present invention have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present application belongs.

[0054] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0055] Embodiment 1

[0056] In one or more embodiments, a method for calculating the eigenvalues of a distributed power system is disclosed. Combining Figure 1 , it specifically includes the following steps:

[0057] S101: Based on the linearized state - space equations of each region in the distributed power system, calculate the eigenvalues and right - eigenvectors of the region locally. Then, transform the input matrix and output matrix of the linearized state - space equation based on the right - eigenvectors, and transmit the eigenvalues of the region and the transformed input matrix and output matrix to the eigenvalue calculation center.

[0058] In this embodiment, the linearized state - space equations of each region include a state equation and an output equation. The input variables of the state equation and the output equation are the column vectors composed of the terminal voltages of the region in the d - q rotating coordinate system, and the output variables are the column vectors composed of the output currents of the region in the d - q rotating coordinate system.

[0059] Taking the k - th region as an example, the linearized state - space equation of this region is:

[0060]

[0061] In the formula, the subscript k represents the k - th region; is the state variable of this region, is the small - signal form of the state variable of this region; n k is the total number of state variables of this region; U k = [u kd , u kq T is the terminal voltage of this region, u kd and u kq are the d - axis component and q - axis component respectively, is the small - signal form of the terminal voltage of this region; I k = [i kd , i kq T is the output current of this region, i kd and i kq are the d - axis component and q - axis component respectively, is the small - signal form of the output current of this region; is the state matrix of this region; is the input matrix of this region; is the output matrix of this region.

[0062] In this embodiment, the process of calculating the eigenvalues and right - eigenvectors of each region includes: establishing the characteristic equation about the right - eigenvector of the state matrix of each region, and obtaining the eigenvalues and right - eigenvectors of the system by solving the characteristic equation.

[0063] Taking the k - th region as an example, the characteristic equation of this region about the right - eigenvector is:

[0064] Α k vj = λ j v j (2)

[0065] where λ j is the j-th eigenvalue, and each eigenvalue corresponds to a mode. Real eigenvalues correspond to non-oscillatory modes, and complex eigenvalues correspond to oscillatory modes. Its real part represents damping, and its imaginary part represents the oscillation frequency; is the right eigenvector corresponding to the j-th eigenvalue.

[0066] In this embodiment, the process of processing the input matrix and output matrix in the state space equation based on the right eigenvector matrix includes: the right eigenvectors of each regional power grid are arranged by column to form a right eigenvector matrix, which is used as the transformation matrix. The input matrix in the state space equation is left-multiplied by the inverse matrix of the transformation matrix, and the output matrix is right-multiplied by the transformation matrix to obtain the transformed input matrix and the transformed output matrix respectively.

[0067] Taking the k-th region as an example, the expression of the transformation matrix is:

[0068]

[0069] where is the transformation matrix of the k-th region; is the right eigenvector corresponding to the first eigenvalue of the k-th region; is the right eigenvector corresponding to the n k -th eigenvalue of the k-th region.

[0070] The expressions of the transformed input matrix and the transformed output matrix are:

[0071]

[0072] where is the transformed input matrix of the k-th region; is the transformed output matrix of the k-th region.

[0073] This embodiment transmits the eigenvalues of this region and the transformed input matrix and output matrix to the eigenvalue calculation center, which can avoid directly transmitting the original matrix information of the state space equations of each region and effectively ensure the confidentiality of the core information of each region.

[0074] S102: Arrange the eigenvalues and the transformed input matrix and output matrix transmitted from each region diagonally to obtain a diagonal eigenvalue matrix, a block diagonal transformed input matrix, and a block diagonal transformed output matrix respectively. The above matrices integrate the information transmitted from all regions for subsequent calculation of the eigenvalues of this distributed power system.

[0075] In this embodiment, the eigenvalue, the transformed input matrix, and the transformed output matrix transmitted in each area are arranged diagonally respectively to form a diagonal eigenvalue matrix, a block diagonal transformed input matrix, and a block diagonal transformed output matrix. Assume that there are m areas in this distributed power system, and the expressions of each block diagonal matrix are as follows:

[0076]

[0077] In the formula, is a diagonal matrix composed of the eigenvalues of the first area, and n1 is the total number of state variables in the first area; is a diagonal matrix composed of the eigenvalues of the k-th area; is a diagonal matrix composed of the eigenvalues of the m-th area, and n m is the total number of state variables in the m-th area;

[0078] is a diagonal matrix composed of the eigenvalues of all areas, and N is the total number of state variables of all areas;

[0079] is the transformed input matrix of the first area; is the transformed input matrix of the m-th area; is the block diagonal transformed input matrix; is the transformed output matrix of the first area; is the transformed output matrix of the m-th area; is the block diagonal transformed output matrix.

[0080] S103: Construct a network differential equation including the terminal voltage and output current of each area to obtain a network impedance matrix and a network inductance matrix.

[0081] In this embodiment, consider a system containing m distributed power sources. This system is connected in parallel by h branches to a Point of Common Coupling (PCC), and then connected to the AC power grid via a line. The l-th branch contains t l series-connected distributed power sources. Taking this distributed system as an example, the derivation process of the network differential equation, the network inductance matrix, and the network impedance matrix is introduced.

[0082] There is a relationship between the terminal voltages of the w-th and (w + 1)-th distributed power sources on the l-th branch:

[0083]

[0084] In the formula, U w = [u wd , u wq Tis the terminal voltage of the w-th distributed power source, u wd and u wq are its d-axis component and q-axis component respectively; U w+1 =[u (w+1)d ,u (w+1)q T is the terminal voltage of the (w + 1)-th distributed power source, u (w+1)d and u (w+1)q are its d-axis component and q-axis component; I line,w =[i line,wd ,i line,wq T is the current flowing through the line between the w-th and the (w + 1)-th distributed power sources, i line,wd and i line,wq are its d-axis component and q-axis component, is its derivative; is the inductance matrix of the line between the w-th and the (w + 1)-th distributed power sources; is the impedance matrix of the line between the w-th and the (w + 1)-th distributed power sources.

[0085] The specific expressions of the inductance matrix and the impedance matrix are:

[0086]

[0087] In the formula, L w is the inductance of the line; R w is the resistance of the line; X w =ωL w is the reactance of the line, ω is the angular frequency.

[0088] And so on, write out the relationships between the terminal voltages of all distributed power sources from the (w + 1)-th distributed power source to the PCC point on this branch, as well as the relationship between the PCC point voltage and the AC grid voltage, and substitute all voltage relationships into Equation (6), the expression of the terminal voltage of the w-th distributed power source on the l-th branch can be obtained:

[0089]

[0090] In the formula, is the inductance matrix of the line between the (w + 1)-th and the (w + 2)-th distributed power sources; is the impedance matrix of the line between the (w + 1)-th and the (w + 2)-th distributed power sources; I line,w+1 =

[0091] [i line,(w+1)d ,i line,(w+1)q T is the current flowing through the line between the (w + 1)-th and the (w + 2)-th distributed power sources, i line,(w+1)d and i​​​line,(w+1)q are its d-axis component and q-axis component, is its derivative; is the serial number of the last distributed power source on the l-th branch; is the inductance matrix of the line between it and the PCC point; is the impedance matrix of the line between it and the PCC point;

[0092] is the current flowing through the line between it and the PCC point, and

[0093] are its d-axis component and q-axis component, is its derivative; is the inductance matrix of the line between the PCC point and the AC power grid; is the impedance matrix of the line between the PCC point and the AC power grid; is the current flowing through the line between the PCC point and the AC power grid, i line,gd and i line,gq are its d-axis component and q-axis component, is its derivative; U g =[u gd ,u gq T is the voltage of the AC power grid, u gd and u gq are its d-axis component and q-axis component.

[0094] The current flowing through the line is the sum of the output currents of all the distributed power sources in front of this branch. Replace all the line currents in Equation (8) with the output currents of the distributed power sources, and take the output current of each distributed power source as a common factor to organize it, then the form of the terminal voltage of the w-th distributed power source expressed by the output currents of all the distributed power sources can be obtained. Similarly, the expressions of the terminal voltages of other distributed power sources can be obtained, and they are combined and written in the form of a vector to obtain the network differential equation:

[0095]

[0096] In the formula, is the column vector composed of the terminal voltages of all the distributed power sources; is the column vector composed of the output currents of all the distributed power sources; is the column vector composed of m AC power grid voltages; is the network inductance matrix, which is a block matrix composed of m 2 2×2 matrices, and its diagonal element L ww is the sum of the inductance matrices of the lines connecting the w-th distributed power source and the AC power grid, and the non-diagonal element L wv ​is the sum of the inductance matrices of the common parts of the lines connecting the w-th distributed power source and the v-th distributed power source to the AC grid; is the network impedance matrix, which is a block matrix composed of m 2 2×2 matrices, and its diagonal element Z ww is the sum of the impedance matrices of the lines connecting the w-th distributed power source to the AC grid, and the off-diagonal element Z wv is the sum of the impedance matrices of the common parts of the lines connecting the w-th distributed power source and the v-th distributed power source to the AC grid.

[0097] Linearize Equation (9) at the steady-state point to obtain the network differential equation in small-signal form:

[0098]

[0099] where, is the column vector composed of the small-signal forms of the terminal voltages of each distributed power source; is the column vector composed of the small-signal forms of the output currents of each distributed power source; is the column vector composed of the small-signal forms of the voltages of m AC grids.

[0100] In this embodiment, a network differential equation including the terminal voltages and output currents of each region is constructed, and the current differential terms introduced by the dynamic line inductance are considered, avoiding the risks of inaccurate network modeling and loss of certain oscillation modes caused by ignoring the differential terms in traditional network algebraic equations, and ensuring that all oscillation modes can be accurately calculated.

[0101] S104: Based on the diagonal eigenvalue matrix, the block-diagonal transformed input matrix, the block-diagonal transformed output matrix, the network impedance matrix, and the network inductance matrix, construct an equivalent state matrix.

[0102] S105: Calculate the eigenvalues of the equivalent state matrix, which are the eigenvalues of the distributed power system.

[0103] Specifically, the equivalent state matrix of this embodiment is specifically:

[0104] A s,eq = Λ + B t (E 2m - LC t B t ) -1 (LC t Λ + ZC t ) (11)

[0105] where, is the equivalent state matrix; is the identity matrix.

[0106] Calculate the equivalent state matrix A eq The eigenvalues of are the eigenvalues of the distributed power system. Arrange the transformation matrices of each area in diagonal form to construct a block diagonal transformation matrix, i.e.:

[0107] T = diag[T1 … T k … T m (12)

[0108] In the formula, is the block diagonal transformation matrix; is the transformation matrix of the first area; is the transformation matrix of the m-th area.

[0109] Left multiply the equivalent state matrix A s,eq by the block diagonal transformation matrix and right multiply by the inverse matrix of the block diagonal transformation matrix, we can get:

[0110]

[0111] In the formula, is the block diagonal matrix composed of the state matrices in the linearized state space equations of each area arranged in diagonal form; is the block diagonal matrix composed of the input matrices of each area arranged in diagonal form; is the block diagonal matrix composed of the output matrices of each area arranged in diagonal form.

[0112] Combining the linearized state space equations of each area shown in formula (1) and the network differential equation shown in formula (10), the state matrix of the distributed power system can be deduced:

[0113] A s = A + B(E 2m - LCB) -1 (LCA + ZC) (14)

[0114] In the formula, is the state matrix.

[0115] It can be seen from formula (13) and formula (14) that the equivalent state matrix A s,eq is essentially a similarity transformation of the state matrix A s , so it can be proved that the eigenvalues of the equivalent state matrix A s,eq obtained are the eigenvalues of the state matrix A s .

[0116] Next, a grid-connected system with distributed power sources is used to verify the effectiveness of the proposed method for calculating the eigenvalues of the distributed power system. All analyses are carried out in Matlab and on an Inter 2.20GHz 16GB laptop computer.

[0117] The grid-connected system with distributed power sources is as follows Figure 2 shown. The grid-connected system with distributed power sources includes 4 distributed power sources. In the figure is the AC grid voltage, is the terminal voltage of each distributed power source, is the output current of each distributed power source; R i (i = 1, 2, 3, 4) and X i = ω g L i (i = 1, 2, 3, 4) are respectively the resistance and reactance of the line between each distributed power source and the PCC point, ω g is the angular frequency of the grid, L i (i = 1, 2, 3, 4) is the inductance of the line; R g and X g = ω g L g are respectively the resistance and reactance of the line between the PCC point and the AC grid, L g is the inductance of the line.

[0118] By means of the linearized state space equations of each distributed power source, the eigenvalues and right eigenvector matrices are calculated locally respectively, and then the input matrix and output matrix are transformed, and they are provided to the eigenvalue calculation center together with the eigenvalues. The eigenvalue calculation center constructs an equivalent state matrix that does not contain the information of the original state space equation matrix of each distributed power source based on the network inductance matrix and network impedance matrix derived from the network differential equation, and the eigenvalues of this matrix are the eigenvalues of the entire system.

[0119] The state space equations of each distributed power source are as follows:

[0120]

[0121] In the formula, is the state variable of each distributed power source, is the small signal form of the state variable of each distributed power source; n i is the total number of state variables of each distributed power source; is the small signal form of the terminal voltage of each distributed power source, is the small signal form of the output current of each distributed power source;

[0122] is the state matrix of each distributed power source; is the input matrix of each distributed power source; is the output matrix of each distributed power source.

[0123] Calculate the state matrix A of each distributed power source separately i for its eigenvalues and right eigenvectors, and obtain the eigenvalue Λ i of each distributed power source and the transformation matrix T i composed of right eigenvectors. Then, transform the input matrix and output matrix to obtain the transformed input matrix B t,i and the transformed output matrix C t,i :

[0124]

[0125] Arrange the eigenvalues Λ i of each distributed power source, the transformed input matrix B t,i and the transformed output matrix C t,i diagonally respectively to form the diagonal eigenvalue matrix Λ, the block diagonal transformed input matrix B t and the block diagonal transformed output matrix C t :

[0126]

[0127] According to the network topology, obtain the network differential equation of the grid-connected system containing distributed power sources:

[0128]

[0129] where ΔU = [ΔU1, ΔU2, ΔU3, ΔU4] T , ΔI = [ΔI1, ΔI2, ΔI3, ΔI4] T , ΔU g4 = [ΔU g , ΔU g , ΔU g , ΔU g T .

[0130] The system network inductance matrix L and network impedance matrix Z are:

[0131]

[0132] where L g and L i (i = 1, 2, 3, 4) are the inductance matrices of each line respectively; Z g and Z i (i = 1, 2, 3, 4) are the impedance matrices of each line respectively, and the specific expressions are:

[0133]

[0134] Based on the diagonal eigenvalue matrix Λ, the block diagonal transformed input matrix B​t and the block diagonal transformed output matrix C t , as well as the network inductance matrix L and the network impedance matrix Z, to construct the equivalent state matrix A s,eq :

[0135] A s,eq = Λ + B t (E8 - LC t B t ) -1 (LC t Λ + ZC t ) (21)

[0136] Wherein, is the identity matrix.

[0137] Calculate the eigenvalues of A s,eq , that is, the eigenvalues of the grid-connected system with distributed power sources. The information transfer of this calculation process is as Figure 3 shown, achieving the goal of calculating the accurate eigenvalues of the system without obtaining the information of the original state equation matrix of each distributed power source.

[0138] Figure 4 This is the eigenvalue distribution diagram of this system, which respectively shows the eigenvalues calculated by the method of the present invention and the eigenvalues calculated after obtaining all the matrices of the original state space equation under the condition of fully transparent information. By comparison, it can be seen that the eigenvalues calculated by the method of the present invention are consistent with the results of the fully transparent method. Calculate the relative error of each eigenvalue, and the maximum relative error is only 4.2280×10 -11 , which can verify the accuracy of the method of the embodiment of the present invention.

[0139] In addition, differential equations are used to describe the lines in the above calculations. However, in the traditional method of deriving network equations, algebraic equations are mostly used to describe the lines, ignoring the line dynamics, which may lead to some oscillation modes not being accurately reflected. The method of the present invention establishes network differential equations, fully considering the line dynamics, and avoiding the risk of losing oscillation modes. Simulate this system in Matlab Simulink, adjust the parameters of the control links in the distributed power sources, and calculate the eigenvalues respectively by the traditional method using algebraic equations of the lines and the method described in this embodiment. The results are shown in Table 1.

[0140] Table 1 Comparison of eigenvalue calculations between the traditional method and the method of this embodiment

[0141]

[0142]

[0143] As can be seen from Table 1, in Case 3, there are no eigenvalues with positive real parts in the calculation results of the traditional method, and this oscillation mode is lost. However, the method described in this embodiment can correctly reflect this oscillation mode.

[0144] Embodiment 2

[0145] In one or more embodiments, a calculation system for eigenvalues of a distributed power system is disclosed, including:

[0146] A regional local calculation module, configured to calculate eigenvalues and right eigenvectors of each region locally based on the linearized state-space equations of the respective regions in the distributed power system, transform the input matrix and output matrix of the linearized state-space equations based on the right eigenvectors, and transmit the eigenvalues of the region and the transformed input matrix and output matrix to the eigenvalue calculation center;

[0147] A matrix reconstruction module, configured to arrange the eigenvalues and the transformed input matrix and output matrix transmitted from each region in a diagonal manner respectively to obtain a diagonal eigenvalue matrix, a block-diagonal transformed input matrix, and a block-diagonal transformed output matrix;

[0148] A network matrix construction module, configured to construct a network differential equation including the terminal voltages and output currents of each region to obtain a network impedance matrix and a network inductance matrix;

[0149] An equivalent state matrix construction module, configured to construct an equivalent state matrix based on the diagonal eigenvalue matrix, the block-diagonal transformed input matrix, the block-diagonal transformed output matrix, the network impedance matrix, and the network inductance matrix;

[0150] An eigenvalue calculation module, configured to calculate the eigenvalues of the equivalent state matrix, which are the eigenvalues of the distributed power system.

[0151] The specific implementation manners of the above modules are the same as those in Embodiment 1 and will not be elaborated here.

[0152] Embodiment 3

[0153] In one or more embodiments, a terminal device is disclosed, which includes a processor and a memory. The processor is configured to implement instructions; the memory is configured to store multiple instructions, and the instructions are adapted to be loaded and executed by the processor to perform the method for calculating eigenvalues of the distributed power system described in Embodiment 1.

[0154] It should be understood that in this embodiment, the processor may be a central processing unit (CPU), and the processor may also be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or any conventional processor, etc.

[0155] The memory may include a read-only memory and a random access memory, and provide instructions and data to the processor. A part of the memory may also include a non-volatile random access memory. For example, the memory may also store information about the device type.

[0156] In the implementation process, each step of the above method may be completed by the integrated logic circuit in the hardware of the processor or the instructions in the form of software.

[0157] Embodiment 4

[0158] In one or more embodiments, a computer-readable storage medium is disclosed, in which multiple instructions are stored, and the instructions are adapted to be loaded and executed by the processor of the terminal device to perform the method for calculating the characteristic values of the distributed power system described in Embodiment 1.

[0159] Although the specific implementation manners of the present invention are described above in conjunction with the drawings, it is not a limitation to the protection scope of the present invention. Those skilled in the art should understand that based on the technical solutions of the present invention, various modifications or deformations that can be made by those skilled in the art without creative efforts are still within the protection scope of the present invention.

Claims

1. A calculation method for eigenvalues of a distributed power system, characterized in that, including: Based on the linearized state space equations of each region in the distributed power system, the eigenvalues and right eigenvectors of each region are calculated locally. The input matrix and output matrix of the linearized state space equation are transformed based on the right eigenvectors, and the eigenvalues of each region and the transformed input matrix and output matrix are transmitted to the eigenvalue calculation center; The eigenvalues transmitted by each region and the transformed input matrix and output matrix are arranged diagonally respectively to obtain a diagonal eigenvalue matrix, a block diagonal transformed input matrix, and a block diagonal transformed output matrix; Construct a network differential equation including the terminal voltage and output current of each region to obtain a network impedance matrix and a network inductance matrix; Based on the diagonal eigenvalue matrix, the block diagonal transformed input matrix, the block diagonal transformed output matrix, the network impedance matrix, and the network inductance matrix, construct an equivalent state matrix; Calculate the eigenvalues of the equivalent state matrix, which are the eigenvalues of the distributed power system.

2. The calculation method of the eigenvalues of a distributed power system according to claim 1, characterized in that The linearized state space equation includes a state equation and an output equation. The input variables of the state equation and the output equation are both column vectors composed of the terminal voltages of the region in the d-q rotating coordinate system, and the output variables are both column vectors composed of the output currents of the region in the d-q rotating coordinate system.

3. The calculation method of the eigenvalue of a distributed power system according to claim 1, characterized in that Calculate the right eigenvector of the region, specifically: Taking the kth region as an example, the characteristic equation of the region with respect to the right eigenvector is: Α k v j = λ j v j ; Among them, A k is the state matrix of this region; λ j is the j-th eigenvalue, and each eigenvalue corresponds to a mode. The real eigenvalue corresponds to a non-oscillatory mode, and the complex eigenvalue corresponds to an oscillatory mode. Its real part represents damping, and its imaginary part represents the oscillation frequency; v j is the right eigenvector corresponding to the j-th eigenvalue.

4. The calculation method of eigenvalues of a distributed power system according to claim 1, characterized in that, Transform the input matrix and output matrix of the linearized state space equation based on the right eigenvector, specifically: The right eigenvectors of each region in the distributed power system are arranged by column to form a right eigenvector matrix, and the right eigenvector matrix is used as the transformation matrix; The input matrix in the state space equation is left-multiplied by the inverse matrix of the transformation matrix to obtain a transformed input matrix; The output matrix in the state space equation is right-multiplied by the transformation matrix to obtain a transformed output matrix.

5. The calculation method of eigenvalues of a distributed power system according to claim 1, characterized in that The diagonal eigenvalue matrix Λ, the block diagonal transformed input matrix B t and the block diagonal transformed output matrix C t are respectively: where diag represents a block diagonal matrix formed by the matrices within its square brackets; assuming that there are m regions in the distributed power system, Λ k is a diagonal matrix composed of the eigenvalues of the k-th region; B t,k is the conversion input matrix of the k-th region; C t,k is the conversion output matrix of the k-th region; k = 1, 2, …, m.

6. The calculation method of the eigenvalues of a distributed power system according to claim 1, characterized in that Construct a network differential equation including the terminal voltage and output current of each region, specifically: Among them, U is a column vector composed of the terminal voltages of all distributed power sources; I is a column vector composed of the output currents of all distributed power sources; U gm is a column vector composed of m AC grid voltages; L is the network inductance matrix, which is a block matrix composed of m 2 2×2 matrices. Its diagonal element L ww is the sum of the line inductance matrices connecting the w-th distributed power source to the AC grid. The off-diagonal element L wv is the sum of the inductance matrices of the common parts of the lines connecting the w-th distributed power source and the v-th distributed power source to the AC grid; Z is the network impedance matrix, which is a block matrix composed of m 2 2×2 matrices. Its diagonal element Z ww is the sum of the line impedance matrices connecting the w-th distributed power source to the AC grid. The off-diagonal element Z wv is the sum of the impedance matrices of the common parts of the lines connecting the w-th distributed power source and the v-th distributed power source to the AC grid.

7. The calculation method of the eigenvalues of a distributed power system according to claim 1, characterized in that, The equivalent state matrix is specifically: A s,eq = Λ + B t (E 2m - LC t B t ) -1 (LC t Λ + ZC t ); Among them, A s,eq is the equivalent state matrix; E 2m is the identity matrix, Λ, B t and C t are the diagonal eigenvalue matrix, the block diagonal transformed input matrix, and the block diagonal transformed output matrix respectively, Z is the network impedance matrix, and L is the network inductance matrix.

8. A calculation system for eigenvalues of a distributed power system, characterized in that, including: A regional local calculation module, which is used to calculate the eigenvalues and right eigenvectors of each region locally based on the linearized state space equations of each region in the distributed power system, transform the input matrix and output matrix of the linearized state space equation based on the right eigenvectors, and transmit the eigenvalues of each region and the transformed input matrix and output matrix to the eigenvalue calculation center; A matrix reconstruction module, which is used to arrange the eigenvalues transmitted by each region and the transformed input matrix and output matrix diagonally respectively to obtain a diagonal eigenvalue matrix, a block diagonal transformed input matrix, and a block diagonal transformed output matrix; A network matrix construction module, which is used to construct a network differential equation including the terminal voltage and output current of each region to obtain a network impedance matrix and a network inductance matrix; An equivalent state matrix construction module, which is used to construct an equivalent state matrix based on the diagonal eigenvalue matrix, the block diagonal transformed input matrix, the block diagonal transformed output matrix, the network impedance matrix, and the network inductance matrix; An eigenvalue calculation module, which is used to calculate the eigenvalues of the equivalent state matrix, which are the eigenvalues of the distributed power system.

9. A terminal device, comprising a processor and a memory, the processor being configured to implement instructions; the memory being configured to store a plurality of instructions, characterized in that, The instruction is adapted to be loaded and executed by a processor to calculate the characteristic values of the distributed power system according to any one of claims 1-7.

10. A computer-readable storage medium storing multiple instructions, characterized in that, The instruction is adapted to be loaded and executed by a processor of a terminal device to calculate the characteristic values of the distributed power system according to any one of claims 1-7.

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