A method for identifying dominant bifurcation mode of transient synchronization stability of an inverter grid-connected system

Abstract

The application provides a transient synchronous stability dominant bifurcation mode identification method for an inverter grid-connected system, and relates to the field of power systems and their automation, and the steps of the method are as follows: obtaining inverter parameters and power parameters of the inverter grid-connected system and obtaining bifurcation equivalent parameters; based on a stable equilibrium point, obtaining a Hopf complex normal form coefficient real part and a normalized bifurcation parameter according to a generalized swing equation and the bifurcation equivalent parameters; obtaining a limit cycle amplitude according to the bifurcation equivalent parameters, the Hopf complex normal form coefficient real part and the normalized bifurcation parameter; obtaining a transient stability margin according to a geometric distance between a stable manifold at an unstable equilibrium point and the stable equilibrium point; and identifying a dominant bifurcation mode of the inverter grid-connected system according to the limit cycle amplitude and the transient stability margin. The method can effectively improve the efficiency and precision of transient synchronous instability mode identification, realizes quantitative evaluation of the stability margin, and provides accurate transient synchronous stability criteria for power systems.

Description

Technical Field

[0001] This invention relates to the field of power systems and their automation technology, specifically to a method for identifying the dominant bifurcation mode of transient synchronization stability in inverter grid-connected systems. Background Technology

[0002] With the high proportion of renewable energy integration, the number of inverters connected to the grid in the power system is growing rapidly. Their dynamic response characteristics are significantly different from those of traditional synchronous generators. Especially when the system is subjected to disturbances (such as short circuits or sudden load changes), they are prone to transient synchronization instability. This type of instability is mainly manifested in the inability of the converter output phase angle to maintain synchronization with the grid, thereby triggering the inverter to disconnect from the grid and affecting the safe and stable operation of the system.

[0003] Most current stability assessment methods rely on linearization analysis or ergodic calculations based on time-domain simulation, which fail to reveal the deep dynamic mechanisms in inverter systems, such as changes in the attraction domain, the formation of limit cycles, and the evolution of manifold structures caused by nonlinear bifurcation. Furthermore, practical engineering applications lack methods for identifying the dominant bifurcation mechanisms in different operating regions, resulting in low accuracy and severely limited efficiency in stability margin assessments.

[0004] Especially when system operating parameters approach the critical region, nonlinear phenomena such as Hopf bifurcation and homoclinic bifurcation often become key triggering factors for transient instability. Therefore, there is an urgent need to develop a method that can accurately identify the dominant bifurcation type of the system, quantify the boundary structure of the attraction domain, and on this basis, achieve rapid estimation of stability margin, in order to meet the stability analysis requirements under high-proportion inverter access. Summary of the Invention

[0005] This invention addresses the problems existing in the prior art by providing a method for identifying the dominant bifurcation mode of transient synchronization stability in inverter grid-connected systems. This method effectively solves the problem of accurately identifying transient synchronization instability modes in inverter grid-connected systems. Specifically, based on nonlinear dynamic characteristics such as Hopf bifurcation and homodextrous bifurcation, this disclosure proposes a method for identifying the dominant instability mechanism of transient synchronization instability in inverter grid-connected systems, thereby enabling rapid assessment of transient synchronization stability margin.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows: a method for identifying the transient synchronous stability dominant bifurcation mode of an inverter grid-connected system, comprising the following steps: obtaining inverter parameters and the power parameters of the inverter grid-connected system;

[0007] The bifurcation equivalent parameters are obtained based on the inverter parameters and the electrical parameters.

[0008] Based on the stable equilibrium point, the real part of the Hopf complex normal form coefficients and the normalized bifurcation parameters are obtained according to the generalized rocking equation and the bifurcation equivalent parameters.

[0009] The limiting cycle amplitude value is obtained based on the bifurcation equivalent parameter, the real part of the Hopf complex normal form coefficient, and the normalized bifurcation parameter;

[0010] The transient stability margin is obtained based on the geometric distance between the stable manifold at the unstable equilibrium point and the stable equilibrium point.

[0011] The dominant bifurcation mode of the inverter grid-connected system is identified based on the limiting loop amplitude and the transient stability margin.

[0012] In some embodiments, identifying the dominant bifurcation mode of the inverter grid-connected system based on the limiting loop amplitude and the transient stability margin includes:

[0013] When the limiting loop amplitude is less than the transient stability margin, the inverter grid-connected system is in a transient synchronous instability mode dominated by Hopf bifurcation.

[0014] When the limiting loop amplitude is equal to the transient stability margin, the inverter grid-connected system is in a critical state of homogeneous bifurcation.

[0015] When the limiting loop amplitude is greater than the transient stability margin, the inverter grid-connected system is in a transient synchronous instability mode dominated by co-homogeneous bifurcation.

[0016] In some embodiments, the step of obtaining the transient stability margin based on the geometric distance between the stable manifold at the unstable equilibrium point and the stable equilibrium point is as follows: obtaining an identity matrix; obtaining a first coordinate and a second coordinate, wherein the first coordinate is the coordinate of the stable equilibrium point and the second coordinate is the coordinate of the unstable equilibrium point;

[0017] Linearize the inverter grid-connected system at the second coordinate and obtain the Jacobian matrix;

[0018] Based on the Jacobian matrix, obtain the unit eigenvectors corresponding to the negative eigenvalues;

[0019] The projection operator is obtained based on the unit eigenvector;

[0020] The transient stability margin is obtained based on the identity matrix, the projection operator, the first coordinate, and the second coordinate.

[0021] In some embodiments, the step of obtaining the projection operator based on the unit feature vector is as follows:

[0022] Obtain the transpose of the unit eigenvector based on the unit eigenvector;

[0023] The projection operator is obtained by multiplying the unit eigenvector and the transpose vector.

[0024] In some embodiments, the steps of obtaining the real part of the Hopf complex normal form coefficients and the normalized bifurcation parameters based on the stable equilibrium point, according to the generalized rocking equation and the bifurcation equivalent parameters, are as follows:

[0025] The generalized rocking equation is simplified to the Hopf normal form;

[0026] Based on the stable equilibrium point, the real part and imaginary part of the Hopf complex normal coefficients are obtained by solving the Hopf normal form.

[0027] Based on the real part of the coefficients of the Hopf complex normal form and the imaginary part of the coefficients of the Hopf complex normal form, the polar coordinate Hopf normal form is obtained according to the generalized rocking equation;

[0028] The normalized bifurcation parameters are obtained based on the polar coordinate Hopf canonical form.

[0029] In some embodiments, the limiting cycle amplitude is obtained by taking the square root of the ratio of the normalized bifurcation parameter to the real part of the Hopf complex normal form coefficient.

[0030] In some embodiments, the inverter parameters include the proportional coefficient of the phase-locked loop PI control, the integral coefficient of the phase-locked loop PI control, and the current reference value, and the electrical parameters include the reference angular frequency, the equivalent inductance of the transmission line, and the grid connection point voltage.

[0031] In some embodiments, the bifurcation equivalent parameters include a first equivalent parameter, a second equivalent parameter, a third equivalent parameter, and a fourth equivalent parameter;

[0032] The first equivalent parameter is:

[0033]

[0034] The second equivalent parameter is:

[0035]

[0036] The third equivalent parameter is:

[0037]

[0038] The fourth equivalent parameter is:

[0039]

[0040] In the formula, P α As the first equivalent parameter, P I As the second equivalent parameter, P D As the third equivalent parameter, PDc k is the fourth equivalent parameter. ppll k is the proportional coefficient of the phase-locked loop PI control. ipll i represents the integral coefficient of the phase-locked loop PI control. dref For current reference value, L g U is the equivalent inductance of the transmission line. g ω0 is the grid connection point voltage, and ω0 is the reference angular frequency.

[0041] In some embodiments, the real part of the Hopf complex normal form coefficients is:

[0042]

[0043] In the formula, Let ω1 be the real part of the coefficients in the Hopf complex normal form, and ω1 be an intermediate expression.

[0044] In some embodiments, the normalized bifurcation parameter is obtained by halving the difference between the third equivalent parameter and the fourth equivalent parameter.

[0045] Compared with the prior art, the present invention has the following beneficial effects:

[0046] 1. This disclosure can solve for the limiting loop amplitude and transient stability margin based on inverter parameters and power parameters, and identify the dominant bifurcation mode of the inverter grid-connected system through the limiting loop amplitude and transient stability margin. It can effectively improve the efficiency and accuracy of transient synchronous instability mode identification, and provide theoretical basis and technical support for the optimization of control parameters and operation safety assessment of inverter grid-connected systems. It has good engineering adaptability and promotion prospects.

[0047] 2. This disclosure derives the scaling law of the limit cycle amplitude based on Hopf regularity theory, and establishes an analytical expression for the boundary of the attraction domain by combining the homoclinic orbit construction method, thereby realizing a quantitative assessment of the stability margin and providing an accurate criterion for transient synchronous stability of the power system;

[0048] 3. The dominant bifurcation pattern recognition method proposed in this disclosure combines manifold structure and limit cycle characteristics, avoiding the high computational burden of traditional point-by-point simulation, and is suitable for real-time stability monitoring under large-scale parameter changes in engineering practice;

[0049] 4. This disclosure proposes an efficient and accurate method for identifying the dominant bifurcation mode of transient synchronous stability in inverter grid-connected systems. This method can comprehensively solve the problems of difficulty in identifying instability modes and high computational complexity in stability margin assessment in existing technologies. It has significant engineering practical value and scalability, and can provide strong support for inverter control parameter tuning and system safety boundary construction. Attached Figure Description

[0050] Figure 1 This is a schematic diagram of the transient synchronous stability dominant bifurcation mode identification method for inverter grid-connected systems disclosed in this paper.

[0051] Figure 2a The phase-locked loop PI control parameters and the limiting loop amplitude M os A three-dimensional graph of correlations;

[0052] Figure 2b The phase-locked loop PI control parameters and transient stability margin M ts A three-dimensional graph of correlations;

[0053] Figure 3a The phase-locked loop PI control parameters and the limiting loop amplitude M os A relational plane diagram;

[0054] Figure 3b The phase-locked loop PI control parameters and transient stability margin M ts A relational plane diagram;

[0055] Figure 4 The limiting loop amplitude M under different phase-locked loop PI control parameters os With transient stability margin M ts Comparison chart;

[0056] Figure 5a For the power parameters and the limiting loop amplitude M os A three-dimensional graph of correlations;

[0057] Figure 5b For the electric charge parameter and transient stability margin M ts A three-dimensional graph of correlations;

[0058] Figure 6a For the power parameters and the limiting loop amplitude M os A relational plane diagram;

[0059] Figure 6b For the electric charge parameter and transient stability margin M ts A relational plane diagram;

[0060] Figure 7 The limiting loop amplitude value M under different electrical parameters os With transient stability margin M ts The comparison chart. Detailed Implementation

[0061] To address the shortcomings of existing methods in identifying transient synchronization instability mechanisms in inverter-connected grid systems, this disclosure proposes a dominant bifurcation pattern identification method based on attraction domains. By characterizing the attraction domain boundaries corresponding to Hopf bifurcations and homodextrous bifurcations, a quantitative assessment of transient synchronization stability margin is achieved. This method not only overcomes the limitations of traditional methods in analyzing nonlinear instability mechanisms but also effectively reduces the reliance on extensive time-domain simulations, providing a more theoretically profound and engineering-adaptable solution for stability analysis and parameter optimization of new energy power systems.

[0062] To clearly illustrate the technical features of this solution, the implementation methods of this application will be described in detail below with reference to the accompanying drawings and embodiments. This will allow for a full understanding and implementation of how this application uses technical means to solve technical problems and achieve corresponding technical effects. The embodiments of this application and the various features within them can be combined with each other without conflict, and the resulting technical solutions are all within the protection scope of this application.

[0063] See Figure 1 This disclosure provides a method for identifying the transient synchronous stability dominant bifurcation mode in an inverter grid-connected system, comprising the following steps: acquiring inverter parameters and the power parameters of the inverter grid-connected system; in some embodiments, the inverter parameters include phase-locked loop (PLL) PI control parameters and current reference value i. dref The phase-locked loop (PLL) PI control parameters include the proportional coefficient k of the PLL PI control. ppll The integral coefficient k of the phase-locked loop PI control ipll The electrical parameters include the reference angular frequency ω0 and the equivalent inductance L of the transmission line. g and grid connection point voltage U g ;

[0064] The bifurcation equivalent parameters are obtained based on the inverter parameters and the power parameters; in some embodiments, the bifurcation equivalent parameters include a first equivalent parameter, a second equivalent parameter, a third equivalent parameter, and a fourth equivalent parameter;

[0065] The first equivalent parameter is:

[0066]

[0067] The second equivalent parameter is:

[0068]

[0069] The third equivalent parameter is:

[0070]

[0071] The fourth equivalent parameter is:

[0072]

[0073] In the formula, P α As the first equivalent parameter, P I As the second equivalent parameter, P D As the third equivalent parameter, P Dc It is the fourth equivalent parameter, and simultaneously satisfies condition P. α ≥0, P I ≥0, P D ≥0, P Dc ≥0;

[0074] Based on the stable equilibrium point, the real part of the Hopf complex normal form coefficients and the normalized bifurcation parameters are obtained according to the generalized rocking equation and the bifurcation equivalent parameters.

[0075] The limiting cycle amplitude is obtained from the bifurcation equivalent parameter, the real part of the Hopf complex normal form coefficient, and the normalized bifurcation parameter. The limiting cycle amplitude is the stability margin under the Hopf bifurcation dominance.

[0076] The transient stability margin is obtained by the geometric distance between the stable manifold at the unstable equilibrium point and the stable equilibrium point. The transient stability margin is the stability margin under the dominance of homoclinic bifurcation.

[0077] Identify the dominant bifurcation mode of the inverter grid-connected system based on the limit cycle amplitude and transient stability margin.

[0078] Beneficially, this disclosure can solve for the limiting loop amplitude and transient stability margin based on inverter parameters and power parameters, and identify the dominant bifurcation mode of the inverter grid-connected system through the limiting loop amplitude and transient stability margin. This can effectively improve the efficiency and accuracy of transient synchronous instability mode identification, and provide theoretical basis and technical support for the optimization of control parameters and operation safety assessment of inverter grid-connected systems. It has good engineering adaptability and promotion prospects.

[0079] Based on nonlinear dynamics theory, and given that there are multiple bifurcation types in the known inverter grid-connected system, we identify the transient synchronous instability region dominated by Hopf bifurcation and homodextral bifurcation. Specifically, the unstable limit cycle caused by Hopf bifurcation constitutes the boundary of the attraction domain, and the homodextral orbit caused by homodextral bifurcation constitutes the attraction domain of the system's transient synchronous stability.

[0080] In the transient process, the phase-locked loop plays a major role in the grid-connected inverter. The transient synchronization stability of the grid-connected inverter system can be explained by the generalized swing equation, as shown in equation (1):

[0081]

[0082] In the formula, For phase angle difference, θ pllω is the direct output phase angle of the phase-locked loop, t is time, and ω is the output angular frequency of the phase-locked loop.

[0083]

[0084] In the formula, For a linear transformation of time t;

[0085] According to equation (1), the conditions for the generation of Hopf bifurcation and homoclinic bifurcation can be analyzed. Hopf bifurcation refers to the appearance or disappearance of periodic orbits, i.e., limit cycles. The appearance or disappearance of periodic orbits is manifested by the appearance of a pair of conjugate imaginary eigenvalues ​​in the Jacobian matrix. The bifurcation point parameter conditions are shown in equation (2):

[0086]

[0087] Homic bifurcation is usually associated with the generation and disappearance of homomic orbits. Homic bifurcation occurs when the distance between the stable and unstable manifolds at a saddle point is zero, leading to the generation of homomic orbits. Therefore, the parameter conditions for homomic bifurcation points can be derived as shown in equation (3):

[0088]

[0089] In summary, the generalized oscillating equation may exhibit Hopf bifurcation and homoclinic bifurcation in different parameter regions. Hopf bifurcation corresponds to oscillatory instability due to transient synchronous instability, while homoclinic bifurcation corresponds to out-of-step divergence due to transient synchronous instability. Therefore, the regions dominated by Hopf bifurcation and homoclinic bifurcation (i.e., regions where transient synchronous instability may occur) can be identified based on the parameter conditions at the Hopf bifurcation and homoclinic bifurcation points.

[0090] Transient synchronous stability depends on the relationship between the system's initial state and its state after fault clearing, and is essentially determined by the equilibrium point and its attraction domain. Therefore, transient synchronous stability can be assessed by determining whether the system state after fault clearing is within the attraction domain, and the distance between the equilibrium point and the attraction domain can be used to characterize the system's stability margin. However, the attraction domain structure differs within different bifurcation dominance regions. Within the Hopf bifurcation dominance region, the limit cycle is the attraction domain of the equilibrium point. When the limit cycle collides with and disappears from the stable manifold of the saddle point, the system undergoes homoclinic bifurcation, and the resulting homoclinic trajectory constitutes the attraction domain of the equilibrium point. Therefore, the system has two types of attraction domains: one is the unstable limit cycle induced by Hopf bifurcation, whose instability manifests as oscillatory divergence; the other is the homoclinic trajectory formed by homoclinic bifurcation, whose instability corresponds to system out-of-step.

[0091] In some embodiments, the steps for obtaining the real part of the Hopf complex normal form coefficients and the normalized bifurcation parameters based on the stable equilibrium point, according to the generalized rocking equation and the bifurcation equivalent parameters, are as follows:

[0092] For the dominant region of Hopf bifurcation, based on the coefficients of Hopf normal form and complex normal form, the scaling law of limit cycle is derived to achieve a quantitative assessment of stability margin.

[0093] The occurrence of Hopf bifurcation is often accompanied by the appearance or disappearance of limit cycles. Supercritical Hopf bifurcation forms stable limit cycles, and the surrounding states are attracted to the limit cycle. Subcritical Hopf bifurcation forms unstable limit cycles, where points inside the limit cycle are attracted to the equilibrium point, while points outside the limit cycle move away from the limit cycle.

[0094] Suppose that at the critical bifurcation parameter, the Jacobian matrix has exactly one pair of purely imaginary eigenvalues ​​±iω1, where i is an imaginary number and ω1 is an intermediate expression. With appropriate coordinate transformation, the system can be simplified to a second-order Hopf normal form with respect to the complex variable z, as shown in equation (4).

[0095]

[0096] In the formula For the complex normal form coefficients, the real part of C1 can be used to determine whether the limit cycle generated by the bifurcation is stable, thus identifying the Hopf bifurcation type; the imaginary part of C1 represents the second-order correction of the amplitude with respect to frequency, λ is the real part of the characteristic roots, O represents higher-order infinitesimals, and here represents z. 4 A higher-order infinitesimal. Let q is the right eigenvector corresponding to +iω1. q is the right eigenvector of -iω1, p is the left eigenvector corresponding to -iω1, and q and p satisfy the following condition:<p,q> =1. Simultaneously, define the Jacobian matrix as A, the second-order multilinear mapping of the Jacobian matrix A as B, and the third-order multilinear mapping as C. The second-order multilinear mapping B is composed of second-order differentials, and the third-order multilinear mapping C is composed of third-order differentials. Therefore, the complex normality coefficients are shown in equation (5):

[0097]

[0098] In the formula, I is the identity matrix;

[0099] The generalized oscillation equation is established in the Cartesian coordinate system, therefore equation (4) needs to be converted to the Hopf normal form in the Cartesian coordinate system, as shown in equation (6). In the equation, ±iω1 are the conjugate imaginary roots.

[0100]

[0101] In the formula, u is the first state variable in the Cartesian coordinate system, v is the second state variable in the Cartesian coordinate system, g is the first nonlinear function, f is the second nonlinear function, g and f are abstract functions, respectively, representing the derivatives of state variables u and v and the functional relationships between the derivative variables;

[0102] Real part of Hopf complex normal coefficients in Cartesian coordinates The imaginary part of the Hopf complex normal coefficients As shown in equations (7) and (8) respectively.

[0103]

[0104] In the formula, f uv The second-order partial derivative of the second nonlinear function obtained by taking partial derivatives with respect to u and v, f vv The second-order partial derivative of the second nonlinear function obtained by taking partial derivatives with respect to v and v', f' ... uu The second-order partial derivative of the second nonlinear function obtained by taking partial derivatives with respect to u and u', g uv The second-order partial derivatives of the first nonlinear function obtained by taking partial derivatives with respect to u and v are given by g. vv The second-order partial derivatives of the first nonlinear function obtained by taking partial derivatives with respect to v and v' are given by g. uu The second-order partial derivatives of the first nonlinear function obtained by taking partial derivatives with respect to u and u', f' vvv The third partial derivative of the second nonlinear function obtained by taking partial derivatives with respect to v, v, and v' in sequence, f' vuu The third partial derivative of the second nonlinear function obtained by taking partial derivatives with respect to v, u, and u in sequence, g vvu The third-order partial derivative of the first nonlinear function obtained by taking partial derivatives with respect to v, v, and u in sequence is g. uuu The third-order partial derivative of the first nonlinear function obtained by taking partial derivatives with respect to u, u, and u in sequence is g. vvv The third partial derivative of the first nonlinear function obtained by taking partial derivatives with respect to v, v, and v is g. uvv The third-order partial derivative of the first nonlinear function obtained by taking partial derivatives with respect to u, v, and v' in sequence is f. vvu The third-order partial derivatives of the second nonlinear function are obtained by taking the partial derivatives of the second nonlinear function with respect to v, v, and u in sequence.

[0105] The generalized rocking equation is simplified to the Hopf normal form;

[0106] Based on the stable equilibrium point, the real and imaginary parts of the Hopf complex normal form coefficients are obtained by solving the Hopf normal form. Specifically, a third-order Taylor expansion is performed at the stable equilibrium point, as shown in equation (9):

[0107]

[0108] In the formula, Let Δω be the change in phase angle difference, and Δω be the change in the output angular frequency of the phase-locked loop. Here, only the third-order and lower-order terms are retained in equation (9), and the stable equilibrium point has been moved to the origin. The eigenvalue λ of equation (9) is... 1,2 As shown in equation (10):

[0109]

[0110] The coefficients of the complex normal form are obtained as shown in equation (11):

[0111]

[0112] The real part of the coefficients in the Hopf complex normal form determines the Hopf bifurcation type. Corresponding to subcritical, This corresponds to supercriticality. Clearly, the Hopf bifurcation of the inverter grid-connected system is a subcritical Hopf bifurcation.

[0113] Based on the real part and imaginary part of the coefficients of the Hopf complex normal form, in order to solve the amplitude and frequency of the limit cycle, the polar coordinate Hopf normal form is obtained according to the generalized rocking equation, as shown in equation (12).

[0114]

[0115] In the formula, r is the first state variable in polar coordinates, r represents the distance from the point on the polar coordinate plane to the origin, and μ norm For the normalized bifurcation parameter, θ is the second state variable in polar coordinate form, where θ represents the angle of a point on the polar coordinate plane;

[0116] The normalized bifurcation parameter μ is obtained from the polar coordinate Hopf canonical form. norm The normalized bifurcation parameter is obtained by halving the difference between the third and fourth equivalent parameters. The normalized bifurcation parameter μ... norm See equation (13):

[0117]

[0118] Thus, the scaling law of the limit cycle can be obtained as shown in equation (14); the limit cycle amplitude is the stability margin under the dominance of Hopf bifurcation, that is, the limit cycle amplitude is obtained by taking the square root of the ratio of the normalized bifurcation parameter to the real part of the Hopf complex normal form coefficient.

[0119]

[0120] In the formula, M os Ω represents the limiting loop amplitude, and Ω represents the limiting loop frequency.

[0121] Equation (14) shows that the limiting cycle frequency Ω depends not only on the linear frequency ω1 at the bifurcation point, but also on the correction of the nonlinear effect, which is caused by... The determination of the correction for nonlinear effects and the limiting cycle amplitude M os It is proportional to the square of. If Then the limiting cycle frequency Ω and the limiting cycle amplitude M os Irrelevant.

[0122] For the dominant region of homoclinic bifurcation, the tangent space of the equilibrium point unstable manifold and the saddle point stable manifold is constructed to estimate the homoclinic orbit formation conditions, thereby achieving rapid assessment of stability margin;

[0123] Trajectories within the homoclinic orbit region converge to stable equilibrium points. Trajectories outside the homoclinic orbits diverge along the unstable manifolds of unstable equilibrium points. The boundaries of the attraction domain are precisely formed by the stable manifolds of unstable equilibrium points; therefore, transient synchronization stability can be assessed based on their positions in the phase plane.

[0124] Since the boundary of the attraction domain in the homoclinic orbit region is precisely formed by the stable manifold of the unstable equilibrium point, an approximate analytical expression of the attraction domain can be obtained by solving for this stable manifold. In nonlinear dynamical systems, the phase space manifold near any equilibrium point can be approximated by its tangent space at that point, i.e., obtained through a linearized description of the system. Specifically, the stable manifold is the curve or surface formed by all trajectories that eventually converge to the equilibrium point. At the equilibrium point, its tangent direction is precisely determined by the stable subspace of the linearized system, which is determined by the corresponding eigenvectors.

[0125] To achieve stability margin assessment dominated by homoclinic bifurcation, this disclosure uses the geometric distance between the stable manifold at the saddle point and the stable equilibrium point as the transient stability margin M. ts The saddle point is an unstable equilibrium point.

[0126] In some embodiments, the step of obtaining the transient stability margin based on the geometric distance between the stable manifold at the unstable equilibrium point and the stable equilibrium point includes: obtaining the identity matrix I; obtaining the first coordinate system. Second coordinate in The x-coordinate value of the first coordinate. The x-coordinate of the second coordinate is the x-coordinate of the first coordinate. e The coordinates of the stable equilibrium point, the second coordinate x s The coordinates of the unstable equilibrium point;

[0127] Second coordinate x s The inverter grid-connected system is linearized and the Jacobian matrix J is obtained;

[0128] Obtain the negative eigenvalues ​​λ of the Jacobian matrix J. s The corresponding unit eigenvector v s ;

[0129] Based on the linearization approximation, the stable manifold is defined by the second coordinate x. s The eigenvector v of the cut unit s The straight line slants the line, thus allowing the stable manifold W at the saddle point to be represented. s (x s Consider it as the second coordinate x passing through the point. s And tangent to the unit eigenvector v s The straight line is shown in equation (15):

[0130]

[0131] In the formula, L is the second coordinate x passing through the point. s And tangent to the unit eigenvector v s The straight line, where ξ is the coefficient of the unit eigenvector. It is the set of real numbers;

[0132] The straight line L in equation (15) approximates the first-order tangent of the stable manifold at the saddle point.

[0133] The projection operator v is obtained from the unit eigenvector. s v s T superscript T Indicates transpose;

[0134] The transient stability margin is obtained based on the identity matrix, projection operator, first coordinate, and second coordinate; the stable equilibrium point x e The shortest Euclidean distance to the straight line L can be directly used as the transient stability margin, as shown in equation (16):

[0135]

[0136] In the formula, min is the minimization function;

[0137] In the formula, the projection operator v s v s T Project the vector onto the unit eigenvector v s Direction, operator (Iv) s v s T Project the vector onto the unit eigenvector v s The orthogonal filler is then used to extract the second coordinate x. s The orthogonal distance to line L.

[0138] The advantage is that this method relies only on local linearization information at saddle points and stable equilibrium points, avoiding the computational burden of point-by-point numerical simulation, and providing theoretical support for the rapid assessment of stability margins of large-scale power systems.

[0139] In some embodiments, identifying the dominant bifurcation mode of the inverter grid-connected system based on the limiting loop amplitude and transient stability margin includes:

[0140] When the limiting loop amplitude is less than the transient stability margin, the inverter grid-connected system is in a transient synchronous instability mode dominated by Hopf bifurcation.

[0141] When the limiting loop amplitude is equal to the transient stability margin, the inverter grid-connected system is in a critical state where a bifurcation will occur.

[0142] When the limiting loop amplitude is greater than the transient stability margin, the inverter grid-connected system is in a transient synchronous instability mode dominated by the same-origin bifurcation.

[0143] A dominant bifurcation pattern recognition method is proposed. By judging the characteristics of limit cycles and the geometry of manifolds, the dominant instability mechanism of inverter grid-connected systems can be automatically identified, which significantly reduces the computational burden of traditional point-by-point simulation.

[0144] Based on the system equilibrium point and manifold distribution, transient synchronous stability can be classified into the following modes:

[0145] (1) Before the occurrence of homologous bifurcation

[0146] At this stage, the inverter grid-connected system has undergone Hopf bifurcation and generated an amplitude value of the limit loop amplitude M. os The limiting cycle. On the phase plane, the distance between the stable equilibrium point and the limiting cycle is less than the distance between the limiting cycle and the stable manifold of the unstable equilibrium point. At this point, the limiting cycle has not yet come into contact with the stable manifold of the unstable equilibrium point, and the amplitude M of the limiting cycle... os It must be less than the transient stability margin M ts .

[0147] When the state trajectory of the inverter grid-connected system falls outside the limit cycle after being disturbed, although it will be rejected by the limit cycle, the state of the inverter grid-connected system will not diverge directly because the subcritical Hopf bifurcation exhibits oscillatory divergence when unstable. Instead, it will circle the limit cycle several times before being rejected. Therefore, the inverter grid-connected system is dominated by the Hopf bifurcation in this stage.

[0148] (2) Homoclinic bifurcation point

[0149] As the unstable limit cycle gradually expands, when it comes into contact with the stable manifold at the unstable equilibrium point, a bifurcation occurs in the inverter grid-connected system. At this point, the limit cycle amplitude M... os Equal to transient stability margin Mts .

[0150] (3) After the bifurcation of the same host,

[0151] After the homodextral bifurcation occurs, the original unstable limit cycle disappears, and the attraction domain boundary of the inverter grid-connected system transforms into a homodextral orbit. When the state trajectory of the inverter grid-connected system after being disturbed falls outside the homodextral orbit, it will directly diverge and lose synchronization. Therefore, the inverter grid-connected system is dominated by the homodextral bifurcation during this stage.

[0152] In summary, by comparing the limiting loop amplitude M os With transient stability margin M ts The relationship between the two can identify the morphology of the attraction domain, thereby enabling the determination of the dominant bifurcation mode of the inverter grid-connected system. The dominant roles of Hopf bifurcation and homoclinic bifurcation in the transient synchronous instability process are clarified, and the characteristic regions of the attraction domain dominated by different bifurcation types are identified, filling the gap in existing research regarding the insufficient understanding of the dominant instability mechanism.

[0153] Calculation example

[0154] To verify the bifurcation characteristics and analyze the correlation between parameters and stability margin indices, we first fix the grid inductance, i.e., the equivalent L of the transmission line. g =0.16pu and current reference value i dref =0.7pu, change the proportional coefficient k of the phase-locked loop PI control ppll The integral coefficient k of the phase-locked loop PI control ipll Analyze the proportional coefficient k of the phase-locked loop PI control. ppll The integral coefficient k of the phase-locked loop PI control ipll With transient stability margin M ts and the limiting ring amplitude M os The relationship between them is shown in Figures 2 and 3.

[0155] As shown in the figure, with the increase of the proportional coefficient k in the phase-locked loop PI control... ppll The integral coefficient k of the phase-locked loop PI control ipll The increase of transient stability margin M ts The gradual decrease indicates a reduction in the transient stability margin of the inverter grid-connected system, while the limiting loop amplitude M... os The proportional coefficient k of the phase-locked loop PI control ppll The integral coefficient k of the phase-locked loop PI control ipll There is no monotonic relationship among these parameters. It is worth noting that the overall stability margin of the inverter grid-connected system does not depend solely on the limiting loop amplitude M. os or transient stability margin M ts When the limiting cycle amplitude M osWhen the voltage exceeds the range of the homologous orbit, homologous bifurcation will occur, causing a fundamental change in the stability characteristics of the inverter grid-connected system. Therefore, the actual stability margin of the inverter grid-connected system is affected by the limiting loop amplitude M. os and transient stability margin M ts The constraints of the relationship between them. Figure 4 Further comparison of the limiting loop amplitude M under different control parameters os and transient stability margin M ts Size. From Figure 4 As can be seen, with the increase of the proportional coefficient of the phase-locked loop (PLL), homocentric bifurcation is more likely to become the dominant bifurcation mode; while with the increase of the proportional coefficient k of the PLL PI control, homocentric bifurcation is more likely to become the dominant bifurcation mode. ppll With the increase of [unclear], the inverter grid-connected system is more likely to exhibit oscillation and instability characteristics.

[0156] Based on this, the impact of the power parameters of the inverter grid-connected system on the stability margin is further analyzed. The proportional coefficient k of the fixed phase-locked loop PI control is used. ppll =20 and the integral coefficient k of the phase-locked loop PI control ipll =10000, studying the electrical distance and current reference values ​​and the limiting loop amplitude M os and transient stability margin M ts The relationship between these factors is shown in Figures 5 and 6. The figures indicate that as the electrical distance and current reference value increase, the limiting loop amplitude M... os and transient stability margin M ts Both margins show a decreasing trend. Similarly, relying solely on the limiting cycle amplitude M... os or transient stability margin M ts No single indicator can fully measure the stability margin of an inverter grid-connected system. Figure 7 This demonstrates the limiting loop amplitude M under varying electrical parameters of the inverter-grid-connected system. os and transient stability margin M ts The comparison shows that as the electrical distance and current reference value increase, oscillation instability is more likely to become the main instability mode of the inverter grid-connected system.

[0157] This disclosure proposes a method for identifying the dominant bifurcation pattern in transient synchronous stability of inverter grid-connected systems. Addressing the problems of low computational efficiency and unclear physical mechanisms in existing methods for instability mechanism identification and stability margin assessment, this method systematically analyzes the changes in the attraction domain structure caused by Hopf bifurcation and homoclinic bifurcation from a nonlinear dynamics perspective. By constructing a limit cycle scaling law and a manifold tangent space, the boundary of the attraction domain of the inverter grid-connected system is accurately characterized, enabling rapid assessment of transient synchronous stability margins within different bifurcation dominant regions. This method effectively reveals the mapping relationship between nonlinear bifurcation mechanisms and the dynamic behavior of inverter grid-connected systems, transforming the complex time-domain stability problem into a geometric identification problem of manifold structure and bifurcation characteristics, significantly reducing the simulation burden and improving identification efficiency and criterion clarity. This disclosure can provide a theoretical foundation and engineering support for inverter control strategy optimization, operational boundary determination, and disturbance response assessment in power systems, and has broad application prospects.

[0158] Finally, it should be noted that the above content is only used to illustrate the technical solution of the present invention, and is not intended to limit the scope of protection of the present invention. Simple modifications or equivalent substitutions made by those skilled in the art to the technical solution of the present invention do not depart from the essence and scope of the technical solution of the present invention.

Claims

1. A method for identifying the dominant bifurcation mode of transient synchronous stability in an inverter grid-connected system, characterized in that: Includes the following steps: Obtain inverter parameters and power parameters of the inverter grid-connected system; the inverter parameters include the proportional coefficient of the phase-locked loop PI control, the integral coefficient of the phase-locked loop PI control, and the current reference value; the power parameters include the reference angular frequency, the equivalent inductance of the transmission line, and the grid connection point voltage. The bifurcation equivalent parameters are obtained based on the inverter parameters and the electrical parameters; the bifurcation equivalent parameters include a first equivalent parameter, a second equivalent parameter, a third equivalent parameter, and a fourth equivalent parameter; The first equivalent parameter is: ； The second equivalent parameter is: ； The third equivalent parameter is: ； The fourth equivalent parameter is: ； In the formula, As the first equivalent parameter, The second equivalent parameter, As the third equivalent parameter, The fourth equivalent parameter, This is the proportional coefficient for phase-locked loop PI control. The integral coefficient of the phase-locked loop PI control is . This is the current reference value. For the equivalent inductance of the transmission line, The voltage at the grid connection point. The reference angular frequency; Based on the stable equilibrium point, the real part of the Hopf complex normal form coefficients and the normalized bifurcation parameters are obtained according to the generalized rocking equation and the bifurcation equivalent parameters; the real part of the Hopf complex normal form coefficients is: ； In the formula, For the real part of the coefficients of the Hopf complex normal form, This is an intermediate expression. ; The normalized bifurcation parameter is obtained by subtracting half the difference between the third equivalent parameter and the fourth equivalent parameter; The limiting cycle amplitude is obtained by taking the square root of the ratio of the normalized bifurcation parameter to the real part of the Hopf complex normal form coefficient; The transient stability margin is obtained based on the geometric distance between the stable manifold at the unstable equilibrium point and the stable equilibrium point. Obtaining the transient stability margin based on the geometric distance between the stable manifold at the unstable equilibrium point and the stable equilibrium point includes: obtaining the identity matrix; obtaining a first coordinate and a second coordinate, wherein the first coordinate is the coordinate of the stable equilibrium point and the second coordinate is the coordinate of the unstable equilibrium point; Linearize the inverter grid-connected system at the second coordinate and obtain the Jacobian matrix; Based on the Jacobian matrix, obtain the unit eigenvectors corresponding to the negative eigenvalues; The projection operator is obtained based on the unit eigenvector; The transient stability margin is obtained based on the identity matrix, the projection operator, the first coordinate, and the second coordinate; the transient stability margin is: ； In the formula, For transient stability margin, As a unit array, For unit eigenvectors, For projection operators, superscript Indicates transpose. As the first coordinate, The second coordinate; The dominant bifurcation mode of the inverter grid-connected system is identified based on the limiting loop amplitude and the transient stability margin.

2. The method for identifying the dominant bifurcation mode of transient synchronization stability in an inverter grid-connected system according to claim 1, characterized in that: Identifying the dominant bifurcation mode of the inverter grid-connected system based on the limiting loop amplitude and the transient stability margin includes: When the limiting loop amplitude is less than the transient stability margin, the inverter grid-connected system is in a transient synchronous instability mode dominated by Hopf bifurcation. When the limiting loop amplitude is equal to the transient stability margin, the inverter grid-connected system is in a critical state of homogeneous bifurcation. When the limiting loop amplitude is greater than the transient stability margin, the inverter grid-connected system is in a transient synchronous instability mode dominated by co-homogeneous bifurcation.

3. The method for identifying the dominant bifurcation mode of transient synchronization stability in an inverter grid-connected system according to claim 1 or 2, characterized in that: Based on a stable equilibrium point, the steps for obtaining the real part of the Hopf complex normal form coefficients and the normalized bifurcation parameters according to the generalized rocking equation and the bifurcation equivalent parameters are as follows: The generalized rocking equation is simplified to the Hopf normal form; Based on the stable equilibrium point, the real part and imaginary part of the Hopf complex normal coefficients are obtained by solving the Hopf normal form. Based on the real part of the coefficients of the Hopf complex normal form and the imaginary part of the coefficients of the Hopf complex normal form, the polar coordinate Hopf normal form is obtained according to the generalized rocking equation; The normalized bifurcation parameters are obtained based on the polar coordinate Hopf canonical form.

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