Small signal stability analysis method and system for large-scale new energy power system

Abstract

The invention discloses a small signal stability analysis method and system for a large-scale new energy power system, and relates to the technical field of power system stability analysis, and the method comprises the steps: constructing a discrete state space model of the whole power system for the large-scale new energy power system, and determining a discrete state matrix; converting a characteristic value of a system state matrix expected to be solved into a system dominant characteristic value by utilizing a preprocessing technology; the preprocessing technology is displacement inverse transformation or rotation transformation; based on the discrete state matrix, calculating and solving a system dominant characteristic value by using an iterative algorithm in combination with sparse implementation; converting the solved dominant characteristic value of the system into a characteristic value of a continuous state matrix, judging the small signal interference stability of the power system according to the converted characteristic value, and comparing the converted characteristic value with a distribution diagram of all the characteristic values of the system for verification. According to the method, the problems of difficulty in solving discrete space state matrix eigenvalues and low calculation efficiency are solved.

Description

Technical Field

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

[0002] With the energy transformation and the increasing proportion of installed capacity of power electronic power sources such as photovoltaic and wind power, the stability 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-site groups and the power grid has become increasingly prominent, seriously threatening the safety of the power grid and equipment. In the electromechanical transient model of the traditional power system, the eigenvalue analysis method is widely used. However, for the electromagnetic transient model of the system, especially the large-scale new energy power system, the system structure is complex, and there are problems such as high dimension, difficulty in calculating the equilibrium point and difficulty in selecting state variables. To this end, the existing patent CN202210230373.2 proposes a small signal stability analysis method for medium-voltage DC system based on 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 electromagnetic transient models, especially large-scale power systems, the order of their state matrices is very high, and there are still problems such as convergence difficulties and low computational efficiency when calculating and solving their eigenvalues.

[0003] In response to the difficulty in calculating the eigenvalues ​​of large-scale renewable energy power systems, existing research has proposed a preprocessing technology for calculating the eigenvalues ​​of large-scale power systems based on continuous state space models. This technology can determine the stability of the system by solving some eigenvalues ​​of the system. However, this method is only applicable to continuous state space models, but not to discrete state space models. Therefore, the small signal stability analysis of large-scale power systems based on discrete state space modeling still has the above-mentioned problems of difficulty in calculating eigenvalues ​​and low calculation efficiency. Summary of the invention

[0004] In order to address the deficiencies of the above-mentioned prior art, the present invention provides a method and system for small-signal stability analysis of a large-scale renewable energy power system. For a large-scale renewable energy power system containing a high proportion of power electronic devices, a discrete state space modeling method is adopted for analysis, and preprocessing techniques such as inverse displacement transform and rotation transform are applied to the small disturbance stability analysis based on the discrete state space model. The sparse implementation method based on the discrete state space model is combined to efficiently solve the system eigenvalues, thereby solving the problems of difficulty in solving the eigenvalues ​​of the discrete space state matrix and low computational efficiency.

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

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

[0007] For large-scale renewable energy power systems, discrete state space models of each component in the power system are established to construct a discrete state space model of the entire power system and determine the discrete state matrix;

[0008] 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 an inverse shift transformation or a rotation transformation;

[0009] Based on the discrete state matrix, the dominant eigenvalue of the system is calculated and solved by using an iterative algorithm combined with sparse implementation;

[0010] The solved dominant eigenvalue of the system is converted into the eigenvalue of the continuous state matrix. The strength of the small signal interference stability of the power system is judged according to the converted eigenvalue, and the converted eigenvalue is compared and verified with the distribution diagram of all 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 large-scale new energy power system small signal stability analysis system, comprising:

[0013] The discrete model building module is used to establish the discrete state space model of each component in the power system for large-scale renewable energy power systems, so as to construct the discrete state space model of the entire power system and determine the discrete state matrix;

[0014] A conversion module, used for converting the eigenvalues ​​of the system state matrix to be solved into the dominant eigenvalues ​​of the system by using a preprocessing technique; the preprocessing technique is an inverse shift transformation or a rotation transformation;

[0015] The dominant eigenvalue solving module is used to calculate and solve the dominant eigenvalue of the system based on the discrete state matrix using an iterative algorithm combined with sparse implementation;

[0016] The stability analysis module is used to convert the solved dominant eigenvalues ​​of the system into 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.

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

[0018] In a fourth aspect, the present invention further 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] One or more of the above technical solutions have the following beneficial effects:

[0020] The present invention provides a method and system for analyzing small-signal stability of 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 to perform small-signal stability analysis. This method has the characteristics of high accuracy and easy selection of state variables. On this basis, preprocessing technologies such as inverse displacement transform and rotation transform are applied to small-disturbance stability analysis based on a discrete state space model. The system eigenvalues ​​to be solved are converted into eigenvalues ​​with the largest modulus through the preprocessing technology, and the system eigenvalues ​​are efficiently solved in combination with a sparse implementation method based on a discrete state space model, thereby solving the problem of difficulty in solving the eigenvalues ​​of a 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 accompanying drawings in the specification, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0022] Figure 1 This is a flow chart of a method for analyzing small signal stability of a large-scale new energy power system according to an embodiment of the present invention;

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

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

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

[0026] Figure 5 Schematic diagram of inverse shift transformation in an embodiment of the present invention;

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

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

[0029] Figure 8 It is a distribution diagram of the eigenvalues ​​calculated by the IRA algorithm after the rotation transformation in the embodiment of the present invention and all the eigenvalues ​​of the system in the z domain;

[0030] Fig. 9 It is a distribution diagram of the eigenvalues ​​calculated by the IRA algorithm after the rotation transformation in the embodiment of the present invention and all the eigenvalues ​​of the system in the s domain. DETAILED DESCRIPTION

[0031] It should be noted that the following detailed descriptions are exemplary only, are intended to describe specific embodiments, are intended to provide further explanation of the present invention, and are not intended to limit exemplary embodiments according to the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those of ordinary skill in the art 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, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0032] Embodiment 1

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

[0034] 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, so as to construct a discrete state space model of the entire power system and determine a discrete state matrix;

[0035] Step S2, using a preprocessing technique to convert the eigenvalues ​​of the system state matrix to be solved into the system dominant eigenvalues; the preprocessing technique is an inverse shift transform or a rotation transform;

[0036] Step S3, based on the discrete state matrix, using an iterative algorithm combined with sparse implementation, calculate and solve the dominant eigenvalue of the system;

[0037] Step S4, convert the solved dominant eigenvalue of the system into the eigenvalue of the continuous state matrix, judge the strength of the small signal interference stability of the power system according to the converted eigenvalue, and compare and verify the converted eigenvalue with the distribution diagram of all eigenvalues ​​of the system.

[0038] Through the above method, a discrete state space model of each component and the entire system in a large-scale renewable energy power system is established, and preprocessing techniques such as rotation transformation and inverse displacement transformation are applied to the small signal stability analysis of a large-scale renewable energy power system containing a high proportion of power electronic devices, so as to achieve accurate and fast solution and acquisition of the eigenvalues ​​of the discrete space state matrix, and realize accurate and effective system small signal interference stability analysis.

[0039] In step S1, for a large-scale new energy power system, discrete state space models of each component in the power system are established respectively, so as to construct a discrete state space model of the entire power system and determine a discrete state matrix. The construction of the discrete state space model specifically includes the following steps:

[0040] Step S1.1: Figure 2 For the large-scale power system shown in FIG, a continuous state space model of each component in the power system is established, wherein the components include the converter, the RL series line and the load, and the parallel capacitor C; and then the continuous state space model of each component is discretized and converted into a discrete state space model, such as Figure 3 As shown, the discrete state space model includes a discrete equivalent circuit and an iterative expression of a historical current source vector.

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

[0042]

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

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

[0045]

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

[0047] The continuous state space model of RL series lines and loads is:

[0048]

[0049] In the formula, u RLx and u RLyIt represents the x-axis and y-axis components of the voltage at both ends of the line in the xy common rotating coordinate system, i RLx and i RLy It represents the x-axis and y-axis components of the line current in the xy rotating coordinate system; ω is the rotation speed of the xy common rotating coordinate system.

[0050] The discretized state space model of RL series lines and loads is:

[0051]

[0052] In the formula, h RL (t) represents the vector related to the state at time (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 parallel capacitor C is:

[0054]

[0055] In the formula, u pcx and u pcy represents the xy-axis component of the voltage of the parallel capacitor branch in the xy rotating coordinate system, i pcx and i pcy It represents the xy-axis component of the parallel capacitor branch current in the xy rotating coordinate system.

[0056] The discrete 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 time (t-Δt) in the current discrete expression, or is called the historical current source vector of the parallel 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 of the discrete equivalent circuit of the discrete state space model of each component and its connection mode, a node conductance matrix and a branch-node association matrix of the system are established.

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

[0061]

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

[0063] Based on Figure 3 The topological structure and connection mode of the discrete equivalent circuit shown in the figure are used to establish the branch-node association matrix L of the system, where L T It can be expressed as:

[0064]

[0065] Where I represents the identity matrix and the subscript 2 represents 2-dimension.

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

[0067] Specifically, the historical current source vector iterative expressions of each component are combined into a new state vector, 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 a vector composed of the branch voltage vectors of all the branches where the components are located in the system, and k and g are 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.

[0070] Step S1.4: Based on the system's node conductance matrix, branch-node association matrix and state vector, a discrete state space model of the entire power system is constructed to determine the discrete system state matrix (referred to as discrete state matrix).

[0071] Specifically, according to 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 and state matrix A of the system are obtained: d ,for:

[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, a discrete state space model of the entire system is established. On this basis, the discrete state matrix A is calculated and analyzed. d The eigenvalue of is used to judge the small disturbance stability of the system.

[0075] In step S2, the eigenvalues ​​of the system state matrix to be solved are converted into the dominant eigenvalues ​​of the system by using a preprocessing technique, wherein the preprocessing technique is an inverse shift transformation or a rotation transformation, that is, the system state matrix and the eigenvalues ​​are converted by using an inverse shift transformation, or the system state matrix and the eigenvalues ​​are converted by using a rotation transformation.

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

[0077] Firstly, 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, the continuous state matrix A is determined by the discretization process of the continuous system c and the discrete state matrix A d There are conversion relationships, including:

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

[0080]

[0081] Applying the implicit trapezoidal integral formula to equation (12) yields:

[0082]

[0083] Where Δt is the discrete time step, usually 50 μs, and Ω is 2 / Δt;

[0084] Further rearranging formula (13) yields:

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

[0086] Comparing equation (14) with the discrete state space equation, we can obtain:

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

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

[0089]

[0090] like Figure 4 It can be seen from the (a) continuous system eigenvalues ​​and (b) discrete system eigenvalues ​​and the corresponding relationship between the eigenvalues ​​of the continuous system and the discrete system that the eigenvalues ​​of the continuous system located on the left side of the imaginary axis will be mapped to 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 to the outside of the unit circle in the discrete system; the eigenvalues ​​of the continuous system located on the imaginary axis will be mapped to the unit circle in the discrete system. Furthermore, when judging the stability of the power system under small signal interference, for the continuous system, the stable state is that the eigenvalues ​​are all located on the left side of the imaginary axis; for the discrete system, the stable state is that the eigenvalues ​​are all located within the unit circle; and the stable states of the continuous system and the discrete system are corresponding. For stable systems, they can also be divided into systems with strong stability and systems with weak stability. Therefore, this embodiment uses a preprocessing technology based on inverse shift transformation or rotation transformation to achieve the judgment of the stability of the power system.

[0091] On the basis of the above, the inverse shift transform is used to transform the system state matrix and eigenvalues, that is, the discrete state matrix is ​​transformed into a continuous state matrix, and the displacement point is selected, and the inverse shift transform is performed on the transformed continuous state matrix, and the eigenvalue of the transformed continuous state matrix closest to the displacement point is mapped to the eigenvalue with the largest system modulus, wherein the eigenvalue of the continuous state matrix closest to the displacement point is the eigenvalue of the system state matrix desired to be solved (referred to as the system eigenvalue), and the eigenvalue with the largest modulus of the continuous system after the inverse shift transform is the dominant eigenvalue of the system. Afterwards, the dominant eigenvalue of the system is calculated through the solution process of step S3. Preferably, the eigenvalue with the largest modulus can be a plurality of maximum values ​​arranged in sequence.

[0092] Specifically, Figure 5 As shown, the inverse shift transform is to transform the discrete system state matrix A d The continuous system state matrix A obtained by conversion cThe eigenvalue closest to the displacement point is mapped as the dominant eigenvalue. On this basis, an iterative algorithm can be used to calculate the eigenvalue with the largest modulus of the first r eigenvalues ​​of the continuous system state matrix after the inverse displacement transformation. This eigenvalue is the approximate value of the r eigenvalues ​​in the system from near to far from the displacement point. The specific steps are as follows;

[0093] First, the discrete state matrix A is converted into d Transformed into a continuous state matrix A c ,for:

[0094] A c =Ω(A d -I)(A d +I) -1 (17)

[0095] Choose the complex constant as the displacement point λ s , for A c Applying the shift-inverse transform, we get:

[0096] A c ′=(A c -λ S I) -1 (18)

[0097] From formula (18), we can get the continuous state matrix A c The relationship between the eigenvalue λ and the eigenvalue λ′ of the system after the inverse shift transformation is:

[0098]

[0099] Substituting formula (17) into formula (18), we get:

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

[0101] Formula (20) can be further organized as:

[0102]

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

[0104]

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

[0106]

[0107] Furthermore, by rearranging formula (23), we can obtain:

[0108]

[0109] From the above formula, we can see that when the iteration method is used to obtain A c When calculating the eigenvalue of A c The process of ′v involves multiple calculations of matrix-vector products (MVP):

[0110] z=(αA d ±βI)v (25)

[0111] And the matrix inverse-vector product (MIVP):

[0112] z=(αA d ±βI) -1 v (26)

[0113] Where α and β are complex constants.

[0114] (2) Using rotation transformation to transform the system state matrix and eigenvalue

[0115] Firstly, the discrete state space model of the whole system is rotated and modified to obtain the rotated discrete state space model of the whole system, and then the discrete state matrix after the rotation transformation 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 rotated, we can start with the continuous state space model / equation and transform the state matrix A of the continuous state space model. c Multiply by e -jθ , infer the transformation mode of the differential equations of the inverter and network after linearization, and then derive the change mode of the differential equations of the inverter and network before linearization. Finally, the transformed new differential equations of the inverter and network are discretized by implicit trapezoidal integration to obtain the discrete state space model of the whole system after rotation.

[0117] In fact, according to the discretization process of the continuous system, the state matrix A of the discrete state space equation can be determined d and the state matrix A of the continuous state space equation cThere is a conversion relationship shown in formula (15) between them, so the rotated discrete state matrix A directly obtained by the above method d ′, and A obtained by the following formula (27) d ' are the same, namely:

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

[0119] Based on the above-mentioned discrete state matrix after rotation, according to the conversion relationship between the continuous state matrix and the discrete state matrix after rotation, the discrete state matrix A can be calculated d The eigenvalue μ′ of ′ is equivalent to the continuous state matrix A c The eigenvalue λ of is rotated clockwise by an angle θ to λ′, and then mapped to the z domain, that is, the discrete state matrix A can be determined d ′ eigenvalue μ′ and continuous state matrix A c There is a conversion relationship between the eigenvalues ​​λ shown in formula (28), which is:

[0120]

[0121] Furthermore, the above step of directly obtaining the rotated discrete state matrix is ​​specifically as follows:

[0122] The algebraic equations shown in equations (1), (3), (5), (29) and (30) are:

[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] In the formula, the matrix M inv 、M load and M lineis the branch-node association matrix of the branch where the inverter, RL load and RL line are located, R N A virtual resistance to ground set to ensure that the voltage at the tie node or load node is well defined.

[0126] remember Δy=[(Δi pcDQ ) T ,(Δv interDQ ) T ] T , the above formula constitutes the continuous state space model of the whole system:

[0127]

[0128] In the formula, the expression of each coefficient matrix is:

[0129]

[0130] Wherein, matrix B1 and matrix B1″ together constitute the coefficient matrix B.

[0131] Eliminating the algebraic variable Δy from the continuous state space equation of the whole system shown in formula (31) yields:

[0132]

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

[0134]

[0135] Therefore, A c The rotation is equivalent to the coefficient matrix A in equations (1), (3) and (5) inv , A line , A load , A pc and B inv , B line , B load , B pc Multiply by e -jθ .

[0136] Therefore, after rotation preprocessing, the changes in the coefficient matrix are located in each element, and the changes in the original differential equation are inferred, including:

[0137] For the inverter, the continuous state space equation coefficient matrix A of the inverter shown in equation (1) is inv and B inv Matrix direct multiplication e-jθ Then, the implicit trapezoidal method is applied for discretization, and its discrete state space model after rotation preprocessing 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 , frequency ω multiplied by e -jθ , as in formula (3) L / e -jθ and frequency ω multiplied by e -jθ Then, the implicit trapezoidal method is applied for discretization to obtain the discrete state space model of each part of the network after rotation preprocessing;

[0139] After obtaining the discrete state space models of each part of the system after rotation preprocessing, according to the generation method of the discrete state space model of the whole system, the algebraic variables are eliminated to obtain the new discrete state space model of the whole system after rotation.

[0140] Secondly, after obtaining the rotated discrete state matrix, set the damping ratio, which refers to 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 eigenvalue of the continuous state matrix with a damping ratio less than the set damping ratio is converted into the dominant eigenvalue of the system, wherein the eigenvalue of the continuous system with a damping ratio less than the set damping ratio is the eigenvalue 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. Afterwards, the dominant eigenvalue of the system is calculated through the solution process of step S3. Preferably, the eigenvalue with the largest modulus can be a plurality of maximum values ​​arranged in sequence.

[0141] In step S3, based on the discrete state matrix, the dominant eigenvalue of the system is calculated and solved by using an iterative algorithm combined with sparse implementation. That is, the discrete state matrix is ​​first sparsely implemented, and then iteratively solved by using an iterative algorithm, and the dominant eigenvalue of the system is solved in the order of decreasing module value. In this embodiment, the iterative algorithm adopts an implicit restart Arnoldi algorithm (i.e., IRA algorithm).

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

[0143] First, the system's discretized state matrix A d Rewrite it as formula (11), substitute formula (11) into formula (25) and formula (26) to get:

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

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

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

[0147]

[0148] The above formula can be equivalently converted to:

[0149]

[0150] Where w is the middle vector.

[0151] Secondly, the discrete state matrix after the above transformation, that is, equation (37), is sparsely realized, and then iteratively solved using an iterative algorithm. Before iteratively calculating equation (37), only a sparse triangular decomposition is performed on G, that is, G = LU; then, in each iteration, it is only necessary to first obtain the intermediate vector w by forward-backward calculation, and then obtain z by multiplying the sparse matrix with the vector v.

[0152] Similarly, formula (36) can be equivalently converted to:

[0153]

[0154] Formula (39) has the same form as Formula (38), so the iterative calculation process is also similar: First, calculate (αk±βI) -1 , since αk±βI is a block diagonal matrix, (αk±βI) -1 It can be obtained by inverting each diagonal sub-block separately; secondly, calculate the block sparse matrix G′=GL T B(αk±βI) -1 αgL, which has the same sparsity as G; then, sparse triangular decomposition is performed on G′, w is calculated, and finally z is obtained.

[0155] After the system state matrix has been subjected to the preprocessing technology proposed in step S2, the desired system eigenvalue is converted into the dominant eigenvalue of the system, and the eigenvalue of the system is efficiently solved by the IRA algorithm based on the sparse implementation method proposed in step S3. Then, through step S5, the solved eigenvalue is converted into the eigenvalue of the original continuous system (i.e., the original continuous state matrix) using equation (19) or equation (28), and the stability of the small signal interference of the system and its strength are judged according to the converted eigenvalue. In the above manner, this embodiment solves part of the eigenvalue of the system to judge the stable state of the system, and solves the problem that the state matrix order is high and it is difficult to solve its eigenvalue in the existing system small signal stability analysis method based on discrete state space.

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

[0157] Specifically, after the preprocessed system eigenvalue is iteratively calculated using the IRA algorithm, the eigenvalue and its converted value are compared and verified with the distribution diagram of all eigenvalues ​​of the system:

[0158] (1) Figure 6 As shown, firstly, all the eigenvalues ​​of the system are expressed on the complex plane, and the displacement point is selected as j314. After the displacement inverse 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 This is a local enlarged diagram. After being converted into the original system eigenvalue, a circle is drawn with the displacement point as the center and the distance between the rth eigenvalue calculated by IRA iteration and the displacement point as the radius. The r eigenvalues ​​with the largest modulus values ​​calculated by IRA are all located within the circle.

[0159] (2) Figure 8 As shown, the eigenvalues ​​calculated by IRA iteration and all the eigenvalues ​​of the system are plotted in the z domain, as shown in Fig. 9 As shown, the eigenvalues ​​obtained by IRA iteration and all the eigenvalues ​​of the system are plotted on the s domain, where the first r = 10 eigenvalues ​​with the largest modulus values ​​of the rotated discrete state space system are obtained by IRA iteration. They are all outside the circle with the origin as the center and the modulus value of the rth eigenvalue |μ| = 1.0139 as the radius, that is, their moduli are greater than or equal to 1.0139; Fig. 9: The eigenvalue distribution diagram after converting the eigenvalues ​​in the z domain to the s domain, where the r key eigenvalues ​​calculated using IRA iteration are all located to the upper right of the isomolar value line |μ|=1.0139.

[0160] Embodiment 2

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

[0162] The discrete model building module is used to establish the discrete state space model of each component in the power system for large-scale power systems, so as to construct the discrete state space model of the entire power system and determine the discrete state matrix;

[0163] A conversion module, used for converting the eigenvalues ​​of the system state matrix to be solved into the dominant eigenvalues ​​of the system by using a preprocessing technique; the preprocessing technique is an inverse shift transformation or a rotation transformation;

[0164] The dominant eigenvalue solving module is used to calculate and solve the dominant eigenvalue of the system based on the discrete state matrix using an iterative algorithm combined with sparse implementation;

[0165] The stability analysis module is used to convert the solved dominant eigenvalues ​​of the system into 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.

[0166] Embodiment 3

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

[0170] The steps involved in the above embodiments 2 to 4 correspond to the method embodiment 1, and the specific implementation methods can refer to the relevant description part of embodiment 1. The term "computer-readable storage medium" should be understood as 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 modules or steps of the present invention described above can be implemented by a general-purpose computer device, or alternatively, they can be implemented by a program code 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 made into individual integrated circuit modules, or multiple modules or steps therein can be made 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 description is only a preferred embodiment of the present invention. Although the specific implementation mode of the present invention is described in conjunction with the accompanying drawings, it is not a limitation of the protection scope of the present invention. Those skilled in the art should understand that on the basis of the technical solution of the present invention, various modifications or variations that can be made by those skilled in the art without creative work are still within the protection scope of the present invention.

Claims

1. A method for analyzing small signal stability of a large-scale renewable energy power system, characterized in that: include: For large-scale renewable energy power systems, discrete state space models of each component in the power system are established to construct a discrete state space model of the entire power system and determine the discrete state matrix; By using preprocessing technology, the eigenvalues ​​of the system state matrix to be solved are converted into the dominant eigenvalues ​​of the system; The preprocessing technique is an inverse displacement transform or a rotation transform; Based on the discrete state matrix, the dominant eigenvalue of the system is calculated and solved by using an iterative algorithm combined with sparse implementation; The solved dominant eigenvalue of the system is converted into the eigenvalue of the continuous state matrix. The strength of the small signal interference stability of the power system is judged according to the converted eigenvalue, and the converted eigenvalue is compared and verified with the distribution diagram of all eigenvalues ​​of the system.

2. A method for analyzing small signal stability of a large-scale new energy power system according to claim 1, characterized in that: Construct a discrete state space model of the entire power system and determine the discrete state matrix, including: For large-scale power systems, continuous state space models of various components in the power system are established respectively; the components include converters, RL series lines and loads, and parallel capacitors C; The continuous state space model of each element is discretized and converted into a discrete state space model; the discrete state space model includes an iterative expression of a discrete equivalent circuit and a historical current source vector; Based on the topological structure of the discrete equivalent circuit of the discrete state space model of each component and its connection mode, the node conductance matrix and branch-node association matrix of the system are established; Iterative expressions of historical current source vectors based on discrete state space models of each component form a state vector; Based on the system's node conductance matrix, branch-node association matrix and state vector, a discrete state space model of the entire power system is constructed and the discrete state matrix is ​​determined.

3. A method for analyzing small signal stability of a large-scale renewable energy power system according to claim 1, characterized in that: Using preprocessing technology, the eigenvalues ​​of the system state matrix that is expected to be solved are converted into the dominant eigenvalues ​​of the system, including: The inverse shift transform is used to transform the system state matrix and eigenvalue, which is: convert the discrete state matrix into a continuous state matrix, select a shift point, perform an inverse shift transform on the transformed continuous state matrix, and map the eigenvalue of the transformed continuous state matrix closest to the shift point to the eigenvalue with the largest system modulus; wherein the eigenvalue of the continuous state matrix closest to the shift point is the eigenvalue of the system state matrix to be solved, and the eigenvalue with the largest modulus of the continuous system after the inverse shift transform is the dominant eigenvalue of the system.

4. A method for analyzing small signal stability of a large-scale renewable energy power system according to claim 1, characterized in that: Using preprocessing technology, the eigenvalues ​​of the system state matrix that is expected to be solved are converted into the dominant eigenvalues ​​of the system, including: Rotation transformation is used to convert the system state matrix and eigenvalue, which is: setting the damping ratio, and rotating and modifying the discrete state space model, converting the eigenvalue of the continuous state matrix with a damping ratio less than the set damping ratio into the system dominant eigenvalue; wherein, the eigenvalue of the continuous system with a damping ratio less than the set damping ratio is the eigenvalue of the system state matrix desired to be solved, and the eigenvalue with the largest modulus value of the discrete state matrix after rotation is the system dominant eigenvalue.

5. A method for analyzing small signal stability of a large-scale renewable energy power system according to claim 1, characterized in that: Using iterative algorithms combined with sparse implementation, the dominant eigenvalues ​​of the system are calculated and solved, including: The discrete state matrix is ​​sparsely realized, and then an iterative algorithm is used to iteratively solve the system dominant eigenvalue in the order of decreasing module value; the iterative algorithm adopts an implicit restart Arnoldi algorithm.

6. A method for analyzing small signal stability of a large-scale renewable 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: After the eigenvalue conversion is performed using the inverse shift transform, the relationship between the eigenvalue λ of the continuous state matrix and the eigenvalue λ′ of the transformed system is:

7. A method for analyzing small signal stability of a large-scale renewable energy power system according to claim 1, characterized in that: After the eigenvalue conversion is performed using the rotation transformation, the relationship between the eigenvalue λ of the continuous state matrix and the eigenvalue μ′ of the discrete state matrix after the rotation transformation is:

8. A large-scale new energy power system small signal stability analysis system, characterized in that: include: The discrete model building module is used to establish the discrete state space model of each component in the power system for large-scale renewable energy power systems, so as to construct the discrete state space model of the entire power system and determine the discrete state matrix; A conversion module, used for converting the eigenvalues ​​of the system state matrix to be solved into the system dominant eigenvalues ​​by using a preprocessing technology; The preprocessing technique is an inverse displacement transform or a rotation transform; The dominant eigenvalue solving module is used to calculate and solve the dominant eigenvalue of the system based on the discrete state matrix using an iterative algorithm combined with sparse implementation; The stability analysis module is used to convert the solved dominant eigenvalues ​​of the system into 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.

9. An electronic device, characterized in that: The invention comprises a memory and a processor and computer instructions stored in the memory and executed on the processor. When the computer instructions are executed by the processor, the steps of a method for analyzing small signal stability of a large-scale new energy power system as described in any one of claims 1 to 7 are completed.

10. A computer-readable storage medium, characterized in that: Used to store computer instructions, which, when executed by a processor, complete the steps of a large-scale new energy power system small signal stability analysis method as described in any one of claims 1-7.

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