A small-signal stability analysis method and system for a large-scale new energy power system

Abstract

The present invention discloses a small-signal stability analysis method and system for a large-scale new energy power system, relating to the technical field of power system stability analysis, including: for a large-scale new energy power system, constructing a discrete state space model of the entire power system and determining a discrete state matrix; using a preprocessing technique to convert the eigenvalues of the system state matrix to be solved into the dominant eigenvalues of the system; the preprocessing technique is a displacement inverse transformation or a rotation transformation; based on the discrete state matrix, using an iterative algorithm combined with sparsity implementation to calculate and solve the dominant eigenvalues of the system; converting the solved dominant eigenvalues of the system into the eigenvalues of the continuous state matrix, judging the strength of the small-signal interference stability of the power system according to the converted eigenvalues, and comparing and verifying the converted eigenvalues with the distribution diagram of all the eigenvalues of the system. The present invention solves the problems of difficult solution of the eigenvalues of the discrete space state matrix and low calculation efficiency.

Description

Technical Field

[0001] The present invention relates to the technical field of power system stability analysis, and particularly to a small-signal stability analysis method and system for a large-scale new energy power system. Background Art

[0002] With the continuous improvement of the proportion of power electronic type power sources such as energy transformation and photovoltaic and wind power in the installed capacity, the stable characteristics of the power system have changed significantly. The electromagnetic transient small disturbance stability problem caused by the complex interaction between large-scale new energy multi-station groups and the power grid has become increasingly prominent, seriously threatening the safety of the power grid and equipment. In the traditional power system electromechanical transient model, the eigenvalue analysis method is widely used. However, for the system electromagnetic transient model, especially for a large-scale new energy power system, the system structure is complex, and there are problems such as high dimension, difficult calculation of the equilibrium point, and difficult selection of state variables. Therefore, the existing patent CN202210230373.2 proposes a small-signal stability analysis method for a medium-voltage DC system based on a discrete state space. The proposed discrete state space model has the characteristics of high accuracy and easy selection of state variables, and this method has begun to be gradually applied to solve practical problems. However, for the electromagnetic transient model, especially for a large-scale power system, the order of its state matrix is very high, and there are still problems such as difficult convergence and low calculation efficiency when calculating its eigenvalues.

[0003] In view of the problems such as difficult eigenvalue calculation for a large-scale new energy power system, the existing research has proposed a preprocessing technology for eigenvalue calculation of a large-scale power system based on a continuous state space model. This technology can judge the stable state of the system by solving some eigenvalues of the system. However, this method is only applicable to the continuous state space model and is not applicable to the discrete state space model. Therefore, for the small-signal stability analysis of a large-scale power system based on discrete state space modeling, there are still problems such as difficult eigenvalue calculation and low calculation efficiency. Summary of the Invention

[0004] To solve the deficiencies of the above-mentioned existing technologies, the present invention provides a small-signal stability analysis method and system for a large-scale new energy power system. For a large-scale new energy power system containing a high proportion of power electronic devices, a discrete state space modeling method is used for analysis, and preprocessing technologies such as displacement inverse transformation and rotation transformation are applied to the small disturbance stability analysis based on the discrete state space model. Combined with a sparse implementation method based on the discrete state space model, the system eigenvalues are efficiently solved to solve the problems of difficult eigenvalue solution and low calculation efficiency of the discrete space state matrix.

[0005] In the first aspect, the present invention provides a small-signal stability analysis method for a large-scale new energy power system.

[0006] A small-signal stability analysis method for a large-scale new energy power system, comprising:

[0007] For a large-scale new energy power system, discrete state space models of each component in the power system are respectively established, and based on this, a discrete state space model of the entire power system is constructed, and a discrete state matrix is determined;

[0008] Using a preprocessing technique, the eigenvalues of the system state matrix to be solved are converted into system dominant eigenvalues; the preprocessing technique is displacement inverse transformation or rotation transformation;

[0009] Based on the discrete state matrix, using an iterative algorithm combined with sparsity implementation, the system dominant eigenvalues are calculated and solved;

[0010] The solved system dominant eigenvalues are converted into the eigenvalues of the continuous state matrix, and the small-signal interference stability of the power system is judged according to the converted eigenvalues, and the converted eigenvalues are compared and verified with the distribution diagram of all the eigenvalues of the system.

[0011] In a second aspect, the present invention provides a small-signal stability analysis system for a large-scale new energy power system.

[0012] A small-signal stability analysis system for a large-scale new energy power system, comprising:

[0013] A discrete model construction module, configured to, for a large-scale new energy power system, respectively establish discrete state space models of each component in the power system, and based on this, construct a discrete state space model of the entire power system, and determine a discrete state matrix;

[0014] A conversion module, configured to use a preprocessing technique to convert the eigenvalues of the system state matrix to be solved into system dominant eigenvalues; the preprocessing technique is displacement inverse transformation or rotation transformation;

[0015] A dominant eigenvalue solving module, configured to, based on the discrete state matrix, use an iterative algorithm combined with sparsity implementation to calculate and solve the system dominant eigenvalues;

[0016] A stability analysis module, configured to convert the solved system dominant eigenvalues into the eigenvalues of the continuous state matrix, judge the strength of the small-signal interference stability of the power system according to the converted eigenvalues, and compare and verify the converted eigenvalues with the distribution diagram of all the eigenvalues of the system.

[0017] In a third aspect, the present invention further provides an electronic device, including a memory, a processor, and computer instructions stored on the memory and running on the processor. When the computer instructions are run by the processor, the steps of the method described in the first aspect are completed.

[0018] In a fourth aspect, the present invention also provides a computer-readable storage medium for storing computer instructions, which, when executed by a processor, complete the steps of the method described in the first aspect.

[0019] The above one or more technical solutions have the following beneficial effects:

[0020] The present invention provides a small-signal stability analysis method and system for a large-scale new energy power system. For a large-scale power system containing a high proportion of power electronic devices, a discrete state-space modeling method is used for small-signal stability analysis. This method has the characteristics of high accuracy and easy selection of state variables. On this basis, preprocessing techniques such as displacement inverse transformation and rotation transformation are applied to the small-signal stability analysis based on the discrete state-space model. Through this preprocessing technique, the system eigenvalues to be solved are converted into the eigenvalues with the largest modulus, and a sparse implementation method based on the discrete state-space model is combined to efficiently solve the system eigenvalues, so as to solve the problem of difficult solution of the eigenvalues of the discrete space state matrix. Finally, the accurate judgment of the system stable state is completed according to the solved system eigenvalues. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] The specification drawings forming a part of the present invention are used to provide a further understanding of the present invention. The schematic embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation to the present invention.

[0022] Figure 1 is a flowchart of the small-signal stability analysis method for the large-scale new energy power system according to the embodiment of the present invention;

[0023] Figure 2 is a schematic diagram of the large-scale new energy power system used as an example in the embodiment of the present invention;

[0024] Figure 3 is a discrete equivalent circuit diagram of the power system obtained by discretization in the embodiment of the present invention;

[0025] Figure 4 is a corresponding diagram of the eigenvalues of the continuous system and the discrete system in the embodiment of the present invention;

[0026] Figure 5 is a schematic diagram of the displacement inverse transformation in the embodiment of the present invention;

[0027] Figure 6 is a global distribution diagram of the eigenvalues calculated by the IRA algorithm after the displacement inverse transformation and all the eigenvalues of the system in the embodiment of the present invention;

[0028] Figure 7 is an enlarged distribution diagram of the eigenvalues calculated by the IRA algorithm after the displacement inverse transformation and all the eigenvalues of the system in the embodiment of the present invention;

[0029] Figure 8 This is the distribution diagram in the z-domain of the eigenvalues calculated by the IRA algorithm after rotation transformation and all the eigenvalues of the system in the embodiments of the present invention;

[0030] Figure 9 This is the distribution diagram in the s-domain of the eigenvalues calculated by the IRA algorithm after rotation transformation and all the eigenvalues of the system in the embodiments of the present invention. Specific Embodiments

[0031] It should be noted that the following detailed description is exemplary only for describing specific embodiments, aiming to provide further illustration of the present invention and is not intended to limit the exemplary embodiments of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present invention belongs. In addition, it should also 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.

[0032] Embodiment 1

[0033] This embodiment provides a method for analyzing the small-signal stability of a large-scale new energy power system, as Figure 1 shown, including the following steps:

[0034] Step S1: For a large-scale new energy power system, discrete state-space models of each component in the power system are established respectively to construct the discrete state-space model of the entire power system and determine the discrete state matrix;

[0035] Step S2: Using a preprocessing technique, the eigenvalues of the system state matrix to be solved are converted into the dominant eigenvalues of the system; the preprocessing technique is displacement inverse transformation or rotation transformation;

[0036] Step S3: Based on the discrete state matrix, the dominant eigenvalues of the system are calculated and solved by using an iterative algorithm in combination with sparsity implementation;

[0037] Step S4: The dominant eigenvalues of the system obtained by solving are converted into the eigenvalues of the continuous state matrix, and the small-signal disturbance stability of the power system is judged according to the converted eigenvalues, and the converted eigenvalues are compared and verified with the distribution diagram of all the eigenvalues of the system.

[0038] By the above method, a discrete state space model of each component and the entire system in a large-scale new energy power system is established, and preprocessing technologies such as rotation transformation and displacement inverse transformation are applied to the small-signal stability analysis of a large-scale new energy power system with a high proportion of power electronic devices, so as to accurately and quickly solve and obtain the eigenvalues of the discrete space state matrix, and realize accurate and effective small-signal interference stability analysis of the system.

[0039] In step S1, for a large-scale new energy power system, a discrete state space model of each component in the power system is established respectively, and based on this, the discrete state space model of the entire power system is constructed, and the discrete state matrix is determined. The construction of this discrete state space model specifically includes the following steps:

[0040] In step S1.1, for the large-scale power system as Figure 2 shown, a continuous state space model of each component in this power system is established respectively. Among them, the components include converters, RL series lines and loads, and shunt capacitor C; then, after discretizing the continuous state space model of each component, it is converted into a discrete state space model, as Figure 3 shown, and this discrete state space model includes a discrete equivalent circuit and an iterative expression of the historical current source vector.

[0041] Specifically, the continuous state space model of the converter in the x-y common rotating coordinate system is:

[0042]

[0043] In the formula, x inv is the state vector of the converter, i oxy is the port output current of the converter in the x-y common rotating coordinate system, and u bxy is the port voltage of the converter in the x-y common rotating coordinate system.

[0044] The discretized state space model of the converter is:

[0045]

[0046] In the formula, h represents the vector related to the state at the (t - Δt) moment in the discrete expression of the converter, or is called the RL line historical current source vector; the first formula represents the iterative expression of the historical current source vector, and the second formula represents the discrete equivalent circuit.

[0047] The continuous state space model of the RL series line and the load is:

[0048]

[0049] In the formula, u RLx and u RLyrepresent the x-axis and y-axis components of the voltages at both ends of the line in the x-y common rotating coordinate system, i RLx and i RLy represent the x-axis and y-axis components of the line current in the x-y rotating coordinate system; ω is the rotational speed of the x-y common rotating coordinate system.

[0050] The discretized state-space model of the RL series line and the load is:

[0051]

[0052] In the formula, h RL (t) represents the vector related to the state at the moment (t - Δt) in the current discrete expression, or is called the historical current source vector of the RL line. The first formula represents the iterative expression of the historical current source vector, and the second formula represents the discrete equivalent circuit.

[0053] The continuous state-space model of the shunt capacitor C is:

[0054]

[0055] In the formula, u pcx and u pcy represent the x-y axis components of the shunt capacitor branch voltage in the x-y rotating coordinate system, i pcx and i pcy represent the x-y axis components of the shunt capacitor branch current in the x-y rotating coordinate system.

[0056] The discretized state-space model of the shunt capacitor C is:

[0057]

[0058] In the formula, h pc (t) represents the vector related to the state at the moment (t - Δt) in the current discrete expression, or is called the historical current source vector of the shunt capacitor C. The first formula represents the iterative expression of the historical current source vector, and the second formula represents the discrete equivalent circuit.

[0059] Step S1.2: Based on the topological structure and connection mode of the discrete equivalent circuit of the discrete state-space model of each component, establish the node conductance matrix and branch-node incidence matrix of the system.

[0060] Specifically, based on the topological structure of the equivalent circuit of the discrete state-space model as Figure 3 shown, establish the node conductance matrix of the system, which is:

[0061]

[0062] In the formula, g inv1 、g inv2 and ginv3 is the equivalent conductance matrix of three converters, g line1 and g line2 is the equivalent conductance matrix of two lines, g load1 and g load2 is the equivalent conductance matrix of two loads, g pc1 , g pc2 and g pc3 are the equivalent conductance matrices of three shunt capacitors C.

[0063] Based on the topology and connection mode of the discrete equivalent circuit as Figure 3 shown, establish the branch-node incidence matrix L of the system, where L T can be expressed as:

[0064]

[0065] In the formula, I represents the identity matrix, and the subscript 2 represents two dimensions.

[0066] Step S1.3, based on the iterative expression of the historical current source vector of the discrete state space model of each component, form the state vector.

[0067] Specifically, form a new state vector from the iterative expressions of the historical current source vectors of each component, which is:

[0068] h(t) = kh(t - Δt) + gu xy (t - Δt) (9)

[0069] In the formula, h = [(h inv ) T , (h RL ) T , (h pc ) T T , u xy = [(u invxy ) T , (u RLxy ) T , (u pcxy ) T T is the vector composed of the branch voltage vectors of all the branches where the components in the system are located, and k and g are the block diagonal matrices composed of the coefficient matrices of the iterative expressions of the historical current source vectors of the discrete models of each component respectively.

[0070] Step S1.4, based on the node conductance matrix, branch-node incidence matrix and state vector of the system, construct the discrete state space model of the entire power system and determine the discrete system state matrix (abbreviation: discrete state matrix).

[0071] ​​Specifically, based on the relationship between the node voltage and the branch voltage, and the relationship between the node injection current and the historical current source, the discrete state space model of the system and the state matrix A are obtained. d , which is:

[0072] h(t) = (k - gLG -1 L T B)h(t - Δt) (10)

[0073] A d = k - gLG -1 L T B (11)

[0074] Based on the above method, the discrete state space model of the entire system is established. On this basis, the discrete state matrix A is analyzed by calculation. d The eigenvalues of are calculated to judge the small-signal stability of the system.

[0075] In step S2, using the preprocessing technology, the eigenvalues of the system state matrix to be solved are converted into the dominant eigenvalues of the system. Among them, the preprocessing technology is the displacement inverse transformation or the rotation transformation, that is, the displacement inverse transformation is used to transform the system state matrix and eigenvalues, or the rotation transformation is used to transform the system state matrix and eigenvalues.

[0076] (1) Using the displacement inverse transformation to transform the system state matrix and eigenvalues

[0077] First, according to the discretization process of the continuous system, the conversion relationship between the continuous state matrix and the discrete state matrix is determined, and the conversion relationship between the eigenvalues of the continuous state matrix and the eigenvalues of the discrete state matrix is determined.

[0078] Specifically, from the discretization process of the continuous system, it is determined that there is a conversion relationship between the continuous state matrix A c and the discrete state matrix A d , including:

[0079] Suppose the continuous state space equation of the system is:

[0080]

[0081] Applying the implicit trapezoidal integration formula to Equation (12) gives:

[0082]

[0083] where Δt is the discrete time step, usually taken as 50 μs, and let Ω be 2 / Δt;

[0084] Further arranging Equation (13) gives:

[0085] x(t + Δt) = (ΩI - Ac ) -1 (ΩI + A c )x(t) (14)

[0086] Comparing Equation (14) with the discrete state - space equation gives:

[0087] A d =(ΩI - A c ) -1 (ΩI + A c ) (15)

[0088] Therefore, the eigenvalues of the continuous system and the discrete system can be converted into each other and satisfy:

[0089]

[0090] As shown in Figure 4 the (a) eigenvalues of the continuous system, (b) eigenvalues of the discrete system, and the corresponding relationship between the eigenvalues of the continuous system and the discrete system, it can be seen that the eigenvalues of the continuous system located on the left side of the imaginary axis will be mapped inside the unit circle in the discrete system; the eigenvalues of the continuous system located on the right side of the imaginary axis will be mapped outside the unit circle in the discrete system; the eigenvalues of the continuous system located on the imaginary axis will be mapped on the unit circle in the discrete system. Further, when judging the small - signal disturbance stability of the power system, for the continuous system, the stable state is that all eigenvalues are located on the left side of the imaginary axis; for the discrete system, the stable state is that all eigenvalues are located inside the unit circle; and the stable states of the continuous system and the discrete system correspond to each other. For a stable system, it can also be divided into a system with strong stability and a system with weak stability. Therefore, in this embodiment, the pre - processing technology based on the inverse displacement transformation or rotation transformation is used to realize the judgment of the strength of the power system stability.

[0091] On the above basis, the inverse displacement transformation is used to perform the conversion of the system state matrix and eigenvalues, that is: convert the discrete state matrix into a continuous state matrix, select a displacement point, perform the inverse displacement transformation on the converted continuous state matrix, and map the eigenvalue closest to the displacement point in the converted continuous state matrix to the eigenvalue with the largest modulus of the system. Among them, the eigenvalue closest to the displacement point in the continuous state matrix is the eigenvalue of the system state matrix to be solved (abbreviated as the system eigenvalue), and the eigenvalue with the largest modulus of the continuous system after the inverse displacement transformation is the dominant eigenvalue of the system. Then, through the solution process of step S3, the dominant eigenvalue of the system is calculated. Preferably, the eigenvalue with the largest modulus can be multiple maximum values arranged in sequence.

[0092] Specifically, as shown in Figure 5 the inverse displacement transformation is to transform the continuous - system state matrix A d converted from the discrete - system state matrix A cThe eigenvalue closest to the displacement point is mapped to the dominant eigenvalue. Based on this, an iterative algorithm can be used to calculate the first r eigenvalues with the largest modulus of the continuous system state matrix after the displacement inverse transformation. These eigenvalues are approximate values of the r eigenvalues in the system from the displacement point in order of proximity. The specific steps are as follows;

[0093] First, transform the discrete state matrix A by equation (15) d into the continuous state matrix A c , which is:

[0094] A c = Ω(A d - I)(A d + I) -1 (17)

[0095] Select the complex constant as the displacement point λ s , and apply the displacement - inverse transformation to A c , obtaining:

[0096] A c ′ = (A c - λ S I) -1 (18)

[0097] From equation (18), the relationship between the eigenvalue λ of the continuous state matrix A c and the eigenvalue λ′ of the system after the displacement inverse transformation is:

[0098]

[0099] Substitute equation (17) into equation (18), obtaining:

[0100] A c ′ = [Ω(A d - I)(A d + I) -1 - λ S I] -1 (20)

[0101] Equation (20) can be further arranged as:

[0102]

[0103] For the matrix where M and N are n×m - order matrices, a is an m×m - order non - singular matrix, m ≤ n, when a -1 + N T A -1 M is invertible, there is the following matrix inversion auxiliary theorem:

[0104]

[0105] Applying the above theorem to Equation (21), we get:

[0106]

[0107] Furthermore, by rearranging Equation (23), we get:

[0108]

[0109] It can be seen from the above equation that when using the iterative method to obtain the eigenvalues of A c ′, in the process of calculating A c ′v, there are multiple matrix-vector products (MVPs) involved:

[0110] z = (αA d ±βI)v (25)

[0111] and matrix inverse-vector products (MIVPs):

[0112] z = (αA d ±βI) -1 v (26)

[0113] where α and β are complex constants.

[0114] (2) Using rotation transformation for system state matrix and eigenvalue conversion

[0115] First, rotate and modify the discrete state space model of the entire system to obtain the rotated discrete state space model of the entire system, and then the rotated discrete state matrix can be directly obtained.

[0116] Specifically, considering that the continuous state space equation is obtained by linearizing the differential equations of the inverter and the network, and the discrete state space equation is obtained by discretizing the differential equations of the inverter and the network using the implicit trapezoidal method. In order to directly obtain the discretized state matrix and make the discrete state matrix already rotated, we can start from the continuous state space model / equation. Multiply the state matrix A c of the continuous state space model by e -jθ , reverse-deduce the transformation method of the linearized differential equations of the inverter and the network, then obtain the change method of the differential equations of the inverter and the network before linearization. Finally, discretize the transformed new differential equations of the inverter and the network using the implicit trapezoidal method to obtain the rotated discrete state space model of the entire system.

[0117] In fact, according to the continuous system discretization process, the state matrix A d of the discrete state space equation and the state matrix A c of the continuous state space equation can be determined.There is a conversion relationship shown in formula (15). Therefore, the rotated discrete state matrix A directly obtained by the above method d ′, is the same as the A d ′ obtained from the following formula (27), which is:

[0118] A d ′ = (ΩI - A c e -jθ ) -1 (ΩI + A c e -jθ ) (27)

[0119] Based on the above-obtained rotated discrete state matrix, according to the conversion relationship between the continuous state matrix and the rotated discrete state matrix, the discrete state matrix A d ′ can be calculated. The eigenvalue μ′ of the discrete state matrix A c is equivalent to rotating the eigenvalue λ of the continuous state matrix A d ′ by an angle θ clockwise to λ′, and then mapping it to the z-domain. That is, the conversion relationship shown in formula (28) between the eigenvalue μ′ of the discrete state matrix A c and the eigenvalue λ of the continuous state matrix A

[0120]

[0121] Furthermore, the steps to directly obtain the rotated discrete state matrix are specifically as follows:

[0122] From the algebraic equations shown in formula (1), formula (3), formula (5), formula (29), and formula (30):

[0123] Δi pcDQ = M′ inv Δi oDQ + M′ line Δi lineDQ + M′ load Δi loadDQ (29)

[0124] Δv interDQ = R N (M″ inv Δi oDQ + M″ line Δi lineDQ + M″ load Δi loadDQ ) (30)

[0125] Wherein, the matrices M inv 、M load and M lineThe branch-node incidence matrix of the branch where the inverter, RL load, and RL line are located, R N The grounding virtual resistance set to ensure well-defined voltages at the connection nodes or load nodes.

[0126] Denote Δy = [(Δi pcDQ ) T ,(Δv interDQ ) T T , and the continuous state space model of the entire system is composed of the above formula:

[0127]

[0128] In the formula, the expressions of each coefficient matrix are:

[0129]

[0130] In the formula, matrix B1 and matrix B1″ together form coefficient matrix B.

[0131] Eliminating the algebraic variable Δy from the continuous state space equation of the entire system shown in Equation (31) gives:

[0132]

[0133] Rotating the continuous state space equation A c to A c e -jθ , which can also be obtained by multiplying matrices A and B in Equation (31) by e -jθ :

[0134]

[0135] Therefore, rotating A c is equivalent to multiplying the coefficient matrices A inv , A line , A load , A pc and B inv , B line , B load , B pc in Equations (1), (3), and (5) by e -jθ .

[0136] Therefore, after the rotation preprocessing, localize the changes in the coefficient matrices to each component, and inversely deduce the changes in the original differential equation, including:

[0137] For the inverter, directly multiply the A inv and B inv matrices of the continuous state space equation coefficient matrix of the inverter shown in Equation (1) by e​-jθ After that, the implicit trapezoidal method integration is applied for discretization, and then the discrete state - space model after rotational pre - processing can be obtained;

[0138] For the network part (i.e., RL branch, RL load, and shunt capacitor branch), multiply the line parameter L or C by e jθ , and multiply the frequency ω by e -jθ , such as L / e in Equation (3) -jθ , and multiply the frequency ω by e -jθ , then apply the implicit trapezoidal method integration for discretization to obtain the discrete state - space model of each part of the network after rotational pre - processing;

[0139] After obtaining the discrete state - space models of each part of the system after rotational pre - processing, according to the generation method of the discrete state - space model of the whole system, the new discrete state - space model of the rotated whole system is obtained after eliminating the algebraic variables.

[0140] Secondly, after obtaining the rotated discrete state matrix, set the damping ratio. The damping ratio is the ratio of the opposite of the real part of the eigenvalue to the modulus of the eigenvalue. The smaller the damping ratio, the weaker the system stability; through the above - mentioned rotation operation on the discrete state matrix, the eigenvalues of the continuous state matrix with a damping ratio less than the set damping ratio are converted into the dominant eigenvalues of the system. Among them, the eigenvalues of the continuous system with a damping ratio less than the set damping ratio are the eigenvalues of the system state matrix to be solved. The eigenvalue with the largest modulus of the rotated discrete state matrix is the dominant eigenvalue of the system. Then, through the solution process of step S3, the dominant eigenvalue of the system is calculated. Preferably, the eigenvalue with the largest modulus can be multiple maximum values in sequence.

[0141] In step S3, based on the discrete state matrix, use the iterative algorithm combined with sparsity implementation to calculate and solve the dominant eigenvalue of the system. That is, first perform sparsity implementation on the discrete state matrix, and then use the iterative algorithm for iterative solution to obtain the dominant eigenvalue of the system in the order of decreasing modulus. In this embodiment, the iterative algorithm uses the implicit restarted Arnoldi algorithm (i.e., IRA algorithm).

[0142] The above - mentioned step S3 is an efficient implementation of Equations (25) and (26) based on step S2, and specifically includes the following steps:

[0143] First, rewrite the discretized state matrix A of the system d as Equation (11), and substituting Equation (11) into Equations (25) and (26) gives:

[0144] z = [(αk ± βI)-αgLG -1 L T B]v (35)

[0145] z = [(αk ± βI) - αgLG -1 L T B] -1 v (36)

[0146] Equation (35) can be decomposed into the following two steps:

[0147]

[0148] The above equation can be equivalently transformed into:

[0149]

[0150] where w is an intermediate vector.

[0151] Secondly, perform sparse implementation on the above transformed discrete state matrix, i.e., Equation (37), and then use the iterative algorithm for iterative solution. Among them, before the iterative calculation of Equation (37), only perform a sparse triangular decomposition on G once, i.e., G = LU; furthermore, in each iteration, only need to first calculate the intermediate vector w through forward substitution - back substitution, and then obtain z through the product of the sparse matrix and the vector v.

[0152] Similarly, Equation (36) can be equivalently transformed into:

[0153]

[0154] Equation (39) has the same form as Equation (38), so its iterative calculation process is also similar, which is: First, calculate (αk ± βI) -1 , since αk ± βI is a block diagonal matrix, so (αk ± βI) -1 can be obtained by taking the inverse of each diagonal sub - block respectively; Secondly, calculate the block sparse matrix G′ = G - L T B(αk ± βI) -1 αgL, which has the same sparsity as G; Then, perform sparse triangular decomposition on G′, calculate w, and finally obtain z.

[0155] After the system state matrix undergoes the preprocessing technique proposed in the above step S2, the system eigenvalues to be solved are converted into the dominant eigenvalues of the system, and the IRA algorithm based on the sparse implementation method proposed in S3 is used to efficiently solve the eigenvalues of the system. Then, through step S5, the solved eigenvalues are converted into the eigenvalues of the original continuous system (i.e., the original continuous state matrix) using Equation (19) or Equation (28), and the small-signal disturbance stability and its strength of the system are judged based on the converted eigenvalues. In this way, in this embodiment, some eigenvalues of the system are solved to judge the stable state of the system, solving the problem that it is difficult to solve the eigenvalues due to the high order of the state matrix in the existing small-signal stability analysis method based on the discrete state space.

[0156] Furthermore, in this embodiment, the preprocessing technique is to convert the eigenvalues to be solved into the eigenvalues with the largest modulus, and the IRA iterative algorithm solves the eigenvalues one by one in decreasing order of the eigenvalue modulus. Therefore, to verify whether the eigenvalues solved by the IRA algorithm are the eigenvalues to be solved, in this embodiment, the eigenvalues solved by the IRA iterative algorithm are compared with the eigenvalue distribution diagram of the entire system to verify the correctness of this method.

[0157] Specifically, after iteratively calculating the eigenvalues of the preprocessed system using the IRA algorithm, the eigenvalues and their converted values are compared and verified with the eigenvalue distribution diagram of the entire system:

[0158] (1) As Figure 6 shown, first, all the eigenvalues of the system are represented on the complex plane. The displacement point is selected as j314. After the inverse displacement transformation, the IRA algorithm is used to obtain the first r = 10 eigenvalues with the largest modulus, that is, the r eigenvalues closest to the displacement point. Figure 7 is a local enlarged view. After being converted into the eigenvalues of the original system, a circle is drawn with the displacement point as the center and the distance between the rth eigenvalue calculated by the IRA iteration and the displacement point as the radius. Among them, the r eigenvalues with the largest modulus calculated by the IRA are all located inside the circle;

[0159] (2) As Figure 8 shown, the eigenvalues calculated by the IRA iteration and all the eigenvalues of the system are plotted on the z-domain. As Figure 9 shown, the eigenvalues calculated by the IRA iteration and all the eigenvalues of the system are plotted on the s-domain. Among them, the first r = 10 eigenvalues with the largest modulus of the rotated discrete state space system calculated by the IRA iteration are all located outside the circle with the origin as the center and the modulus of the rth eigenvalue |μ| = 1.0139 as the radius, that is, their moduli are greater than or equal to 1.0139; Figure 9It is the eigenvalue distribution diagram after converting the eigenvalues in the z domain to the s domain respectively, where r key eigenvalues calculated by IRA iteration are all located above the equal modulus line |μ| = 1.0139.

[0160] Embodiment 2

[0161] This embodiment provides a small-signal stability analysis system for a large-scale new energy power system, including:

[0162] A discrete model construction module, which is used to establish discrete state space models of each component in the power system for a large-scale power system respectively, thereby constructing the discrete state space model of the entire power system and determining the discrete state matrix;

[0163] A conversion module, which is used to convert the eigenvalues of the system state matrix to be solved into system dominant eigenvalues by using preprocessing technology; the preprocessing technology is displacement inverse transformation or rotation transformation;

[0164] A dominant eigenvalue solving module, which is used to calculate and solve the system dominant eigenvalues based on the discrete state matrix by using an iterative algorithm combined with sparsity implementation;

[0165] A stability analysis module, which is used to convert the solved system dominant eigenvalues into the eigenvalues of the continuous state matrix, judge the strength of the small-signal disturbance stability of the power system according to the converted eigenvalues, and compare and verify the converted eigenvalues with the eigenvalue distribution diagram of all system eigenvalues.

[0166] Embodiment 3

[0167] This embodiment provides an electronic device, including a memory, a processor, and computer instructions stored on the memory and running on the processor. When the computer instructions are run by the processor, the steps in a small-signal stability analysis method for a large-scale new energy power system as described above are completed.

[0168] Embodiment 4

[0169] This embodiment also provides a computer-readable storage medium for storing computer instructions. When the computer instructions are executed by the processor, the steps in a small-signal stability analysis method for a large-scale new energy power system as described above are completed.

[0170] The steps involved in Embodiments 2 to 4 above correspond to those in Method Embodiment 1. For specific implementation manners, reference may be made to the relevant description part of Embodiment 1. The term "computer-readable storage medium" should be understood to include a single medium or multiple media including one or more instruction sets; it should also be understood to include any medium that can store, encode, or carry an instruction set for execution by a processor and enable the processor to execute any method in the present invention.

[0171] Those skilled in the art should understand that the various modules or steps of the present invention described above can be implemented by a general-purpose computer device. Optionally, they can be implemented by program codes executable by a computing device, so that they can be stored in a storage device and executed by the computing device, or they can be separately fabricated into individual integrated circuit modules, or multiple modules or steps among them can be fabricated into a single integrated circuit module for implementation. The present invention is not limited to any specific combination of hardware and software.

[0172] The above are only the preferred embodiments of the present invention. Although the specific implementation manners of the present invention have been described in conjunction with the accompanying drawings, it is not a limitation to the protection scope of the present invention. Those skilled in the art should understand that various modifications or deformations that can be made without creative efforts on the basis of the technical solutions of the present invention are still within the protection scope of the present invention.

Claims

1. A small-signal stability analysis method for a large-scale new energy power system, characterized in that Including: For a large-scale new energy power system, discrete state space models of each component in the power system are established respectively, and based on this, the discrete state space model of the entire power system is constructed, and the discrete state matrix is determined, including: For a large-scale power system, continuous state space models of each component in the power system are established respectively; the components include converters, RL series lines and loads, and shunt capacitors C; After discretizing the continuous state space models of each component, they are converted into discrete state space models; the discrete state space models include discrete equivalent circuits and iterative expressions of historical current source vectors; Based on the topological structures and connection methods of the discrete equivalent circuits of the discrete state space models of each component, the nodal conductance matrix and branch-node incidence matrix of the system are established; Based on the iterative expressions of the historical current source vectors of the discrete state space models of each component, a state vector is formed; Based on the nodal conductance matrix, branch-node incidence matrix and state vector of the system, the discrete state space model of the entire power system is constructed, and the discrete state matrix is determined; Using a preprocessing technique, the eigenvalues of the system state matrix to be solved are converted into the dominant eigenvalues of the system; the preprocessing technique is displacement inverse transformation or rotation transformation; Based on the discrete state matrix, using an iterative algorithm combined with sparsity implementation, the dominant eigenvalues of the system are calculated and solved; The dominant eigenvalues of the system obtained by solving are converted into the eigenvalues of the continuous state matrix, and the small-signal disturbance stability of the power system is judged according to the converted eigenvalues, and the converted eigenvalues are compared and verified with the distribution map of all eigenvalues of the system.

2. The small-signal stability analysis method for a large-scale new energy power system according to claim 1, characterized in that Using a preprocessing technique, the eigenvalues of the system state matrix to be solved are converted into the dominant eigenvalues of the system, including: Performing system state matrix and eigenvalue conversion using displacement inverse transformation, which is: converting the discrete state matrix into a continuous state matrix, selecting a displacement point, performing displacement inverse transformation on the converted continuous state matrix, and mapping the eigenvalue closest to the displacement point of the converted continuous state matrix to the eigenvalue with the largest modulus of the system; among them, the eigenvalue closest to the displacement point of the continuous state matrix is the eigenvalue of the system state matrix to be solved, and the eigenvalue with the largest modulus of the continuous system after displacement inverse transformation is the dominant eigenvalue of the system.

3. A small-signal stability analysis method for a large-scale new energy power system according to claim 1, characterized in that Using a preprocessing technique, the eigenvalues of the system state matrix to be solved are converted into the dominant eigenvalues of the system, including: Performing system state matrix and eigenvalue conversion using rotation transformation, which is: setting a damping ratio, and performing rotational modification on the discrete state space model, and converting the eigenvalues of the continuous state matrix with a damping ratio less than the set damping ratio into the dominant eigenvalues of the system; among them, the eigenvalues of the continuous system with a damping ratio less than the set damping ratio are the eigenvalues of the system state matrix to be solved, and the eigenvalue with the largest modulus of the discrete state matrix after rotation is the dominant eigenvalue of the system.

4. A small-signal stability analysis method for a large-scale new energy power system according to claim 1, characterized in that, Using an iterative algorithm combined with sparsity implementation, the dominant eigenvalues of the system are calculated and solved, including: Perform sparse implementation on the discrete state matrix, and then use an iterative algorithm for iterative solution to obtain the dominant eigenvalues of the system in the order of decreasing modulus values; the iterative algorithm uses the implicit restart Arnoldi algorithm.

5. A small-signal stability analysis method for a large-scale new energy power system according to claim 1, characterized in that, The conversion relationship between the eigenvalue λ of the continuous state matrix and the eigenvalue μ of the discrete state matrix is as follows: After performing eigenvalue conversion using displacement inverse transformation, the relationship between the eigenvalues λ of the continuous state matrix and the eigenvalues λ′ of the transformed system is as follows: where λ s represents the displacement point.

6. The small-signal stability analysis method for a large-scale new energy power system according to claim 1, characterized in that After performing eigenvalue transformation using rotation transformation, the relationship between the eigenvalue λ of the continuous state matrix and the eigenvalue μ' of the discrete state matrix after rotation transformation is as follows:

7. A small-signal stability analysis system for a large-scale new energy power system, characterized in that, Execute the steps of a small-signal stability analysis method for a large-scale new energy power system according to any one of claims 1-6, including: A discrete model construction module, which is used to establish discrete state space models for each component in the power system for a large-scale new energy power system, thereby constructing the discrete state space model of the entire power system and determining the discrete state matrix; A conversion module, which is used to convert the eigenvalues of the system state matrix to be solved into the dominant eigenvalues of the system by using preprocessing techniques; the preprocessing techniques are displacement inverse transformation or rotation transformation; A dominant eigenvalue solving module, which is used to calculate and solve the dominant eigenvalues of the system based on the discrete state matrix by using an iterative algorithm in combination with sparse implementation; A stability analysis module, which is used to convert the solved dominant eigenvalues of the system into the eigenvalues of the continuous state matrix, judge the strength of the small-signal interference stability of the power system according to the converted eigenvalues, and compare and verify the converted eigenvalues with the distribution diagram of all eigenvalues of the system.

8. An electronic device, characterized in that, It includes a memory, a processor, and computer instructions stored on the memory and running on the processor. When the computer instructions are run by the processor, the steps of a small-signal stability analysis method for a large-scale new energy power system according to any one of claims 1-6 are completed.

9. A computer-readable storage medium, characterized in that, Used to store computer instructions, and when the computer instructions are executed by the processor, the steps of a small-signal stability analysis method for a large-scale new energy power system according to any one of claims 1-6 are completed.

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