Phase-locked loop stability boundary method, device and medium for a grid-following converter

Abstract

The application belongs to the field of power system optimal operation, and specifically discloses a grid-following converter phase-locked loop stability boundary optimal power flow method, equipment and medium. The application constructs a system damping matrix related to the dynamic characteristics of the phase-locked loop, explicitly represents the change of synchronous damping margin caused by the change of the operating state, and converts the phase-locked loop synchronous stability criterion into an explicit mathematical inequality about the operating variable by using the Gerschgorin disc theorem, so that the phase-locked loop synchronous stability requirement can be directly embedded into the optimal power flow model. Thus, the traditional operation mode of "first optimization, then checking, and then adjustment" is changed into joint optimization under the synchronous stability constraint, the synchronous instability operating point is actively avoided in the optimization process, the synchronous stability of the phase-locked loop is ensured, the calculation process of repeated stability checking and adjustment under different operating states is reduced, the instability hidden danger after the large-scale grid-following converter is connected to the system is eliminated, and the system safety margin is improved.

Description

Technical Field

[0001] This application belongs to the field of power system optimization operation, specifically involving a method, equipment, and medium for optimal power flow at the stability boundary of a grid-connected converter phase-locked loop. Background Technology

[0002] Currently, a large amount of renewable energy is connected to the grid via grid-connected converters. This has significantly changed the power system structure, exhibiting characteristics of a weak grid. Under weak grid conditions, the phase-locked loop (PLL) of the grid-connected converter is highly susceptible to coupling with the grid impedance, causing the converter ports to exhibit negative damping characteristics at specific frequency bands. This, in turn, can induce PLL-dominated synchronization instability. Therefore, to ensure stable power system operation under the backdrop of large-scale converter integration, it is essential to consider the synchronization stability problems caused by PLL dynamics.

[0003] Currently, research on phase-locked loop (PLL) synchronization stability mainly focuses on two aspects: equipment-level control and system-level optimization. In terms of equipment-level control, common methods include PLL controller parameter tuning, additional damping control, virtual impedance control, and coordinated control of network equipment. These methods can improve grid-connected stability by addressing the control characteristics of the converter itself, but they struggle to cope with the global synchronous instability risk caused by time-varying system topology and the coupling interaction of multiple converters. In terms of system-level optimization, a common approach is "optimize first, then verify, then adjust." This involves first determining the system operating scheme through optimal power flow, then conducting PLL synchronization stability analysis based on the optimization results; when the operating point does not meet stability requirements, the operating states such as converter output and node voltage are readjusted, and stability verification is performed again until a stable operating scheme is obtained. This approach separates economic operation optimization from stability analysis. Under conditions of frequent changes in system operating modes and converter output, optimization, stability verification, and operation adjustment need to be repeatedly performed for different operating points, resulting in a complex calculation process. Furthermore, it is difficult to proactively avoid potential synchronous instability operating points during the optimization process.

[0004] To address the aforementioned issues, some studies have directly embedded small-disturbance stability constraints into optimal power flow models, primarily including methods based on eigenvalue sensitivity, data-driven surrogate models, and distributed stability criteria. These methods comprehensively consider the synchronization stability of the phase-locked loop (PLL) within an optimization framework that takes into account the small-disturbance stability constraints of the grid-connected converter. They can reflect the overall dynamic stability margin of the system to some extent, but lack explicit characterization of the PLL's dynamic characteristics, making it difficult to directly describe the impact of system decision variables and PLL control parameters on the system's synchronization stability boundary. Therefore, current research on optimization methods considering the synchronization stability boundary of the PLL in grid-connected converters is very limited. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this application aims to provide a method, device, and medium for optimal power flow at the stable boundary of the phase-locked loop (PLL) in a grid-connected converter. The goal is to solve the problems that existing operation optimization methods lack explicit characterization of the PLL dynamic characteristics and synchronous stability boundary, and that synchronous stability criteria are difficult to directly embed into the optimal power flow model, making it difficult to actively avoid synchronous instability points during the optimization process.

[0006] The first aspect of this application relates to an optimal power flow method for the stability boundary of a grid-connected converter phase-locked loop (PLL), comprising: step S10, constructing a damping matrix of the power system based on network data and load data of the power system, and a frequency domain admittance model of the grid-connected converter; the frequency domain admittance model is a complex frequency domain function characterizing the change of the PLL damping characteristics with operating state; step S20, obtaining the available damping margin of the grid-connected node of the converter based on the damping matrix and load data, according to Gell's disk theorem; the available damping margin is the effective damping capacity actually possessed by the grid-connected node after deducting network coupling effects; step S30, constructing synchronous stability constraints for the PLL of the grid-connected converter based on the available damping margin and the real part of the frequency domain admittance model; step S40, embedding the synchronous stability constraints into the optimal power flow model of the power system and solving it to obtain the optimized output result of the converter that meets the synchronous stability requirements of the PLL.

[0007] In one embodiment, before step S10, the following steps are included: constructing the output power equation in the actual grid coordinate system based on the grid-connected topology of the grid-connected converter; constructing the small-signal linearized control equation based on the phase-locked loop control loop of the grid-connected converter; performing small-signal linearization on the coordinate transformation relationship of the grid-connected node voltage and the mapping relationship of the output current in the actual grid coordinate system based on the phase deviation relationship between the actual grid coordinate system and the phase-locked loop control coordinate system; and obtaining the frequency domain admittance model by simultaneously solving the output power equation, the small-signal linearized control equation, the voltage coordinate transformation relationship after small-signal linearization, and the current mapping relationship.

[0008] In one embodiment, step S10 includes: constructing the system's node admittance matrix and the load admittance model of each node based on the network data and load data of the power system; adding the load admittance model and frequency domain admittance model of each node to the node admittance matrix to obtain the system node admittance augmented matrix; and constructing the system damping matrix based on the system node admittance augmented matrix and the corresponding Hermitian matrix.

[0009] In one embodiment, the off-diagonal elements of the damping matrix are determined based on the branch conductance of the target node and each of the other nodes in the network data; the diagonal elements of the damping matrix are determined based on the branch conductance connected to the target node, load data, and the real part of the frequency domain admittance model.

[0010] In one embodiment, step S20 includes: obtaining the node's own equivalent damping based on the conductance and load data of each branch connected to the target node; determining the network coupling damping based on the branch conductance of the target node and each of the other nodes in the network data; and determining the available damping margin of the grid-connected node based on the calculation result of subtracting the network coupling damping from the node's own equivalent damping.

[0011] In one embodiment, the synchronization stability constraint of the phase-locked loop is that the real part of the frequency domain admittance model is less than the available damping margin.

[0012] In one embodiment, the optimal power flow model of the power system includes an objective function and constraints; the objective function is to minimize the system network loss; the constraints include at least node power balance constraints, branch power flow constraints, synchronous generator output constraints, grid-connected converter output constraints, node voltage amplitude constraints, line capacity transmission constraints, and synchronous stability constraints.

[0013] In one embodiment, step S40 includes: initializing the active power output of the grid-connected converter and the voltage amplitude of the grid-connected node as initial decision variables; based on the initial decision variables, obtaining the real part and available damping margin of the frequency domain admittance model, and constructing synchronous stability constraints; embedding the synchronous stability constraints into the optimal power flow model of the power system, performing iterative solutions through a solver, and updating the decision variables; repeatedly obtaining the real part and available damping margin of the frequency domain admittance model, and updating the synchronous stability constraints, until the decision variables meet the convergence condition, and outputting the optimized output result of the converter.

[0014] Secondly, this application provides an electronic device, comprising: a communication interface configured to acquire network data, load data, and the real part of a frequency domain admittance model of a grid-connected converter; a memory connected to the communication interface configured to store the network data, load data, the real part of the frequency domain admittance model, and computer-executable instructions; and a processor connected to the communication interface and the memory configured to execute computer-executable instructions to control the electronic device to implement the optimal power flow method of the stable boundary of the grid-connected converter phase-locked loop of the first aspect.

[0015] Thirdly, this application provides a computer-readable storage medium storing a computer program that, when run on a processor, causes the processor to perform the method described in the first aspect or any possible implementation thereof.

[0016] Fourthly, this application provides a computer program product that, when run on a processor, causes the processor to perform the method described in the first aspect or any possible implementation thereof.

[0017] It is understood that the beneficial effects of the second to fourth aspects mentioned above can be found in the relevant descriptions in the first aspect mentioned above, and will not be repeated here.

[0018] Overall, the technical solutions conceived in this application have the following beneficial effects compared with the prior art: This application constructs a system damping matrix related to the dynamic characteristics of the phase-locked loop (PLL), explicitly characterizing the change in synchronization damping margin caused by changes in operating state. Furthermore, it utilizes Gell's disk theorem to transform the PLL synchronization stability criterion into an explicit mathematical inequality concerning the operating variables, allowing the synchronization stability requirement to be directly embedded into the optimal power flow model. This transforms the traditional "optimize first, then verify, then adjust" operating method into joint optimization under synchronization stability constraints. During the optimization process, it actively avoids synchronization instability points, ensuring the synchronization stability of the PLL and reducing the need for repeated stability verification and adjustment calculations under different operating states. Attached Figure Description

[0019] Figure 1 This is a flowchart illustrating the optimal power flow method for the stable boundary of the phase-locked loop in a grid converter provided in this application embodiment; Figure 2 This is a topology diagram of a 39-node system provided in an embodiment of this application; Figure 3 This is a schematic diagram of the grid-connected topology of the grid-connected converter provided in the embodiments of this application; Figure 4 This is a schematic diagram of the control loop of the phase-locked loop of the grid-connected converter provided in the embodiments of this application; Figure 5 This is a schematic diagram of the active power output boundary characteristics of a grid-connected converter solved by the optimal power flow model without phase-locked loop synchronous stability constraints provided in this application embodiment; Figure 6 This is a schematic diagram of the active power output boundary characteristics of a grid-connected converter solved by the optimal power flow model with phase-locked loop synchronous stability constraints provided in the embodiments of this application. Figure 7 This is an eigenvalue distribution diagram of the system's generalized admittance matrix when the active power output of the grid-connected converter is output according to the solution result of the optimal power flow model with synchronous stability constraints without phase-locked loop, provided in the embodiments of this application. Figure 8 This is a partially enlarged view of the eigenvalue distribution of the generalized admittance matrix of the system when the active power output of the grid-connected converter is output according to the solution result of the optimal power flow model with synchronous stability constraints without phase-locked loop provided in the embodiments of this application; Figure 9 This is an eigenvalue distribution diagram of the system's generalized admittance matrix when the active power output of the grid-connected converter is output according to the solution result of the optimal power flow model with phase-locked loop synchronous stability constraints provided in the embodiments of this application. Figure 10 This is a partially enlarged view of the eigenvalue distribution of the generalized admittance matrix of the system when the active power output of the grid-connected converter is output according to the solution result of the optimal power flow model with phase-locked loop synchronous stability constraints provided in the embodiments of this application; Figure 11 This is a schematic diagram of the structure of the electronic device provided in the embodiments of this application.

[0020] In all the accompanying drawings, the same reference numerals are used to denote the same elements or structures, wherein: 100 is the communication interface; 200 is the memory; 300 is the processor; 400 is the communication bus. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0022] In this application, the term "and / or" describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent three cases: A existing alone, A and B existing simultaneously, and B existing alone. In this application, the symbol " / " indicates that the related objects are in an "or" relationship, for example, A / B means A or B.

[0023] In this application, the terms "first" and "second," etc., are used to distinguish different objects, not to describe a specific order of objects. For example, "first response message" and "second response message," etc., are used to distinguish different response messages, not to describe a specific order of response messages.

[0024] In the embodiments of this application, the terms "exemplary" or "for example" are used to indicate that something is an example, illustration, or description. Any embodiment or design that is described as "exemplary" or "for example" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or designs. Specifically, the use of the terms "exemplary" or "for example" is intended to present the relevant concepts in a specific manner.

[0025] In the description of the embodiments of this application, unless otherwise stated, "multiple" means two or more, for example, multiple processing units means two or more processing units, multiple elements means two or more elements, etc.

[0026] Based on the background technology, this application proposes an embodiment of an optimal power flow method for the stable boundary of a grid-type converter using a phase-locked loop. Please refer to... Figure 1 , Figure 1This is a flowchart illustrating the optimal power flow method for the stable boundary of the phase-locked loop in a grid converter provided in this application embodiment.

[0027] In this embodiment, the method includes: Step S10: Based on the network data and load data of the power system, as well as the frequency domain admittance model of the grid-connected converter, construct the damping matrix of the power system.

[0028] Among them, the network data of the power system refers to the topological connections of the power grid, line impedance parameters, transformer parameters, etc.; the load data of the power system refers to the active and reactive power demands of each node. The frequency domain admittance model of a grid-connected converter is a complex frequency... s The transfer function is a complex frequency domain function that characterizes the change of the phase-locked loop's damping characteristics with operating conditions. Its real part reflects the positive or negative damping components that the phase-locked loop can provide at different frequencies.

[0029] Specifically, nodes i The frequency domain admittance model of a grid-connected converter can be expressed as: ;in, For the real part of the frequency domain model of the grid converter; This is the imaginary part of the frequency domain model of the grid converter.

[0030] It should be noted that the core idea of ​​constructing this damping matrix in this application is to directly incorporate the frequency domain admittance model characterizing the dynamic characteristics of the phase-locked loop and the node load admittance model characterizing the constant power characteristics into the power system node admittance matrix composed of network data and load data, forming an augmented matrix. Then, the augmented matrix and the corresponding Hermitian matrix are added together and divided by 2 to construct the system's damping matrix.

[0031] Understandably, in any complex admittance matrix, this method extracts the energy dissipation or conductance portion, which corresponds precisely to the system's damping characteristics; the remaining antisymmetric portion corresponds to energy storage or susceptance characteristics and does not provide damping. The resulting matrix is ​​a pure damping correlation matrix, which can be used to directly calculate the overall system damping level and determine stability.

[0032] Specifically, nodes i The load admittance model can be expressed as: ;in, Let be the real part of the nodal equivalent load admittance, and its magnitude is . , Let be the imaginary part of the nodal equivalent load admittance, and its size is . , and For nodes i The active and reactive loads can be determined. These parameters can be obtained from the power system's network data and load data.

[0033] Similarly, the nodal admittance matrix of the system can be written as: (1).

[0034] in, For nodes i Self-guided absorbance, For nodes i With nodes j Mutual admittance between them i =1, 2, ..., n; j =1, 2, ..., n; n is the number of system nodes.

[0035] At this point, the frequency domain admittance model of the grid converter and the load admittance models of each node are added to the node admittance matrix to obtain the system node admittance augmented matrix. : (2).

[0036] Add the augmented matrix and the corresponding Hermitian matrix and divide by 2: Construct the system damping matrix D : (3).

[0037] in, It is the Hermitian matrix of the augmented admittance matrix of the system nodes.

[0038] Therefore, before implementing step S10, it is necessary to obtain the frequency domain admittance model of the grid-connected converter. This application proposes a model construction method that does not directly use existing transfer functions or data-driven proxy models. Instead, it starts from the physical topology and control loop of the converter and constructs four sub-models sequentially through analytical derivation: the output power equation, the small-signal linearized control equation, the small-signal linearized form of the voltage coordinate transformation relationship, and the small-signal linearized form of the current mapping relationship. These are then solved simultaneously to obtain the frequency domain admittance model at complex frequencies. s Frequency domain admittance model with variables.

[0039] Specifically, based on the grid-connected topology of the grid-connected converter, the output power equation is constructed in the actual grid coordinate system.

[0040] It should be noted that grid-connected topology refers to the connection method between the converter and the power grid, including the wiring configuration and parameters of components such as filter inductors, transformers, and line impedance. Based on this topology, a mathematical expression for the converter's output power needs to be established in the actual coordinate system of the power grid.

[0041] The output power equation is usually expressed as: (4).

[0042] in, and These are the active power and reactive power output of the grid-connected converter, respectively. and These are the direct-axis and quadrature-axis components of the voltage at the grid connection point of the grid-connected converter in steady state under the actual coordinate system of the power grid. and These represent the direct-axis and quadrature-axis components of the output current of the grid-connected converter in steady state, respectively, within the actual coordinate system of the power grid. This equation reflects the relationship between the active and reactive power injected into the grid by the converter and its port electrical quantities; it provides a benchmark equation for the steady-state operating point for subsequent small-signal linearization, ensuring that the model can accurately reflect the power transmission characteristics at different operating points.

[0043] Therefore, under the control of the phase-locked loop, the following exists in steady state: (5).

[0044] in, For nodes The voltage amplitude.

[0045] Specifically, based on the phase-locked loop control circuit of the grid-type converter, a small-signal linearized control equation is constructed.

[0046] It should be noted that a phase-locked loop (PLL) control circuit typically consists of a phase detector, a loop filter (PI controller), and a voltage-controlled oscillator (VCO). The small-signal linearized control equation approximates the nonlinear dynamics of the PLL as a linear transfer function using a first-order Taylor expansion near the steady-state operating point.

[0047] Specifically, the small-signal linearization control equation is: (6).

[0048] in, The deviation between the phase-locked loop output phase and the system synchronization phase. and Indicates the first The proportional and integral coefficients of the phase-locked loop controller for the converter. s For the Laplace operator, To control the quadrature axis small disturbance component of the voltage at the grid connection point of the grid-type converter in the coordinate system.

[0049] Understandably, the construction of this equation depends on the proportional-integral coefficients of the phase-locked loop (PLL) and the feedforward compensation parameters. Transforming the closed-loop dynamics of the PLL into an analytically expressible linear element provides the PLL's own response to phase disturbances for subsequent simultaneous solutions.

[0050] Specifically, based on the phase deviation relationship between the actual grid coordinate system and the phase-locked loop control coordinate system, small-signal linearization is performed on the coordinate transformation relationship of the grid connection point voltage of the grid-connected converter and the mapping relationship of the output current in the actual grid coordinate system.

[0051] It is understandable that the actual grid coordinate system is a rotating coordinate system oriented towards the grid voltage vector, while the phase-locked loop (PLL) control coordinate system is oriented towards the PLL output phase. There is a phase deviation angle between the two. Therefore, voltage and current have a transformation relationship between the two coordinate systems. By performing small-signal linearization on this transformation relationship—that is, assuming the phase deviation angle is very small and substituting cosine as 1 and sine as itself—a linearized transformation matrix is ​​obtained.

[0052] Specifically, the small-signal coordinate transformation relationship of the cross-axis component of the grid connection point voltage is as follows: (7).

[0053] in, It represents the quadrature-axis small disturbance component of the voltage at the grid connection point of the grid-type converter in the actual coordinate system of the power grid.

[0054] Similarly, the mapping relationship of the output current in the actual coordinate system of the power grid also needs to be linearized. That is, the current command is generated in the phase-locked loop control coordinate system, and after PWM modulation, the current component is actually output to the actual coordinate system of the power grid, which is also affected by the phase deviation angle.

[0055] Specifically, the relationship with the output current projection of the grid converter is as follows: (8).

[0056] in, It represents the quadrature-axis small disturbance component of the output current of the grid-type converter in the actual coordinate system of the power grid.

[0057] Understandably, the key to this step is to retain the phase deviation as a small-signal variable in the linearized equation, thereby establishing a coupling channel between the phase-locked loop dynamics and the electrical quantities at the converter port; it reveals how the phase deviation of the phase-locked loop affects the coordinate transformation of voltage and current, which is a crucial step for subsequent models to reflect the negative damping mechanism of the phase-locked loop.

[0058] Specifically, by combining the output power equation, the small-signal linearization control equation, the voltage coordinate transformation relationship after small-signal linearization, and the current mapping relationship, the frequency domain admittance model is obtained.

[0059] It should be noted that the simultaneous equation-making process refers to treating the above four sub-models (output power equation, phase-locked loop small-signal control equation, small-signal form of voltage coordinate transformation relationship, and small-signal form of current mapping relationship) as a set of algebraic equations, eliminating intermediate variables, and finally obtaining the equations with only complex frequency as the equation. s The transfer function with operating state parameters as variables is the frequency domain admittance model.

[0060] Understandably, the output of this model is a complex number, and its real part is the damping margin provided by the phase-locked loop at a given frequency. Simultaneous solutions typically employ symbolic derivation or numerical elimination methods, such as using the Mason gain formula or state-space transformation. Alternative options include: directly constructing the converter port impedance model using the frequency domain impedance method and then extracting the damping component from it; or using system identification methods to obtain frequency response data by injecting a swept-frequency signal and then fitting a rational function to obtain the frequency domain admittance model. However, neither of the latter two methods can explicitly preserve the analytical relationships of all operating state parameters as in this application.

[0061] Understandably, the direct effect of this step is to obtain a complex frequency domain function with a clear physical meaning, which can be directly used to construct the damping matrix in step S10, and its analytical form makes sensitivity analysis and constraint embedding in subsequent optimization feasible.

[0062] Finally, the real part of the frequency domain admittance model for the grid converter is: (9).

[0063] in: (10); (11).

[0064] in, Represents a node The real part of the frequency domain admittance model of the grid-type converter. Represents a node The real part of the frequency domain admittance model of the grid converter is a function of the angular frequency. , and the active power output of the grid converter and node voltage The function, This represents the denominator of the real part of the frequency domain admittance model for a grid-type converter. The molecule represents the real part of the frequency domain admittance model of a grid-type converter.

[0065] Understandably, the real part of the frequency domain admittance model for a grid-connected converter is expressed as a function of angular frequency, converter active power output, and grid-connected node voltage amplitude. In this real part expression, angular frequency represents the oscillation frequency of interest to the system and is a key variable for analyzing low-frequency oscillation characteristics. Active power output reflects the current power transmission level of the converter and is a core operating parameter determining the system's steady-state power angle and power transmission limits. Voltage amplitude reflects the strength of the grid and the voltage support at the converter ports.

[0066] Regarding the internal control parameters of the phase-locked loop (PLL), the proportional control parameters determine the PLL's instantaneous response speed to phase errors, directly affecting the system's inertial damping characteristics. The integral control parameters determine the PLL's ability to eliminate steady-state phase errors, and their values ​​alter the system's low-frequency phase characteristics. The denominator and numerator polynomials are essentially frequency-domain characteristic polynomials composed of the aforementioned control parameters and system electrical parameters. They implicitly contain information about the PLL's closed-loop pole and zero distribution, directly determining the magnitude of the damping margin and the phase change trend.

[0067] Step S20: Based on the damping matrix and load data, obtain the available damping margin of the converter grid-connected node according to Gell's disk theorem.

[0068] The available damping margin is defined as the net damping capacity that the node's own phase-locked loop can actually provide after deducting the damping effect of other nodes on the node through grid coupling. Its physical meaning is equivalent to the node's remaining ability to resist synchronous oscillations at the system's current operating point.

[0069] The calculation method typically relies on the Gell's disk theorem to analyze the damping matrix. Since the eigenvalues ​​of the damping matrix directly determine the system's damping level, the Gell's disk theorem states that all eigenvalues ​​of the matrix must lie within the union of the circular regions (i.e., the Gell's disks) formed by the moduli of the elements in each row (or column) on its complex plane. By calculating the center position of the Gell's disk for each node (i.e., the diagonal elements, representing the node's inherent damping) and the disk radius (i.e., the sum of the absolute values ​​of the off-diagonal elements, representing the coupling damping with other nodes), the sign and magnitude of the node's eigenvalues ​​(i.e., the actual equivalent damping) can be intuitively determined. If the Gell's disk corresponding to a node is completely located to the right of the imaginary axis of the complex plane, it indicates that the node has a positive damping margin under the current operating state; otherwise, there is a risk of instability. Furthermore, by combining load data to correct for damping changes caused by load fluctuations, the net damping capacity that the node's own phase-locked loop can actually provide is accurately extracted.

[0070] Alternatively, by performing matrix decomposition (such as LU decomposition) on the damping matrix or solving a system of linear equations, the damping contribution factor of each node relative to the overall network disturbance can be obtained, and then the damping changes caused by load fluctuations can be corrected by combining load data.

[0071] Understandably, the benefit of this step is that it provides a scalar index, namely the available damping margin, which can intuitively reflect the stability margin of each converter grid connection point under the current operating conditions. This avoids the tedious process of observing all oscillation modes required by the traditional eigenvalue analysis method, and is easy to embed the constraints of the optimization problem.

[0072] Step S30: Based on the available damping margin and the real part of the frequency domain admittance model, construct the synchronization stability constraints of the phase-locked loop of the grid converter.

[0073] Understandably, the mathematical form of this constraint can be expressed as: for each grid-connected node i Its available damping margin must be greater than or equal to the critical threshold determined by the real part of the frequency domain admittance model (usually zero or a positive safety margin). In other words, the net damping of each node must be positive to ensure that the phase-locked loop does not experience oscillatory instability caused by negative damping. This constraint is usually written in inequality form, which includes decision variables such as the active / reactive power output of the converter and the proportional-integral coefficient of the phase-locked loop.

[0074] Combining the damping matrix and Gell's disk theorem mentioned earlier, we know that all eigenvalues ​​of the matrix lie in the union of Gell's disk, which is centered on its diagonal elements and has the sum of the absolute values ​​of the off-diagonal elements in the same row as its radius.

[0075] but (12). That is: (13).

[0076] Understandable For the eigenvalues ​​of the damping matrix, to ensure the synchronous stability of the phase-locked loop, they must be greater than 0, i.e. Guaranteed It is positive. This expression can be rearranged as: (14).

[0077] In summary, the left side of equation (14) is the real part of the frequency domain admittance model of the grid-connected converter, and the right side is the grid-connectable damping margin, which is the available damping margin.

[0078] It should be noted that the data sources required to construct this constraint include the available damping margin output in step S20 and the real part of the frequency domain admittance model in step S10. Alternative constraint forms include: using the ratio of the available damping margin to the real part of the frequency domain admittance model as a stability index to set a lower limit; or introducing a robustness adjustment factor to account for measurement errors and parameter drift.

[0079] Understandably, the technical effect of this step is to transform the phase-locked loop synchronization stability problem, which originally belonged to the field of small-disturbance stability analysis, into an algebraic inequality constraint that can be directly handled by conventional optimization solvers, thereby achieving an organic integration of stability analysis and economic scheduling.

[0080] Step S40: Embed the synchronization stability constraint into the optimal power flow model of the power system and solve it to obtain the optimized output result of the converter that meets the synchronization stability requirements of the phase-locked loop.

[0081] It should be noted that the optimal power flow model here refers to a nonlinear programming model with the objective of minimizing the total system generation cost (or minimizing network losses, maximizing renewable energy absorption, etc.), and constraints such as nodal power balance equations, branch power flow limits, and generator output upper and lower limits. Adding the synchronous stability constraints constructed in step S30 as an additional set of inequality constraints to this model constitutes an enhanced optimal power flow problem with phase-locked loop stability boundaries. This problem can be solved using interior-point methods, sequential quadratic programming, or heuristic algorithms (such as particle swarm optimization). If the model is large, a decomposition coordination strategy (such as the Alternating Direction Multiplier Method, ADMM) can be used for distributed solution.

[0082] It should be noted that typical devices for implementing this step include: high-performance computers deployed in scheduling centers, running commercial optimization software (such as Gurobi, CPLEX) or open-source solvers (such as Ipopt); lightweight optimization engines can also be used on edge computing nodes to achieve local fast rescheduling. Alternative solution approaches include: linearizing the synchronous stability constraints into mixed-integer linear programming, or using machine learning surrogate models to replace the original constraints to accelerate the solution speed.

[0083] Understandably, the direct effect of this step is to output a set of converter active / reactive power commands that simultaneously satisfy both economic efficiency and phase-locked loop (PLL) synchronization stability. These commands can be sent to the actuators (such as converter controllers) of each energy storage power station via a communication network. Its benefits are twofold: firstly, it avoids the risk of instability caused by neglecting PLL dynamics; secondly, it avoids overly conservative stability reserves, improving the economic efficiency of system operation. It is particularly suitable for system optimization under various operating conditions, not limited to a single operating scenario, and provides technical support for the safe and stable operation of the power system.

[0084] In this embodiment, a system damping matrix related to the dynamic characteristics of the phase-locked loop (PLL) is constructed to explicitly characterize the change in synchronization damping margin caused by changes in operating state. Furthermore, the Gale disk theorem is used to transform the PLL synchronization stability criterion into an explicit mathematical inequality concerning the operating variables, allowing the synchronization stability requirement to be directly embedded into the optimal power flow model. This transforms the traditional "optimize first, then verify, then adjust" operating method into joint optimization under synchronization stability constraints. During the optimization process, synchronization instability points are actively avoided, ensuring the synchronization stability of the PLL and reducing the need for repeated stability verification and adjustment calculations under different operating states.

[0085] Furthermore, based on the above embodiments, this application provides specific implementation methods.

[0086] In this embodiment, the off-diagonal elements of the damping matrix are determined based on the branch conductance of the target node and each of the other nodes in the network data; the diagonal elements of the damping matrix are determined based on the branch conductance connected to the target node, load data, and the real part of the frequency domain admittance model. This process is essentially the result of outputting the damping matrix as described above.

[0087] It should be noted that the target node refers to the grid-connected node of the grid-connected converter whose diagonal elements of the damping matrix are currently to be determined in the power system. Branch conductance refers to the conductance parameter of the transmission line or transformer connecting two nodes in the power network; it reflects the resistive loss and damping characteristics during active power transmission. Off-diagonal elements are elements in the damping matrix whose row and column indices differ, representing the damping interaction between different grid-connected converter nodes through grid impedance coupling. Diagonal elements are elements in the damping matrix whose row and column indices are the same, representing the damping capacity provided by each node's own phase-locked loop, and taking into account corrections for load consumption and coupling effects.

[0088] Specifically, the damping matrix for: (15).

[0089] in, For nodes The set of all directly connected nodes. for A node in, Represents a node To the node The conductance of the branch between them For nodes To the node The conductance of the branch between them For nodes Active load, For nodes The voltage amplitude.

[0090] It is understandable that for non-diagonal elements, i.e., row indexes... With column index For different elements, the formula specifies two assignment cases: when And nodes With nodes There are direct-connection transmission lines or transformers between them, i.e., branch conductance. When, the elements of the damping matrix Assigned value The physical meaning of this assignment method is that the negative sign indicates the directionality of the damping interaction between nodes through the grid impedance. Its absolute value is determined by the branch conductance between the two nodes; the larger the conductance (i.e., the greater the resistive loss), the stronger the damping coupling between the nodes. When And nodes With nodes There are no direct branches between them, that is At time 0, the elements of the damping matrix The value is set to 0. This indicates that there is no direct damping coupling through the grid impedance between node pairs that are not directly electrically connected.

[0091] Understandably, for diagonal elements, the summation term in the first part covers the nodes. The resistive path radiating to all neighboring nodes reflects the inherent damping basis that the node provides to the system through the grid topology; the second part is the equivalent damping contribution of the local active load: in the synchronous small-signal analysis scenario, the dynamic characteristics of the node's active load changing with frequency are equivalent to positive damping (the larger the load, the stronger the braking effect caused by power changes during oscillation); the third part, the real part, reflects the positive or negative damping component that the phase-locked loop can provide under the current operating state, and is the core contribution of the converter's own control dynamics to the node damping. The sum of these three parts comprehensively determines the diagonal elements. The value represents the node. i The effective damping capacity provided by the phase-locked loop itself, and the load consumption and coupling effects are corrected.

[0092] It should be noted that the damping matrix constructed using the above formula (15) achieves the following technical effects: each element of the matrix has a clear physical correspondence; the negative conductance of the off-diagonal elements reflects the direction and strength of damping coupling between nodes; the sum of the three terms of the diagonal elements corresponds to the inherent damping of the power grid, the load damping effect, and the phase-locked loop control damping, respectively; at the same time, this formula avoids the complex linearization and inversion operation of the entire network admittance matrix in traditional methods, and only requires extracting the branch conductance, load data, and the real part of the phase-locked loop frequency domain admittance model to complete the matrix construction, significantly reducing the computational load and satisfying the requirements of... The real-time requirements of line applications are met; and since the diagonal elements are directly related to the real part of the frequency domain admittance model, which is an analytical function of the converter's operating state, the elements of the damping matrix can be expressed as explicit functions of decision variables, providing a convenient mathematical basis for subsequently constructing synchronous stability constraints and embedding them into the optimal power flow model; in addition, by setting the off-diagonal elements, the formula fully preserves the damping interaction between grid-connected nodes of different grid-type converters through the grid impedance, avoiding the optimistic estimation that may occur when independently evaluating the stability margin of a single node, and ensuring the accuracy of system-level synchronous stability assessment.

[0093] In this embodiment, according to Gale's disk theorem, step S20 includes: obtaining the node's own equivalent damping based on the conductance and load data of each branch connected to the target node; determining the network coupling damping based on the branch conductance of the target node and each of the other nodes in the network data; and determining the available damping margin of the grid-connected node based on the calculation result of subtracting the network coupling damping from the node's own equivalent damping.

[0094] Among them, the node's own equivalent damping refers to the damping capacity that the node can theoretically provide after considering only the damping contribution of its own phase-locked loop and local load consumption. Its value comes from the remaining part of the diagonal elements of the damping matrix after deducting the sum of the branch conductance terms. Network coupling damping refers to the total damping coupling generated by the interaction between the node and other nodes through the grid impedance, which is represented by the sum of the conductance of all branches related to the node in the damping matrix.

[0095] Therefore, the available damping margin refers to the effective damping capacity that the node can actually use to suppress synchronous oscillations during actual operation, which is the remaining value after subtracting the network coupling damping from the node's own equivalent damping. When this margin is positive, it indicates that the node can provide sufficient positive damping to maintain synchronous stability; when it is negative, there is a risk of instability.

[0096] Specifically, the available damping margin The expression is: (16).

[0097] It is understandable that the first two terms reflect the equivalent damping of the node itself; This reflects the network coupling damping. It accumulates the absolute values ​​of the branch conductance of the target node and all non-self nodes in the entire network. Taking the absolute value is to be compatible with the intermediate results of signed network calculations, to ensure that the coupling loss is always a positive deduction item, and to avoid the problem of the margin being artificially high due to the loss being negative.

[0098] Compared to the matrix decomposition and conjugate gradient methods proposed earlier, the available damping margin expression proposed in this embodiment is a quantitative evaluation tool designed specifically for engineering applications. It transforms complex matrix operations into intuitive physical indicators, significantly reducing the computational and data thresholds while ensuring accuracy. It has significant advantages in transparency, computational lightweightness, and engineering practicality.

[0099] In this embodiment, the synchronization stability constraint of the phase-locked loop is: the real part of the frequency domain admittance model is less than the available damping margin. That is: (17).

[0100] Understandably, this constraint means that the damping contribution provided by the phase-locked loop itself must not exceed the upper limit of the effective damping that the system node can currently accommodate; otherwise, the excess damping contribution will manifest as negative damping, leading to synchronization instability.

[0101] It is understandable that the real part of the frequency domain admittance model proposed in this embodiment is no greater than the available damping margin synchronous stability constraint. It realizes the explicit correlation between the dynamic characteristics of the phase-locked loop and the system-level stability boundary in a concise mathematical form. This lays a solid theoretical foundation and engineering implementation path for embedding the constraint into the optimal power flow model and providing the converter optimized output result that meets the synchronous stability requirements of the phase-locked loop in subsequent steps.

[0102] In this embodiment, the optimal power flow model of the power system includes an objective function and constraints; the objective function is to minimize the system network loss; the constraints include at least node power balance constraints, branch power flow constraints, synchronous generator output constraints, grid-connected converter output constraints, node voltage amplitude constraints, line capacity transmission constraints, and synchronous stability constraints.

[0103] Specifically, the objective function is: (18).

[0104] in, This indicates that the system's network loss is minimized. and They are nodes and The active power flow injected at both ends of the line.

[0105] The constraints include: (19); (20); (twenty one); (twenty two); (twenty three); (twenty four); (25).

[0106] Equation (19) represents the node power balance constraint. , and System nodes The active power output of the synchronous generator, the active power output of the grid converter, and the system nodes Active load at the location, , and System nodes The reactive power output of synchronous generators, the reactive power output of grid-connected converters, and system nodes reactive load at the location, Represents a node Flow to Node The unproductive current.

[0107] Wherein, equation (20) represents the branch power flow constraint. and System nodes and The conductance and susceptance of the lines between them. and System nodes and voltage amplitude, For system nodes and The voltage phase difference between them.

[0108] Wherein, equation (21) represents the output constraint of the synchronous generator unit. and The first The upper and lower limits of the active power output of the synchronous generator unit. and The first The upper and lower limits of reactive power output of the synchronous generator unit.

[0109] Wherein, equation (22) represents the output constraint of the grid-connected converter. and The first The power output of the grid-type converter has an upper and lower limit. and The first The upper and lower limits of reactive power output of grid-type converters.

[0110] Wherein, equation (23) represents the system node voltage amplitude constraint. and System nodes The upper and lower limits of the voltage amplitude. Equation (24) is the transmission capacity constraint of the line. For system nodes and The maximum apparent power capacity of the line between them. Equation (25) is the synchronous stability constraint of the phase-locked loop of the grid converter.

[0111] The optimal power flow model for power systems with grid-connected converter phase-locked loop synchronization stability proposed in this application requires solving for the following variables: , , , and .

[0112] When a solver is used to solve the optimal power flow model of a power system oriented towards synchronous stability with a grid-connected converter phase-locked loop, the solution obtained is the unique global optimal solution. Other methods can also be used to solve the problem.

[0113] Specifically, step S40 includes: initializing the active power output of the grid-connected converter and the voltage amplitude of the grid-connected node as initial decision variables; based on the initial decision variables, obtaining the real part and available damping margin of the frequency domain admittance model and constructing synchronous stability constraints; embedding the synchronous stability constraints into the optimal power flow model of the power system, iteratively solving the model through a solver, and updating the decision variables; repeatedly obtaining the real part and available damping margin of the frequency domain admittance model and updating the synchronous stability constraints until the decision variables meet the convergence condition, and outputting the optimized output result of the converter.

[0114] Based on the above, a specific running example is given.

[0115] This embodiment was tested in an improved 39-node system. The topology of the 39-node system is as follows: Figure 2 As shown, the system contains 39 nodes. Nodes 31 and 39 are each connected to a thermal power unit, and nodes 30, 32, 33, 34, 35, 36, 37 and 38 are each connected to a grid-connected converter.

[0116] Among them, the grid-connected topology of the grid-connected converter and its phase-locked loop control circuit are respectively as follows: Figure 3 and Figure 4 As shown.

[0117] The former topology mainly consists of DC-side energy storage units, switching devices, and an AC grid interface. The DC side is connected to the energy storage battery to provide DC power to the system; the core switching device in the middle adopts the structure of insulated gate bipolar transistor (IGBT) and anti-parallel diode, which is responsible for performing high-frequency switching operations to realize power conversion; the right side is connected to the three-phase AC grid, and the DC power is inverted into AC power that meets the grid requirements by adjusting the switching timing.

[0118] The latter circuit first acquires three-phase voltage signals from the AC side, then converts them into DC signals in a two-phase synchronous rotating coordinate system through Clark and Park transformations, facilitating the controller's extraction of stable phase information. Subsequently, the signal enters the PI controller for regulation to eliminate voltage errors, and an integrator (1 / s) generates an angle accumulation, ultimately outputting the grid's phase angle. This phase angle is fed back to the PWM modulation module to generate precise switching pulse signals for control. Figure 3 The IGBTs in the converter operate synchronously with the power grid.

[0119] Two scenarios are set up to illustrate the validity of this application: The first scenario: Using the traditional optimal power flow method, the active power output of the grid converter is solved according to the optimal power flow model with synchronization and stability constraints without phase-locked loops. Figure 5 The active power output boundary characteristics of the grid converter at this point are given; The second scenario: An optimal power flow method based on the phase-locked loop (PLL) synchronization stability constraints of the grid-connected converter is adopted. The active power output of the grid-connected converter is output according to the solution results of the optimal power flow model with PLL synchronization stability constraints. Figure 6 The active power output boundary characteristics of the grid converter at this time are given.

[0120] It should be noted that in the first case, the active power output of the grid-type converter is output according to the solution result of the optimal power flow model with synchronous stability constraints without phase-locked loops. In this case, the eigenvalue distribution diagram and its local magnified diagram of the system's generalized admittance matrix are as follows: Figure 7 and Figure 8 As shown.

[0121] It should be noted that in the second case, the system is optimized using the method proposed in this application, and the active power output of the grid converter is optimized according to the optimized power output. The specific implementation steps are as described above. At this time, the eigenvalue distribution diagram and its local magnified diagram of the system's generalized admittance matrix are as follows. Figure 9 and Figure 10 As shown.

[0122] Understandably, in comparison Figure 8 and Figure 10It can be seen that in the first case, the active power output of the grid-connected converter is output according to the optimal power flow model with no phase-locked loop (PLL) synchronization stability constraints. In this case, the eigenvalues ​​of the system's generalized admittance matrix have negative real parts, and the system will lose synchronization stability. In the second case, the active power output of the grid-connected converter is output according to the optimal power flow model with PLL synchronization stability constraints. In this case, all the real parts of the eigenvalues ​​of the system's generalized admittance matrix are positive, and the system will tend to stabilize. Therefore, the optimal power flow method for PLL synchronization stability of grid-connected converters proposed in this application can achieve optimal power flow of the power system while effectively ensuring the synchronization stability of the system after grid connection of the grid-connected converter.

[0123] As can be seen, the optimal power flow method for synchronizing the grid-connected converter's phase-locked loop (PLL) synchronously and stably, proposed in this application, accurately characterizes the output power boundary of the grid-connected converter during stable operation by constructing a frequency domain admittance model of the PLL, quantifying the available damping margin of the converter's grid-connected nodes, establishing synchronous stability constraints for the PLL, and embedding these constraints into the optimal power flow model for solution. Through this approach, this application can optimize the output power of the grid-connected converter while avoiding the optimization results falling into the synchronous instability region dominated by the PLL, effectively ensuring the synchronous stability of the power system under large-scale grid-connected scenarios of grid-connected converters. This method is applicable to system optimization under various operating conditions, not limited to a single operating scenario, providing technical support for the safe and stable operation of the power system.

[0124] In addition, this application also proposes an embodiment of an electronic device. Please refer to... Figure 11 , Figure 11 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. The electronic device may include: Communication interface 100 is configured to acquire real-time operating data of the power system from a wide area measurement system (WAMS) or a local monitoring terminal. Specifically, this includes network topology data, load power data, and the real part of the frequency domain admittance model of each node and the grid-type converter, calculated based on the analytical model described above. The hardware implementation of this communication interface can employ an Ethernet interface, a fiber optic communication interface, or a dedicated power line carrier communication module to support low-latency, high-reliability transmission of massive amounts of power grid measurement data.

[0125] The memory 200, optionally connected to the communication interface, is configured to non-transitory store network data, load data, the real part of the frequency domain admittance model, and computer-executable instructions. The memory may include storage media such as solid-state drives (SSDs), random access memory (RAM), or read-only memory (ROM), and its function is to build a stable local data cache, ensuring that the optimization algorithm can quickly retrieve historical data and intermediate variables during iteration.

[0126] The processor 300, optionally connected to a communication interface and a memory, is configured to read and execute the computer-executable instructions to control the electronic equipment to implement the aforementioned grid-connected converter phase-locked loop stability boundary optimal power flow method.

[0127] Specifically, the logic of the processor 300 executing instructions includes: First, based on the acquired power grid data and the real part of the converter frequency domain admittance model, constructing an optimal power flow mathematical model with the goal of minimizing system operating costs and satisfying the nonlinear inequality constraint that the real part of the frequency domain admittance model is no greater than the available damping margin; Second, calling a nonlinear numerical optimization solver such as the Interior Point Method or Sequential Quadratic Programming (SQP) to solve the model in real time; Finally, outputting active and reactive power optimization output scheduling instructions for each converter that satisfy the synchronous stability boundary.

[0128] It should be noted that the memory 200, communication interface 100, and processor 300 communicate with each other via the communication bus 400. The communication bus 400 can adopt a standard internal bus architecture, such as PCI Express, I²C, or SPI. During operation, the processor 300 reads the required data from the memory 200 and data acquisition interface 100, executes optimization algorithms, and outputs the generated scheduling scheme to the power system control center.

[0129] It should be noted that the electronic device may also include other components, such as a display unit for displaying scheduling results, or a communication module for sending scheduling schemes to remote terminal units.

[0130] Furthermore, the logical instructions in the aforementioned memory can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application.

[0131] Based on the methods in the above embodiments, this application provides a computer-readable storage medium storing a computer program that, when run on a processor, causes the processor to execute the methods in the above embodiments.

[0132] Based on the methods in the above embodiments, this application provides a computer program product that, when run on a processor, causes the processor to execute the methods in the above embodiments.

[0133] It is understood that the processor in the embodiments of this application can be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. A general-purpose processor can be a microprocessor or any conventional processor.

[0134] The method steps in this application embodiment can be implemented in hardware or by a processor executing software instructions. The software instructions can consist of corresponding software modules, which can be stored in random access memory (RAM), flash memory, read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), registers, hard disks, portable hard disks, CD-ROMs, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor, enabling the processor to read information from and write information to the storage medium. Of course, the storage medium can also be a component of the processor. The processor and the storage medium can reside in an ASIC.

[0135] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially as a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted through the computer-readable storage medium. The computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state disk (SSD)).

[0136] It is understood that the various numerical designations used in the embodiments of this application are merely for the convenience of description and are not intended to limit the scope of the embodiments of this application.

[0137] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A method for optimal power flow at the stability boundary of a phase-locked loop in a grid-type converter, characterized in that, include: Step S10: Based on the network data and load data of the power system, and the frequency domain admittance model of the grid-connected converter, construct the damping matrix of the power system; The frequency domain admittance model is a complex frequency domain function characterizing the phase-locked loop damping characteristics as a function of operating conditions. Step S20: Based on the damping matrix and the load data, obtain the available damping margin of the converter grid-connected node according to the Gale disk theorem; The available damping margin is the effective damping capacity that the grid-connected node actually possesses after deducting the network coupling effect. Step S30: Based on the available damping margin and the real part of the frequency domain admittance model, construct the synchronization stability constraints of the phase-locked loop of the grid converter. Step S40: Embed the synchronization stability constraint into the optimal power flow model of the power system and solve it to obtain the optimized output result of the converter that meets the synchronization stability requirements of the phase-locked loop.

2. The optimal power flow method for the stable boundary of a grid-connected converter phase-locked loop as described in claim 1, characterized in that, Step S10 includes: Based on the grid-connected topology of the grid-connected converter, the output power equation is constructed in the actual grid coordinate system. Based on the phase-locked loop control circuit of the grid-type converter, a small-signal linearized control equation is constructed. Based on the phase deviation relationship between the actual grid coordinate system and the phase-locked loop control coordinate system, the coordinate transformation relationship of the grid-connected node voltage and the mapping relationship of the output current in the actual grid coordinate system of the grid-connected converter are linearized using small signals. By combining the output power equation, the small-signal linearization control equation, the voltage coordinate transformation relationship after small-signal linearization, and the current mapping relationship, the frequency domain admittance model is obtained.

3. The optimal power flow method for the stability boundary of a grid-connected converter phase-locked loop as described in claim 1, characterized in that, Step S10 includes: Based on the network data and load data of the power system, construct the node admittance matrix of the system and the load admittance model of each node; The load admittance model and the frequency domain admittance model of each node are added to the node admittance matrix to obtain the system node admittance augmented matrix; Construct the system damping matrix based on the system node admittance augmentation matrix and the corresponding Hermitian matrix.

4. The optimal power flow method for the stability boundary of a grid-connected converter phase-locked loop as described in any one of claims 1 to 3, characterized in that, The off-diagonal elements of the damping matrix are determined based on the branch conductance of the target node and each of the other nodes in the network data; the diagonal elements of the damping matrix are determined based on the branch conductance connected to the target node, load data, and the real part of the frequency domain admittance model.

5. The optimal power flow method for the stability boundary of a grid-connected converter phase-locked loop as described in any one of claims 1 to 3, characterized in that, Step S20 includes: Based on the conductance and load data of each branch connected to the target node, obtain the node's own equivalent damping; Determine the network coupling damping based on the branch conductance of the target node and each of the other nodes in the network data; The available damping margin of the grid-connected node is determined based on the calculation result of subtracting the network coupling damping from the node's own equivalent damping.

6. The optimal power flow method for the stability boundary of a grid-connected converter phase-locked loop as described in claim 1, characterized in that, The synchronization stability constraint of the phase-locked loop is: The real part of the frequency domain admittance model is smaller than the available damping margin.

7. The optimal power flow method for the stability boundary of a grid-connected converter phase-locked loop as described in claim 1, characterized in that, The optimal power flow model of the power system includes an objective function and constraints; The objective function is to minimize the system network loss; The constraints include at least node power balance constraints, branch power flow constraints, synchronous generator output constraints, grid-connected converter output constraints, node voltage amplitude constraints, line capacity transmission constraints, and synchronous stability constraints.

8. The optimal power flow method for the stability boundary of a grid-connected converter phase-locked loop as described in claim 1, characterized in that, Step S40 includes: The active power output of the grid-connected converter and the voltage amplitude at the grid-connected node are initialized as initial decision variables; Based on the initial decision variables, the real part of the frequency domain admittance model and the available damping margin are obtained, and the synchronization stability constraints are constructed. The synchronization stability constraint is embedded into the optimal power flow model of the power system, and the decision variables are updated by iteratively solving the problem through a solver. Repeatedly obtain the real part of the frequency domain admittance model and the available damping margin, and update the synchronous stability constraint until the decision variables meet the convergence condition, and output the optimized output result of the converter.

9. An electronic device, characterized in that, include: The communication interface is configured to acquire network data, load data, and the real part of the frequency domain admittance model of the power system. A memory, connected to the communication interface, is configured to store the network data, the load data, the real part of the frequency domain admittance model, and computer-executable instructions; A processor, connected to the communication interface and the memory, is configured to execute the computer-executable instructions to control the electronic device to implement the optimal power flow method for the stable boundary of the grid-connected converter phase-locked loop as described in any one of claims 1 to 8.

10. A computer-readable storage medium comprising instructions, characterized in that: When the instructions are executed on an electronic device, the electronic device causes the electronic device to perform the method as described in any one of claims 1 to 8.

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