Matrix perturbation theory-based virtual inertia optimization method for network construction type converter

Abstract

The invention relates to the technical field of new energy power systems, in particular to a virtual inertia optimization method for a network-building converter based on a matrix perturbation theory, and the method comprises the steps: obtaining a state space matrix through the linear modeling of a power system, so as to build an incidence relation between virtual inertia and a characteristic value. Based on the matrix perturbation theory, the influence of parameter perturbation on the system characteristic value is quantified, a linear programming model with the minimum spectral intercept as the target is constructed, and the optimal perturbation direction is determined. And the optimal perturbation step length is solved by adopting a backtracking iterative algorithm, so that the dynamic correction of the virtual inertia parameter is realized, and the small-interference stability of the power grid is remarkably improved. According to the strategy, parameter configuration is converted into a solvable sub-sequence linear programming problem, a quantitative design framework is provided for parameter setting of a network construction type converter, and the strategy is suitable for an inertia supporting capacity optimization scene of a multi-machine power system.

Description

Technical Field

[0001] The present invention relates to the technical field of new energy power systems, and in particular to a virtual inertia optimization method for a grid-type converter based on matrix perturbation theory. Background Art

[0002] With the increasing proportion of renewable energy generation equipment such as wind and photovoltaic power connected to the grid, power fluctuations and uncertainties in modern power systems are becoming increasingly prominent. Power systems with a high proportion of renewable energy (mostly using grid-following control) suffer from low inertia and weak damping, resulting in poor disturbance immunity and prone to grid disconnection, threatening system safety and stability. Grid-connected converters, which proactively provide inertia support and flexibly distribute inertia, enhance system stability and are widely used. However, when a large number of grid-connected units are connected to the grid, the risk of medium- and low-frequency oscillations increases due to mismatched controller parameters and the system, hindering the efficient use of renewable energy.

[0003] Research has shown that the grid-connected stability of grid-type converters is closely related to the virtual inertia configuration, and improper virtual inertia adjustment will increase the risk of medium and low-frequency oscillations. Therefore, research on optimizing the virtual inertia configuration of grid-type converters is of great significance to improving the security of new energy power systems and enhancing their anti-disturbance capabilities. In the context of the increasing proportion of new energy, ensuring the stable operation of the power grid is particularly critical. The controller parameter configuration of grid-type converters mainly relies on the stability criteria in classical control theory for parameter scanning. However, with the increase in the scale and complexity of power systems, traditional parameter configuration methods can no longer accurately reflect the stability of the system in multiple scenarios, nor can they provide a universal optimization strategy, making it difficult to adapt to the current rapidly changing application needs. Therefore, there is an urgent need for a new method to analyze and optimize the virtual inertia configuration of grid-type converters to ensure the stability of the system under small disturbances.

[0004] Research on control parameter configuration analysis methods for renewable energy converters has made some progress. However, these methods still have limitations in analyzing the small-disturbance stability of renewable energy power systems with a high proportion of power electronics. Currently, the main approaches for optimizing control parameter configuration for renewable energy converters include heuristic algorithms and analytical optimization methods based on small-signal models.

[0005] First, the core idea of ​​heuristic optimization methods is to transform network parameter optimization into a single- or multi-objective nonlinear programming problem, using intelligent algorithms (such as genetic algorithms or particle swarm optimization) to search for local optimal solutions. These methods typically do not involve explicit representation of the parameter optimization model. Currently, researchers in related fields have attempted to combine traditional particle swarm optimization with time-domain participation factor analysis to optimize the configuration of network virtual inertia and damping in alternating virtual synchronous generators (VSGs). Subsequently, researchers have also attempted to use the frequency-domain transfer function as a guide, deriving an equivalent impedance model for the system based on a series of simplifying assumptions. Furthermore, combined with complex torque analysis, they have relatively intuitively studied the system stability under specified parameter configurations recommended by the intelligent algorithm. Furthermore, considering the non-convex optimization characteristics of the system's small-disturbance stability, researchers have specifically proposed an improved particle swarm algorithm based on chaos and differential evolution and applied it to optimize the configuration parameters of a VSG-attached PSS multi-damping controller.

[0006] In contrast, eigenvalue analysis, the most widely used method for small-disturbance stability analysis, offers the advantages of rigorous theory, high accuracy, and the ability to provide stability information, helping to guide the optimization of key system parameters. However, traditional eigenvalue analysis-based methods require repeated calculations of system sensitivity, resulting in complex calculations and limited universality. Consequently, there is currently a lack of an efficient and mature method for collaborative optimization of multi-machine systems to improve the stability and performance of grid-connected converters.

[0007] Currently, the matrix perturbation method has garnered widespread attention in system parameter design and dynamic characteristics analysis due to its efficient sensitivity calculation and eigenvalue estimation. However, existing power system stability analysis based on the matrix perturbation method is mostly limited to approximate eigenvalues ​​within a local perturbation range, failing to address the insufficient small-disturbance stability margin of renewable energy power systems caused by improper allocation of virtual inertia in the grid. Therefore, there is an urgent need to develop a highly accurate and widely applicable parameter configuration optimization method for grid-type converters to address the severe challenge of increasing low-frequency oscillation risks in current power systems with a high proportion of renewable energy. Summary of the Invention

[0008] The technical problem to be solved by the present invention is to address the deficiencies in the above-mentioned prior art and provide a virtual inertia optimization method for a grid-type converter based on matrix perturbation theory, which is used to solve the technical problem of excessively low minimum damping ratio of the system caused by improper setting of power electronic equipment in a high-proportion new energy power system.

[0009] The purpose of the present invention is achieved by the following technical solutions: In a first aspect, the present invention provides a method for optimizing virtual inertia of a grid-type converter based on matrix perturbation theory, comprising: Linearizing the power system to obtain a state space matrix of the power system, and associating the state space matrix with control parameters of the grid-connected converter; Based on matrix perturbation theory, the quantitative relationship between the state space matrix, system eigenvalues ​​and control parameters of the grid-type converter is established; The perturbed eigenvalues ​​are constrained using a linear constraint method, and a linear programming model is constructed with the optimization objective of minimizing the spectral intercept and the real part of the eigenvalues. The linear programming model is solved to obtain the optimal perturbation direction within the neighborhood of the optimization sequence; the spectral intercept is the minimum value of the real part of all eigenvalues; The optimal perturbation step size in the neighborhood of the optimization sequence is solved according to the backtracking iterative algorithm; The optimal perturbation direction is combined with the optimal perturbation step size to correct the virtual inertia parameters in the optimization model, thereby obtaining the optimal virtual inertia parameter configuration within the neighborhood of the current optimization sequence.

[0010] As a further improvement of the present invention, a quantitative relationship between the state space matrix, the system eigenvalues ​​and the control parameters of the grid-type converter is established based on the matrix perturbation theory, specifically including: Calculate the eigenvalues, right eigenvectors, and left eigenvectors corresponding to the state space matrix; According to the matrix perturbation theory, the sensitivity relationship between the state space matrix and the control parameters of the grid-type converter is analyzed. According to the sensitivity relationship, the Taylor expansion is used to obtain the quantitative analytical relationship between the eigenvalue and the virtual inertia parameter, retaining the first-order sensitivity and second-order sensitivity of the Taylor expansion, and realizing the second-order prediction equation of the real and imaginary parts of the eigenvalue relative to the parameter perturbation under the virtual inertia perturbation.

[0011] As a further improvement of the present invention, a linear constraint method is used to constrain the perturbed eigenvalue, specifically constraining the curvature change, the first-order variation, and the damping ratio corresponding to the real part of the eigenvalue; Constraint on curvature change of the real part of the eigenvalue:

[0012] Constraints on the first-order variation of the real part of the eigenvalue:

[0013] Eigenvalue damping ratio constraint:

[0014] Where, is the projection amplitude of the perturbation direction in the feature space; is the column vector of the state space matrix; for; is the upper limit of the real part of the eigenvalue; is the lower limit of the ratio of the imaginary and real parts of the eigenvalue; for; is the ith isolated eigenvalue.

[0015] As a further improvement of the present invention, the linear programming model is:

[0016] Where, is the real part of the maximum eigenvalue after the k-th optimization, is the eigenvalue corresponding to the perturbed state space matrix, for, is the lower limit of the ratio of the imaginary and real parts of the eigenvalue, For the system The damping ratio corresponding to the eigenvalue is, is the lower limit of the eigenvalue damping ratio, is the ith isolated eigenvalue, is the upper limit of the real part of the eigenvalue, is the real part of the eigenvalue after the kth optimization, is the lower limit of the minimum damping ratio constraint of the k-th optimization system, It is the single increase amount of the preset minimum damping ratio of the system.

[0017] As a further improvement of the present invention, the optimal perturbation step size in the neighborhood of the optimization sequence is solved according to the backtracking iterative algorithm, specifically including: After determining the optimal perturbation direction, the virtual inertia parameter optimization direction is determined according to the optimal setting direction; According to the optimization direction and initial step size of the virtual inertia parameters, the change of the objective function after the perturbation and the minimum value of the damping ratio of the power system characteristic value after the perturbation are obtained; When the change of the objective function after perturbation satisfies the first condition and the minimum value of the eigenvalue damping ratio after perturbation satisfies the second condition, the backtracking search algorithm is used to accept the step size and directly enter the next optimization iteration; When the first and second conditions cannot be met at the same time, the backtracking search mechanism is triggered to adjust the perturbation step size until the optimization iteration stop condition is reached and the optimal perturbation step size is obtained.

[0018] As a further improvement of the present invention, the change of the objective function after perturbation is:

[0019] Where, is the change of the objective function after perturbation, is the initial vector of virtual inertia parameters, is the parameter perturbation, is the state space matrix, is the optimal perturbation direction, is the perturbation step length.

[0020] As a further improvement of the present invention, the minimum value of the damping ratio of the power system characteristic value after perturbation is:

[0021] Where, is the minimum value of the eigenvalue damping ratio of the power system after perturbation; is the parameter perturbation; is the state space matrix; is the perturbation step length.

[0022] In a second aspect, the present invention provides a virtual inertia optimization system for a networked converter, which is used to implement the above-mentioned virtual inertia optimization method for a networked converter based on matrix perturbation theory, comprising: A linearization model building module performs linearization processing on the power system to obtain a state space matrix of the power system, and associates the state space matrix with the control parameters of the grid-connected converter; Quantization module, which establishes the quantitative relationship between the state space matrix, system eigenvalues ​​and grid-type converter control parameters based on matrix perturbation theory; Optimal perturbation direction solving module, The perturbed eigenvalues ​​are constrained using a linear constraint method, and a linear programming model is constructed with the optimization objective of minimizing the spectral intercept and the real part of the eigenvalues. The linear programming model is solved to obtain the optimal perturbation direction within the neighborhood of the optimization sequence; the spectral intercept is the minimum value of the real part of all eigenvalues; The optimal perturbation step length solving module solves the optimal perturbation step length in the neighborhood of the optimization sequence based on the backtracking iterative algorithm; The virtual inertia parameter configuration module combines the optimal perturbation direction with the optimal perturbation step size, modifies the virtual inertia parameters in the optimization model, and obtains the optimal virtual inertia parameter configuration in the neighborhood of the current optimization sequence.

[0023] In a third aspect, the present invention provides a computer-readable storage medium storing one or more programs, wherein the one or more programs include instructions, which, when executed by a computing device, enable the computing device to execute the above-mentioned virtual inertia optimization method of the grid-type converter based on matrix perturbation theory.

[0024] In a fourth aspect, the present invention provides a computing device, comprising: One or more processors, a memory, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the one or more programs include steps for executing the above-mentioned virtual inertia optimization method of the grid-type converter based on matrix perturbation theory.

[0025] The present invention provides a virtual inertia optimization method for a grid-type converter based on matrix perturbation theory. By linearizing the power system, a complex nonlinear system can be simplified into a linear system, facilitating analysis and calculation. Associating the state-space matrix with the control parameters of the grid-type converter (such as virtual inertia parameters and eigenvalues) can more accurately reflect the converter's impact on the system's dynamic characteristics. Matrix perturbation theory can quantitatively analyze the impact of parameter changes on the system's eigenvalues, thereby establishing a quantitative relationship between the state-space matrix and the grid-type converter's control parameters. By constraining the perturbed eigenvalues ​​using a linear constraint method and constructing a linear programming model with the real part of the eigenvalue as the optimization objective, the system's stability can be effectively controlled. A backtracking iterative algorithm can effectively determine the optimal perturbation step size within the neighborhood of the optimization sequence, ensuring convergence and accuracy of the optimization process. By combining the optimal perturbation direction and the optimal perturbation step size, the virtual inertia parameters in the optimization model are modified to obtain the optimal virtual inertia parameter configuration within the neighborhood of the current optimization sequence.

[0026] While maintaining the system's minimum damping ratio safety margin, this invention improves the absolute decay rate of the system's slowest oscillation mode under small disturbances, thereby optimizing the virtual inertia configuration. The algorithm can provide recommended inertia configurations for high-proportion renewable energy multi-mechanism networks, enabling the system to maintain high stability under various operating conditions. This is particularly true in renewable energy power systems, effectively addressing issues such as low inertia and improper inertia distribution, and improving the system's robustness and anti-interference capabilities in the face of frequent disturbances and uncertainties. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0028] Figure 1 This is a control structure diagram of the VSG type grid-type converter provided by the present invention.

[0029] Figure 2 This is a control structure diagram of the PQ control type grid-following converter provided by the present invention.

[0030] Figure 3 This is a flow chart of a virtual inertia optimization method for a grid-type converter based on matrix perturbation theory provided by the present invention.

[0031] Figure 4 This is the IEEE 39 100% new energy topology diagram provided by the present invention.

[0032] Figure 5 It is a structural schematic diagram of the electronic device provided by the present invention. DETAILED DESCRIPTION

[0033] In order to make the purpose and technical solution of the present invention clearer and easier to understand, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. The specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0034] The technical solutions of the present invention will be described clearly and completely below with reference to the accompanying drawings and specific embodiments. The described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments.

[0035] Example 1 This embodiment provides a virtual inertia optimization method for a grid-type converter based on matrix perturbation theory. The first purpose is to overcome the difficulty of solving the system damping ratio sensitivity problem of traditional methods with the help of matrix perturbation theory, thereby forming an optimization model based on the Taylor expansion of the system damping ratio with respect to the perturbation of the grid control parameters, and solving the optimal perturbation direction of the parameters. The second purpose is to apply the backtracking algorithm to solve the optimal perturbation step size of the grid parameters in the neighborhood of each optimization subsequence. Considering the non-convex characteristics of the actual expansion of the eigenvalue along the perturbation direction, the optimal perturbation step size in the neighborhood of the current step-by-step optimization subsequence is determined by backtracking search technology combined with strict eigenvalue decomposition. Finally, the obtained optimal perturbation direction and the optimal perturbation step size of the backtracking search are combined to make targeted corrections to the grid parameters, which is the optimal configuration scheme of the grid parameters in the neighborhood of the current optimization subsequence. The following is a specific implementation method of this embodiment.

[0036] First, the power system is linearized to obtain the state-space matrix. This state-space matrix is ​​then associated with the control parameters of the grid-connected converter. These parameters include the inertia time constant of the grid-connected active power outer loop control. The grid-connected converter control process also includes virtual inertia parameters and eigenvalues.

[0037] This embodiment constructs controller models of synchronous machines, grid-following converters, and grid-connecting converters for a high-proportion renewable energy grid-connected system under the electromechanical transient time scale, as well as a network quasi-steady-state model. Through linearization processing, the power system state space matrix and the corresponding stability margin information are obtained.

[0038] This embodiment mainly focuses on the low and medium frequency bands of new energy systems under the electromechanical transient time scale ( Hz) small disturbance stability problem. In view of the time scale separation characteristics of each control link of the unit in the system, for the VSG type network, the voltage and current inner loop control link can be ignored, and the focus is on analyzing the virtual synchronization dynamic characteristics (such as Figure 1 Similarly, for the grid-following converter, its current inner loop is approximated as ideal control, and the focus is on the dynamic response of its phase-locked loop and power outer loop (as shown in Figure 2 (as shown). In a 100% grid-connected / network-building renewable energy scenario. Furthermore, given that the network time constant is relatively short compared to the time scale of the control parameters of each synchronous generator, a quasi-steady-state node admittance matrix of short-distance transmission lines is used to characterize the network dynamics. All loads in the test case system adopt a constant impedance model.

[0039] All constant impedance loads are incorporated into the network admittance matrix in the form of equivalent admittances, and the differential algebraic equations of the system linearization model are written in matrix form. Equation (1) shows the distribution of the virtual inertia parameters of the i-th grid-type converter in the Jacobian matrix, which intuitively demonstrates the quantitative relationship between the grid-type parameters and the state space matrix: (1) The above transient model was built in the MATLAB Simulink platform and automatically linearized to generate the state-space matrix corresponding to the small-signal model of the system. Combined with pattern analysis and the estimated analytical-sequential optimization algorithm developed in the present invention, the optimal configuration of the multi-mechanism network virtual inertia was achieved.

[0040] Secondly, a quantitative relationship between the state-space matrix, system eigenvalues, and the control parameters of the grid-type converter is established based on matrix perturbation theory. By introducing matrix perturbation theory, a sensitivity relationship between the state-space matrix of the power system linearization model and the control parameters is established. A quantitative analytical relationship between the system's small-disturbance eigenvalues ​​and the grid-type virtual inertia is theoretically derived using Taylor expansion. By retaining the first-order and second-order terms in the analytical expression, a second-order indirect estimate of the system's damping ratio relative to the parameter perturbation under the grid-type virtual inertia perturbation is achieved.

[0041] Next, A linear constraint method is used to constrain the perturbed eigenvalues. A linear programming model is constructed with the optimization objective of minimizing the spectral intercept and the real part of the eigenvalues. Solving the linear programming model yields the optimal perturbation direction within the neighborhood of the optimization sequence; the spectral intercept is the minimum real part of all eigenvalues. Linear constraints are employed to constrain the curvature response of the eigenvalue estimate and the system's minimum damping ratio, thereby reducing the error in the eigenvalue estimate caused by nonlinear terms. A linear programming (LP) model is then formed to optimize the perturbation direction that improves the system's minimum damping ratio. This method avoids the complex process of repeatedly solving the sensitivity of the system's damping ratio to the control parameters in traditional network parameter configuration methods (which cannot be analytically solved and is computationally difficult using traditional approximate methods), effectively achieving the optimal solution for the perturbation direction of the network parameters.

[0042] The specific method includes: calculating the eigenvalues, right eigenvectors and left eigenvectors corresponding to the state-space matrix; analyzing the sensitivity relationship between the state-space matrix and the control parameters of the grid-type converter based on matrix perturbation theory; based on the sensitivity relationship, using Taylor expansion to obtain the quantitative analytical relationship between the eigenvalues ​​and the virtual inertia parameters, retaining the first-order sensitivity and second-order sensitivity of the Taylor expansion, and realizing the second-order prediction equation of the damping ratio relative to the parameter perturbation under virtual inertia perturbation.

[0043] Specifically, according to Lyapunov's first method, the basic information of the stability criterion of the whole system is obtained as follows: for any eigenvalue of the whole system : (2) (3) (4) (5) in For the system The damping ratio corresponding to the characteristic value reflects the attenuation rate of the oscillation response under each oscillation mode of the system. It characterizes the lower limit of the damping ratio of the entire system and conveniently characterizes the damping ratio of the system before and after optimization. is the lower limit of the ratio of the imaginary part to the real part of the eigenvalue, corresponding to the lower limit of the damping ratio According to the power system safety and stability guidelines: When , the system small disturbance stability meets the disturbance response suppression capability requirements.

[0044] By adding linear constraints, the ratio of the real and imaginary parts of the perturbed eigenvalues ​​is bounded to ensure that the minimum damping ratio of the system has a certain lower limit during the optimization process. Subsequently, the lower limit of the system's minimum damping ratio is gradually increased during the iterative process until the system's minimum damping ratio is greater than the safety threshold of 0.05. Considering that the real part of the eigenvalue determines the rate at which the oscillation mode recovers to the steady state and the stability margin, this embodiment chooses the real part of the eigenvalue as the optimization target, and in conjunction with the damping ratio safety margin constraint shown in equation (5), a comprehensive optimization problem for the system's small-disturbance stability can be formed.

[0045] Taking into account the different perturbation response trends of the real parts of different eigenvalues, and to avoid adding too strong constraints that lead to insufficient optimization results, this embodiment uses the eigenvalue with the largest real part as the benchmark for the oscillation decay rate of the entire system during each round of iterative optimization (the kth time). While ensuring that the overall system damping ratio tends to increase, the oscillation mode with the slowest decay rate of the system is gradually improved. The linear programming model is: (6) Where, is the real part of the maximum eigenvalue after the k-th optimization, is the eigenvalue corresponding to the perturbed state space matrix, for, is the lower limit of the ratio of the imaginary and real parts of the eigenvalue, For the system The damping ratio corresponding to the eigenvalue is, is the lower limit of the eigenvalue damping ratio, is the ith isolated eigenvalue, is the upper limit of the real part of the eigenvalue, is the real part of the eigenvalue after the kth optimization, is the lower limit of the minimum damping ratio constraint of the k-th optimization system, It is the single increase amount of the preset minimum damping ratio of the system.

[0046] Matrix perturbation theory is a fast eigenvalue estimation and reanalysis method, and is an efficient means to solve problems such as sensitivity calculation and structural dynamic design. Considering that in most cases, the power system parameters are not symmetrical, according to the relevant theory of random matrices of linear systems, its linearized model usually corresponds to a non-defective system, that is, all eigenvalues ​​of the system are isolated eigenvalues. Therefore, according to matrix perturbation theory, for the state space matrix before perturbation Any Isolated eigenvalues , the corresponding right eigenvector is , the corresponding left eigenvector is , then when the matrix Control parameters At the initial value Nearby experience any scalar Column vector of After perturbation: (7) The perturbed state space matrix The corresponding eigenvalue , right eigenvector , left eigenvector satisfy: (8) (9) (10) Let matrix , and carry out relevant deduction based on matrix perturbation theory to obtain the eigenvalue About the perturbation step size First-order and second-order sensitivity The analytical expression of : (11) (12) Control parameter column vector exist Nearby about scalar Any column vector of Under perturbation ,matrix Any eigenvalue of About scalars The first and second order sensitivities can be given by about Sensitivity , And the left and right eigenvectors before perturbation. According to the chain rule of partial derivatives, the matrix is Sensitivity: (13) (14) The above formula shows that the sensitivity of the state space matrix to the perturbation can be solved by Get eigenvalues ​​about a scalar First and second order sensitivity . The first and second order sensitivities Substitute into the expanded formula (9) and keep The quadratic term of the matrix control parameter perturbation can be constructed The analytical relationship with the second-order estimation of the perturbed eigenvalue is shown in formula (15): (15) Combining Equations (2) and (5), we establish a second-order predictive quantitative relationship between the system damping ratio and the control parameter perturbation, thus forming an optimization problem for the parameter configuration of the new energy unit controller. At this point, the key to the optimization problem of the new energy unit controller parameters shifts from solving the sensitivity of the system damping ratio with respect to the control parameters to solving the sensitivity of the system state space with respect to the control parameter perturbation.

[0047] The sensitivity analysis of the state space matrix control parameters of the linearized model of the whole system is carried out. In this embodiment, the differential-algebraic equations of the linearized model of the new energy power system are organized into a general matrix form as shown in (16): (16) in is a column vector consisting of all state variables, is a column vector of all algebraic variables, , , is the block matrix of the Jacobian matrix. Generally, the system state space matrix can be simplified by the following formula : (17) According to the control parameters, the state space matrix is ​​Taylor expanded to obtain the state space matrix with respect to the control parameters. Expanded. Assume that the initial state space matrix before perturbation is , initial value of control parameters , impose a first-order perturbation on the control parameters back, , the state space matrix can be expanded as: (18) (19) in, is the parameter perturbation column vector The k-th dimension element of .

[0048] When considering the meshed virtual inertia as a control parameter, observing the Jacobian matrix shown in matrix (1), and combining it with formula (17), it can be seen that the system state space matrix linearly depends on the inverse of the meshed virtual inertia coefficient , This means that when the reciprocal coefficient of the virtual inertia coefficient of the network is perturbed, the matrix is ​​related to the control parameter The n-th order sensitivity tensor satisfies: (20) where tensor is the perturbation step size A constant tensor of extraneous first-order partial derivatives.

[0049] The expansion of the state space matrix with respect to the inverse of the virtual inertia of the network is: (twenty one) in, is the perturbed state space matrix about Each element in The n-th order partial derivative tensor element of satisfy: (twenty two) Simplifying the analytical expression of the second-order prediction, we get: (twenty three) Estimated eigenvalues: Take the real part of the analytical formula (23) and substitute it into the system small disturbance stability optimization model (6), and then establish the optimization model of the spectral intercept of the whole system with respect to the perturbation direction and perturbation step of the inverse of the virtual inertia of the network (for the convenience of analysis, the optimization model is demonstrated here by taking the eigenvalue with the imaginary part less than 0 in the conjugate eigenvalue as an example):

[0050] Furthermore, in the analysis of the eigenvalue perturbation direction, in order to facilitate analytical derivation, it is assumed that the control parameter perturbation step size is , then the second-order estimated analytical expression of the eigenvalue is, (25) Among them about The first-order term Determines the dominant direction of eigenvalue change, the second-order term It describes the curvature effect caused by the parameter perturbation, which can be used to quantify the nonlinear characteristics of the eigenvalue change. However, the optimization problem constructed based on this second-order prediction formula belongs to the category of second-order cone optimization (SOCP), and the related computational complexity grows superlinearly with the parameter dimension. In order to break through the computational bottleneck in high-dimensional parameter space, the second-order perturbation prediction analytical formula of the eigenvalue is degraded into a linear form by adding constraints on the nonlinear change terms of the estimated eigenvalue, thereby modeling the step-by-step optimization problem as a linear program (LP). According to the formula shown in formula (25), it is retained to the first-order term, and the analytical forms of the real part and imaginary part of the eigenvalue prediction related to the damping ratio are substituted into the optimization model (24) to obtain: (26) Next, to ensure that the first-order term is the dominant direction of the eigenvalue and that the oscillation mode margin after optimization is sufficient, we will use the estimated real part of the eigenvalue as an example to explain how to add linear constraints to limit the curvature response. The analytical expression for estimating the real part of the eigenvalue considering the curvature response is as follows: (27) It is worth noting that the second-order term is a quadratic structure of optimization parameters, and All elements are real numbers, By introducing the correction tensor , ensuring that the estimated eigenvalue quadratic term correlation matrix can be similarly diagonalized. In this case, the quadratic term can be rewritten as: (28) because is a symmetric matrix, which can be transformed into a similarity transformation form about a diagonal matrix: (29) in is an orthogonal matrix, for The diagonal matrix of all eigenvalues ​​of . At this point, the parameter perturbation direction can be Projection to In the feature space of , then the quadratic term of the real part of the estimated eigenvalue can be further expressed as: (30) In order to suppress the nonlinear change trend of the real part of the eigenvalue and ensure the accuracy of the linear quantitative estimation, it is necessary to limit the projection The projection amplitude in the feature space is .

[0051] Under the above conditions, the change of the quadratic term of the eigenvalue caused by the parameter perturbation is close to zero, and the change of the eigenvalue is completely dominated by the change of the first-order term (linear). Based on the above content, a linear programming model of the real part of the system eigenvalue with respect to the control parameter perturbation can be constructed. The model is based on the perturbation direction is the decision variable, and the goal is to minimize the real part of the rightmost eigenvalue and satisfy the following constraints: 1) Constraint on the curvature change of the real part of the eigenvalue: (31) where the column vector Each component element of It's a very small constant.

[0052] 2) Constraints on the first-order variation of the real part of the eigenvalue: (32) 3) Eigenvalue damping ratio constraint: (33) Finally, by integrating the above constraints into a linear programming model, the optimal perturbation direction of the sub-optimization problem can be obtained with the help of a solver, thereby providing optimization guidance for the network parameter setting configuration. Next, after obtaining the optimal perturbation direction, the selection of the actual step size of the parameter perturbation amount will directly determine the convergence speed and numerical stability of the sequence optimization algorithm, and indirectly determine the optimization effect of the algorithm. If a fixed step size strategy is adopted, the real part of the eigenvalue may oscillate due to nonlinear effects, and even iterative divergence may occur. To this end, the present invention adopts a backtracking search strategy to improve the stability and convergence efficiency of the network parameter sequence optimization algorithm by adjusting the dynamic perturbation step size.

[0053] Specifically, after determining the optimization direction of the network parameters, the second-order estimated analytical expressions of the real and imaginary parts of the eigenvalues ​​relative to the parameter perturbation are converted into a quadratic polynomial expansion of the system eigenvalues ​​versus the perturbation step size along the perturbation direction. When perturbing different step sizes along the local optimal perturbation direction obtained by linear programming, since only the first-order response trend of the control parameter perturbation to the eigenvalue is considered when searching for the local optimal perturbation direction, the system spectral intercept and minimum damping ratio considering the second-order (curvature) response may show different optimization effects, or even worsen the system spectral intercept or minimum damping ratio. Therefore, it is necessary to add constraints on the spectral intercept and minimum damping ratio in combination with the second-order response prediction expression to ensure the optimization effect of the perturbation.

[0054] Based on the Armijo criterion, a critical upper bound for the optimal perturbation step size is calculated, providing an efficient backoff search iterative starting point for subsequent step-by-step sequence optimization. Furthermore, considering the non-convex nature of the system's damping ratio as it varies along the perturbation direction, the present invention uses a backtracking search technique combined with a rigorous eigenvalue decomposition method to determine the optimal perturbation step size within the neighborhood of the current step-by-step optimization subsequence.

[0055] Specifically, after determining the optimal perturbation direction, the optimization direction of the virtual inertia parameter is determined according to the optimal setting direction; the change in the objective function after the perturbation and the minimum value of the characteristic value damping ratio of the power system after the perturbation are obtained according to the optimization direction and initial step size of the virtual inertia parameter; when the change in the objective function after the perturbation meets the first condition, and the minimum value of the characteristic value damping ratio after the perturbation meets the second condition, the backtracking search algorithm is used to accept the step size and directly enter the next optimization iteration; when the first condition and the second condition cannot be met at the same time, the backtracking search mechanism is triggered to adjust the perturbation step size until the optimization iteration stop condition is reached and the optimal perturbation step size is obtained. The first condition is , the second condition is .

[0056] If the optimal perturbation direction determined by the LP solver is , initial step length , then the change of the objective function after parameter perturbation is: (34) The minimum damping ratio of the system after perturbation is: (35) like and , the backtracking search algorithm accepts the step size and directly enters the next optimization iteration; otherwise, the backtracking search mechanism is triggered and the perturbation step size is adjusted according to the exponential decay rule: (36) in is the attenuation factor, the default value is 0.5, and it can be dynamically adjusted according to the improvement rate of the objective function. is the optimized perturbation step size, is the perturbation step size before optimization. If the objective function optimization result is not achieved after the backtracking search exceeds the maximum allowed number of times, the backtracking search is automatically exited to avoid invalid searches and improve the efficiency of the optimization algorithm. At this point, the sequential optimization algorithm can comprehensively consider the small-disturbance stability safety requirements of the entire system and determine the optimal perturbation of the network-based control parameters.

[0057] Finally, the optimal perturbation direction and the optimal perturbation step size are combined to modify the virtual inertia parameters in the optimization model, obtaining the optimal virtual inertia parameter configuration within the neighborhood of the current optimization sequence. This method not only provides an innovative quantitative research framework for analyzing the stability mechanism of multi-machine interaction in power systems with a high proportion of renewable energy, but also forms a systematic optimization scheme that improves the grid-connected stability of power systems with a high proportion of renewable energy by optimizing the parameter configuration of grid-connected converters. This provides important theoretical support for analyzing the stable grid-connected requirements of heterogeneous and heterogeneous power electronic equipment and for planning the future transformation of renewable energy stations.

[0058] The advantage of this embodiment is that, under the premise of taking into account the system's minimum damping ratio safety margin requirements, the absolute attenuation rate of the system's slowest oscillation mode with small disturbances is improved, thereby optimizing the virtual inertia configuration. The algorithm of the present invention can provide a recommended scheme for inertia configuration of a high-proportion new energy multi-mechanism network, so that the system can maintain a high stability under different working conditions, especially in new energy power systems, and can effectively deal with problems such as low inertia and improper inertia distribution, and can improve the system's robustness and anti-interference ability when facing frequent disturbances and uncertain factors. By taking into account the improvement of the slowest oscillation mode with small disturbances and the minimum damping ratio safety margin requirements, the multi-machine interaction characteristics of the new energy power system are optimized. Especially in the context of a high proportion of new energy, the present invention can effectively suppress instability modes such as subsynchronous resonance and improve the global suppression capability of the power system.

[0059] Example 2 This embodiment further explains the virtual inertia optimization method for a grid-type converter based on matrix perturbation theory provided in Example 1 in conjunction with an application example.

[0060] To verify the effectiveness of the algorithm proposed in this embodiment, a transient and small-signal model of the power system in a 100% renewable energy scenario was constructed based on IEEE 39 examples. The developed sequence optimization program was applied to the virtual inertia configuration optimization of the grid-connected units. The grid configuration scheme, system spectral intercept, and minimum damping ratio before and after algorithm optimization were recorded.

[0061] The topology connection of the IEEE 39-node high-proportion new energy system after the new energy transformation is as follows: Figure 4 Nodes 31, 32, 33, 35, and 39 are connected to VSG-type grid-forming converters (green), while nodes 30, 34, 36, 37, and 38 are connected to PQ-controlled grid-following converters (blue). All loads in the system adopt a constant impedance model (orange).

[0062] As shown in Tables 1 through 4, Tables 1 and 2 respectively demonstrate the virtual inertia configurations of individual units in the IEEE 39 system before and after the optimization algorithm proposed in this paper. Tables 3 and 4 respectively demonstrate the improvements in key indicators of system small-disturbance stability after each experimental group, as well as the corresponding configurations of all fixed parameters of the networked units during the virtual inertia optimization algorithm.

[0063] Table 1: Virtual inertia time constant configuration scheme of each network unit before optimization (pu)

[0064] Table 2: Optimized virtual inertia time constant configuration scheme for each network benchmark group (pu)

[0065] As can be seen from Tables 1 and 2, the five groups of verification experiments all used the currently common grid-connected homogeneous configuration ideas as the optimization starting point. The statistical results of the grid-connected virtual inertia configuration after algorithm optimization show that: in the process of optimizing and improving the small-disturbance stability of the entire system, the virtual inertia of the grid-connected units in the system shows a trend of heterogeneous distribution. This indicates that in the future, we should consider exploring the combination scheme of grid-connected units under heterogeneous configuration to fully develop the stability of the power system and improve the grid-connected stability and power supply reliability of future high-proportion new energy power systems. In summary, the optimization algorithm proposed in this invention fully considers the various requirements of the power system stability margin and significantly improves the dynamic interaction performance between the grid-connected converter and the power system. Its optimized recommended configuration scheme effectively meets the stable operation requirements of the power system and can provide an effective optimization reference for the design and planning of future new energy power systems.

[0066] Table 3: Improvement of key indicators of small disturbance stability before and after optimization in each experimental group

[0067] Table 4: Fixed parameter configuration of network units during optimization (pu)

[0068] The power flow distribution, system topology and operation mode data in this experiment are derived from the MATPOWER format IEEE 39 standard calculation example. The system benchmark capacity =100MVA, reference voltage =220kV, base frequency =50Hz.

[0069] Among them, the key indicators in Table 3 show that the system's small-disturbance stability was significantly improved after the optimization algorithm was introduced. Among the six experimental groups, the optimization effect of the first group was the most significant. After optimization, the system spectral intercept increased by 38 times and the minimum damping ratio increased by 8.45 times. In addition, after the optimization algorithm was introduced, the corresponding system spectral intercept of all experimental groups was significantly improved, and the minimum damping ratio increased from less than the safety threshold of 0.05 to above 0.05. This proves that the optimization algorithm objective function and the added minimum damping ratio constraint proposed in this invention are functioning properly, and that this invention has strong universal applicability in new energy power systems.

[0070] Example 3 This embodiment provides a virtual inertia optimization system for a grid-type converter, which mainly includes modules for implementing the virtual inertia optimization method for a grid-type converter based on matrix perturbation theory in Example 1. Specifically: a linearization model construction module for linearizing the power system to obtain a state space matrix of the power system, and associating the state space matrix with control parameters of a grid-type converter; the control parameters of the grid-type converter include virtual inertia parameters; Quantization module, which establishes the quantitative relationship between the state space matrix, system eigenvalues ​​and grid-type converter control parameters based on matrix perturbation theory; The optimal perturbation direction solving module uses the linear constraint method to constrain the perturbation eigenvalue, constructs a linear programming model with minimizing the real part of the eigenvalue as the optimization goal, and solves the linear programming model to obtain the optimal perturbation direction within the optimization sequence neighborhood; The optimal perturbation step length solving module solves the optimal perturbation step length in the neighborhood of the optimization sequence based on the backtracking iterative algorithm; The virtual inertia parameter configuration module combines the optimal perturbation direction with the optimal perturbation step size, modifies the virtual inertia parameters in the optimization model, and obtains the optimal virtual inertia parameter configuration in the neighborhood of the current optimization sequence.

[0071] Example 4 In another embodiment of the present invention, a computer-readable storage medium is provided as a storage component within a terminal device, whose primary function is to store programs and data. It should be noted that the computer-readable storage medium herein encompasses not only the terminal device's built-in storage component but also any supported expansion storage components. Essentially, it is a tangible medium capable of containing or storing programs that can be accessed by, or run in conjunction with, an instruction execution system, device, or component.

[0072] The storage medium provides a storage area for the terminal's operating system and stores one or more instructions suitable for the processor to load and execute. These instructions can constitute one or more computer programs containing program codes.

[0073] In particular, examples (a non-exclusive list) of computer-readable storage media include: an electrical connection with one or more wires, a portable magnetic disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM), optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any reasonable combination of the foregoing.

[0074] The storage medium may also include a data signal transmitted as part of a baseband portion or carrier wave, which carries readable program code. Such a transmitted data signal may take a variety of forms, including but not limited to electromagnetic signals, optical signals, or any reasonable combination of the two. In addition, computer-readable storage media may also refer to other readable media other than traditional readable storage media, which are capable of sending, transmitting, or transmitting programs for use by or in conjunction with an instruction execution system, device, or component. The program code on the storage medium may be transmitted via any suitable medium, including but not limited to wireless, wired, optical cable, or any reasonable combination thereof.

[0075] The program code used to implement the operations of the present invention can be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java and C++, as well as conventional procedural programming languages ​​such as "C." The program code can be executed entirely on the user's computing device, partially on the user's device as a standalone software package, partially distributed across the user's device and a remote computing device, or entirely on a remote computing or device server. When a remote computing device is involved, the device can be connected to the user's computing device via any type of network, such as a local area network (LAN) or wide area network (WAN), or connected to an external computing device via the Internet through an Internet service provider (ISP).

[0076] The processor is capable of loading and executing one or more instructions stored in a computer-readable storage medium to implement corresponding steps of the virtual inertia optimization method for a grid-type converter based on matrix perturbation theory described in Example 1.

[0077] Example 5 Reference Figure 5 Another embodiment of the present invention provides a terminal device, which is specifically a computer device 60. This computer device 60 is mainly composed of three parts, namely a processor 61, a memory 62, and a computer program 63 stored in the memory 62 and capable of running on the processor 61. Among them, the processor 61 is responsible for executing the computer program to implement the virtual inertia optimization method of the grid-type converter based on the matrix perturbation theory described in Example 1, and the memory 62 is used to store the computer program and other programs and data required for the operation of the device. When the computer program 63 runs on the processor 61, it can implement the virtual inertia optimization method of the grid-type converter based on the matrix perturbation theory. In order to avoid repetition of content, the relevant details will not be described in detail here.

[0078] The computer device 60 has many different forms. It can be a desktop computer, a notebook computer, a handheld computer, or a computing device such as a cloud server.

[0079] The processor 60 may be a central processing unit, or other types of general-purpose processors, central processing units, graphics processing units, digital signal processors, application-specific integrated circuits, field programmable gate arrays, or other programmable logic devices, discrete gate or transistor logic devices, quantum computing-based data processing logic, discrete hardware components, etc. The general-purpose processor referred to herein refers to a microprocessor or any conventional processor.

[0080] Memory 62 can be an internal storage unit of computer device 60, such as its hard drive or memory, or an external storage device, such as a plug-in hard drive, SmartMediaCard (SMC), SecureDigital (SD) card, or FlashCard. Memory 62 not only stores computer programs but also other programs and data required for device operation, and temporarily stores data that has been or is about to be output.

[0081] In the various embodiments provided herein, references to memory, databases, or other media will encompass at least one of non-volatile memory and volatile memory. There are many types of non-volatile memory, including read-only memory, magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory, magnetic random access memory, ferroelectric memory, phase change memory, graphene memory, and the like. Volatile memory may include random access memory (RAM) or external cache memory. It should be noted that RAM has various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM).

Claims

1. A virtual inertia optimization method for a grid-type converter based on matrix perturbation theory, characterized in that: include: Linearizing the power system to obtain a state space matrix of the power system, and associating the state space matrix with control parameters of the grid-connected converter; Based on matrix perturbation theory, the quantitative relationship between the state space matrix, system eigenvalues ​​and control parameters of the grid-type converter is established; The perturbed eigenvalues ​​are constrained using a linear constraint method, and a linear programming model is constructed with the optimization objective of minimizing the spectral intercept and the real part of the eigenvalues. The optimal perturbation direction within the neighborhood of the optimization sequence is obtained by solving the linear programming model; the spectral intercept is the minimum value of the real part of all eigenvalues; The optimal perturbation step size in the neighborhood of the optimization sequence is solved according to the backtracking iterative algorithm; The optimal perturbation direction is combined with the optimal perturbation step size to correct the virtual inertia parameters in the optimization model, thereby obtaining the optimal virtual inertia parameter configuration within the neighborhood of the current optimization sequence.

2. The virtual inertia optimization method for a networked converter based on matrix perturbation theory according to claim 1 is characterized in that: Based on matrix perturbation theory, the quantitative relationship between the state space matrix, system eigenvalues ​​and grid-type converter control parameters is established, including: Calculate the eigenvalues, right eigenvectors, and left eigenvectors corresponding to the state space matrix; According to the matrix perturbation theory, the sensitivity relationship between the state space matrix and the control parameters of the grid-type converter is analyzed. According to the sensitivity relationship, the Taylor expansion is used to obtain the quantitative analytical relationship between the eigenvalue and the virtual inertia parameter, retaining the first-order sensitivity and second-order sensitivity of the Taylor expansion, and realizing the second-order prediction equation of the real and imaginary parts of the eigenvalue relative to the parameter perturbation under the virtual inertia perturbation.

3. The virtual inertia optimization method for a networked converter based on matrix perturbation theory according to claim 1 is characterized in that: The linear constraint method is used to constrain the perturbed eigenvalues, specifically constraining the curvature change, first-order variation, and damping ratio corresponding to the real part of the eigenvalue. Constraint on curvature change of the real part of the eigenvalue: Constraints on the first-order variation of the real part of the eigenvalue: Eigenvalue damping ratio constraint: Where, is the projection amplitude of the perturbation direction in the feature space; is the column vector of the state space matrix; for; is the upper limit of the real part of the eigenvalue; is the lower limit of the ratio of the imaginary and real parts of the eigenvalue; for; is the ith isolated eigenvalue.

4. The virtual inertia optimization method for a networked converter based on matrix perturbation theory according to claim 3 is characterized in that: The linear programming model is: Where, is the real part of the maximum eigenvalue after the k-th optimization, is the eigenvalue corresponding to the perturbed state space matrix, for, is the lower limit of the ratio of the imaginary and real parts of the eigenvalue, For the system The damping ratio corresponding to the eigenvalue is, is the lower limit of the eigenvalue damping ratio, is the ith isolated eigenvalue, is the upper limit of the real part of the eigenvalue, is the real part of the eigenvalue after the kth optimization, is the lower limit of the minimum damping ratio constraint of the k-th optimization system, It is the single increase amount of the preset minimum damping ratio of the system.

5. The virtual inertia optimization method for a networked converter based on matrix perturbation theory according to claim 1 is characterized in that: The optimal perturbation step size in the neighborhood of the optimization sequence is solved according to the backtracking iterative algorithm, specifically including: After determining the optimal perturbation direction, the virtual inertia parameter optimization direction is determined according to the optimal setting direction; According to the optimization direction and initial step size of the virtual inertia parameters, the change of the objective function after the perturbation and the minimum value of the damping ratio of the power system characteristic value after the perturbation are obtained; When the change of the objective function after perturbation satisfies the first condition and the minimum value of the eigenvalue damping ratio after perturbation satisfies the second condition, the backtracking search algorithm is used to accept the step size and directly enter the next optimization iteration; When the first and second conditions cannot be met at the same time, the backtracking search mechanism is triggered to adjust the perturbation step size until the optimization iteration stop condition is reached and the optimal perturbation step size is obtained.

6. The virtual inertia optimization method for a networked converter based on matrix perturbation theory according to claim 5 is characterized in that: The change of the objective function after perturbation is: Where, is the change of the objective function after perturbation, is the initial vector of virtual inertia parameters, is the parameter perturbation, is the state space matrix, is the optimal perturbation direction, is the perturbation step size.

7. The virtual inertia optimization method for a networked converter based on matrix perturbation theory according to claim 5 is characterized in that: The minimum value of the eigenvalue damping ratio of the power system after perturbation is: Where, is the minimum value of the eigenvalue damping ratio of the power system after perturbation; is the parameter perturbation; is the state space matrix; is the perturbation step size.

8. A virtual inertia optimization system for a grid-type converter, used to implement the virtual inertia optimization method for a grid-type converter based on matrix perturbation theory according to any one of claims 1 to 7, characterized in that: include: A linearization model building module performs linearization processing on the power system to obtain a state space matrix of the power system, and associates the state space matrix with the control parameters of the grid-connected converter; Quantization module, which establishes the quantitative relationship between the state space matrix, system eigenvalues ​​and grid-type converter control parameters based on matrix perturbation theory; Optimal perturbation direction solving module, The perturbed eigenvalues ​​are constrained using a linear constraint method, and a linear programming model is constructed with the optimization objective of minimizing the spectral intercept and the real part of the eigenvalues. The optimal perturbation direction within the neighborhood of the optimization sequence is obtained by solving the linear programming model; the spectral intercept is the minimum value of the real part of all eigenvalues; The optimal perturbation step length solving module solves the optimal perturbation step length in the neighborhood of the optimization sequence based on the backtracking iterative algorithm; The virtual inertia parameter configuration module combines the optimal perturbation direction with the optimal perturbation step size, modifies the virtual inertia parameters in the optimization model, and obtains the optimal virtual inertia parameter configuration in the neighborhood of the current optimization sequence.

9. A computer-readable storage medium storing one or more programs, characterized in that: The one or more programs include instructions, which, when executed by a computing device, enable the computing device to execute the virtual inertia optimization method for a grid-type converter based on matrix perturbation theory as described in any one of claims 1 to 7.

10. A computing device, characterized in that include: One or more processors, a memory, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the one or more programs include steps for executing the virtual inertia optimization method of a grid-type converter based on matrix perturbation theory as described in any one of claims 1 to 7.

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