A method and system for calculating eigenvalues of a distributed power system

Abstract

The application discloses a kind of distributed power system eigenvalue calculation method and system, comprising: distributed power system respectively in local area eigenvalue and right eigenvector of this region are calculated, based on right eigenvector to the input matrix and output matrix of linearization state space equation are transformed;Eigenvalue and the input matrix and output matrix after transformation of this region are transferred to eigenvalue calculation center;Respectively get diagonal eigenvalue matrix, block diagonal conversion input matrix and block diagonal conversion output matrix;Network differential equation including each regional terminal voltage and output current is constructed, and network impedance matrix and network inductance matrix are obtained;Equivalent state matrix is constructed;Eigenvalue of equivalent state matrix is calculated, i.e. the eigenvalue of distributed power system.The original matrix information of each regional state space equation is not needed in the application calculation process, and the confidentiality of each regional core information can be effectively guaranteed.

Description

Technical Field

[0001] This invention relates to the field of power system characteristic value calculation technology, and in particular to a method and system for calculating characteristic values ​​of a distributed power system. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] With the integration of a high proportion of renewable energy and the demand for flexible resource response on the user side, the power system is accelerating its evolution from the traditional centralized "large grid" model to a distributed structure, showing a development trend of more flexible structure, stronger resilience and greater inclusiveness, with distributed power sources becoming its most prominent feature.

[0004] In distributed power systems, different regions adopt a zoned management model to improve local response efficiency and flexibility. Due to differences in management systems, market competition mechanisms, and data privacy protection requirements, core data in each region is not shared, making it difficult to achieve completely transparent data sharing across the entire network, which poses challenges to power system stability analysis.

[0005] In this context, traditional online security analysis often equates other regions to equivalent models to reduce computational complexity. However, this approach can lead to the loss of critical modal information, failing to effectively identify potential system instability risks. For example, dynamic interactions between regional units may generate interval oscillations. If other regions are equated, their dynamic characteristics cannot be accurately reflected by the simplified model, resulting in significant deviations in eigenvalue calculations. Furthermore, when modeling inter-regional connection lines, traditional eigenvalue calculation methods typically ignore the dynamic processes of the lines, using network algebraic equations to reflect the system topology, which also leads to the loss of oscillation modes. Therefore, preserving the dynamic characteristics of each link, avoiding equation errors, accurately calculating each mode, and simultaneously protecting the core information of each region are of great practical significance.

[0006] To address the requirements of both accuracy and confidentiality in distributed eigenvalue calculation, existing technologies propose a distributed eigenvalue calculation method based on the traditional self-excitation method. This method only requires the exchange of a small amount of information between the boundary regions of each area, and iteratively solves the distributed eigenvalues ​​using the principle of self-excitation. The results are consistent with the traditional method and have good accuracy. However, this method has obvious limitations. It can only calculate key eigenvalues ​​related to electromechanical oscillation modes, and is only applicable to low-frequency oscillation scenarios in power systems. It cannot analyze broadband oscillation phenomena in new power systems ranging from subsynchronous to supersynchronous frequencies. Summary of the Invention

[0007] To address the aforementioned issues, this invention proposes a method and system for calculating the eigenvalues ​​of a distributed power system. Each region of the distributed power system provides its locally transformed input and output matrices, along with its eigenvalues, to an eigenvalue calculation center. Based on the information transmitted from each region, the eigenvalue calculation center, in conjunction with the network inductance and impedance matrices, constructs an equivalent state matrix that does not contain the original state-space equation matrix information of each region, thereby obtaining the eigenvalues ​​of the distributed power system. This achieves accurate calculation of the eigenvalues ​​of the distributed power system while maintaining the confidentiality of core information from each region and without losing oscillation modes.

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

[0009] A method for calculating characteristic values ​​of a distributed power system, comprising:

[0010] Each region of the distributed power system calculates its own eigenvalues ​​and right eigenvectors based on its own linearized state space equations. The input and output matrices of the linearized state space equations are then transformed based on the right eigenvectors. Finally, the eigenvalues ​​of the region, along with the transformed input and output matrices, are transmitted to the eigenvalue calculation center.

[0011] The eigenvalues ​​transmitted from each region, as well as the transformed input and output matrices, are arranged diagonally to obtain the diagonal eigenvalue matrix, the block diagonal transformation input matrix, and the block diagonal transformation output matrix, respectively.

[0012] Construct network differential equations that include the terminal voltages and output currents of each region to obtain the network impedance matrix and network inductance matrix;

[0013] Based on the diagonal eigenvalue matrix, the block diagonal transformation input matrix, the block diagonal transformation output matrix, the network impedance matrix, and the network inductance matrix, an equivalent state matrix is ​​constructed.

[0014] The eigenvalues ​​of the equivalent state matrix are the eigenvalues ​​of the distributed power system.

[0015] As a further embodiment, 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 dq rotating coordinate system, and the output variables are both column vectors composed of the output currents of the region in the dq rotating coordinate system.

[0016] As a further step, the right eigenvector of this region is calculated, specifically as follows:

[0017] Taking the k-th region as an example, the characteristic equation of this region with respect to the right eigenvector is:

[0018] A kv j =λ j v j ;

[0019] Among them, A k Let λ be the state matrix of this region. j Let v be the j-th eigenvalue. Each eigenvalue corresponds to a mode. Real eigenvalues ​​correspond to non-oscillatory modes, and complex eigenvalues ​​correspond to oscillatory modes. The real part represents damping, and the imaginary part represents the oscillation frequency. j Let be the right eigenvector corresponding to the j-th eigenvalue.

[0020] As a further approach, the input and output matrices of the linearized state-space equations are transformed based on the right eigenvectors, specifically as follows:

[0021] The right eigenvectors of each region of the distributed power system are arranged in columns to form a right eigenvector matrix, which is then used as a transformation matrix.

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

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

[0024] As a further solution, the diagonal eigenvalue matrix Λ and the block diagonal transformation input matrix B... t The output matrix C is transformed by dividing the block diagonally. t They are respectively:

[0025]

[0026] Where, diag represents a block diagonal matrix consisting of the matrices within its square brackets; assuming the distributed power system has m regions, Λ k B is a diagonal matrix composed of the eigenvalues ​​of the k-th region; t,k C is the transformation input matrix for the k-th region; t,k Let be the transformation output matrix for the k-th region; k = 1, 2, ..., m.

[0027] As a further approach, a network differential equation is constructed that includes the terminal voltage and output current of each region, specifically:

[0028]

[0029] Where U is a column vector consisting of the terminal voltages of all distributed power sources; I is a column vector consisting of the output currents of all distributed power sources; U gm Let L be a column vector consisting of m AC grid voltages; L is the network inductance matrix, composed of m... 2A block matrix consisting of 2×2 matrices, with diagonal elements L ww The sum of the line inductance matrices connecting the w-th distributed power source to the AC grid, with off-diagonal elements L wv Z is the sum of the inductance matrices of the common sections of the lines connecting the w-th and v-th distributed power sources to the AC grid; Z is the network impedance matrix, formed by m 2 A block matrix consisting of 2×2 matrices, with diagonal elements Z ww The sum of the line impedance matrices connecting the w-th distributed power source to the AC grid, with off-diagonal elements Z wv This is the sum of the impedance matrices of the common sections 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 as follows:

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

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

[0033] In other embodiments, the following technical solutions are adopted:

[0034] A system for calculating characteristic values ​​of a distributed power system, comprising:

[0035] The regional local calculation module is used to calculate the eigenvalues ​​and right eigenvectors of each region in the distributed power system based on the linearized state space equation of the region. Based on the right eigenvector, the input matrix and output matrix of the linearized state space equation are transformed, and the eigenvalues ​​of the region and the transformed input matrix and output matrix are transmitted to the eigenvalue calculation center.

[0036] The matrix reconstruction module is used to arrange the eigenvalues ​​transmitted from each region, as well as the transformed input and output matrices, along the diagonal to obtain the diagonal eigenvalue matrix, the block diagonal transformed input matrix, and the block diagonal transformed output matrix, respectively.

[0037] The network matrix construction module is used to construct network differential equations that include the terminal voltages and output currents of each region, and to obtain the network impedance matrix and the network inductance matrix.

[0038] The equivalent state matrix construction module is used to construct an equivalent state matrix based on the diagonal eigenvalue matrix, the block diagonal transformation input matrix, the block diagonal transformation output matrix, the network impedance matrix, and the network inductance matrix.

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

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

[0041] A terminal device includes a processor and a memory, the processor being used to implement instructions; the memory being used to store multiple instructions adapted for loading and execution by the processor of the above-described method for calculating characteristic values ​​of a distributed power system.

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

[0043] A computer-readable storage medium storing a plurality of instructions adapted for loading and execution by a processor of a terminal device of the above-described method for calculating characteristic values ​​of a distributed power system.

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

[0045] (1) In this invention, the input matrix and output matrix are linearly transformed locally in each region. The transformed input matrix and output matrix, along with the eigenvalues ​​of the region, are then transmitted to the eigenvalue calculation center. The eigenvalue calculation center combines the network inductance matrix and the network impedance matrix to construct the 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, which can effectively ensure the confidentiality of the core information of each region.

[0046] (2) The present invention writes differential equations for the connecting lines between regions, takes into account the current differential terms introduced by the line inductance, and further derives the network differential equations for the calculation of system eigenvalues. This avoids the risk of inaccurate network modeling and loss of some oscillation modes caused by neglecting differential terms in traditional network algebraic equations, and ensures that all oscillation modes can be accurately calculated.

[0047] (3) This invention makes full use of the eigenvalues ​​of each region, the input matrix, the output matrix and the network topology between regions to obtain the equivalent state matrix of the distributed power system. This matrix is ​​essentially a similar 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, thus ensuring the accuracy of the eigenvalue calculation.

[0048] Other features and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0049] Figure 1 This is a flowchart of the method for calculating characteristic values ​​of a distributed power system in an embodiment of the present invention;

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

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

[0052] Figure 4 This is a schematic diagram of the feature value distribution in an embodiment of the present invention. Detailed Implementation

[0053] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used in this invention have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0054] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, 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] Example 1

[0056] In one or more embodiments, a method for calculating characteristic values ​​of a distributed power system is disclosed, combined with Figure 1 Specifically, it includes the following steps:

[0057] S101: Each region of the distributed power system calculates its own eigenvalues ​​and right eigenvectors based on its own linearized state space equations. Based on the right eigenvectors, it transforms the input and output matrices of the linearized state space equations and transmits the eigenvalues ​​of its region, as well as the transformed input and output matrices, 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 column vectors composed of the terminal voltages of the region in the dq rotating coordinate system, and the output variables are column vectors composed of the output currents of the region in the dq rotating coordinate system.

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

[0060]

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

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

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

[0064] A k vj =λ j v j (2)

[0065] In the formula, λ j Let be the j-th eigenvalue. Each eigenvalue corresponds to a mode. Real eigenvalues ​​correspond to non-oscillatory modes, and complex eigenvalues ​​correspond to oscillatory modes. The real part represents damping, and the imaginary part represents the oscillation frequency. Let be 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: arranging the right eigenvectors of each regional power grid into a right eigenvector matrix, using it as the transformation matrix, multiplying the input matrix in the state space equation by the inverse of the transformation matrix on the left, and multiplying the output matrix by the transformation matrix on the right, to obtain the transformed input matrix and transformed output matrix respectively.

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

[0068]

[0069] In the formula, Let be the transformation matrix for the k-th region; This is the right eigenvector corresponding to the first eigenvalue of the k-th region; For the k-th region n-th k The right eigenvector corresponding to each eigenvalue.

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

[0071]

[0072] In the formula, This is the transformation input matrix for the k-th region; This is the transformation output matrix for the k-th region.

[0073] This embodiment transmits the eigenvalues ​​of the region, as well as the transformed input and output matrices, to the eigenvalue calculation center. This avoids directly transmitting the original matrix information of the state space equations of each region, effectively ensuring the confidentiality of the core information of each region.

[0074] S102: Arrange the eigenvalues ​​transmitted from each region, as well as the transformed input and output matrices, along the diagonal to obtain the diagonal eigenvalue matrix, the block diagonal transformation input matrix, and the block diagonal transformation output matrix. These matrices integrate the information transmitted from all regions for subsequent calculation of the eigenvalues ​​of the distributed power system.

[0075] In this embodiment, the eigenvalues, transformation input matrices, and transformation output matrices transmitted from each region are arranged diagonally to form a diagonal eigenvalue matrix, a block-diagonal transformation input matrix, and a block-diagonal transformation output matrix. Assuming the distributed power system has m regions, the expression for each block-diagonal matrix is ​​as follows:

[0076]

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

[0078] Let N be a diagonal matrix consisting of the eigenvalues ​​of all regions, and N be the total number of state variables of all regions.

[0079] This is the transformation input matrix for the first region; This is the transformation input matrix for the m-th region; Transform the input matrix into a block diagonal; This is the transformation output matrix for the first region; This is the transformation output matrix for the m-th region; The output matrix is ​​transformed by dividing the blocks diagonally.

[0080] S103: Construct network differential equations that include the terminal voltages and output currents of each region to obtain the network impedance matrix and network inductance matrix.

[0081] In this embodiment, a system with m distributed power sources is considered. This system consists of h branches connected in parallel to the Point of Common Coupling (PCC), and then connected to the AC power grid via lines. The l-th branch contains t l A series-connected distributed power source. Taking this distributed system as an example, the derivation process of the network differential equations and the network inductance matrix and 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 in the l-th branch:

[0083]

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

[0085] The specific expressions for the inductance matrix and impedance matrix are as follows:

[0086]

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

[0088] Similarly, write down the relationship between the terminal voltages of all distributed power sources along the branch from the (w+1)th distributed power source to the PCC point, as well as the relationship between the voltage at the PCC point and the AC grid voltage. Substituting all voltage relationships into equation (6), we can obtain the expression for the terminal voltage of the wth distributed power source along the l-th branch:

[0089]

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

[0091] [i line,(w+1)d i line,(w+1)q ] T Let i be the current flowing through the line between the (w+1)th and (w+2)th distributed power sources. line,(w+1)d and iline,(w+1)q Let its d-axis and q-axis components be... Its derivative; It is the sequence number of the last distributed power source on the l-th branch; Let the inductance matrix of the line between it and point PCC be given. Let the impedance matrix be the line between it and point PCC.

[0092] Let the current flowing through the line between it and point PCC be the current. and

[0093] Let its d-axis and q-axis components be... Its derivative; The inductance matrix of the line between point PCC and the AC power grid; This is the impedance matrix of the line between point PCC and the AC power grid; i represents the current flowing through the line between point PCC and the AC power grid. line,gd and i line,gq Let its d-axis and q-axis components be... Its derivative; U g =[u gd ,u gq ] T The voltage of the AC power grid, u gd and u gq Let its d-axis and q-axis components be defined.

[0094] The current flowing through the line is the sum of the output currents of all distributed power sources preceding that branch. By replacing all line currents in equation (8) with the output currents of the distributed power sources, and rearranging them using the output current of each distributed power source as a common factor, we can obtain the form of the terminal voltage of the w-th distributed power source expressed in terms of the output currents of each distributed power source. Similarly, we can obtain the expressions for the terminal voltages of other distributed power sources. Combining them into a vector form, we obtain the network differential equation:

[0095]

[0096] In the formula, This is a column vector consisting of the terminal voltages of all distributed power sources. This is a column vector consisting of the output currents of all distributed power sources. It is a column vector consisting of m AC grid voltages; For a network inductance matrix, it is composed of m 2 A block matrix consisting of 2×2 matrices, with diagonal elements L ww The sum of the line inductance matrices connecting the w-th distributed power source to the AC grid, with off-diagonal elements L wvThe sum of the inductance matrices of the common portion of the lines connecting the w-th distributed power source and the v-th distributed power source to the AC power grid; The network impedance matrix is ​​formed by m 2 A block matrix consisting of 2×2 matrices, with diagonal elements Z ww The sum of the line impedance matrices connecting the w-th distributed power source to the AC grid, with off-diagonal elements Z wv This is the sum of the impedance matrices of the common sections of the lines connecting the w-th distributed power source and the v-th distributed power source to the AC power grid.

[0097] Linearizing equation (9) at the steady-state point yields the network differential equation in small-signal form:

[0098]

[0099] In the formula, A column vector consisting of the small-signal forms of the voltages at the terminals of each distributed power source; A column vector consisting of the small-signal form of the output current of each distributed power source; It is a column vector consisting of m small-signal forms of AC grid voltages.

[0100] This embodiment constructs a network differential equation that includes the terminal voltage and output current of each region. It takes into account the current differential term dynamically introduced by the line inductance, avoiding the risk of inaccurate network modeling and loss of some oscillation modes caused by neglecting differential terms in traditional network algebraic equations, and ensuring that all oscillation modes can be accurately calculated.

[0101] S104: Construct an equivalent state matrix based on the diagonal eigenvalue matrix, the block diagonal transformation input matrix, the block diagonal transformation output matrix, the network impedance matrix, and the network inductance 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 in this embodiment is as follows:

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

[0105] In the formula, This is the equivalent state matrix; It is an identity matrix.

[0106] Calculate the equivalent state matrix A eq The eigenvalues ​​are the eigenvalues ​​of the distributed power system. The transformation matrices of each region are arranged diagonally to construct a block-diagonal transformation matrix, i.e.:

[0107] T = diag[T1 … T] k … T m (12)

[0108] In the formula, This is a block diagonal transformation matrix; This is the transformation matrix for the first region; Let be the transformation matrix for the m-th region.

[0109] The equivalent state matrix A s,eq Multiplying the block diagonal transformation matrix on the left and on the inverse of the block diagonal transformation matrix on the right, we get:

[0110]

[0111] In the formula, This is a block diagonal matrix composed of the state matrices arranged diagonally in the linearized state-space equations of each region. Input a block diagonal matrix composed of matrices arranged diagonally for each region; The output matrices for each region are arranged diagonally to form a block diagonal matrix.

[0112] Combining the linearized state-space equations for each region shown in equation (1) with the network differential equations shown in equation (10), the state matrix of the distributed power system can be derived:

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

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

[0115] From equations (13) and (14), it can be seen that the equivalent state matrix A s,eq Essentially, it is the state matrix A s The similarity transformations can be used to prove that the equivalent state matrix A is... s,eq The desired eigenvalues ​​are the state matrix A. s eigenvalues.

[0116] The effectiveness of the proposed method for calculating the characteristic values ​​of distributed power systems is then verified using a grid-connected system with distributed power sources. All analyses were performed in Matlab and on an Intel 2.20GHz 16GB laptop.

[0117] Grid-connected systems with distributed power sources, such as Figure 2 As shown in the figure, the grid-connected system with distributed power sources includes four distributed power sources. AC grid voltage, The terminal voltage of each distributed power source. R represents the output current of each distributed power source; i (i = 1, 2, 3, 4) and X i =ω g L i (i = 1, 2, 3, 4) represent the resistance and reactance of the lines between each distributed power source and the PCC point, respectively, ω g L is the angular frequency of the power grid. i (i = 1, 2, 3, 4) represents the inductance of the line; R g and X g =ω g L g These represent the resistance and reactance of the line between point PCC and the AC power grid, respectively. g The inductance of the circuit.

[0118] By using the linearized state-space equations of each distributed power source, the eigenvalues ​​and right eigenvector matrices are calculated locally. Then, the input and output matrices are transformed and provided to the eigenvalue calculation center along with the eigenvalues. Based on the information provided by each distributed power source and combined with the network inductance matrix and network impedance matrix derived from the network differential equations, the eigenvalue calculation center constructs an equivalent state matrix that does not contain the original state-space equation matrix information of each distributed power source. The eigenvalues ​​of this matrix are the eigenvalues ​​of the entire system.

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

[0120]

[0121] In the formula, These are the state variables of each distributed power source. For each distributed power source's state variable, the form is small-signal; n i This represents the total number of state variables for all distributed power sources. For the small-signal form of the voltage at each distributed power source terminal, This represents the small-signal form of the output current of each distributed power source.

[0122] The state matrix of each distributed power source; For each distributed power source, there is an input matrix; This represents the output matrix of each distributed power source.

[0123] Calculate the state matrix A of each distributed power source respectively. i From the eigenvalues ​​and right eigenvectors, the eigenvalues ​​Λ of each distributed power source are obtained. i The transformation matrix T composed of the right eigenvectors i Then, the input and output matrices are transformed to obtain the transformed input matrix B. t,i and the transformation output matrix C t,i :

[0124]

[0125] The characteristic value Λ of each distributed power source i Transform input matrix B t,i and the transformation output matrix C t,i Arrange them diagonally to form a diagonal eigenvalue matrix Λ and a block diagonal transformation input matrix B. t The output matrix C is transformed by dividing the block diagonally. t :

[0126]

[0127] Based on the network topology, the network differential equations of a grid-connected system containing distributed power sources are obtained:

[0128]

[0129] In the formula, 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] In the formula, L g and L i (i = 1, 2, 3, 4) represent the inductance matrices of each line; Z g and Z i (i = 1, 2, 3, 4) represent the impedance matrices of each line, with the specific expressions as follows:

[0133]

[0134] Based on the diagonal eigenvalue matrix Λ and the block diagonal transformation input matrix Bt The output matrix C is transformed by dividing the block diagonally. t And the network inductance matrix L and the network impedance matrix Z, 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 ) (twenty one)

[0136] In the formula, It is an identity matrix.

[0137] Calculate A s,eq The characteristic values ​​are those of a grid-connected system containing distributed power sources. The information transfer in this calculation process is as follows: Figure 3 As shown, the goal of calculating the precise eigenvalues ​​of the system without obtaining the original state equation matrix information of each distributed power source is achieved.

[0138] Figure 4 The eigenvalue distribution diagrams for this system show the eigenvalues ​​calculated by the method of this invention and the eigenvalues ​​calculated after obtaining all matrices of the original state-space equation under conditions of complete information transparency. A comparison shows that the eigenvalues ​​calculated by the method of this invention are consistent with those calculated by the fully transparent method. The relative errors of each eigenvalue are calculated, with the maximum relative error being only 4.2280 × 10⁻⁶. -11 This can verify the accuracy of the method in the embodiments of the present invention.

[0139] Furthermore, the circuits in the above calculations are all described using differential equations. However, in traditional methods, when deriving network equations, circuits are often described using algebraic equations, neglecting circuit dynamics. This may lead to some oscillation modes not being accurately reflected. The method of this invention establishes network differential equations, fully considering circuit dynamics and avoiding the risk of losing oscillation modes. The system was simulated in Matlab Simulink, and the parameters of the control loop in the distributed power supply were adjusted. The eigenvalues ​​were calculated using both the traditional method of circuit algebraic equations and the method described in this embodiment. The results are shown in Table 1.

[0140] Table 1 Comparison of eigenvalue calculation using traditional methods and the method of this embodiment.

[0141]

[0142]

[0143] As can be seen from Table 1, in Case 3, the calculation results of the traditional method do not contain positive real part eigenvalues, and this oscillation mode is lost, while the method described in this embodiment can correctly reflect this oscillation mode.

[0144] Example 2

[0145] In one or more embodiments, a system for calculating characteristic values ​​of a distributed power system is disclosed, comprising:

[0146] The regional local calculation module is used to calculate the eigenvalues ​​and right eigenvectors of each region in the distributed power system based on the linearized state space equation of the region. Based on the right eigenvector, the input matrix and output matrix of the linearized state space equation are transformed, and the eigenvalues ​​of the region and the transformed input matrix and output matrix are transmitted to the eigenvalue calculation center.

[0147] The matrix reconstruction module is used to arrange the eigenvalues ​​transmitted from each region, as well as the transformed input and output matrices, along the diagonal to obtain the diagonal eigenvalue matrix, the block diagonal transformed input matrix, and the block diagonal transformed output matrix, respectively.

[0148] The network matrix construction module is used to construct network differential equations that include the terminal voltages and output currents of each region, and to obtain the network impedance matrix and the network inductance matrix.

[0149] The equivalent state matrix construction module is used to construct an equivalent state matrix based on the diagonal eigenvalue matrix, the block diagonal transformation input matrix, the block diagonal transformation output matrix, the network impedance matrix, and the network inductance matrix.

[0150] The eigenvalue calculation module is used to calculate the eigenvalues ​​of the equivalent state matrix, which are the eigenvalues ​​of the distributed power system.

[0151] The specific implementation methods of the above modules are the same as those in Example 1, and will not be described in detail again.

[0152] Example 3

[0153] In one or more embodiments, a terminal device is disclosed, comprising a processor and a memory, wherein the processor is used to implement instructions; and the memory is used to store multiple instructions adapted to be loaded by the processor and executed by the method for calculating characteristic values ​​of a distributed power system as described in Embodiment 1.

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

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

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

[0157] Example 4

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

[0159] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for calculating characteristic values ​​of a distributed power system, characterized in that, include: Each region of the distributed power system calculates its own eigenvalues ​​and right eigenvectors based on its own linearized state space equations, and transforms the input and output matrices of the linearized state space equations based on the right eigenvectors. The eigenvalues ​​of this region, along with the transformed input and output matrices, are passed to the eigenvalue calculation center. The input and output matrices of the linearized state-space equations are transformed based on the right eigenvectors, specifically as follows: The right eigenvectors of each region of the distributed power system are arranged in columns to form a right eigenvector matrix, which is then used as a transformation matrix. The input matrix in the state-space equation is multiplied by the inverse of the transformation matrix on the left to obtain the transformed input matrix; The output matrix in the state-space equation is right-multiplied by the transformation matrix to obtain the transformed output matrix; The eigenvalues ​​transmitted from each region, as well as the transformed input and output matrices, are arranged diagonally to obtain the diagonal eigenvalue matrix, the block diagonal transformation input matrix, and the block diagonal transformation output matrix, respectively. Construct network differential equations that include the terminal voltages and output currents of each region to obtain the network impedance matrix and network inductance matrix; Based on the diagonal eigenvalue matrix, the block diagonal transformation input matrix, the block diagonal transformation output matrix, the network impedance matrix, and the network inductance matrix, an equivalent state matrix is ​​constructed. The eigenvalues ​​of the equivalent state matrix are the eigenvalues ​​of the distributed power system.

2. The method for calculating characteristic values ​​of a distributed power system as described in claim 1, characterized in that, The linearized state-space equations include state equations and output equations. The input variables of the state equations and output equations are both column vectors composed of the terminal voltages of the region in the dq rotating coordinate system, and the output variables are both column vectors composed of the output currents of the region in the dq rotating coordinate system.

3. The method for calculating characteristic values ​​of a distributed power system as described in claim 1, characterized in that, Calculate the right eigenvector of this region as follows: With the first k Taking a region as an example, the characteristic equation of this region with respect to the right eigenvector is: ； in, A k This is the state matrix for this region; λ j For the first j There are 1 eigenvalues, each corresponding to a modulus. The real eigenvalues ​​correspond to non-oscillatory modes, and the complex eigenvalues ​​correspond to oscillatory modes. The real part represents damping, and the imaginary part represents the oscillation frequency. v j For the first j The right eigenvector corresponding to each eigenvalue.

4. The method for calculating characteristic values ​​of a distributed power system as described in claim 1, characterized in that, The diagonal eigenvalue matrix Λ Transform the input matrix by dividing it into blocks and diagonals. B t Transform the output matrix by dividing the block into diagonals C t They are: ； Where, diag represents a block diagonal matrix formed by the matrices within its square brackets; assuming the distributed power system has a total of m Each region Λ k For the first k A diagonal matrix composed of the eigenvalues ​​of each region; B t,k For the first k Transformation input matrix for each region; C t,k For the first k Transformation output matrix for each region; k = 1, 2, …, m .

5. The method for calculating characteristic values ​​of a distributed power system as described in claim 1, characterized in that, Construct the network differential equations that include the terminal voltages and output currents of each region, specifically as follows: in, U This is a column vector consisting of the terminal voltages of all distributed power sources. I This is a column vector consisting of the output currents of all distributed power sources. U gm for m A column vector consisting of AC grid voltages; L For the network inductance matrix, by m 2 2 A block matrix composed of 2 matrices, whose diagonal elements L ww To connect the first w The sum of the line inductance matrices of the distributed power sources and the AC power grid, and the off-diagonal elements. L wv To connect the first w The first distributed power source and the first v The sum of the inductance matrices of the common parts of the lines of a distributed power source and an AC power grid; Z The network impedance matrix is ​​formed by... m 2 2 A block matrix composed of 2 matrices, whose diagonal elements Z ww To connect the first w The sum of the line impedance matrices of the distributed power sources and the AC power grid, with off-diagonal elements. Z wv To connect the first w The first distributed power source and the first v The sum of the impedance matrices of the common parts of the lines of a distributed power source and the AC power grid.

6. The method for calculating characteristic values ​​of a distributed power system as described in claim 1, characterized in that, The equivalent state matrix is ​​specifically: ； in, A s,eq This is the equivalent state matrix; E 2m It is the identity matrix. , and These are the diagonal eigenvalue matrix, the block diagonal transformation input matrix, and the block diagonal transformation output matrix, respectively. The network impedance matrix, This is the network inductance matrix.

7. A system for calculating characteristic values ​​of a distributed power system, characterized in that, include: The regional local computation module is used to compute the eigenvalues ​​and right eigenvectors of each region in the distributed power system based on the linearized state space equation of that region, and to transform the input matrix and output matrix of the linearized state space equation based on the right eigenvector. The eigenvalues ​​of this region, along with the transformed input and output matrices, are passed to the eigenvalue calculation center. The input and output matrices of the linearized state-space equations are transformed based on the right eigenvectors, specifically as follows: The right eigenvectors of each region of the distributed power system are arranged in columns to form a right eigenvector matrix, which is then used as a transformation matrix. The input matrix in the state-space equation is multiplied by the inverse of the transformation matrix on the left to obtain the transformed input matrix; The output matrix in the state-space equation is right-multiplied by the transformation matrix to obtain the transformed output matrix; The matrix reconstruction module is used to arrange the eigenvalues ​​transmitted from each region, as well as the transformed input and output matrices, along the diagonal to obtain the diagonal eigenvalue matrix, the block diagonal transformed input matrix, and the block diagonal transformed output matrix, respectively. The network matrix construction module is used to construct network differential equations that include the terminal voltages and output currents of each region, and to obtain the network impedance matrix and the network inductance matrix. The equivalent state matrix construction module is used to construct an equivalent state matrix based on the diagonal eigenvalue matrix, the block diagonal transformation input matrix, the block diagonal transformation output matrix, the network impedance matrix, and the network inductance matrix. The eigenvalue calculation module is used to calculate the eigenvalues ​​of the equivalent state matrix, which are the eigenvalues ​​of the distributed power system.

8. A terminal device comprising a processor and a memory, the processor for implementing instructions; the memory for storing multiple instructions, characterized in that, The instructions are adapted to be loaded by a processor and executed by the method for calculating the characteristic values ​​of a distributed power system according to any one of claims 1-6.

9. A computer-readable storage medium storing a plurality of instructions, characterized in that, The instructions are adapted to be loaded by the processor of the terminal device and executed by the method for calculating the characteristic values ​​of the distributed power system according to any one of claims 1-6.

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