Transient stability boundary determination method and device of network construction type converter system and medium

Abstract

The invention provides a transient stability boundary determination method and device of a network-forming converter system and a medium, and belongs to the technical field of transient stability boundary determination. The method comprises the following steps: constructing a nonlinear autonomous system model of a network construction type new energy generator group; solving all I-class unstable equilibrium points of the nonlinear autonomous system model; constructing a local stable manifold along the stable feature vector direction of the I-type unstable equilibrium point; constructing a global stable manifold of the I-type unstable equilibrium point; and combining global stability manifolds of all I-type unstable equilibrium points to form a transient stability boundary of the system, and verifying a closed state at an infinity position based on an infinity singular point theory. According to the method, through the constructed nonlinear autonomous system model, influence factors of a stability boundary and a stability domain after the system is subjected to large disturbance are researched based on a nonlinear stability manifold theory, and forms of a saddle point boundary line and a trajectory of the system at infinity are researched, so that the transient synchronization stability of the system is improved.

Description

Technical Field

[0001] This invention relates to the field of transient stability boundary determination technology, and specifically to a method, apparatus and medium for determining the transient stability boundary of a grid-type converter system. Background Technology

[0002] Currently, relevant departments are vigorously developing new energy sources, represented by wind power and photovoltaics. Unlike traditional synchronous generator sets, new energy generator sets connect to the grid through power electronic interfaces, such as grid-connected converters, exhibiting characteristics like low inertia and poor disturbance rejection capabilities, profoundly altering the dynamic characteristics of the power system. The continuous increase in the penetration rate of new energy sources reduces the stability of the power system under large disturbances, posing a significant challenge to its stable operation. In recent years, some transient faults have occurred due to the loss of synchronization between new energy equipment and the grid after experiencing large disturbances such as voltage dips. When grid-connected converters are connected to a strong grid, the interaction between the power synchronization loop and the grid may cause low-frequency oscillations in the grid, further leading to power angle instability, which has a significant impact on the safe and reliable operation of the grid.

[0003] Currently, research on grid-connected renewable energy systems lacks sufficient information regarding the stability boundary of the system after large disturbances. Most studies rely on the equal area rule and energy function method to solve the stability boundary, which is relatively conservative. There is a lack of theoretical support for accurate quantification methods of the stability boundary of grid-connected nonlinear systems with grid-connected converters. Therefore, determining the stability boundary of grid-connected renewable energy systems under large disturbances is of great significance, as it facilitates rapid assessment of stability margin during fault processes and enhances the grid's security and defense capabilities. Summary of the Invention

[0004] The purpose of this invention is to provide a method, apparatus, and medium for determining the transient stability boundary of a grid-connected converter system, which is used to accurately quantify the transient stability boundary of the grid-connected converter system under large disturbances, so as to accurately evaluate the system stability performance and guide the optimization of grid parameters, thereby improving the safety and stability of the grid with a high proportion of new energy.

[0005] To achieve the above objectives, this invention provides a method for determining the transient stability boundary of a grid-connected converter system, comprising: constructing a nonlinear autonomous system model of a grid-connected renewable energy generator group based on a grid-connected renewable energy generator group scenario; solving for all Type I unstable equilibrium points in the nonlinear autonomous system model; for each solved Type I unstable equilibrium point, performing local linearization using Taylor expansion, and constructing a local stable manifold along the direction of the stable eigenvector of the Type I unstable equilibrium point; at each Type I unstable equilibrium point, selecting an initial set of points on the local stable manifold, and performing numerical integration on the system trajectory in the reverse time direction to construct the global stable manifold of the Type I unstable equilibrium point; merging the global stable manifolds of all Type I unstable equilibrium points to form the transient stability boundary of the system, and verifying the closure state of the transient stability boundary of the system at infinity based on the singularity theory at infinity.

[0006] Optionally, the nonlinear autonomous system model for constructing a grid-connected new energy generator group includes: defining virtual power angle and angular velocity; establishing a power balance equation containing virtual inertia and damping; and embedding grid strength parameters into the electromagnetic power of the power balance equation to obtain the nonlinear autonomous system model.

[0007] Optionally, solving for all Type I unstable equilibrium points of the nonlinear autonomous system model includes: constructing equilibrium condition equations based on the nonlinear autonomous system model; using the unique equilibrium point as a reference, constructing an initial unstable equilibrium point adjacent to the target saddle point by applying perturbations to the complementary directions of the work angles; iteratively solving for the equilibrium position using the Newton-Raphson method; and verifying that the equilibrium point satisfies the dynamic characteristics of Type I unstable equilibrium points.

[0008] Optionally, the construction of equilibrium condition equations based on the nonlinear autonomous system model includes: establishing a set of differential equations containing virtual power angle and angular velocity dual state variables based on the nonlinear autonomous system model; and degenerating the dynamic differential constraint into a static power-power angle balance relationship by forcing the virtual angular velocity and its derivative to be zero.

[0009] Optionally, the step of performing local linearization using Taylor expansion for each solved type I unstable equilibrium point and constructing a locally stable manifold along the direction of the stable eigenvector of the type I unstable equilibrium point includes: performing a Taylor series expansion for each type I unstable equilibrium point; solving the Jacobian matrix at the type I unstable equilibrium point, selecting eigenvalues ​​with negative real parts, and calculating the stable eigenvectors corresponding to the eigenvalues ​​with negative real parts; and uniformly sampling within a preset neighborhood radius of the type I unstable equilibrium point along the direction of the stable eigenvector to obtain the discrete point set of the locally stable manifold.

[0010] Optionally, at each of the Type I unstable equilibrium points, selecting an initial set of points on the locally stable manifold and numerically integrating the system trajectory along the reverse time direction to construct the globally stable manifold of the Type I unstable equilibrium point includes: selecting initial points for driving the inverse time integration based on the discrete point set of the locally stable manifold; reconstructing the time evolution direction of the nonlinear autonomous system model based on the initial points, replacing the forward time variables with reverse time variables; integrating the system trajectory along the reverse time axis using the fourth-order Runge-Kutta algorithm; dynamically truncating the integration path by setting a dual-channel termination criterion; and merging all valid integration trajectories to construct the globally stable manifold of the Type I unstable equilibrium point.

[0011] Optionally, the step of reconstructing the time evolution direction of the nonlinear autonomous system model based on the initial point and replacing the forward time variable with the reverse time variable includes: introducing the reverse time variable to replace the original time variable and establishing a mapping relationship between the reverse time variable and the original time variable; keeping the original nonlinear autonomous system model structure unchanged, reversing the sign of the derivative term in the original system state equation to construct the reverse system; and verifying that there is no explicit time term in the reverse system.

[0012] Optionally, the step of merging the global stable manifolds of all Type I unstable equilibrium points to form the system transient stability boundary, and verifying the closure state of the system transient stability boundary at infinity in phase space based on the singularity theory at infinity, includes: integrating the global stable manifolds of all Type I unstable equilibrium points, constructing the system transient stability boundary through topological union, and verifying the closure state of the stability boundary at infinity in phase space based on the singularity theory at infinity; calculating the limit cut-off angle based on the system transient stability boundary, and solving the limit cut-off time through linear interpolation of the fault process power angle sequence; and scanning the influence of four-dimensional parameters—virtual inertia, damping coefficient, active power command, and grid strength—on the system transient stability boundary using the control variable method, generating a parameter optimization map to guide grid planning and controller tuning.

[0013] According to a second aspect of this application, a control device is provided for implementing a transient stability boundary determination method for a grid-type converter system. The control device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. The processor executes the computer program to implement the transient stability boundary determination method.

[0014] According to a third aspect of this application, a machine-readable storage medium is provided, on which instructions are stored, causing a machine to execute the transient stability boundary determination method for the grid-type converter system described above.

[0015] The above technical solution, based on the constructed nonlinear autonomous system model, studies the stability boundary and stability domain influencing factors after the system is subjected to large disturbances based on the nonlinear stable manifold theory, judges the closure state of the stability boundary trajectory at infinity based on the singularity theory at infinity, and further studies the saddle point boundary line and the shape of the trajectory at infinity. Thus, it can provide a clearer understanding of the transient stability mechanism of the grid-connected system of grid-connected converters and improve the transient synchronous stability of the system.

[0016] Other features and advantages of the present invention will be described in detail in the following detailed description section. Attached Figure Description

[0017] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the following detailed description to explain the invention, but do not constitute a limitation thereof. In the drawings:

[0018] Figure 1 A flowchart is drawn to illustrate the transient stability boundary of a grid-connected renewable energy system.

[0019] Figure 2 A schematic diagram showing the positions of the sphere at infinity and the phase plane α;

[0020] Figure 3 Equivalent circuit diagram of a grid-connected system for a grid-connected converter;

[0021] Figure 4 This is a schematic diagram of the GFM-VSC voltage and current dual closed-loop control strategy;

[0022] Figure 5 This is a schematic diagram of the GFM-VSC virtual synchronization control strategy;

[0023] Figure 6 Transient stability boundary and phase trajectory diagram of a grid-type converter;

[0024] Figure 7 Stability boundary diagrams of GFM after perturbation under different virtual inertia;

[0025] Figure 8 Stability boundary diagrams of GFM after disturbance under different damping coefficients;

[0026] Figure 9 Stability boundary diagrams of GFM after disturbance under different active power reference commands;

[0027] Figure 10 This is a stability boundary diagram of GFM after disturbance under different electrical distances. Detailed Implementation

[0028] The following is in conjunction with the appendix Figure 1 -Appendix Figure 10The specific implementation methods of the embodiments of the present invention will be described in detail below. It should be understood that the specific implementation methods described herein are only for illustrating and explaining the embodiments of the present invention, and are not intended to limit the embodiments of the present invention.

[0029] It should be noted that the acquisition, transmission, storage, use, and processing of data in the technical solution of this application all comply with the relevant provisions of national laws and regulations. In the embodiments of this application, certain existing industry solutions such as software, components, and models may be mentioned. These should be considered exemplary, intended only to illustrate the feasibility of implementing the technical solution of this application, and do not imply that the applicant has already used or necessarily used such solutions.

[0030] In the process of realizing this invention, the inventors of this application discovered that traditional transient stability analysis methods for power systems are mostly based on the equal area rule and energy function method to solve the stability boundary. Neglecting damping leads to overly conservative evaluation results and lacks accurate quantitative theoretical support for the stability boundary of grid-connected nonlinear systems with grid-connected converters.

[0031] Example 1

[0032] Reference Figure 1 , Figure 2 This is the first embodiment of the present invention, which provides a method for determining the transient stability boundary of a grid-connected system with a grid-connected converter, including:

[0033] S100: Based on the grid connection scenario of grid-connected new energy generator groups, a nonlinear autonomous system model of grid-connected new energy generator groups is constructed.

[0034] In this embodiment, virtual power angle and angular velocity are defined; a power balance equation containing virtual inertia and damping is established, and the power grid strength parameters are embedded into the electromagnetic power of the power balance equation to obtain a nonlinear autonomous system model.

[0035] In this embodiment of the application, the expression for the nonlinear autonomous system model is as follows:

[0036]

[0037] Where δ represents the virtual power angle of the converter, J represents the virtual moment of inertia coefficient, D represents the virtual damping coefficient, and P ref P represents the active power reference value. em This refers to the electromagnetic power transmitted from new energy sources to the power grid through a grid-connected converter.

[0038] In the above nonlinear autonomous system model, the electromagnetic power transmitted from new energy sources to the power grid through grid-connected converters is calculated as follows:

[0039]

[0040] Among them, U g U represents the voltage amplitude of the power grid. pcc X represents the voltage amplitude at the grid connection point. Σ δ represents the total reactance of the system. m This represents the virtual power angle of a grid-type converter.

[0041] S200: Solve for all Type I unstable equilibrium points in the nonlinear autonomous system model.

[0042] In this embodiment, equilibrium condition equations are constructed based on a nonlinear autonomous system model; an initial unstable equilibrium point adjacent to the target saddle point is constructed by applying a perturbation to the complementary direction of the work angle using a unique equilibrium point as a reference; the equilibrium position is solved iteratively using the Newton-Raphson method; and the equilibrium point is verified to satisfy the dynamic characteristics of a type I unstable equilibrium point.

[0043] In a preferred embodiment of this application, a system of differential equations containing virtual power angle and angular velocity dual state variables is established based on a nonlinear autonomous system model; by forcing the virtual angular velocity and its derivative to be zero, the dynamic differential constraint is degenerated into a static power-power angle balance relationship.

[0044] In this embodiment, the equilibrium condition equation is as follows:

[0045]

[0046] Where, δ m The virtual power angle of the grid-type converter is represented by ω, the actual angular velocity by ω0, the rated angular velocity by Δω, the difference between the actual and rated angular angular velocities by J, the virtual moment of inertia coefficient by D, and the virtual damping coefficient by P. ref P represents the active power reference value. em This refers to the electromagnetic power transmitted from new energy sources to the power grid through a grid-connected converter.

[0047] The above equilibrium condition equations can be simplified into transcendental equations, which are as follows:

[0048] g(δ)=P ref -P em sinδ m =0

[0049] Where g(δ) represents the transcendental equation corresponding to the above equilibrium condition, δ m P represents the virtual power angle of a grid-type converter. ref P represents the active power reference value. em This refers to the electromagnetic power transmitted from new energy sources to the power grid through a grid-connected converter.

[0050] In a preferred embodiment of this application, an initial unstable equilibrium point adjacent to the target saddle point is constructed by applying a disturbance to the direction of complementary power angles, based on a unique equilibrium point.

[0051] The formula for calculating the work angle value corresponding to the stable equilibrium point is as follows:

[0052]

[0053] Where, δ SEP P represents the work angle value corresponding to the stable equilibrium point. ref P represents the active power reference value. em This refers to the electromagnetic power transmitted from new energy sources to the power grid through a grid-connected converter.

[0054] The formula for constructing the initial unstable equilibrium point adjacent to the target saddle point by applying a perturbation to the direction of complementary power angle is as follows:

[0055] δ0=π-δ SEP +Δ

[0056] Where δ0 represents the initial unstable equilibrium point obtained after applying a perturbation at the unstable equilibrium point, δ SEP The value represents the work angle corresponding to the stable equilibrium point, and Δ represents the disturbance.

[0057] The equilibrium position is determined iteratively using the Newton-Raphson method, with the initial value calculated as x0 = [δ0, 0]. T x0 represents the initial value calculated by the Newton-Raphson method, T represents the transpose, and the iterative formula is as follows:

[0058] x n+1 =x n -J -1 (x n )·f(x n )

[0059]

[0060] Among them, X n X represents the state vector at the current iteration point. n =[δ n ,ω n ] T X n+1 X represents the state vector at the next iteration point. n+1 =[δ n+1 ,ω n+1 ] T n represents the iteration step index, f(x) represents the nonlinear autonomous system function, J(x) represents the Jacobian matrix, and x represents any point in the continuous state space. n ) represents the Jacobian matrix in X nThe value at J -1 (x n ) represents the inverse of the Jacobian matrix, ω represents the angular velocity of the grid converter, and P ref P represents the active power reference value. em This represents the electromagnetic power transmitted from new energy sources to the grid through a grid-connected converter, where D represents the virtual damping coefficient, and δ... m J represents the virtual power angle of the grid-type converter, and J represents the virtual inertia.

[0061] It should be noted that f1 represents the first term in f(x), namely the rate of change of the work angle. f2 represents the second term in f(x), namely angular acceleration.

[0062] In this embodiment of the application, the conditions for iterative convergence are as follows:

[0063] ||f(x n )||2<10 -6 And ||x n+1 -x n ||2<10 -6

[0064] In a preferred embodiment of this application, the equilibrium point is verified to satisfy the dynamic characteristics of a Type I unstable equilibrium point. If the Jacobian matrix J(x) has one and only one positive real eigenvalue and the real parts of the other eigenvalues ​​are strictly negative, and the ratio of the absolute value of the imaginary part to the absolute value of the real part of the eigenvalues ​​of the unstable mode is less than 0.1, ensuring that the instability of the system is mainly dominated by non-oscillatory monotonic divergence, then the unstable equilibrium point is a Type I unstable equilibrium point.

[0065] S300: For each solved Type I unstable equilibrium point, local linearization is performed using Taylor expansion, and a locally stable manifold is constructed along the direction of the stable eigenvector of the Type I unstable equilibrium point.

[0066] In this embodiment, a Taylor series expansion is performed on each type I unstable equilibrium point; the Jacobian matrix at the type I unstable equilibrium point is solved, eigenvalues ​​with negative real parts are selected, and stable eigenvectors corresponding to the eigenvalues ​​with negative real parts are calculated; along the direction of the stable eigenvectors, uniform sampling is performed within a preset neighborhood radius of the type I unstable equilibrium point, centered on the unstable equilibrium point, to obtain a discrete set of points of the local stable manifold.

[0067] In a preferred embodiment of this application, a Taylor series expansion is performed on each type I unstable equilibrium point, and local linearization is achieved using the Taylor expansion to solve for the Jacobian matrix at the type I unstable equilibrium point:

[0068]

[0069] Where J represents the Jacobian matrix, J represents the virtual inertia, and δ u The value represents the work angle corresponding to the unstable equilibrium point, and D represents the virtual damping coefficient.

[0070] Solve for the stable eigenvalues ​​and their corresponding eigenvectors at the unstable equilibrium points using the Jacobian matrix:

[0071]

[0072] Re(λ s )<0

[0073] Jv s =λ s v s

[0074] Where det() represents solving for the eigenvalues ​​of the characteristic equation, λ represents the eigenvalue, and λ s V represents the eigenvalue of the stable equilibrium point. S Let J represent the eigenvector corresponding to the stable equilibrium point, J represent the virtual inertia, J represent the Jacobian matrix, I represent the identity matrix, Re() represent the real part of the eigenvalues, and δ represent the eigenvectors. u The work angle value corresponding to the unstable equilibrium point is represented by D, and the damping coefficient is represented by P. em This refers to the electromagnetic power transmitted from new energy sources to the power grid through a grid-connected converter.

[0075] The formula for constructing a locally stable manifold at an unstable equilibrium point is as follows:

[0076]

[0077] in, This represents the locally stable manifold at the unstable equilibrium point UEP, where x represents the state variable, x = [δ m ,ω] T x UEP Represents an unstable equilibrium point, v s Let represent the stable eigenvector, corresponding to the negative real part eigenvalue, α represent the displacement coefficient along the stable eigenvector, and ε represent the local neighborhood radius.

[0078] S400: At each type I unstable equilibrium point, an initial set of points is selected on the local stable manifold, and the system trajectory is numerically integrated in the reverse direction of time to construct the global stable manifold of that type I unstable equilibrium point.

[0079] In this embodiment, based on the discrete point set of the locally stable manifold, initial points for driving inverse-time integration are selected; based on the initial points, the time evolution direction of the nonlinear autonomous system model is reconstructed, and the forward time variables are replaced with inverse time variables; the fourth-order Runge-Kutta algorithm is used to integrate the system trajectory along the inverse time axis; a dual-channel termination criterion is set to dynamically truncate the integration path; all valid integration trajectories are merged to construct the globally stable manifold of the type I unstable equilibrium point.

[0080] In a preferred embodiment of this application, an inverse time variable is introduced to replace the original time variable, and a mapping relationship between the inverse time variable and the original time variable is established; the original nonlinear autonomous system model structure remains unchanged, the sign of the derivative term in the original system state equation is reversed, and an inverse system is constructed; it is verified that there is no explicit time term in the inverse system.

[0081] In this embodiment, the time evolution direction of the nonlinear autonomous system model is reconstructed by replacing the forward time variable with the reverse time variable, as shown in the following formula:

[0082]

[0083] Where x represents the system state variable, τ represents the inverse time variable, f(x) represents the state-space equation of the system integral, and P M P represents mechanical input power. em t represents electromagnetic power, and t represents real time.

[0084] With a step size Δτ = 0.01s, numerical integration is performed using the fourth-order Runge-Kutta method (RK4):

[0085]

[0086] Where, x n Let x represent the current step state vector. n =[δ n ,ω n ] T x n+1 Let x represent the next state vector. n+1 =[δ n+1 ,ω n+1 ] T Δτ represents the reverse time integration step size, and k1~k4 represent the slope of the current point.

[0087] Take N points (N>50) uniformly on the locally stable manifold, and for each Integrate until the termination condition is met.

[0088]

[0089] in, This represents the initial value chosen for integration, x. UEP Let ε represent a type I unstable equilibrium point, ε represent the neighborhood radius, N represent the number of sampling points, and α represent the number of sampling points. i This represents the offset coefficient along the direction of the stable eigenvector.

[0090] It should be noted that a globally stable manifold is the set of all trajectories that converge to the same unstable equilibrium point. The globally stable manifold is obtained by collecting all valid trajectories generated by inverse integration along time from the neighborhood of the unstable equilibrium point, covering all paths that asymptotically converge to that unstable equilibrium point.

[0091] S500: The global stable manifold that merges all Type I unstable equilibrium points forms the transient stable boundary of the system, and the closed state of the transient stable boundary at infinity in the phase space is verified based on the singularity theory at infinity.

[0092] In this embodiment, the global stable manifold of all Type I unstable equilibrium points is integrated, and the transient stability boundary of the system is constructed by topological union. The closed state of the stability boundary at infinity in phase space is verified based on the theory of singularities at infinity. The limit cut-off angle is calculated based on the transient stability boundary of the system, and the limit cut-off time is solved by linear interpolation of the power angle sequence of the fault process. The influence of four-dimensional parameters of virtual inertia, damping coefficient, active power command and grid strength on the transient stability boundary of the system is scanned by the control variable method, and a parameter optimization map is generated to guide grid planning and controller tuning.

[0093] It should be noted that a stable manifold is the set of all solution curves that tend towards an equilibrium point x0. For this equilibrium point x0, there exists an attractive region, within which every trajectory gradually tends towards that point over time, denoted as set A(x0), whose boundary... This is the boundary of the stability region at that equilibrium point.

[0094] If x0 is the hyperbolic equilibrium point of the system, then the stable manifold of x0 is defined as:

[0095]

[0096] An unstable manifold of x0 can be defined as:

[0097]

[0098] Where φ(t,x) is the solution function of the nonlinear autonomous system model, t represents the time variable, t→+∞ indicates that time approaches positive infinity, t→-∞ indicates that time approaches negative infinity, i.e., inverse integration to infinity, x represents the system state variable, and R n Let W represent an n-dimensional real vector space, x0 represent an equilibrium point of the system, and W s (x0) denotes the stable manifold of x0, Wu (x0) denotes an unstable manifold of x0.

[0099] By merging the stable manifolds of all unstable equilibrium points, the stable boundary of the system is formed:

[0100]

[0101] in, This represents the locally stable manifold of the system at the unstable equilibrium point. This represents the union of the trajectories generated from N initial points. Indicates the system starts from the initial point The starting stream function, τ∈[0,τ max ] indicates the time range of the inverse integration.

[0102] In a preferred embodiment of this application, for a given two-dimensional system Where x and y represent the system's state variables, corresponding to the system's power angle δ. m and angular velocity ω, Let P and Q denote the derivative of the corresponding function, and let P and Q denote the nonlinear functions of the state variables. The system trajectory is presented in the xy plane, denoted as plane α. To study the distribution of the phase trajectory at infinity, the trajectory is mapped onto the sphere S. 2- ={(X,Y,Z):X 2 +Y 2 +Z 2 =1, Z≤0}, (X,Y,Z) represents the mapping to the sphere S 2- Points on X, when X 2 +Y 2 As the distance approaches infinity (→∞), Z→0, meaning the point at infinity in the plane maps to the equator of the sphere. This sphere is tangent to plane α at the South Pole. For any point N on the plane, the line connecting the center O of the sphere to that point intersects the opposite radial points N′ and N″ on the sphere. Except for points on the equator, there is a one-to-one correspondence between the opposite radial points on the sphere and points on plane α. For example... Figure 2 As shown, the three points O(0,0,0), N(x,y,-1), and N(X,Y,Z) satisfy the coordinate transformation relationship.

[0103]

[0104] Where X, Y, and Z represent the sphere S, respectively. 2- The three-dimensional coordinates on the phase plane α, x and y represent the state variable coordinates on the two-dimensional phase plane α, and Δxy represents the scaling factor used to ensure that the mapped coordinates satisfy the following conditions: 2 +Y 2 +Z 2 =1.

[0105] In the above formula, Δxy=(1+x 2 +y 2 ) 1 / 2 According to the above formula, all points on the plane can be mapped to the sphere.

[0106] In a preferred embodiment of this application, in order to indirectly obtain the relationship between the point at infinity and the point on the equator, a Poincaré mapping is performed, first letting:

[0107]

[0108] The first transformation converts the (x, y) coordinates to the new coordinates (u, z), which, when rearranged, yields:

[0109]

[0110] In the above formula, This represents the derivative of variable u with respect to time t. Let represent the derivative of variable z with respect to time t, where u and z are both variables of the first transformation, u represents the slope variable used to describe the trajectory direction, and z represents the scaling variable, and n is a non-negative integer; P * Q * These are the irreducible polynomials after the first transformation, the singularity at infinity (i.e., the singularity at the equator), and the corresponding system of equations {P}. * (u,0)=0,Q * The solution to (u,0)=0} is given by:

[0111]

[0112] The second transformation changes the (x, y) coordinates to the new coordinates (v, z), which, when rearranged, yields:

[0113]

[0114] In the above formula This represents the derivative of variable v with respect to time t. Let v represent the derivative of variable z with respect to time t, v and z represent the variables of the second transformation, and m be a non-negative integer; if the system of equations If the system contains a zero solution, then the intersection points D and D' of the Y-axis with the equator are both singularities at infinity.

[0115] It should be noted that traditional transient stability analysis methods suffer from openness defects in the stability region boundary because they do not consider the asymptotic behavior of the system trajectory at infinity. By introducing the Poincaré spherical mapping, the dynamic characteristics at infinity are transformed into an analytical problem at the equatorial singularity. The characteristics of the singularity at infinity, together with the saddle point boundary, form a closed curve, rigorously delineating the stable and unstable regions. If the singularity at infinity is stable, it is the endpoint of a finite divergent trajectory; if it is unstable, it is the starting point of a finite convergent trajectory.

[0116] In a preferred embodiment of this application, the Runge-Kutta algorithm is used to calculate the power angle sequence [δ0, δ1, δ2 ~ δ] of the grid-connected (GFM) inverter during a fault. n ] and the fault duration sequence [t0, t1, t2~t n The dynamic equation for calculating the inverter's limit cut-off time is shown below:

[0117]

[0118] Where δ0 and t0 are the initial values ​​of the fault duration sequence and the power angle sequence, respectively; t0 = 0 indicates that the fault start time is set as the zero point, and δ0 = δ SEP This indicates that the power angle of the initialized GFM inverter is the stable equilibrium point before the fault, δ SEP Let dδ / dt be the power angle value corresponding to the power balance point of the GFM inverter, and let P be the dynamic equation representing the change in the GFM power angle during a fault. ref P represents the active power reference value. em J represents the electromagnetic power transmitted from the new energy source to the power grid through the grid-connected converter, and J represents the virtual inertia.

[0119] It should be noted that the limiting cutoff angle β is the maximum power angle value that the GFM inverter can achieve to maintain transient stability. The output active power of the GFM inverter has an approximately sinusoidal relationship with the power angle. Therefore, in the interval [0,π], the transcendental equation will have two numerical solutions with a value of δ, and the solution between [0,π / 2] is δ. SEP The solution between [π / 2, π] is the limiting cut-off angle β of the GFM inverter.

[0120] In a preferred embodiment of this application, the power angle values ​​of the GFM inverter during the fault period [δ0, δ1, δ2 ~ δ] are... n Compared with the limit resection angle, if δ i If the value is less than β, increment i by 1 and continue iterating and comparing it with β, where i is the index, until δ is determined. i+1 Until ≥β. Since there is a one-to-one correspondence between the values ​​in the fault duration sequence and the power angle sequence, the limiting cut-off time of the grid-type inverter satisfies t. i ≤t cc ≤t i+1 , t cc The limiting cut-off time of a grid-connected inverter is represented by the mean value theorem. Therefore, the formula for calculating the limiting cut-off time of a grid-connected inverter is as follows:

[0121]

[0122] Among them, t i-1 , t iδ represents the discrete fault time point generated by the Runge-Kutta method iteration. i δ i-1 Indicates the corresponding t i , t i-1 , where β is the power angle value of the grid-type converter at time t, and β represents the limit cut-off angle of the grid-type converter.

[0123] The proposed method for calculating the limit cut-off time is a significant improvement over traditional techniques. It generates a dynamic sequence of power angles during a fault through the Runge-Kutta method of discrete iteration. Combined with the limit cut-off angle constraint and linear interpolation algorithm, the limit cut-off time can be accurately located directly from the discrete sequence. This overcomes the complex defects of methods such as the Newton-Raphson method, which require repeated solutions to high-dimensional nonlinear equations. It provides an efficient theoretical tool for online evaluation of transient stability of grid-type converters.

[0124] Example 2

[0125] Reference Figures 3-10 This is the second embodiment of the present invention, which provides a method for determining the transient stability boundary of a grid-connected system with a grid-connected converter, taking a wind farm grid-connected system with a grid-connected converter as an example.

[0126] In the embodiments of this application, Figure 3 This is the equivalent circuit diagram of the grid-connected system. The grid-connected converter employs a virtual synchronous generator (VSG) control strategy, such as... Figure 4 and Figure 5 As shown, its grid-type (GFM) control section consists of an active power loop and voltage and current dual closed loops. The VSG simulates the motion characteristics of the synchronous generator rotor through a swing equation, autonomously generates the output voltage phase, and actively constructs the grid frequency reference. Reactive power-voltage control and inner loop voltage control realize the terminal voltage control of the VSG and provide a current reference. The dynamic characteristics of the GFM can be changed by changing the parameters of the power control loop.

[0127] For example, assuming the system is in a stable operating state before the fault occurs, a 90% voltage drop occurs at 2.0s, and the fault is cleared after 0.3s, calculate the system Jacobian matrix based on the system operating conditions and control parameters:

[0128]

[0129] Regarding the equilibrium point (δ) s ,0), exists Therefore, the characteristic equation of the Jacobian matrix at this equilibrium point is:

[0130]

[0131] Where, p(λ) s This represents the characteristic equation of the Jacobian matrix at a stable equilibrium point.

[0132] Solve for p(λ). s The eigenvalues ​​are:

[0133]

[0134] Where, λ 1,2 Indicates that the system is in (δ) s The eigenvalues ​​of the characteristic equation at (0) are P. M This represents the mechanical power input to the grid-type converter.

[0135] Continuing with the example above, regarding the stable equilibrium point (δ) s If damping is ignored, i.e., D = 0, the eigenvalue λ 1,2 For a pair of conjugate imaginary roots, the stable equilibrium point is (δ). s With λ as the center; if the system has negative damping D < 0, λ 1,2 There must be a stable equilibrium point (δ) with a positive real part. s λ(0) represents an unstable node or focus; if the system has positive damping D > 0, λ 1,2 The real parts are all negative, and the stable equilibrium point is (δ). s ,0) is a stable node or focus.

[0136] For the unstable equilibrium point (δ) u ,0), by The relation can be obtained Therefore, the characteristic equation of the Jacobian matrix at this equilibrium point is:

[0137]

[0138] Where, p(λ) u The characteristic equation of the Jacobian matrix at the unstable equilibrium point is given.

[0139] Its characteristic values ​​are:

[0140]

[0141] Where, λ' 1,2 Indicates that the system is in (δ) u The eigenvalues ​​of the characteristic equation at (0, 0).

[0142] Clearly, regardless of whether the system has positive damping, no damping, or negative damping, λ' 1,2 All are real roots with opposite signs, and the equilibrium point (δ) u ,0) is a saddle point.

[0143] In this embodiment, based on the established nonlinear autonomous system model of grid-connected new energy, the stability boundary of the system under large disturbance is determined using the nonlinear stable manifold method. The correctness of the stability boundary is judged by combining the phase trajectory of the system after the disturbance. Figure 6 As shown, when the initial operating point is in the stable region, the state trajectory is attracted due to damping consumption and eventually converges to the stable equilibrium point. Otherwise, the state trajectory will diverge, the angular velocity will continue to increase, and eventually lead to transient instability.

[0144] In a preferred embodiment of this application, the influencing factors of the stability boundary of a grid-type converter are studied:

[0145] Example 1: By changing the virtual inertia J and damping coefficient D of a grid-type converter, the influence of different active power control loop parameters on the stability boundary is studied, such as... Figure 7 , Figure 8 As shown.

[0146] Example 2: Changing the system operating conditions, setting different active power commands, grid impedances, and voltage sag depths, will cause the system equilibrium point and stability region to change accordingly, such as... Figure 9 , Figure 10 As shown.

[0147] It should be noted that the stability boundaries plotted using the steady manifold method under different control parameters and operating conditions yield the following results: When the active power loop control parameters J or D change, the system equilibrium point remains unchanged, and the stability boundary gradually increases as J decreases or D increases, thus improving the system stability margin; when the operating conditions change, the initial active power reference command increases, causing both the stable and unstable equilibrium points to shift to the right, the stability boundary to contract, and the system transient stability margin to improve; when the grid impedance decreases, the system short-circuit ratio increases, the grid strength increases, the equilibrium point shifts to the left, the stability boundary to expand, and the system transient stability margin to improve.

[0148] In summary, for grid-connected new energy systems, changing control parameters or adopting better operating conditions, such as appropriately reducing the virtual inertia of the converter or increasing the damping effect, or appropriately reducing the active power command or reducing the line impedance, can significantly improve the transient synchronous stability of the system.

[0149] The present invention also provides a control device for implementing a transient stability boundary determination method for a grid-type converter system. The control device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. The processor executes the computer program to implement the transient stability boundary determination method.

[0150] This invention provides a machine-readable storage medium storing instructions that cause a machine to execute the transient stability boundary determination method for the grid-type converter system described above.

[0151] This invention provides a processor for running a program, wherein the program executes a method for determining the transient stability boundary of a grid-connected system with a grid-connected converter.

[0152] This invention provides a device including a processor, a memory, and a program stored in the memory and executable on the processor. When the processor executes the program, it implements a method for determining the transient stability boundary of a grid-connected system with a grid-connected converter. The device described herein can be a server, PC, tablet, mobile phone, etc.

[0153] This application also provides a computer program product that, when executed on a data processing device, is suitable for performing a method for determining the transient stability boundary of a grid-connected system with a grid-connected converter.

[0154] Those skilled in the art will understand that embodiments of this application can provide methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0155] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0156] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0157] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0158] In a typical configuration, a computing device includes one or more processors (CPU), input / output interfaces, network interfaces, and memory.

[0159] Memory may include non-persistent memory in computer-readable media, such as random access memory (RAM) and / or non-volatile memory, such as read-only memory (ROM) or flash RAM. Memory is an example of computer-readable media.

[0160] Computer-readable media includes both permanent and non-permanent, removable and non-removable media that can store information using any method or technology. Information can be computer-readable instructions, data structures, modules of programs, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other non-transferable medium that can be used to store information accessible by a computing device. As defined herein, computer-readable media does not include transient computer-readable media, such as modulated data signals and carrier waves.

[0161] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0162] The above are merely embodiments of this application and are not intended to limit the scope of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of the claims of this application.

Claims

1. A method for determining the transient stability boundary of a grid-connected converter system, characterized in that, include: Based on the grid-connected renewable energy scenario, a nonlinear autonomous system model for grid-connected renewable energy is constructed. Solve for all Type I unstable equilibrium points of the nonlinear autonomous system model; For each of the solved Type I unstable equilibrium points, local linearization is performed using Taylor expansion, and a local stable manifold is constructed along the direction of the stable eigenvector of the Type I unstable equilibrium point. At each of the Type I unstable equilibrium points, an initial set of points is selected on the local stable manifold, and the system trajectory is numerically integrated in the reverse direction of time to construct the global stable manifold of that Type I unstable equilibrium point; The global stable manifolds of all type I unstable equilibrium points are merged to form the transient stable boundary of the system, and the closure state of the transient stable boundary of the system at infinity is verified based on the singularity theory at infinity.

2. The method for determining transient stability boundaries according to claim 1, characterized in that, The nonlinear autonomous system model for grid-connected new energy sources includes: Define virtual work angle and angular velocity; A power balance equation with virtual inertia and damping is established, and the power grid strength parameters are embedded into the electromagnetic power of the power balance equation to obtain a nonlinear autonomous system model.

3. The method for determining transient stability boundaries according to claim 1, characterized in that, The solution to the nonlinear autonomous system model includes all type I unstable equilibrium points: Equilibrium condition equations are constructed based on the aforementioned nonlinear autonomous system model; Using a unique equilibrium point as a reference, an initial unstable equilibrium point adjacent to the target saddle point is constructed by applying a perturbation in the direction of complementary power angles. The equilibrium position is determined iteratively using the Newton-Raphson method. Verify that the equilibrium point satisfies the dynamic characteristics of a type I unstable equilibrium point.

4. The method for determining the transient stability boundary according to claim 3, characterized in that, The construction of equilibrium condition equations based on the nonlinear autonomous system model includes: Based on the aforementioned nonlinear autonomous system model, a system of differential equations containing virtual work angle and angular velocity dual state variables is established. By forcing the virtual angular velocity and its derivative to zero, the dynamic differential constraint is degenerated into a static power-power angle balance relationship.

5. The method for determining transient stability boundaries according to claim 1, characterized in that, The step of performing local linearization using Taylor expansion for each of the solved Type I unstable equilibrium points, and constructing a locally stable manifold along the direction of the stable eigenvector of the Type I unstable equilibrium point, includes: Perform a Taylor series expansion for each type I unstable equilibrium point; Solve for the Jacobian matrix at the unstable equilibrium point of type I, filter out the eigenvalues ​​with negative real parts, and calculate the stable eigenvectors corresponding to the eigenvalues ​​with negative real parts; Along the direction of the stable feature vector, with the unstable equilibrium point as the center, uniform sampling is performed within the neighborhood radius of the preset type I unstable equilibrium point to obtain the discrete point set of the local stable manifold.

6. The method for determining transient stability boundaries according to claim 5, characterized in that, At each of the Type I unstable equilibrium points, an initial set of points is selected on the locally stable manifold, and the system trajectory is numerically integrated along the reverse time direction to construct the globally stable manifold for that Type I unstable equilibrium point, including: Based on the discrete point set of the locally stable manifold, initial points for driving inverse-time integration are selected; Based on the initial point, the time evolution direction of the nonlinear autonomous system model is reconstructed, and the forward time variable is replaced with the reverse time variable; The fourth-order Runge-Kutta algorithm is used to integrate the system trajectory along the reverse time axis; Set a dual-channel termination criterion to dynamically truncate the integration path; By merging all valid integral trajectories, a globally stable manifold is constructed for this type I unstable equilibrium point.

7. The method for determining transient stability boundaries according to claim 6, characterized in that, The step of reconstructing the time evolution direction of the nonlinear autonomous system model based on the initial point, and replacing the forward time variable with the reverse time variable, includes: Introduce a reverse time variable to replace the original time variable, and establish a mapping relationship between the reverse time variable and the original time variable; Keeping the original nonlinear autonomous system model structure unchanged, the sign of the derivative terms in the original system state equation is reversed to construct the inverse system; Verify that there is no explicit time term in the reverse system.

8. The method for determining transient stability boundaries according to claim 1, characterized in that, The globally stable manifold that merges all Type I unstable equilibrium points constitutes the transient stable boundary of the system. The closure state of this transient stable boundary at infinity in phase space is verified based on the singularity theory, including: By integrating the global stable manifolds of all Type I unstable equilibrium points, the transient stable boundary of the system is constructed through topological union, and the closed state of the stable boundary at infinity in phase space is verified based on the theory of singularities at infinity. The limiting cut-off angle is calculated based on the transient stability boundary of the system, and the limiting cut-off time is solved by linear interpolation of the fault process power angle sequence. By using the controlled variable method to scan the influence of four-dimensional parameters—virtual inertia, damping coefficient, active power command, and grid strength—on the transient stability boundary of the system, a parameter optimization map is generated to guide grid planning and controller tuning.

9. A control device, characterized in that, The control device includes: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the transient stability boundary determination method according to any one of claims 1-8.

10. A machine-readable storage medium, characterized in that, The machine-readable storage medium stores instructions that cause the machine to perform the transient stability boundary determination method according to any one of claims 1-8.

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