Multi-converter parameter collaborative optimization method for improving small interference stability of active power distribution network

Abstract

The invention discloses a multi-converter parameter collaborative optimization method for improving the small interference stability of an active power distribution network, and belongs to the technical field of power systems, and the method comprises the steps: building a differential algebraic equation model, and carrying out the linearization of a steady-state operation point, and obtaining a state space model; and a control parameter optimization problem taking the minimization of the spectrum intercept construction as a target is defined, and control parameters are a GFL converter phase-locked loop parameter and a GFM converter virtual damping parameter. First-order sensitivity and second-order sensitivity of eigenvalues to control parameters are calculated based on a matrix perturbation theory and are converted into local quadratic constraint sub-problems. And performing convexity solution by adopting a positive semidefinite relaxation method, adjusting the step length in combination with a line search mechanism, iteratively updating control parameters, and outputting an optimization result after a convergence condition is met. According to the method, the spectral intercept is reduced through multi-converter parameter collaborative optimization, and the weak stability characteristic is improved; the convergence and solvability are improved by utilizing matrix perturbation and positive semidefinite relaxation; and the stability is enhanced and optimized by adopting line search step length adjustment.

Description

Technical Field

[0001] This invention relates to the field of power system technology, specifically to a method for collaborative optimization of multi-converter parameters to improve the stability of active distribution networks under small disturbances. Background Technology

[0002] Power electronic converters are widely used as energy conversion interfaces in active distribution networks. The coupling of their diverse control strategies and dynamic elements causes the system to exhibit strong nonlinearity and time-varying characteristics. The dynamic interaction of control elements at different time scales among multiple converters can easily induce system oscillations, becoming a key technical bottleneck restricting the high proportion of new energy consumption and stable operation of active distribution networks.

[0003] The control structure and parameter configuration of converters are core factors affecting the stability of active distribution networks under small disturbances. Existing research mainly focuses on improving system stability through two directions: control structure improvement and control parameter optimization. Control structure improvement methods suppress system instability modes by introducing additional control loops or reconfiguring the controller structure. However, these methods rely on specific system operating scenarios, and the additional control loops increase the difficulty of parameter tuning and the burden of robustness design, making them difficult to adapt to the coordinated control requirements of large-scale converter clusters. In contrast, parameter optimization methods, without changing the control structure, can specifically improve the system's eigenvalue distribution and stability margin by precisely adjusting parameters such as the power outer loop and phase-locked loop. They have the advantages of strong engineering compatibility and low implementation cost, making them a research focus.

[0004] Current research on control parameter optimization mainly focuses on two approaches: frequency domain analysis and time domain modeling. Frequency domain methods establish a system transfer function model and, combined with frequency domain indices, evaluate system stability and dynamic performance, forming a feasible region for parameter tuning. However, they struggle to accurately identify the dominant mode and its mapping relationship with control parameters, limiting the targeted optimization performance for the dominant mode. Eigenmode analysis in the time domain can directly reveal the distribution characteristics and evolution patterns of system eigenvalues, clarifying the direction and intensity of the influence of control parameters on the dominant mode, and is widely used in the controller design of new energy converters. Summary of the Invention

[0005] In view of the above-mentioned problems, the present invention is proposed.

[0006] Therefore, the technical problem solved by this invention is that, on the one hand, existing parameter optimization frameworks are mostly based on the assumption of a single-loop structure, which makes it difficult to fully characterize the dynamic coupling relationship between the control loops of multiple converters, resulting in limited generalization ability in the scenario of multi-converter collaborative operation; on the other hand, the mapping of eigenvalues ​​to control parameters is non-convex and non-smooth, which can easily lead to discontinuous behaviors such as dominant mode oscillation and jumps during the optimization process, seriously affecting the optimization path stability of existing algorithms in the scenario of multi-converter operation.

[0007] To address the aforementioned technical problems, this invention provides the following technical solution: a method for collaborative optimization of multi-converter parameters to improve the stability of active distribution networks under small disturbances, comprising, A differential algebraic equation model of an active distribution network is established. The differential algebraic equation model consists of an AC grid model, a GFL converter model, a GFM converter model, and a ZIP load model. The AC grid model, GFL converter model, GFM converter model, and ZIP load model are simplified mathematical models derived based on the principle of time scale separation. The differential-algebraic equation model of the active distribution network is linearized at the steady-state operating point and the algebraic variables are eliminated to obtain the state-space model of the active distribution network. In the state-space model of the active distribution network, the maximum value of the real part of the eigenvalue is defined as the spectral intercept. A control parameter optimization problem is constructed with the goal of minimizing the spectral intercept. The control parameters include the phase-locked loop parameters of the GFL converter model and the virtual damping parameters of the GFM converter model. Value boundaries are set for the control parameters. Based on matrix perturbation theory, the first-order and second-order sensitivities of the eigenvalues ​​of the state-space model of the active distribution network with respect to the control parameters are calculated, and the control parameter optimization problem is transformed into a local quadratic constraint subproblem with respect to the direction of parameter perturbation. The local quadratic constraint subproblem is solved by convexification using semi-positive definite relaxation to obtain the update direction of the control parameters. The parameter update step size is determined by a line search mechanism, and the control parameters are iteratively updated. After each update, the convergence condition is determined based on the spectral intercept. When the convergence condition is met, the co-optimized phase-locked loop parameters and the virtual damping parameters are output to reduce the spectral intercept and improve the small-disturbance stability margin of the active distribution network.

[0008] As a preferred embodiment of the multi-converter parameter collaborative optimization method for improving the small-disturbance stability of active distribution networks described in this invention, the AC power grid model is represented as follows: in, It is the system node admittance matrix. Let n represent the set of complex numbers, n represent the total number of nodes, and i represent the node number. For each node, there is a complex voltage vector; , and These represent the injected currents of the GFL converter, GFM converter, and ZIP load in the global coordinate system, respectively. Indicates the first An n-dimensional unit vector with one component equal to 1 and the rest equal to 0. Number the nodes.

[0009] As a preferred embodiment of the multi-converter parameter collaborative optimization method for improving the stability of active distribution networks under small disturbances as described in this invention, the GFL converter model is represented as follows: in, Indicates the first Intermediate state variables of the phase-locked loop integrator of a GFL converter The phase angle calculated for the phase-locked loop. The reference angular frequency of the power grid. This refers to the frequency deviation of the phase-locked loop output. These are the integral coefficients of the phase-locked loop. This represents the integral state variable of the active power control channel. This represents the integral state variable of the reactive power control channel. This refers to the set of nodes connected to the GFL type converter. The first The d-axis and q-axis components of the voltage at the grid-connected node of a converter. For the first The d-axis current injected into the grid by a ZIP load For the first The q-axis current injected into the grid by a ZIP load. The voltage amplitude at the grid connection point. The complex output current injected into the grid for the GFL converter, The imaginary unit satisfies .

[0010] As a preferred embodiment of the multi-converter parameter collaborative optimization method for improving the stability of active distribution networks under small disturbances as described in this invention, the GFM converter model is represented as follows: in, Indicates the first The power angle of a GFM converter For its frequency deviation, The system's reference angular frequency, The equivalent inertia coefficient, This represents the reference value for active power. This represents the actual output value of active power. The active power damping coefficient is... The reactive control inertia coefficient, For voltage amplitude deviation, This represents the reference value for reactive power. This represents the actual output value of reactive power. The reactive power damping coefficient and voltage amplitude are given. The stable value of the voltage amplitude at the grid connection node voltage amplitude deviation The result of superposition is that , This refers to the voltage amplitude at the grid connection node. For filter reactance, For the complex output current injected into the power grid, This represents the set of nodes connected to the GFM type converter.

[0011] As a preferred embodiment of the multi-converter parameter collaborative optimization method for improving the small-disturbance stability of active distribution networks described in this invention, the ZIP load model is represented as follows: in, Indicates the first The amplitude of the voltage at each ZIP load node. The load component factor representing the constant impedance (Z) corresponding to active power. The load component factor represents the constant current (I) corresponding to the active power. This represents the load component factor of constant power (P) corresponding to active power. This represents the load component factor of the constant impedance (Z) corresponding to reactive power. This represents the load component factor of the constant current (I) corresponding to reactive power. This represents the load component factor of the constant power (P) corresponding to reactive power. The d-axis current component at the reference operating point. The q-axis current component at the reference operating point. The complex current injected into the grid for the ZIP load. The phase angle of the node voltage. This represents the set of nodes connected to a ZIP-type load.

[0012] As a preferred embodiment of the multi-converter parameter collaborative optimization method for improving the stability of active distribution networks under small disturbances as described in this invention, the method involves simultaneously establishing an AC power grid model, a GFL converter model, a GFM converter model, and a ZIP load model to construct a system of differential-algebraic equations characterizing the dynamic behavior of the system, expressed as follows: in, Represents state variables, Let T be an algebraic variable, representing transpose. It is the intermediate state variable of the phase-locked loop integrator of all GFL converters. It is the phase angle of the phase-locked loop of all GFL converters. These are the integral state variables of the active power control channels of all GFL converters. These are the integral state variables of the reactive power control channels of all GFL converters. It is the power angle of all GFM converters. It is the frequency deviation of all GFM converters. It is the voltage amplitude deviation of all GFM converters. It is a vector function. It is the algebraic constraint of the system.

[0013] As a preferred embodiment of the multi-converter parameter collaborative optimization method for improving the stability of active distribution networks under small disturbances as described in this invention, the linearization of the differential-algebraic equation model of the active distribution network at the steady-state operating point includes: in, This represents the rate of change corresponding to a small change in the state variables of the power system. Represents the state matrix of a linearized system. Represents the input matrix of the linearized system. This represents the output matrix of the linearized system. Represents the feedforward matrix of the linearized system. For small changes in the state variables of a power system, For small changes in the algebraic variables of the power system; As a preferred embodiment of the multi-converter parameter collaborative optimization method for improving the small-disturbance stability of active distribution networks described in this invention, wherein: due to the matrix Having nonsingularity, elimination of algebraic variables yields a reduced-order state-space form, expressed as: in, This is the reduced-order state matrix of the system; According to Lyapunov's first method, small-disturbance stability can be achieved through... The eigenvalues ​​are used to determine if all real parts of the eigenvalues ​​are negative, in which case the system is stable under small disturbances at the current equilibrium point.

[0014] As a preferred embodiment of the multi-converter parameter collaborative optimization method for improving the small-disturbance stability of active distribution networks according to the present invention, the step of extracting the maximum value of the real part of the eigenvalues ​​from the state-space model of the active distribution network as the spectral intercept, and constructing a control parameter optimization problem with the objective of minimizing the spectral intercept, is expressed as follows: in, Indicates the optimization operator; It is a decision variable vector, containing the control parameters that need to be adjusted, specifically... , and These are the proportional gain and integral gain of the PLL. These are virtual damping parameters; It is a slack variable; This represents the maximum value of the real part of all eigenvalues ​​of the matrix. It is the first of the matrix 1 eigenvalue, It is the set of all characteristic values ​​of the system; and These are the lower and upper limits of the decision variable, respectively.

[0015] As a preferred embodiment of the multi-converter parameter collaborative optimization method for improving the stability of small disturbances in active distribution networks as described in this invention, the step of using semi-positive definite relaxation for convexity solution to obtain the update direction of the control parameters includes: performing variable boosting on the parameter disturbance direction vector, mapping the disturbance direction vector to a symmetric matrix space, defining matrix variables, and using trace operation to transform the non-convex quadratic terms into matrix form; By introducing a positive semidefinite condition under the matrix variable constraint, the rank constraint is relaxed to a positive semidefinite constraint, thereby transforming the local quadratic constraint subproblem into a convex optimization problem and solving it. A line search mechanism is introduced during the control parameter update process. The update step size is dynamically adjusted based on the monotonically decreasing criterion. When the current step size does not meet the decreasing condition, the step size is reduced until the step size decays to the set threshold.

[0016] The beneficial effects of this invention are as follows: By jointly optimizing the virtual damping of the GFM converter and the phase-locked loop parameters of the GFL converter, this invention significantly improves the system spectral intercept, effectively suppresses the low-damping oscillation of the system, and greatly improves the weak stability characteristics and dynamic recovery capability of the system.

[0017] This invention utilizes matrix perturbation theory and semidefinite relaxation methods to transform non-smooth eigenvalue constraint problems into convex optimization subproblems that can be solved efficiently. These subproblems possess good gradient information and convergence, avoiding the numerical instability and solution difficulties faced by traditional non-convex optimization methods.

[0018] The algorithm of this invention introduces a line search mechanism to dynamically adjust the step size, effectively suppressing the accumulation of higher-order sensitivity errors and relaxation errors, and enhancing the stability and adaptability of the optimization process. Simultaneously, the algorithm framework supports collaborative optimization of multiple control parameters, is applicable to various types of converters and different control structures, and has good engineering practicality and promotional value. Attached Figure Description

[0019] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 This is a schematic diagram of a typical active distribution network structure, illustrating a method for collaborative optimization of multi-converter parameters to improve the stability of active distribution networks under small disturbances, as provided in an embodiment of the present invention.

[0021] Figure 2 The diagram below shows the structure of a GFL-type converter control system, which provides a method for collaborative optimization of multi-converter parameters to improve the stability of active distribution networks under small disturbances, as an embodiment of the present invention.

[0022] Figure 3 The diagram below shows the structure of a GFM converter control system, which provides a method for collaborative optimization of multi-converter parameters to improve the stability of active distribution networks under small disturbances, as an embodiment of the present invention.

[0023] Figure 4 The flowchart of an eigenvalue optimization algorithm based on matrix perturbation theory and semidefinite relaxation is provided as an embodiment of the present invention to improve the stability of active distribution networks under small disturbances.

[0024] Figure 5 This is a schematic diagram of an IEEE 33-node active distribution network, illustrating a method for collaborative optimization of multi-converter parameters to improve the stability of active distribution networks under small disturbances, as provided in an embodiment of the present invention.

[0025] Figure 6 This is a comparison of the characteristic value distribution of an active distribution network system before and after optimization, provided by a multi-converter parameter collaborative optimization method to improve the stability of active distribution networks under small disturbances, as an embodiment of the present invention.

[0026] Figure 7 This is a comparison diagram of the characteristic value distribution before and after optimization of an active distribution network system, provided by a multi-converter parameter collaborative optimization method to improve the stability of active distribution networks under small disturbances, as an embodiment of the present invention.

[0027] Figure 8 This is a comparison of the changes in the spectral intercept mode participation factor before and after optimization of a multi-converter parameter collaborative optimization method to improve the stability of active distribution networks under small disturbances, provided as an embodiment of the present invention.

[0028] Figure 9This is a comparison of the changes in the spectral intercept mode participation factor before and after optimization of a multi-converter parameter collaborative optimization method to improve the stability of active distribution networks under small disturbances, provided as an embodiment of the present invention.

[0029] Figure 10 This is a schematic diagram illustrating the evolution of the spectral intercept change with the number of optimization iterations in a multi-converter parameter collaborative optimization method for improving the stability of active distribution networks under small disturbances, as provided in an embodiment of the present invention.

[0030] Figure 11 This is a schematic diagram illustrating the evolution of the GFM virtual damping coefficient as a function of the number of optimization iterations in a multi-converter parameter collaborative optimization method for improving the stability of active distribution networks under small disturbances, provided as an embodiment of the present invention.

[0031] Figure 12 This is a schematic diagram illustrating the evolution of the PLL proportional coefficient change with the number of optimization iterations in a multi-converter parameter collaborative optimization method for improving the stability of active distribution networks under small disturbances, as provided in an embodiment of the present invention.

[0032] Figure 13 This is a schematic diagram illustrating the evolution of the PLL integral coefficient as a function of the number of optimization iterations in a multi-converter parameter collaborative optimization method for improving the stability of active distribution networks under small disturbances, provided as an embodiment of the present invention.

[0033] Figure 14 This is a comparison diagram of the power angle response of a GFM converter under disturbance conditions before optimization, provided by a multi-converter parameter collaborative optimization method to improve the stability of active distribution networks under small disturbances, as an embodiment of the present invention.

[0034] Figure 15 A comparison diagram of the power angle response of the optimized GFM converter under disturbance conditions, provided by an embodiment of the present invention, for a method of collaborative optimization of multi-converter parameters to improve the stability of active distribution networks under small disturbances. Detailed Implementation

[0035] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of the present invention.

[0036] Example 1, referring to Figures 1-4 This is one embodiment of the present invention, which provides a method for collaborative optimization of multi-converter parameters to improve the stability of active distribution networks under small disturbances, including: Active distribution network structure such as Figure 1As shown, the main equipment includes grid-following (GFL) converters, grid-forming (GFM) converters, and ZIP loads. GFL converters are the primary interface for grid connection of new energy sources and are widely used for power transmission in distributed new energy systems. GFM converters actively establish voltage and frequency references through virtual synchronization control, enhancing the inertia and dynamic regulation capabilities of the power system. ZIP loads dynamically combine weighted coefficients to characterize the actual load characteristics. ZIP loads are a commonly used constant impedance, constant current, and constant power load model in power systems, corresponding to the English term Impedance-Current-Power (ZIP) load. The converters in the system are coupled through the power network, forming a typical multi-timescale, strongly coupled nonlinear system.

[0037] The dynamic characteristics of an active distribution network can be described by a system of differential-algebraic equations, and it exhibits significant multi-time-scale dynamic coupling characteristics. Since this embodiment studies low-to-medium frequency oscillations, a simplified mathematical model of the GFL, GFM converter, ZIP load, and AC power grid is derived based on the time-scale separation principle.

[0038] Specifically, in the AC power grid model, the active distribution network is assumed to contain n nodes, with GFL converters, GFM converters, and ZIP loads connected to the node set respectively. , and , This represents the set of nodes in a GFL converter. This represents the set of nodes in a GFM converter. This represents the set of nodes representing the ZIP load. In low-to-medium frequency oscillation problems, the network can be modeled as a steady-state model globally. In a coordinate system, the relationship between node voltage and injected current can be expressed as: (1) in, It is the system node admittance matrix. Let n represent the set of complex numbers, n represent the total number of nodes, and i represent the node number. For each node, there is a complex voltage vector; , and These represent the injected currents of the GFL converter, GFM converter, and ZIP load in the global coordinate system, respectively. Indicates the first An n-dimensional unit vector with one component equal to 1 and the rest equal to 0. Number the nodes.

[0039] The control system of a GFL converter typically consists of a power outer loop, a phase-locked loop, and a current inner loop, and its structure is as follows: Figure 2 As shown in the figure. The phase-locked loop (PLL) achieves phase synchronization with the grid by detecting the q-axis component of the grid-connected voltage. The outer power loop and the inner current loop work together to maintain the steady-state output of the target power. Figure 2 Among the controller parameters shown, , and These represent the change in the phase-locked loop output angular frequency, the rated angular frequency of the power grid, and the power angle, respectively. and For the proportional and integral gains of the PLL, and The proportional and integral coefficients of the active power controller. and These are the proportional and integral coefficients of the reactive power controller. and These represent reference values ​​for active and reactive power. and This represents the actual output values ​​of active power and reactive power. and These are the d-axis and q-axis components of the grid-connected node voltage and current, respectively. This refers to the output current of the GFL converter. This refers to the voltage amplitude at the grid connection point. The reactance of the filter inductor is represented by its inductance. This indicates the line impedance, while PWM stands for Pulse Width Modulation, which is used to drive the converter to achieve the control objective.

[0040] Considering the time response characteristics of each control loop, the bandwidth of the inner current loop is typically designed to be several hundred hertz, far exceeding the tens of hertz bandwidth of a PLL. Therefore, in analyzing low-frequency oscillation problems, the dynamics of the inner current loop can be ignored, and it is reasonably assumed that it has reached a quasi-steady state. Based on this, the output current of the i-th GFL converter... It can be described by the following system of differential-algebraic equations: (2) in, Indicates the first Intermediate state variables of the phase-locked loop integrator of a GFL converter The phase angle calculated for the phase-locked loop. The reference angular frequency of the power grid. This refers to the frequency deviation of the phase-locked loop output. These are the integral coefficients of the phase-locked loop. and These represent the integral state variables of the active power and reactive power control channels, respectively. This refers to the set of nodes connected to the GFL type converter. The first The d-axis and q-axis components of the voltage at the grid-connected node of a converter. These are the corresponding current components. The voltage amplitude at the grid connection point. The complex output current injected into the grid for the GFL converter; where, The imaginary unit satisfies .

[0041] The control system of the GFM converter mainly consists of a virtual synchronous control loop and a voltage and current dual closed loop, and its structure is as follows: Figure 3 As shown in the figure. Among them, the virtual synchronization loop supports the system frequency and voltage by simulating the inertial response and reactive-voltage regulation characteristics of a synchronous generator; the voltage and current dual closed loop precisely controls the output with high bandwidth, and collaboratively constructs the voltage source characteristics of the equipment. Figure 3 Among the controller parameters shown, , and These represent the changes in the converter's power angle, angular frequency, and voltage amplitude, respectively. , and , These are the reference values ​​and actual output values ​​for active and reactive power, respectively. , and , These are the inertia coefficient and damping coefficient of the active and reactive power control channels, respectively. This is the initial value of the converter voltage amplitude; This represents the connection impedance between the converter and the grid connection node.

[0042] Due to the high bandwidth characteristics of the voltage and current dual closed-loop circuits, its dynamic process can be considered as quasi-steady state within the low-to-medium frequency oscillation timescale. At this time, the output current of the i-th GFM converter... It can be described by the following system of differential-algebraic equations: (3) in, Indicates the first The power angle of a GFM converter For its frequency deviation, This is the system's reference angular frequency. The equivalent inertia coefficient, and These represent the reference value and the actual output value of active power, respectively. This is the active power damping coefficient. The reactive control inertia coefficient, For voltage amplitude deviation, and These represent the reference value and the actual output value of reactive power, respectively. This represents the reactive power damping coefficient. Voltage amplitude. The stable value of the voltage amplitude at the grid connection node voltage amplitude deviation The result of superposition is that The voltage amplitude at the grid-connected node is The filter reactance is The complex output current injected into the power grid is . This represents the set of nodes connected to the GFM type converter.

[0043] ZIP loads are composed of three types of loads: constant impedance (Z), constant current (I), and constant power (P), linearly superimposed in a certain proportion, characterizing the load's sensitivity to voltage amplitude. The input current of the i-th ZIP load... Represented as: (4) in, Indicates the first The amplitude of the voltage at each ZIP load node, of which This is the complex form of the node voltage. and The first The d-axis and q-axis currents injected into the grid by a ZIP load are calculated using linearity coefficients. and The control corresponds to the superposition of constant impedance (Z), constant current (I), and constant power (P) load components, respectively. and This represents the current component at the reference operating point. The complex current injected into the grid by the ZIP load is... ,in The phase angle of the node voltage. This represents the set of nodes connected to a ZIP-type load.

[0044] , , and , , These are the Z / I / P component coefficients corresponding to active power and reactive power, respectively, and they satisfy: (5) in, The component coefficients of the constant impedance (Z) corresponding to the active power are represented. The component coefficients of the constant current (I) corresponding to the active power are represented. The component coefficients representing the constant power (P) corresponding to active power. The component coefficients of the constant impedance (Z) corresponding to reactive power are represented. The component coefficients representing the constant current (I) corresponding to reactive power. The component coefficient representing the constant power (P) corresponding to reactive power.

[0045] Finally, by combining equations (1) to (4), a system of differential-algebraic equations characterizing the dynamic behavior of the system can be constructed, the compact form of which is shown below: (6) Among them, state variables , Let T be an algebraic variable, representing the transpose of the vector. It is the intermediate state variable of the phase-locked loop integrator of all GFL converters. It is the phase angle of the phase-locked loop of all GFL converters. These are the integral state variables of the active power control channels of all GFL converters. It is the integral state variable of the reactive power control channel of all GFL converters. It is the power angle of all GFM converters. It is the frequency deviation of all GFM converters. It is the voltage amplitude deviation of all GFM converters. It is a vector function that represents the dynamic equations of the system and describes the state variables. rate of change (i.e. How does it depend on the current state variable? and algebraic variables . This represents the algebraic constraints of the system. A set of constraints must always be applied to the state variables. and algebraic variables Constraints that are satisfied simultaneously.

[0046] Furthermore, in active distribution networks, the system's dynamic characteristics exhibit control-dominated features. Converter control parameters not only determine the local response characteristics of individual converters but also profoundly influence the overall modal distribution and small-disturbance stability of the system. When the key parameters of the PLL and power loop control are improperly configured, oscillating modes are easily induced in the low-to-medium frequency range, leading to cross-node oscillation propagation and cascading instability, seriously threatening the operational safety of the distribution network. Therefore, it is urgent to improve the system's small-disturbance stability by coordinating the control parameters of each converter.

[0047] The small-disturbance stability of active distribution networks is often analyzed through the eigenvalue distribution of a linearized model at the system equilibrium point. First, equation (6) is linearized at the system's steady-state operating point, resulting in a linear differential-algebraic system with the following structure: (7) in, This represents the rate of change corresponding to a small change in the state variables of the power system. and These are the state matrix and input matrix of the linearized system, respectively, and their structure is influenced by both the converter control parameter configuration and the operating point location. and These are the output matrix and feedforward matrix of the linearized system, respectively, determined by the system network structure and operating point. For small changes in the state variables of a power system, This represents a small change in the algebraic variables of a power system. In practical engineering systems, matrices... It is usually nonsingular, so the algebraic variables can be eliminated to obtain a reduced-order state-space form: (8) in, This represents the reduced-order state matrix of the system. According to Lyapunov's first method, the small-disturbance stability can be achieved through... Eigenvalue judgment: If the real part of all eigenvalues ​​is negative, then the system is stable under small disturbances at the current equilibrium point.

[0048] To quantitatively assess the stability margin of the system, this embodiment introduces the spectral intercept as an evaluation metric. The spectral intercept is defined as a matrix... The maximum value of the real part of all eigenvalues, i.e.: (9) in, The spectral intercept is a numerical value used to measure the stability of a system. The operator that retrieves the maximum value among all values ​​within the parentheses; This means taking the real part of the complex number inside the parentheses; while Representation matrix The The system has several eigenvalues, which are typically complex numbers consisting of real and imaginary parts. A smaller spectral intercept indicates a faster recovery speed after a disturbance, signifying a higher stability margin.

[0049] Based on this, the method in this embodiment uses the spectral intercept of the linearized system as a performance index. By adjusting the PLL parameters of the GFL converter and the virtual damping parameters of the GFM, the system spectral intercept value is minimized, thereby improving the system's disturbance rejection performance. Let the decision variable vector be... The optimization problem can then be expressed as: (10) in, This represents an optimization operator whose goal is to find a set of parameters that minimizes the objective function. It is a decision variable vector, containing the control parameters that need to be adjusted, specifically... ,in and These are the proportional gain and integral gain of the PLL (phase-locked loop). These are virtual damping parameters; It is a slack variable used to transform complex constraints into a workable form. In the constraint, it is set to be greater than or equal to the maximum value of the real part of all eigenvalues. The spectral intercept represents the maximum value of the real part of all eigenvalues ​​of the matrix. It is the first of the matrix Each eigenvalue varies with the decision variable. Change with change; It is the set of all characteristic values ​​of the system; and These are the lower and upper bounds of the decision variables, used to constrain the control parameters within the range allowed by design specifications or hardware capabilities. It is worth noting that this type of eigenvalue-driven control parameter optimization problem is inherently a non-convex, non-smooth optimization problem, making it difficult to directly apply conventional gradient-based optimization methods.

[0050] This embodiment combines the analytical nature of matrix perturbation theory with the convex optimization advantages of semidefinite relaxation methods, proposing an eigenvalue sequence optimization algorithm based on perturbation theory and semidefinite relaxation. Its overall framework is as follows: Figure 4 As shown. The core idea of ​​this algorithm is to transform the problem of minimizing the non-smooth, non-convex spectral intercept into a series of structurally controllable and asymptotically solvable local subproblems through sensitivity analysis and constraint reconstruction.

[0051] A closed-loop optimization architecture employing local second-order modeling, semi-definite relaxation, and parameter updates is adopted. Specifically, firstly, using the system state matrix corresponding to the current control parameters as a benchmark, matrix perturbation theory is used to accurately analyze the first and second-order sensitivities of the system eigenvalues ​​with respect to the control parameters, thereby establishing local analytical expressions for the eigenvalues. Based on this, the originally non-smooth spectral intercept constraint is transformed into a set of low-dimensional, smooth, and structurally clear quadratic constraints, ensuring that each subproblem possesses clear gradient information and optimization direction.

[0052] To address the non-convex quadratic constraints remaining in the subproblem, the algorithm proposes a positive semidefinite relaxation strategy. By introducing auxiliary variables, the original non-convex quadratic constraints are elevated to matrix space and positive semidefinite constraints are applied, thereby relaxing the subproblem into an efficiently solvable convex optimization problem and obtaining the optimal perturbation direction for the converter parameters. Subsequently, the algorithm dynamically adjusts the parameter step size using a line search mechanism and gradually corrects the perturbation amplitude by constructing a monotonically decreasing criterion for the objective function, ensuring that each parameter update increases the system spectral intercept, thus avoiding the numerical instability caused by the superposition of perturbation approximation errors and relaxation errors.

[0053] Matrix perturbation theory reveals the changes in eigenvalues ​​of a linear system's state matrix when subjected to small perturbations. It treats matrix eigenvalues ​​as implicit functions of control parameters and expands them into Taylor series form within their local neighborhoods, thus quantifying the sensitivity of eigenvalues ​​to parameter perturbations. Let the system have initial parameters... The state space matrix under ,in, Let the integer domain be the real number field. Perform eigenvalue decomposition on it: (11) in, and These are the i-th eigenvalues The corresponding right and left eigenvectors satisfy the normalization condition: (12) When the control parameter is along a certain disturbance direction With step size After the change, the updated control parameters can be expressed as follows: As can be seen from the system modeling, the phase-locked loop parameters of the GFL converter, the GFM virtual damping, and the matrix in the formula... and There exists a linear mapping relationship. Because... and Once the system's equilibrium point is determined, it remains fixed and can be considered a constant matrix. Therefore, the state matrix obtained after reducing the system's order is... Each element also maintains a linear dependence on the control parameters. Based on this, the system state matrix... This can be represented as the direction of the disturbance. Linear combination form: (13) in, This represents the partial derivative matrix of the state matrix with respect to the k-th control parameter. According to matrix perturbation theory, the state matrix... eigenvalues and eigenvectors All are expanded to perturbation step length Taylor series form: (14) To obtain analytical expressions for the first and second-order sensitivities of the system eigenvalues ​​with respect to the control parameters, equation (14) is combined with the system eigenvalue decomposition formula. and according to the perturbation step size After expanding and matching the coefficients of each order, we can obtain: (15) (16) Multiply by the left side of both sides of equation (15) After simplification, the first-order sensitivity expression for the eigenvalues ​​is obtained as follows: (17) in, , Similarly, multiplying by the left side of equation (16) The second-order sensitivity expression for the eigenvalues ​​is obtained as follows: (18) The expression is: (19) The combined equations (11) and (17)-(19) can be used to... Further expressed as: (20) in, The second-order sensitivity matrix is ​​the eigenvalue, and its specific construction form is given by... , and The three components reflect the influence of the disturbance direction on the curvature of the system's eigenvalues. At this point, the second-order analytical expression of the real part of the eigenvalues ​​with respect to the converter control parameters is: (twenty one) in This indicates the operation of taking the real part. It is a real symmetric matrix and is The following relationship exists: (twenty two) Here, H represents the conjugate transpose of a complex matrix.

[0054] To address the non-smoothness of the objective function in the small-disturbance stability problem, the method in this embodiment reconstructs the spectral intercept constraint into n parameters related to the perturbation direction based on the above analytical expression. The quadratic inequality constraints allow us to construct a local sub-optimization problem of the following form: (twenty three) The objective function and constraints of this subproblem both have good local smoothness, which effectively alleviates the solution difficulties caused by the original non-smooth constraints.

[0055] Due to the second-order sensitivity correction matrix of the eigenvalues Generally, these problems are not positive definite, and the constraints in the subproblems are essentially non-convex quadratic inequalities, making it difficult to guarantee global convergence. Therefore, this embodiment introduces a semi-positive definite relaxation strategy, transforming the non-convex subproblems into efficiently solvable convex optimization forms through variable lifting and constraint reconstruction.

[0056] First, variable lifting techniques are used to adjust the perturbation direction vector. Mapping to a symmetric matrix space, defining matrix variables And by utilizing the properties of matrix inner product operations, the non-convex quadratic terms in the original constraints are rewritten as: (twenty four) in, This represents the trace operation of a matrix. It then transforms the original constraints into constraints about the variables. The linear matrix inequality form: (25) Note the equality constraints Equivalent to Given a rank-one matrix, to relax this constraint, the method in this embodiment employs a positive semidefinite envelope strategy to relax it into a convex constraint. This is equivalent to introducing linear matrix inequality constraints: (26) This relaxation method essentially extends the original non-convex feasible region into a convex hull containing its solution set. Based on this, the parameter perturbation amplitude is further increased. Setting it to 1, the final constructed local subproblem takes the following form: (27) This problem exhibits good convexity and solvability, and can be efficiently solved using existing convex optimization tools to find the local optimal perturbation direction. .

[0057] Because the eigenvalue estimation formula contains high-order truncation errors, and the solution to the relaxation problem may not strictly satisfy the rank-one constraint, using a fixed step size to update parameters will affect the convergence of the overall optimization process. Therefore, the algorithm introduces a line search mechanism based on the monotonically decreasing objective function during iteration to dynamically adjust the parameter update step size. In the online search strategy, when the optimal perturbation direction of the k-th subproblem... Once determined, the candidate values ​​are updated using the construction parameters: (28) in, Let be the step size factor. To measure the impact of changes in step size on the objective function, its decrease rate is defined as: (29) like If the current step size update does not lead to a decrease in the objective function, then the line search mechanism is triggered to update the step size. (30) And recalculate the parameters The process continues until the objective function meets the descent condition or the step size decays to the set minimum threshold. This mechanism not only effectively suppresses eigenvalue fluctuations caused by sensitivity estimation errors, but also ensures that the spectral intercept index continuously decreases during iteration, thereby improving the overall convergence and robustness of the algorithm.

[0058] Example 2, refer to Figures 5-15 This invention provides a method for collaborative optimization of multi-converter parameters to improve the stability of active distribution networks during small disturbances. To verify the effectiveness of the proposed eigenvalue sequence optimization algorithm in improving system stability during small disturbances, this embodiment selects the following parameters: Figure 5 The IEEE 33-node active distribution network system shown is used as a test case for simulation verification. The system has a rated voltage of 12.66kV and a base power of 10MW. A total of 10 converters are connected to the system, including 6 GFL converters connected to nodes 6, 9, 12, 15, 30 and 32 respectively; and 4 GFM converters configured at nodes 5, 16, 22 and 27. The initial configuration scheme of the control parameters of the GFL and GFM converters is shown in Table 1.

[0059] This invention relates to the phase-locked loop parameters of GFL converters. , and GFM virtual damping coefficient As optimization variables, among which and The range of variation is set to [50, 1000]. The range of variation is [1, 20]. System modeling and simulation were performed using the MATLAB / Simulink platform. The optimization problem was constructed based on the YALMIP modeling language, and the MOSEK solver was used to efficiently solve the semidefinite programming problem. All simulation tests were run on a computing platform equipped with an Intel i7-13700K CPU and 32GB of memory.

[0060] Table 1 Control Parameters for GFM and GFL Converters

[0061] Under the initial control parameter settings, the eigenvalue distribution of the system state matrix is ​​as follows: Figure 6 As shown. From Figure 6 The system's spectral intercept was observed to be only -0.094. The modal eigenvalues ​​dominated by the active power control loop of the GFM converter are distributed in the left half of the complex plane near the imaginary axis, resulting in a significant weak damping characteristic. At the same time, the modes dominated by the phase-locked loop are also distributed on the left side of the complex plane near the imaginary axis, indicating insufficient system stability margin and a tendency to induce oscillating modes under the dynamic interaction of multiple converters.

[0062] To improve the stability of the system under small disturbances, the method in this embodiment uses an eigenvalue sequence optimization algorithm to jointly optimize the phase-locked loop parameters of the GFL converter and the virtual damping coefficient of the GFM. Figure 7 The eigenvalue distribution of the optimized system state matrix is ​​shown, with the system spectral intercept improved to -1.534, more than 16 times higher than the initial value. Simultaneously, the real parts of the three pairs of GFM active power loop oscillation dominant modes have all shifted significantly to the left, increasing to -1.562, -1.589, and -1.611 respectively, effectively improving the system's low-damping modes. Furthermore, the modes dominated by the GFL converter control loop have also shifted to the left overall, verifying the effectiveness of the proposed optimization algorithm in improving the stability of active distribution networks under small disturbances.

[0063] Figure 8 and Figure 9 The evolution of the participation factors of the spectral intercept mode before and after optimization is shown. Before optimization, the participation factors of the spectral intercept mode were mainly concentrated in the active power control loop of the GFM converter, indicating that this part of the control channel lacked sufficient damping support. After optimization, the spectral intercept shifted significantly to the left, and the dominant participation factor of the spectral intercept mode also changed. At this time, the voltage control loop of the GFM converter became dominant, and the system stability bottleneck shifted from the active power loop of the GFM converter to the voltage dynamic regulation level. This result shows that the optimization algorithm, by fully exploiting the synergistic effect of the GFL and GFM control parameters, makes the system's small-disturbance stability margin approach the optimal boundary under the current control structure.

[0064] To further analyze the convergence of the proposed algorithm, Figures 10-13 The changes in spectral intercept and control parameters with the number of iterations are shown. For example... Figure 10 As shown, the spectral intercept increases rapidly in the initial stage, but after the 16th iteration, its increase is less than the pre-set convergence threshold, at which point the optimization process automatically terminates. Figure 11 The results show that the virtual damping coefficient of the GFM converter continuously increases during the optimization process, and all converters exhibit a consistent isomorphic evolution trend, indicating that enhancing virtual damping is beneficial to improving the overall oscillation suppression capability of the system. Meanwhile, from... Figure 12 and Figure 13 Discover the proportional parameters of the phase-locked loop The integral coefficient shows a decreasing trend with increasing spectral intercept. The overall increase indicates that reducing the proportional gain and increasing the integral gain of the PLL can effectively improve the dynamic characteristics of the control loop. However, due to differences in factors such as the location of each node in the power grid topology, voltage support capacity, and load characteristics, the PLL parameters exhibit a significant heterogeneous configuration. This phenomenon reflects that differentiated control strategies are more conducive to tapping the potential of local controllers and synergistically improving the small-disturbance stability of the entire system.

[0065] To verify the effectiveness of the proposed optimization algorithm in improving the dynamic performance of the system under disturbance conditions, time-domain simulation analysis was conducted in a typical scenario. The simulation test was based on the control parameter configuration before and after optimization. At simulation time t=0.05s, a three-phase short-circuit fault with a duration of 0.05s was introduced at bus 16, and node 5 was set as the reference balance node. Figure 14 and Figure 15 The power angle response curves of a typical GFM converter before and after optimization during disturbances are presented.

[0066] from Figure 14 As can be seen, before optimization, the GFM converter exhibited a rapid shift in power angle after a short-circuit fault, with high oscillation amplitude and long duration, requiring more than 50 seconds to recover to steady state. The system displayed obvious low-damping and weak stability characteristics. However, after optimization... Figure 15 The response of the power angle of the GFM converter to disturbances is significantly improved. The initial offset of the power angle is suppressed to 0.025 rad, and the damping effect after the system enters the oscillation state is significantly enhanced. The power angle recovers to near the steady state within about 4 seconds and no longer exhibits obvious zero-crossing swing, indicating that the optimized control parameter configuration effectively enhances the dynamic recovery capability of the system.

[0067] To verify the necessity of parameter co-optimization, this embodiment designed and compared three optimization strategies: Strategy 1 optimizes only the GFM virtual damping coefficient; Strategy 2 optimizes only the GFL converter PLL parameters; and Strategy 3 co-optimizes the virtual damping and PLL parameters. The system spectrum intercepts under each scheme are shown in Table 2.

[0068] Table 2 Comparison of system spectral intercept under different optimized parameters

[0069] As shown in Table 2, the system spectral intercept improved from -0.094 to -1.354 after optimization in Strategy 1, indicating that enhancing virtual damping can effectively improve the low-damped modes of the system. However, the dominant participating factor in the optimized spectral intercept mode has changed from the active control loop of the GFM converter to the PLL control loop, and the system stability is approaching the upper limit achievable by adjusting the virtual damping parameter, indicating that the optimization space of a single control path has reached saturation. The system spectral intercept after optimization in Strategy 2 remains at -0.094, unchanged from before optimization. Combined with... Figure 6 Participation factor analysis revealed that before optimization, the participation rate of PLL parameters in the spectral intercept mode was less than 1%, resulting in parameter changes failing to improve system stability. However, in Strategy 3, the synergistic optimization of virtual damping and PLL parameters further increased the spectral intercept to -1.534, exceeding the optimization results of Strategy 1 and Strategy 2. At this point, the dominant participation factor in the spectral intercept mode shifted to the GFM voltage control loop, indicating that the optimization algorithm fully utilized the synergy among multiple control parameters, breaking through the optimization upper limit of a single control path. This verifies the significant role and necessity of joint adjustment of multi-source control parameters in improving the stability of active distribution networks during small disturbances.

[0070] This embodiment further selects three typical optimization methods for comparative analysis: Monte Carlo search, genetic algorithm, and eigenvalue first-order approximation. All methods use the same initial control parameter configuration, with maximizing the system spectral intercept as the optimization objective. Specifically, the Monte Carlo search randomly generates 1000 sets of control parameters within the feasible region and selects the combination with the largest spectral intercept as the optimal solution; the genetic algorithm has a population size of 100, a maximum number of iterations of 100, a crossover probability of 0.9, and a mutation probability of 0.1; the eigenvalue first-order approximation method constructs a linear optimization model based on the first-order sensitivity of eigenvalues ​​and adjusts the parameters through a subproblem sequential iteration strategy. Table 3 presents the comparison results of the four algorithms in terms of optimal spectral intercept and computational efficiency.

[0071] As shown in Table 3, the algorithm in this embodiment significantly outperforms the other three algorithms with a spectral intercept of -1.534, representing improvements of 75.9%, 32.4%, and 58.0% respectively. Furthermore, the computation time of this algorithm is only 0.082 seconds, far shorter than other methods. This is attributed to the algorithm's use of eigenvalue serialization to transform the non-smooth optimization problem into a series of semi-positive definite programming problems, avoiding the random search process of traditional heuristic algorithms and overcoming the tendency of first-order approximation methods to get trapped in local optima in strongly nonlinear systems. This achieves a synergistic improvement in optimization accuracy and computational efficiency.

[0072] Table 3 Performance Comparison of Different Optimization Methods

[0073] Based on the above description of the implementation methods, those skilled in the art can clearly understand that the present invention can be implemented using software and necessary general-purpose hardware, and of course, it can also be implemented using hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as a computer floppy disk, read-only memory (ROM), random access memory (RAM), flash memory, hard disk, or optical disk, etc., including several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods of the various embodiments of the present invention.

[0074] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for collaborative optimization of multi-converter parameters to improve the stability of active distribution networks under small disturbances, characterized in that: include, A differential algebraic equation model of an active distribution network is established. The differential algebraic equation model consists of an AC grid model, a GFL converter model, a GFM converter model, and a ZIP load model. The AC grid model, GFL converter model, GFM converter model, and ZIP load model are simplified mathematical models derived based on the principle of time scale separation. The differential-algebraic equation model of the active distribution network is linearized at the steady-state operating point and the algebraic variables are eliminated to obtain the state-space model of the active distribution network. In the state-space model of the active distribution network, the maximum value of the real part of the eigenvalue is defined as the spectral intercept. A control parameter optimization problem is constructed with the goal of minimizing the spectral intercept. The control parameters include the phase-locked loop parameters of the GFL converter model and the virtual damping parameters of the GFM converter model. Value boundaries are set for the control parameters. Based on matrix perturbation theory, the first-order and second-order sensitivities of the eigenvalues ​​of the state-space model of the active distribution network with respect to the control parameters are calculated, and the control parameter optimization problem is transformed into a local quadratic constraint subproblem with respect to the direction of parameter perturbation. The local quadratic constraint subproblem is solved by convexification using semi-positive definite relaxation to obtain the update direction of the control parameters. The parameter update step size is determined by a line search mechanism, and the control parameters are iteratively updated. After each update, the convergence condition is determined based on the spectral intercept. When the convergence condition is met, the co-optimized phase-locked loop parameters and the virtual damping parameters are output to reduce the spectral intercept and improve the small-disturbance stability margin of the active distribution network.

2. The method for collaborative optimization of multi-converter parameters to improve the stability of active distribution networks under small disturbances as described in claim 1, characterized in that: The AC power grid model is represented as follows: in, It is the system node admittance matrix. Let n represent the set of complex numbers, n represent the total number of nodes, and i represent the node number. For each node, there is a complex voltage vector; , and These represent the injected currents of the GFL converter, GFM converter, and ZIP load in the global coordinate system, respectively. Indicates the first An n-dimensional unit vector with one component equal to 1 and the rest equal to 0. Number the nodes.

3. The method for collaborative optimization of multi-converter parameters to improve the stability of active distribution networks under small disturbances as described in claim 2, characterized in that: The GFL converter model is represented as follows: in, Indicates the first Intermediate state variables of the phase-locked loop integrator of a GFL converter The phase angle calculated for the phase-locked loop. The reference angular frequency of the power grid. This refers to the frequency deviation of the phase-locked loop output. These are the integral coefficients of the phase-locked loop. This represents the integral state variable of the active power control channel. This represents the integral state variable of the reactive power control channel. This refers to the set of nodes connected to the GFL type converter. The first The d-axis and q-axis components of the voltage at the grid-connected node of a converter. For the first The d-axis current injected into the grid by a ZIP load For the first The q-axis current injected into the grid by a ZIP load. The voltage amplitude at the grid connection point. The complex output current injected into the grid for the GFL converter, The imaginary unit satisfies .

4. The method for collaborative optimization of multi-converter parameters to improve the stability of active distribution networks under small disturbances as described in claim 3, characterized in that: The GFM converter model is represented as follows: in, Indicates the first The power angle of a GFM converter For its frequency deviation, The system's reference angular frequency, The equivalent inertia coefficient, This represents the reference value for active power. This represents the actual output value of active power. The active power damping coefficient is... The reactive control inertia coefficient, For voltage amplitude deviation, This represents the reference value for reactive power. This represents the actual output value of reactive power. The reactive power damping coefficient and voltage amplitude are given. The stable value of the voltage amplitude at the grid connection node voltage amplitude deviation The result of superposition is that , This refers to the voltage amplitude at the grid connection node. For filter reactance, For the complex output current injected into the power grid, This represents the set of nodes connected to the GFM type converter.

5. The method for collaborative optimization of multi-converter parameters to improve the stability of active distribution networks under small disturbances as described in claim 4, characterized in that: The ZIP load model is expressed as follows: in, Indicates the first The amplitude of the voltage at each ZIP load node. The load component factor representing the constant impedance (Z) corresponding to active power. The load component factor represents the constant current (I) corresponding to the active power. This represents the load component factor of constant power (P) corresponding to active power. This represents the load component factor of the constant impedance (Z) corresponding to reactive power. This represents the load component factor of the constant current (I) corresponding to reactive power. This represents the load component factor of the constant power (P) corresponding to reactive power. The d-axis current component at the reference operating point. The q-axis current component at the reference operating point. The complex current injected into the grid for the ZIP load. The phase angle of the node voltage. This represents the set of nodes connected to a ZIP-type load.

6. The method for collaborative optimization of multi-converter parameters to improve the stability of active distribution networks under small disturbances as described in claim 5, characterized in that: By combining the AC power grid model, GFL converter model, GFM converter model, and ZIP load model, a system of differential-algebraic equations characterizing the dynamic behavior of the system is constructed, expressed as: in, Represents state variables, Let T be an algebraic variable, representing transpose. It is the intermediate state variable of the phase-locked loop integrator of all GFL converters. It is the phase angle of the phase-locked loop of all GFL converters. These are the integral state variables of the active power control channels of all GFL converters. These are the integral state variables of the reactive power control channels of all GFL converters. It is the power angle of all GFM converters. It is the frequency deviation of all GFM converters. It is the voltage amplitude deviation of all GFM converters. It is a vector function. It is the algebraic constraint of the system.

7. The method for collaborative optimization of multi-converter parameters to improve the stability of active distribution networks under small disturbances as described in claim 6, characterized in that: The linearization process of the differential-algebraic equation model of the active distribution network at the steady-state operating point includes, in, This represents the rate of change corresponding to a small change in the state variables of the power system. Represents the state matrix of a linearized system. Represents the input matrix of the linearized system. This represents the output matrix of the linearized system. Represents the feedforward matrix of the linearized system. For small changes in the state variables of a power system, It represents the infinitesimal changes in the algebraic variables of the power system.

8. The method for collaborative optimization of multi-converter parameters to improve the stability of active distribution networks under small disturbances as described in claim 7, characterized in that: Due to the matrix Having nonsingularity, elimination of algebraic variables yields a reduced-order state-space form, expressed as: in, This is the reduced-order state matrix of the system; According to Lyapunov's first method, small-disturbance stability can be achieved through... The eigenvalues ​​are used to determine if all real parts of the eigenvalues ​​are negative, in which case the system is stable under small disturbances at the current equilibrium point.

9. The method for collaborative optimization of multi-converter parameters to improve the stability of active distribution networks under small disturbances as described in claim 8, characterized in that: The maximum value of the real part of the eigenvalues ​​is extracted as the spectral intercept from the state-space model of the active distribution network, and the control parameter optimization problem is constructed with the objective of minimizing the spectral intercept as follows: in, Indicates the optimization operator; It is a decision variable vector, containing the control parameters that need to be adjusted, specifically... , and These are the proportional gain and integral gain of the PLL. These are virtual damping parameters; It is a slack variable; This represents the maximum value of the real part of all eigenvalues ​​of the matrix. It is the first of the matrix 1 eigenvalue, It is the set of all characteristic values ​​of the system; and These are the lower and upper limits of the decision variable, respectively.

10. The method for collaborative optimization of multi-converter parameters to improve the stability of active distribution networks under small disturbances as described in claim 9, characterized in that: The step of using semi-positive definite relaxation to perform convexity solution to obtain the update direction of the control parameters includes: performing variable boosting on the parameter disturbance direction vector, mapping the disturbance direction vector to a symmetric matrix space, defining matrix variables, and using trace operation to transform the non-convex quadratic terms into matrix form; By introducing a positive semidefinite condition under the matrix variable constraint, the rank constraint is relaxed to a positive semidefinite constraint, thereby transforming the local quadratic constraint subproblem into a convex optimization problem and solving it. A line search mechanism is introduced during the control parameter update process. The update step size is dynamically adjusted based on the monotonically decreasing criterion. When the current step size does not meet the decreasing condition, the step size is reduced until the step size decays to the set threshold.

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