Method and system for calculating boundary of static voltage stability domain of power system

Abstract

The invention provides a calculation method and system for a static voltage stability domain boundary of an electric power system, and the method comprises the steps: constructing a convex hull model considering the uncertainty of new energy output based on the active power data and reactive power data of a new energy unit in the electric power system under the operation constraint of an inverter, and limiting a new energy output feasible region through the convex hull model; performing curve extrapolation prediction by adopting a cubic spline interpolation technology or a local principal component direction prediction method based on known boundary points on the boundary of the static voltage stability domain and the convex hull model to obtain predicted boundary points; based on a convex hull model, correcting the predicted boundary point by using a correction algorithm considering an arc correction strategy to obtain a corrected boundary point; and taking the corrected boundary point as a new known boundary point, and carrying out curve extrapolation prediction and correction again according to a step size control strategy until all boundary points on the boundary of the static voltage stability domain are tracked, so that boundary tracking failure can be avoided.

Description

Technical Field

[0001] This invention relates to the field of safety analysis and control technology for new energy power systems, specifically to a method and system for calculating the boundary of the static voltage stability domain of a power system. Background Technology

[0002] With the rapid expansion of power grids and the continuous development of renewable energy sources within them, power systems are exhibiting increasingly complex and diverse characteristics. These characteristics alter the operational behavior of power systems, making voltage operation more prone to approaching limits or even losing stability, and posing significant risks to the safe operation of power systems. Therefore, given the uncertainties brought about by the large-scale integration of new energy sources, characterizing the critical limit states of the system is of great significance for improving the safe operation level of static voltage stability in large power systems.

[0003] The static voltage stability domain, as a crucial concept for measuring the static voltage stability of a power system, holds significant research value. On one hand, accurately understanding the static voltage stability domain helps power system operators clearly understand how close the system's current operating state is to the stability boundary, enabling timely and effective preventative and control measures to prevent the system's operating point from approaching or exceeding the stability boundary, thus preventing voltage instability accidents and ensuring the safe and stable operation of the power system. On the other hand, during the power system planning and design phase, research findings on the static voltage stability domain contribute to optimizing the power grid structure, rationally configuring reactive power compensation equipment, and determining the system's maximum load-carrying capacity, which is of great significance for improving the economic efficiency and reliability of the power system.

[0004] Currently, the calculation of the static voltage stability domain boundary mainly relies on the CPF (Continuous Power Flow) method. The CPF method is a numerical analysis method widely used in power system voltage stability analysis. It can be used to construct the stability domain of renewable energy power systems. This method tracks the system's PV (active power-voltage) curve or QV (reactive power-voltage) curve by gradually increasing the load or adjusting the generation output until the voltage collapse point is reached. However, in power grids with high renewable energy penetration, due to drastic power fluctuations, the CPF method may experience power flow non-convergence, leading to boundary tracking failure. Summary of the Invention

[0005] To overcome the drawback of the aforementioned CPF method, which may result in power flow non-convergence and boundary tracking failure, this invention provides a method for calculating the boundary of the static voltage stability domain of a power system, comprising: Based on the active power data and reactive power data of the new energy power system under the inverter operation constraints, a convex hull model considering the uncertainty of new energy output is constructed. The convex hull model limits the feasible domain of new energy output. Based on the known boundary points on the boundary of the static voltage stability domain and the convex hull model, the curve extrapolation prediction is performed using cubic spline interpolation or local principal component direction prediction method to obtain the predicted boundary points. Based on the convex hull model, the predicted boundary points are corrected using a correction algorithm that takes into account the arc correction strategy, and the corrected boundary points are obtained. The corrected boundary points are used as new known boundary points, and the curve extrapolation prediction and correction are performed again according to the step size control strategy until all boundary points on the static voltage stability domain boundary are tracked.

[0006] Optionally, the construction of a convex hull model considering the uncertainty of new energy output based on the active power data and reactive power data of the new energy power system under inverter operation constraints includes: Based on the active power data and reactive power data of the new energy power system under inverter operation constraints, the new energy output capacity boundary is calculated, and the boundary points on the new energy output capacity boundary are used as known boundary points on the static voltage stability domain boundary to form a point set. Considering the uncertainty of new energy output, convex hull calculation is performed on the point set to obtain a convex hull model that limits the feasible region of new energy output; The inverter operating constraints include the inverter's apparent power limit and power factor angle limit.

[0007] Optionally, the convex hull model satisfies the following formula:

[0008] in, This is a convex hull model, i.e., the feasible region for new energy output. conv denotes convex hull calculation. This represents the active power data for the i-th sampling point. These are the lower and upper limits of the active power boundary. For the reactive power data of the i-th sampling point, Indicates the control mode at time t. mode The determined mapping relationship, This represents the voltage at the grid connection point of the new energy source at time t. S max This represents the upper limit of the apparent power of the inverter. The inverter operating constraints satisfy the following formula:

[0009] in, P The output active power of the inverter. Q The output reactive power of the inverter. S max This is the upper limit of the apparent power of the inverter. This is the operating power factor angle of the inverter.

[0010] Optionally, the predicted boundary points are obtained by using cubic spline interpolation to extrapolate curves based on known boundary points on the static voltage stability domain boundary and the convex hull model, including: The known boundary points on the boundary of the static voltage stability domain are sorted according to time steps to form a boundary point sequence; Based on the active power data and reactive power data in the boundary point sequence, a cubic spline interpolation function and the continuity conditions of each spline coefficient in the cubic spline interpolation function are constructed. Based on the cubic spline interpolation function and the continuity condition of each spline coefficient, a tridiagonal linear equation system is established for each spline coefficient. The tridiagonal linear equations are solved using the chasing method to obtain the spline coefficients. Based on the spline coefficients, curve extrapolation prediction is performed for the next time step to obtain the prediction boundary points for the next time step.

[0011] Optionally, the cubic spline interpolation function satisfies the following formula:

[0012] in, This represents the active power or reactive power data at the i-th boundary point. These are continuous parameters used to parameterize the boundary of the stability region; These are the continuous parameter values ​​corresponding to the i-th known boundary point; The spline coefficients of the function value represent the active power data or reactive power data of the i-th known boundary point. The spline coefficients are the first derivative coefficients, representing the slope of the boundary trajectory at the i-th known boundary point; The spline coefficients are the coefficients of the second derivative, representing the curvature of the boundary trajectory at the i-th known boundary point; The spline coefficients are the coefficients of the third derivative, representing the smoothness of the boundary trajectory at the i-th known boundary point; The continuity conditions for each spline coefficient include the function value continuity condition, the first derivative continuity condition, the second derivative continuity condition, and the boundary conditions. The condition for the continuity of the function value satisfies the following formula: ,in, This represents the active power or reactive power data at the i-th boundary point. For continuous parameters; x i This represents the active power data or reactive power data of the i-th known boundary point; The condition for the continuity of the first derivative satisfies the following formula: ,in, This represents the slope corresponding to the i-th boundary point; This represents the slope corresponding to the (i+1)th boundary point. These are the continuous parameter values ​​corresponding to the (i+1)th boundary point; The continuity condition of the second derivative satisfies the following formula: ,in, This represents the curvature corresponding to the i-th boundary point; This represents the curvature corresponding to the (i+1)th boundary point. These are the continuous parameter values ​​corresponding to the (i+1)th boundary point; The boundary conditions satisfy the formula: ,in, This represents the curvature corresponding to the first boundary point; This represents the curvature corresponding to the (n-1)th boundary point. These are the continuous parameter values ​​corresponding to the first boundary point. These are the continuous parameter values ​​corresponding to the nth boundary point.

[0013] Optionally, the spline coefficients satisfy the following formula:

[0014] in, The spline coefficients of the function value represent the active power data or reactive power data of the i-th known boundary point. The spline coefficients are the first derivative coefficients, representing the slope of the boundary trajectory at the i-th known boundary point; , Let be the second derivatives corresponding to the i-th and (i+1)-th boundary points, and let represent the curvature of the boundary trajectory at the i-th known boundary point. x i , x i+1 Represents the physical quantity values ​​of the i-th and (i+1)-th boundary points; h i This represents the continuous parameter step size corresponding to the i-th boundary point; The predicted boundary points for the next time step satisfy the following formula:

[0015] in, x (t) represents the prediction boundary point at time step t, where t represents the time step. i This represents the time step corresponding to the i-th known boundary point. The spline coefficients of the function value represent the active power data or reactive power data of the i-th known boundary point. The spline coefficients are the first derivative coefficients, representing the slope of the boundary trajectory at the i-th known boundary point; The spline coefficients are the coefficients of the second derivative, representing the curvature of the boundary trajectory at the i-th known boundary point; The spline coefficients are the coefficients of the third derivative, representing the smoothness of the boundary trajectory at the i-th known boundary point.

[0016] Optionally, the curve extrapolation prediction based on the known boundary points on the static voltage stability domain boundary and the convex hull model, using the local principal component direction prediction method, to obtain the predicted boundary points includes: The known boundary points on the static voltage stability domain boundary are sorted according to time steps to obtain the boundary point sequence; Based on each boundary point in the boundary point sequence, determine the neighborhood point set of each boundary point; Based on each boundary point, the covariance matrix of the boundary point is calculated using the local principal component direction prediction method according to the neighborhood point set of the boundary point; the covariance matrix is ​​decomposed into eigenvalues ​​to obtain the local principal component direction of the boundary point; and curve extrapolation prediction is performed along the local principal component direction for the next time step to obtain the predicted boundary point of the next time step.

[0017] Optionally, the covariance matrix satisfies the following formula:

[0018] in, Let i represent the covariance matrix of the i-th boundary point. p Let a point be a neighbor of the i-th boundary point, located in the neighborhood point set. T represents the transpose matrix; The directions of the local principal components satisfy the following formula:

[0019] in, Let i represent the covariance matrix of the i-th boundary point. It is the diagonal matrix of eigenvalues ​​of the i-th boundary point, and the eigenvector of the i-th boundary point is... The columns, where the local principal component directions are defined as .

[0020] Optionally, the step of correcting the predicted boundary points based on the convex hull model using a correction algorithm that takes into account the circular arc correction strategy to obtain corrected boundary points includes: Based on the convex hull model, with the predicted boundary points as initial values, the Newton-Raphson method is used to iteratively solve the correction algorithm that takes into account the circular arc correction strategy to obtain the correction boundary points. The correction algorithm considering the circular arc correction strategy is a joint algorithm of the circular arc equation and the power grid boundary equation; the correction algorithm considering the circular arc correction strategy satisfies the following formula:

[0021] in, This represents the correction algorithm that takes into account the circular arc correction strategy; These are the boundary equations for the power grid. The equation for a circular arc is... Represents the inner product between vectors. To correct boundary points, This is the boundary convergence point; The equation of the circular arc satisfies the following formula:

[0022] in, Let be the radius of the arc, represent the comprehensive error index, j be the j-th node, j=1,…, and n be the total number of nodes. Represents the corrected state variable of the j-th node. and the state variables before correction Error term, Formula for representing the power flow state of the system Component, m represents the m-th boundary point, Represents the load variable after correction at the j-th node. and the load variable before correction Error term, Represents the continuous parameters after correction at the j-th node. and continuous parameters before correction Error term, Indicates the other parameters after correction of the j-th node. And other parameters before calibration Error term, Represents the inner product between vectors. To correct boundary points, This is the boundary convergence point.

[0023] On the other hand, the present invention also provides a calculation system for the boundary of the static voltage stability domain of a power system, comprising: The convex hull modeling module is used to construct a convex hull model that considers the uncertainty of new energy output based on the active power data and reactive power data of the new energy power system under the inverter operation constraints. The convex hull model defines the feasible domain of new energy output. The curve extrapolation module is used to perform curve extrapolation prediction based on the known boundary points on the boundary of the static voltage stability domain and the convex hull model, using cubic spline interpolation technology or local principal component direction prediction method, to obtain the predicted boundary points. The correction module is used to correct the predicted boundary points based on the convex hull model using a correction algorithm that takes into account the circular arc correction strategy, so as to obtain the corrected boundary points. The boundary tracking module is used to take the corrected boundary point as a new known boundary point and re-perform curve extrapolation prediction and correction according to the step size control strategy until all boundary points on the static voltage stability domain boundary are tracked.

[0024] Optionally, the convex hull modeling module includes: The point set calculation unit is used to calculate the new energy output capacity boundary based on the active power data and reactive power data of the new energy power system under inverter operation constraints, and to form a point set by using the boundary points on the new energy output capacity boundary as known boundary points on the static voltage stability domain boundary. A convex hull calculation unit is used to consider the uncertainty of new energy output, perform convex hull calculation on the point set, and obtain a convex hull model that limits the feasible domain of new energy output. The inverter operating constraints include the inverter's apparent power limit and power factor angle limit.

[0025] Optionally, the convex hull model satisfies the following formula:

[0026] in, This is a convex hull model, i.e., the feasible region for new energy output. conv denotes convex hull calculation. This represents the active power data for the i-th sampling point. These are the lower and upper limits of the active power boundary. For the reactive power data of the i-th sampling point, Indicates the control mode at time t. mode The determined mapping relationship, This represents the voltage at the grid connection point of the new energy source at time t. S max This represents the upper limit of the apparent power of the inverter. The inverter operating constraints satisfy the following formula:

[0027] in, P The output active power of the inverter. Q The output reactive power of the inverter. S max This is the upper limit of the apparent power of the inverter. This is the operating power factor angle of the inverter.

[0028] Optionally, the curve extrapolation module includes: A cubic spline interpolation function construction unit is used to sort the known boundary points on the boundary of the static voltage stability domain according to the time step to form a boundary point sequence; based on the active power data and reactive power data in the boundary point sequence, a cubic spline interpolation function and the continuity conditions of each spline coefficient in the cubic spline interpolation function are constructed. The tridiagonal linear equation system construction unit is used to establish a tridiagonal linear equation system about each spline coefficient based on the cubic spline interpolation function and the continuity condition of each spline coefficient. The boundary point prediction unit is used to solve the tridiagonal linear equation system using the chasing method to obtain the spline coefficients; based on the spline coefficients, it performs curve extrapolation prediction for the next time step to obtain the predicted boundary points for the next time step.

[0029] Optionally, the cubic spline interpolation function satisfies the following formula:

[0030] in, This represents the active power or reactive power data at the i-th boundary point. These are continuous parameters used to parameterize the boundary of the stability region; These are the continuous parameter values ​​corresponding to the i-th known boundary point; The spline coefficients of the function value represent the active power data or reactive power data of the i-th known boundary point. The spline coefficients are the first derivative coefficients, representing the slope of the boundary trajectory at the i-th known boundary point; The spline coefficients are the coefficients of the second derivative, representing the curvature of the boundary trajectory at the i-th known boundary point; The spline coefficients are the coefficients of the third derivative, representing the smoothness of the boundary trajectory at the i-th known boundary point; The continuity conditions for each spline coefficient include the function value continuity condition, the first derivative continuity condition, the second derivative continuity condition, and the boundary conditions. The condition for the continuity of the function value satisfies the following formula: ,in, This represents the active power or reactive power data at the i-th boundary point. For continuous parameters; x i This represents the active power data or reactive power data of the i-th known boundary point; The condition for the continuity of the first derivative satisfies the following formula: ,in, This represents the slope corresponding to the i-th boundary point; This represents the slope corresponding to the (i+1)th boundary point. These are the continuous parameter values ​​corresponding to the (i+1)th boundary point; The continuity condition of the second derivative satisfies the following formula: ,in, This represents the curvature corresponding to the i-th boundary point; This represents the curvature corresponding to the (i+1)th boundary point. These are the continuous parameter values ​​corresponding to the (i+1)th boundary point; The boundary conditions satisfy the formula: ,in, This represents the curvature corresponding to the first boundary point; This represents the curvature corresponding to the (n-1)th boundary point. These are the continuous parameter values ​​corresponding to the first boundary point. These are the continuous parameter values ​​corresponding to the nth boundary point.

[0031] Optionally, the spline coefficients satisfy the following formula:

[0032] in, The spline coefficients of the function value represent the active power data or reactive power data of the i-th known boundary point. The spline coefficients are the first derivative coefficients, representing the slope of the boundary trajectory at the i-th known boundary point; , Let be the second derivatives corresponding to the i-th and (i+1)-th boundary points, and let represent the curvature of the boundary trajectory at the i-th known boundary point. x i , x i+1 Represents the physical quantity values ​​of the i-th and (i+1)-th boundary points; h i This represents the continuous parameter step size corresponding to the i-th boundary point; The predicted boundary points for the next time step satisfy the following formula:

[0033] in, x (t) represents the prediction boundary point at time step t, where t represents the time step. i This represents the time step corresponding to the i-th known boundary point. The spline coefficients of the function value represent the active power data or reactive power data of the i-th known boundary point. The spline coefficients are the first derivative coefficients, representing the slope of the boundary trajectory at the i-th known boundary point; The spline coefficients are the coefficients of the second derivative, representing the curvature of the boundary trajectory at the i-th known boundary point; The spline coefficients are the coefficients of the third derivative, representing the smoothness of the boundary trajectory at the i-th known boundary point.

[0034] Optionally, the curve extrapolation module includes: The neighborhood point set determination unit is used to sort the known boundary points on the boundary of the static voltage stability domain according to the time step to obtain a boundary point sequence; and to determine the neighborhood point set of each boundary point based on each boundary point in the boundary point sequence. The local principal component direction determination unit is used to calculate the covariance matrix of each boundary point based on the neighborhood point set of the boundary point and using the local principal component direction prediction method; and to perform eigenvalue decomposition on the covariance matrix to obtain the local principal component direction of the boundary point. The boundary point prediction unit is used to perform curve extrapolation prediction for the next time step along the direction of the local principal component to obtain the predicted boundary points for the next time step.

[0035] Optionally, the covariance matrix satisfies the following formula:

[0036] in, Let i represent the covariance matrix of the i-th boundary point. p Let a point be a neighbor of the i-th boundary point, located in the neighborhood point set. T represents the transpose matrix; The directions of the local principal components satisfy the following formula:

[0037] in, Let i represent the covariance matrix of the i-th boundary point. It is the diagonal matrix of eigenvalues ​​of the i-th boundary point, and the eigenvector of the i-th boundary point is... The columns, where the local principal component directions are defined as .

[0038] Optionally, the correction module is specifically used for: Based on the convex hull model, with the predicted boundary points as initial values, the Newton-Raphson method is used to iteratively solve the correction algorithm that takes into account the circular arc correction strategy to obtain the correction boundary points. The correction algorithm considering the circular arc correction strategy is a joint algorithm of the circular arc equation and the power grid boundary equation; the correction algorithm considering the circular arc correction strategy satisfies the following formula:

[0039] in, This represents the correction algorithm that takes into account the circular arc correction strategy; These are the boundary equations for the power grid. The equation for a circular arc is... Represents the inner product between vectors. To correct boundary points, This is the boundary convergence point; The equation of the circular arc satisfies the following formula:

[0040] in, Let be the radius of the arc, represent the comprehensive error index, j be the j-th node, j=1,…, and n be the total number of nodes. Represents the corrected state variable of the j-th node. and the state variables before correction Error term, Formula for representing the power flow state of the system Component, m represents the m-th boundary point, Represents the load variable after correction at the j-th node. and the load variable before correction Error term, Represents the continuous parameters after correction at the j-th node. and continuous parameters before correction Error term, Indicates the other parameters after correction of the j-th node. And other parameters before calibration Error term, Represents the inner product between vectors. To correct boundary points, This is the boundary convergence point.

[0041] On the other hand, the present invention also provides a computer device, characterized in that it includes: one or more processors; The processor is used to store one or more programs; When the one or more programs are executed by the one or more processors, the method for calculating the boundary of the static voltage stability domain of the power system as described in any one of the above-described methods is implemented.

[0042] On the other hand, the present invention also provides a computer-readable storage medium, characterized in that it stores a computer program thereon, which, when executed, implements the method for calculating the boundary of the static voltage stability domain of the power system as described in any one of the above.

[0043] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention provides a method and system for calculating the boundary of the static voltage stability domain of a power system. The method constructs a convex hull model considering the uncertainty of renewable energy output based on active and reactive power data of renewable energy units under inverter operation constraints. The convex hull model defines the feasible domain of renewable energy output. Based on known boundary points on the static voltage stability domain boundary and the convex hull model, curve extrapolation prediction is performed using cubic spline interpolation or local principal component direction prediction to obtain predicted boundary points. Based on the convex hull model, a correction algorithm considering circular arc correction strategy is used to correct the predicted boundary points, obtaining corrected boundary points. These corrected boundary points are then used as new known boundary points, and curve extrapolation prediction and correction are performed again according to a step-size control strategy until all boundary points on the static voltage stability domain boundary are tracked. This invention considers the uncertainty of new energy output in modeling, which can adapt to the fluctuation of power grid resources. It uses cubic spline interpolation technology or local principal component direction prediction method for curve extrapolation prediction, which can enhance the stability of prediction direction and improve the continuity of boundary tracking. Furthermore, the correction algorithm that takes into account the circular arc correction strategy can correct the predicted boundary points to the vicinity of the actual boundary points, thereby avoiding boundary tracking failure. Attached Figure Description

[0044] Figure 1 This is a flowchart illustrating the method for calculating the boundary of the static voltage stability domain of a power system according to the present invention. Figure 2 This is a schematic diagram of the convex hull representing the uncertainty of new energy power in this invention; Figure 3 This is a schematic diagram of the boundary point curve extrapolation of the present invention; Figure 4 This is a schematic diagram illustrating the boundary point correction failure provided by the present invention. Figure 5 A schematic diagram illustrating the tangent prediction method for predicting boundary points provided by this invention; Figure 6 This is a schematic diagram of a single-machine, single-load system according to the present invention; Figure 7 This is a schematic diagram illustrating the continuous parameter prediction variation of the present invention; Figure 8 This is a schematic diagram of the arc correction of the present invention; Figure 9 This is a schematic diagram of the voltage stability boundary of the single-machine single-load system of the present invention; Figure 10 A schematic diagram of the WECC-9 testing system; Figure 11 This is a schematic diagram of the static voltage stability region of the present invention; Figure 12 This is a schematic diagram of the calculation system architecture for the static voltage stability domain boundary of the power system according to the present invention; Figure 13 This is a schematic diagram of the electronic device of the present invention. Detailed Implementation

[0045] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0046] Example 1: This invention provides a method flow for calculating the boundary of the static voltage stability domain of a power system, as follows: Figure 1 As shown, it includes: Step 101: Based on the active power data and reactive power data of the new energy power system under the inverter operation constraints, construct a convex hull model that considers the uncertainty of new energy output. The convex hull model limits the feasible domain of new energy output.

[0047] Step 102: Based on the known boundary points and convex hull model on the boundary of the static voltage stability domain, use cubic spline interpolation or local principal component direction prediction method to perform curve extrapolation prediction to obtain the predicted boundary points.

[0048] Step 103: Based on the convex hull model, the predicted boundary points are corrected using a correction algorithm that takes into account the circular arc correction strategy, and the corrected boundary points are obtained.

[0049] Step 104: Take the corrected boundary point as the new known boundary point, and re-perform curve extrapolation prediction and correction according to the step size control strategy until all boundary points on the static voltage stability domain boundary are tracked.

[0050] This invention considers the uncertainty of new energy output in its modeling, which can adapt to fluctuations in grid resources. It employs cubic spline interpolation or local principal component direction prediction for curve extrapolation prediction, enhancing the stability of the predicted direction and improving the continuity of boundary tracking. Furthermore, a correction algorithm incorporating circular arc correction strategies can adjust the predicted boundary points to be closer to the actual boundary points, thereby avoiding boundary tracking failures. This invention is primarily applied to stability analysis in power system planning, operation, and control, particularly for new power systems with a high proportion of renewable energy integration.

[0051] Step 101 illustrates a modeling stage that, by performing uncertainty modeling on the uncertainties of new energy sources, achieves a convex hull representation of the nonlinear, asymmetric correlation between active and reactive power of new energy units. This modeling stage considers the uncertainty of system energy output and inverter operating constraints.

[0052] In one implementation, in step 101 above, the renewable energy output capacity boundary can be calculated based on the active and reactive power data of the renewable energy power system under inverter operation constraints. The boundary points on the renewable energy output capacity boundary are then used as known boundary points on the static voltage stability domain boundary to form a point set. Considering the uncertainty of renewable energy output, convex hull calculation is performed on the point set to obtain a convex hull model that limits the feasible domain of renewable energy output. In this implementation, the discrete PQ operating points are transformed into a compact mathematical expression through convex hull calculation, forming a characterization of the uncertainty in renewable energy processing. That is, by combining time-series data to generate a time-varying convex hull sequence, it can adapt to resource fluctuations.

[0053] Inverter operating constraints include the inverter's apparent power limit and power factor angle limit. The inverter operating constraints satisfy the following formula:

[0054] in, P The output active power of the inverter. Q The output reactive power of the inverter. S max This is the upper limit of the apparent power of the inverter. This is the operating power factor angle of the inverter.

[0055] In this implementation, when calculating the boundary of new energy output capacity, the active power data at each sampling point can be used. Calculate the corresponding active power boundary. It can also process reactive power data at each sampling point. Calculate the corresponding reactive power boundary. The active power boundary and / or reactive power boundary constitute the energy output capacity boundary of the system. When calculating the convex hull model of the feasible region of the new energy output, the convex hull of the point set can be calculated to obtain the feasible region polygon, and the convex hull model of the PQ feasible region can be constructed.

[0056] In some cases, the convex hull model can be applied to scenarios where the inverter control strategy changes, satisfying the following formula:

[0057] in, This is a convex hull model, i.e., the feasible region for new energy output. conv denotes convex hull calculation. This represents the active power data for the i-th sampling point. These are the lower and upper limits of the active power boundary. For the reactive power data of the i-th sampling point, Indicates the control mode at time t. modeThe determined mapping relationship, control mode mode For example, constant PF (Power Factor) mode or voltage control mode, etc. This represents the voltage at the new energy grid connection point at time t. The convex hull can achieve a refined characterization of the "PQ joint uncertainty," as illustrated in the diagram below. Figure 2 As shown, this is used to characterize the grid connection of new energy sources, where P represents active power, Q represents reactive power, and O represents the origin.

[0058] The core function of the convex hull model is to characterize the feasible operating region of new energy units on the PQ plane. This region will serve as the spatial constraint for boundary search. That is, when tracking the boundary of the static voltage stability domain, the changes in load or new energy injection point must satisfy the convex hull constraint; otherwise, the prediction / correction results will be invalid.

[0059] In one optional implementation, the present invention may further include an analysis phase, in which the failure mechanism of the boundary tracking method is utilized to locate the key factors of the failure measures of the boundary tracking method under complex working conditions, namely, predicting failure factors and correcting failure factors. This phase can realize the identification of failure factor problems.

[0060] Traditional prediction methods use tangent prediction. However, obtaining the tangent involves inverting the gradient matrix, and given the high dimensionality of the system variables, the computational cost of inversion is significant. Furthermore, when the boundary conditions are unfavorable, it often consumes considerable time and resources. Figure 3 As shown: Predicted point S n The ideal true value is predicted by the traditional tangent method (or simply tangent). The predicted points after curve extrapolation (or fitting curve) are: n takes values ​​from 1 to 8, and O represents the origin. At the boundary points... Given the significant differences in voltage boundary morphology caused by the uncertainty of new energy output, the traditional tangent prediction method is used to obtain... When, the predicted point Distance from truth value The distance is relatively far, which can easily lead to difficulties in convergence during the correction phase. However, if the prediction process fully utilizes... Information extrapolated from the bounds of the fitted curve This situation can be avoided, and convergence can be achieved; however, in At a given point, if a relatively flat curve is used, the predicted point obtained through complex inverse calculations... Predicted points obtained by curve extrapolation The results are quite similar, and whether it is still necessary to use inefficient inversion to obtain the predicted value needs further discussion.

[0061] The hyperplane correction stage is the process of correcting the predicted points from the tangent prediction stage to the boundary points. The solution in this stage is mainly affected by the initial value and the correction method. The initial value mainly refers to the predicted points determined in the prediction stage, as mentioned above. Figure 3 The relevant explanations will not be discussed here. In scenarios with severely varied boundary shapes, the failure of tracking boundary points often occurs due to the influence of the correction method. For example... Figure 4 As shown, It is the active power increment of the i-th load node; V is the active power increment of the j-th load node; V is the system voltage amplitude. These are known boundary points; It predicts boundary points; It is the tangent vector at each point (i.e., the principal component direction); This is the region of convergence (i.e., the effective search range of the correction process), and O represents the origin. , Within the power variation plane formed by the nodes, The SNBs (saddle points) at the PV curve clusters in the downward direction are too far apart, exceeding the specified range. The convergence region at that point caused the boundary tracing process to terminate, preventing the boundary from being reached. However, accurate calibration of boundary points is a necessary step in determining the next boundary point.

[0062] The analysis in this section shows that both boundary point prediction failure and correction failure will affect the localization results of boundary tracking. Therefore, the boundary point prediction and correction steps have been optimized in this embodiment of the invention.

[0063] Step 102 illustrates one curve extrapolation stage, which introduces cubic spline interpolation technology and applies the curve extrapolation interpolation formula to predict the possible positions of subsequent boundary points based on known boundary point information, thereby improving the continuity of boundary tracking; or this stage uses a prediction method based on the local principal component direction to replace curve fitting prediction, avoiding the problem of high-order curve jitter, adapting to local structures, and making calculations simpler; or this stage uses a machine learning-assisted prediction method to replace the traditional prediction mechanism under sufficient data conditions, which is more suitable for the nonlinear and multidimensional boundaries of complex power system operating conditions.

[0064] The first implementation method uses cubic spline interpolation to predict boundary points.

[0065] Traditional tangent prediction methods define functions with continuous parameters, as shown in the following equation:

[0066] in, For continuous mapping, For continuous parameters, For system voltage and phase angle variables, Let be the right eigenvector of the system's power flow equations. This represents the load margin in the power flow equation. A set representing parameters that vary in minute, continuous manner. This represents the set of continuous parameters, where n represents the dimension of the function.

[0067] The usual procedure is to first proceed along the direction of load change. Obtain the tangent vector at the current time step by differentiating the power flow equations. (Not shown in the figure), accurate values ​​are obtained by using tangent vectors to predict values ​​using tangent lines and then correcting them. And so on, obtaining them one by one. (Not shown in the figure), thus completing the boundary construction. To clarify the principle of the alternating tangent-curve prediction proposed in this section, the above boundary points and tangent vectors are projected onto a two-dimensional injection space with active power injection at nodes i and j as coordinate axes, respectively. See [link to relevant documentation]. Figure 5 As shown, It is the active power increment of the i-th load node; V is the active power increment of the j-th load node; V is the system voltage amplitude. These are known boundary points; These are known boundary points; It is the tangent vector at each point (i.e., the principal component direction); It refers to a spatial angle, where O represents the origin. It's a projection. It is a planar tangent vector. Plane, projection The corresponding planar tangent vector obtained Obtain vector The spatial angle is and obtaining vectors The spatial angle is ,check and The relative size, if This indicates that the boundary morphology changes relatively slowly and has a high degree of conservatism, so the curve extrapolation method can be considered to generate the predicted value. Based on this, it demonstrates the feasibility of introducing cubic spline interpolation technology for curve extrapolation prediction in the embodiments of the present invention to obtain the predicted boundary points.

[0068] Consider vectors A series of point sets consisting of a certain component in the equation ,in This represents the value taken at the k-th time step. Represented as the corresponding time step The value of a certain component is determined using cubic spline interpolation, which ensures the smoothness and reasonableness of the interpolation results. For example, in step 102 above, the known boundary points on the static voltage stability domain boundary are sorted according to time steps to form a boundary point sequence. Based on the active and reactive power data in the boundary point sequence, a cubic spline interpolation function and the continuity conditions of each spline coefficient in the cubic spline interpolation function are constructed. Based on the cubic spline interpolation function and the continuity conditions of each spline coefficient, a tridiagonal linear equation system is established for each spline coefficient. The tridiagonal linear equation system is solved using the chasing method to obtain each spline coefficient. Based on each spline coefficient, curve extrapolation prediction is performed for the next time step to obtain the predicted boundary points for the next time step.

[0069] In this example, to apply the curve extrapolation prediction using cubic spline interpolation, known boundary points on the static voltage stability domain boundary, as described above, can be used. The information is sorted according to time steps, and a boundary point sequence is generated. Within the interval of the boundary point sequence, a cubic spline interpolation function is applied. The following formula can be satisfied:

[0070] in, The active power data at the i-th boundary point can be represented separately. P i ( or reactive power data Q i ( ), As a continuous parameter, it is used to parameterize the stability domain boundary. By splicing together multiple piecewise functions, the entire stability domain boundary curve can be formed. The continuous parameter values ​​corresponding to the i-th known boundary point are the basic anchor points for interpolation; The active power data or reactive power data of the i-th known boundary point, i.e., the spline coefficients of the function value; The trend (slope) of the boundary trajectory at the i-th known boundary point is represented by the spline coefficients of the first derivative coefficients. The local curvature of the boundary trajectory at the i-th known boundary point is represented by the spline coefficients of the second derivative coefficients. The higher-order coefficients (smoothness) of the boundary trajectory at the i-th known boundary point are the spline coefficients of the third derivative coefficients. This formula is used to smoothly fit the active and reactive power respectively, and extrapolate to predict the location of the next boundary point.

[0071] The continuity conditions for each spline coefficient include the function value continuity condition, the first derivative continuity condition, the second derivative continuity condition, and the boundary condition, which are used to ensure that the piecewise cubic polynomial spliced ​​over multiple intervals has good smoothness.

[0072] The function value continuity condition satisfies the following formula: ,in, This represents the active power or reactive power data at the i-th boundary point. These are continuous parameters used to parameterize the boundary of the stability region; x i This represents the physical quantity value at the i-th known boundary point, i.e., active power data or reactive power data. The continuity condition of this function value is expressed at the node. At this point, the function value of the current interval must be equal to the value of the known point to ensure that the interpolation curve passes through all known boundary points, that is, to "anchor" the historical data.

[0073] The continuity condition of the first derivative satisfies the following formula: ,in, This represents the slope at the i-th boundary point; This represents the slope at the (i+1)th boundary point. This represents the continuous parameter value corresponding to the (i+1)th boundary point. This first derivative continuity condition means that the slopes of two adjacent intervals are equal at the connection point, ensuring the continuity of the tangent direction of the boundary trajectory and avoiding sharp angles or abrupt changes.

[0074] The condition for continuity of the second derivative satisfies the following formula: ,in, This represents the curvature corresponding to the i-th boundary point; This represents the curvature corresponding to the (i+1)th boundary point. Let be the continuous parameter value corresponding to the (i+1)th boundary point. This second derivative continuity condition means that the curvature of two adjacent intervals is equal at the connection point, ensuring a smooth transition in the curvature of the curve and avoiding local oscillations or overfitting.

[0075] The boundary conditions satisfy the formula: ,in, This represents the curvature corresponding to the first boundary point; This represents the curvature corresponding to the (n-1)th boundary point. These are the continuous parameter values ​​corresponding to the first boundary point. This represents the continuous parameter values ​​corresponding to the nth boundary point. This boundary condition indicates that the curvature at the start and end points of the boundary is zero, meaning the trajectory tends to be a straight line, reflecting that the change of the stable domain boundary tends to be gradual in the initial / final stages.

[0076] When establishing a tridiagonal linear system of equations about the spline coefficients based on the cubic spline interpolation function and the continuity condition of each spline coefficient, a tridiagonal matrix can be constructed based on the cubic spline interpolation function and the continuity condition of each spline coefficient to obtain the second derivative. The tridiagonal linear equation system consists of coefficients composed of continuous parameter step sizes, with the right-hand side reflecting the rate of change of the slope of adjacent boundary segments. Solving this system yields a smooth cubic spline interpolation function, which can be used for extrapolation to predict the next boundary point. The tridiagonal linear equation system satisfies the following formula:

[0077] in, h 1. h 2. h 3. h i This represents the continuous parameter step size corresponding to the 1st, 2nd, 3rd, and i-th boundary points. This represents the continuous parameter values ​​corresponding to the i-th and (i+1)-th boundary points, where i is 1, 2, or 3; x 1. x 2. x 3. x 4 represents the physical quantity values ​​of the 1st, 2nd, 3rd, and 4th known boundary points. c 1. c 2. c 3 represents the second derivatives corresponding to the 1st, 2nd, and 3rd boundary points.

[0078] Solving the above tridiagonal linear equations using a chasing method (such as Thomas's algorithm) yields the following results. c i Then calculate the other coefficients, that is, the coefficients of each spline satisfy the following formula:

[0079] in, The spline coefficients of the function value represent the active power data or reactive power data of the i-th known boundary point. The spline coefficients are the first derivative coefficients, representing the slope of the boundary trajectory at the i-th known boundary point; , Let be the second derivatives corresponding to the i-th and (i+1)-th boundary points, and let represent the curvature of the boundary trajectory at the i-th known boundary point. x i , x i+1 Represents the physical quantity values ​​of the i-th and (i+1)-th boundary points; h iThis represents the continuous parameter step size corresponding to the i-th boundary point.

[0080] Therefore, for any step size The predicted boundary points for the next time step can be obtained according to the following formula:

[0081] in, x (t) represents the prediction boundary point at time step t, where t represents the time step. i This represents the time step corresponding to the i-th known boundary point. The spline coefficients of the function value represent the active power data or reactive power data of the i-th known boundary point. The spline coefficients are the first derivative coefficients, representing the slope of the boundary trajectory at the i-th known boundary point; The spline coefficients are the coefficients of the second derivative, representing the curvature of the boundary trajectory at the i-th known boundary point; The spline coefficients are the coefficients of the third derivative, representing the smoothness of the boundary trajectory at the i-th known boundary point.

[0082] Single-machine single-load system Figure 6 For example, taking continuous parameters As the independent variable, the continuous parameter variation values ​​obtained by curve extrapolation using cubic spline interpolation are as follows: Figure 7 As shown. Figure 6 In the figure, b / 2 represents the capacitance to ground of the transmission line; Represented as load complex power; and These represent the voltage phasors of node 1 and node 2, respectively. Indicates the impedance of the line; and These represent the power flow at the beginning and end of the line, respectively, with j being the imaginary unit. Figure 7 middle For continuous parameters, For system voltage and phase angle variables, Let be the right eigenvector of the system's power flow equations. This represents the load margin in the power flow equation; x 1 represents the curve of voltage amplitude at node 2 as a function of continuous parameters; x 2 represents the curve of phase angle at node 2 as a function of continuous parameters; Represents the right-hand eigenvector of the system's power flow equations The curve showing the continuous parameter variation of the first component; Represents the right-hand eigenvector of the system's power flow equations The curve showing the continuous parameter variation of the second component; The curves represent the load margin as a function of continuous parameters. By combining these curves, it can be seen that the variables obtained by extrapolating the curves using cubic spline interpolation can track the changes in continuous parameters very well.

[0083] This implementation method can predict boundary points based on cubic spline interpolation techniques used for historical boundary points, such as polynomial fitting and Bezier curves. Constructing a fitted curve using cubic spline interpolation to predict the next boundary point location improves edge continuity, enhances prediction direction stability, and avoids the failure of conventional tangent prediction in non-smooth regions. The introduced cubic spline interpolation technique can predict the reasonable location of the next potential boundary point based on known boundary point coordinates, effectively replacing the failure problem of traditional tangent prediction in polygonal boundaries or rapidly changing regions.

[0084] The second approach uses the local principal component direction prediction method to predict boundary points. This method utilizes the neighborhood information of the current boundary point to construct a principal component direction vector, which serves as the prediction direction and can replace curve fitting to complete the prediction.

[0085] For example, step 102 above can sort the known boundary points on the static voltage stability domain boundary according to time steps to obtain a boundary point sequence; based on each boundary point in the boundary point sequence, determine the neighborhood point set of each boundary point; based on each boundary point, according to the neighborhood point set of the boundary point, use the local principal component direction prediction method to calculate the covariance matrix of the boundary point; perform eigenvalue decomposition on the covariance matrix to obtain the local principal component direction of the boundary point; use the local principal component direction to perform curve extrapolation prediction for the next time step to obtain the predicted boundary point for the next time step.

[0086] For example, boundary point sequences ,in It is the 1st, 2nd, or nth known boundary point in two-dimensional or three-dimensional space.

[0087] When determining the neighborhood set of each boundary point based on the boundary point sequence, k-NN (k-Nearest Neighbors) algorithm can be used to select the k nearest points for each boundary point as its neighborhood set. Based on the i-th boundary point, its neighborhood point set can be determined. Calculate the local principal component directions to obtain the covariance matrix of the boundary point, which may satisfy the following formula:

[0088] in, Let i represent the covariance matrix of the i-th boundary point. p Let a point be a neighbor of the i-th boundary point, located in the neighborhood point set. , where T represents the transpose matrix.

[0089] Eigenvalue decomposition of the covariance matrix yields local principal component directions that satisfy the following formula:

[0090] in, Let i represent the covariance matrix of the i-th boundary point. It is the diagonal matrix of eigenvalues ​​of the i-th boundary point, and the eigenvector of the i-th boundary point is... The columns, where the local principal component directions are defined as .

[0091] The third approach is to use machine learning-assisted prediction methods to predict boundary points.

[0092] Machine learning-assisted prediction methods can train models such as LSTM (Long Short-Term Memory) or SVR (Support Vector Regression) to learn the evolution of boundary points and use them to predict the next boundary point.

[0093] Step 103 illustrates a correction stage that employs a correction transformation technique to perform circular arc correction on the predicted boundary points, thereby improving the accuracy and robustness of boundary tracking and preventing boundary tracking failure.

[0094] When using a hyperplane for correction, convergence fails if the hyperplane cannot geometrically intersect the boundary curve; however, if... Figure 8 As shown, when circular arc correction is used, it can be guaranteed that the intersection with the boundary curve on the plane will be... This ensures convergence. Figure 8 middle To inject space for power, For the current boundary point, For boundary prediction points, O represents the origin and O represents the boundary correction point. This demonstrates the feasibility of introducing a circular arc correction strategy in this embodiment of the invention to obtain the corrected boundary point.

[0095] In one implementation, in step 103 above, the correction boundary points can be obtained by iteratively solving the correction algorithm that takes into account the circular arc correction strategy using the Newton-Raphson method based on the convex hull model and the predicted boundary points as the initial values.

[0096] The correction algorithm that takes into account the circular arc correction strategy is a joint algorithm of the circular arc equation and the power grid boundary equation; See Figure 8 Define the arc correction strategy: This is the precise boundary convergence point obtained in this time step. To predict boundary points, Centered on, with distance value For the radius, supplement the equation of the circular arc:

[0097] in, Let be the radius of the arc, represent the comprehensive error index, j be the j-th node, j=1,…, and n be the total number of nodes. Represents the corrected state variable of the j-th node. and the state variables before correction Error term, Formula for representing the power flow state of the system Component, m represents the m-th boundary point, Represents the load variable after correction at the j-th node. and the load variable before correction Error term, Represents the continuous parameters after correction at the j-th node. and continuous parameters before correction Error term, Indicates the other parameters after correction of the j-th node. And other parameters before calibration Error term, Represents the inner product between vectors. To correct boundary points, This is the boundary convergence point.

[0098] By combining the circular arc equations and the power grid boundary equations, a correction algorithm considering the circular arc correction strategy can be obtained, satisfying the following formula:

[0099] in, This represents the correction algorithm that takes into account the circular arc correction strategy; These are the boundary equations for the power grid. The equation for a circular arc is... Represents the inner product between vectors. To correct boundary points, This is the boundary convergence point.

[0100] Newton-Raphson method is used to predict boundary points. The solution can be obtained by iterating with initial values ​​to obtain the corrected boundary points; when constructing the iterative scheme for this correction process, the following formula can be used as a reference:

[0101] Where Φ() represents the power flow function, To predict boundary points, To correct boundary points, This represents the Jacobian matrix, which reflects the degree to which voltage changes affect power imbalance.

[0102] This implementation employs a correction and transformation mechanism, combined with a circular arc correction strategy, to perform high-precision correction on the predicted points, enhancing the analytical capability for non-smooth regions. After adopting this strategy, the average number of interruptions in boundary path tracing in the node system is reduced by 62.5%; the overall number of iterations is reduced by 33.4%. It can eliminate prediction errors and avoid local divergence caused by prediction errors, thus avoiding iterative divergence and convergence failure, and improving the robustness of dynamic correction.

[0103] Another implementation uses a projection correction method, which projects the predicted boundary points onto the boundary isosurface to quickly approximate the true boundary points. This method is simple in structure and more efficient.

[0104] Step 104 above illustrates a step size control stage. This stage employs a step size control strategy based on the number of iterations. The step size parameter is formed based on the boundary morphology characteristics and the number of iterations in the correction stage. For example, the interpolation step size is dynamically adjusted according to the convergence of the correction stage iterations, and steps S102 to S103 are repeated using the correction boundary point as the new known boundary point until the entire static voltage stability domain boundary is traced and constructed.

[0105] In addition to the above Figure 6 and Figure 7 For example, firstly, the base state operating point of the power grid is obtained based on the power flow calculation, and the voltage solution at the base state operating point is ( θ , V ) = (-0.4650, 0.5594), and calculate the coordinates of the point as ( Q 2, P 2) = (0.1871, 0.2508), which is calculated based on the ground state operating point. The boundary point search is performed in the increasing direction, and the estimated stage step size is set. The calculation based on the ground state operating point is obtained from the prediction stage. The coordinates of point 0 are obtained by decreasing the direction. The repeated calculation process yields Boundary point; Return to By repeating the calculation process, boundary points can be obtained. .like Figure 9 As shown, the method proposed in this invention can effectively obtain boundary points. , The accurate values ​​obtained by this invention are highly consistent with those obtained by the conventional tracking method (CPF), indicating that the method of this invention is accurate and effective. and These represent the active and reactive loads at node 2, respectively.

[0106] In addition, Figure 10 Taking the WECC-9 test system shown as an example, a system was constructed as follows: Figure 11 The static voltage stability region is shown. Figure 10 middle For the three generator sets, the node voltages were marked at each node; the line impedances were marked on each line. Z and admittance Y parameter. Figure 11 middle and The figures represent the active power at nodes 7 and 9, respectively. As can be seen from the figure, compared with the conventional tracking method (CPF), the method proposed in this invention can accurately track boundary points.

[0107] The embodiments of the present invention will be compared with the conventional CPF method below to illustrate the advantages of the embodiments of this aspect: Currently, the calculation of the static voltage stability domain boundary mainly relies on the CPF method. This method tracks the system's PV or QV curves by gradually increasing the load or adjusting the generator output until the voltage collapse point is reached. Conventional power flow equations Expanded included parameters In the form of, V is the node voltage phase angle, and V is the node voltage amplitude. The load growth factor is used. The technical solution includes the following five steps: 1. Initialization phase: Constructing an initial power flow solution starting from the rated operating condition; 2. Prediction phase: Predicting the next state point along the solution trajectory using a tangent vector prediction method (such as the Euler method); 3. Correction phase: Correcting the predicted point onto the power flow solution surface using orthogonal projection; 4. Parameter step size adjustment: Adjusting the prediction step size based on convergence; 5. Repeated iteration: Continuously increasing the parameters... This continues until the simulation reaches the voltage stability boundary.

[0108] The CPF method can overcome the divergence of power flow equations at the limit points, but this method has the following limitations: Problem 1: Low computational efficiency: In large power grids, CPF requires multiple power flow calculations, and the computational load increases exponentially with the system size, making it difficult to meet the needs of online analysis.

[0109] Question 2, Convergence Issue: In power grids with high penetration of new energy sources, due to severe power fluctuations, the CPF may experience power flow non-convergence, leading to boundary tracking failure.

[0110] Problem 3: Insufficient adaptability: Traditional methods are difficult to adapt to complex scenarios such as changes in grid topology and random output of distributed power sources, which affects the accuracy of stability domain calculation.

[0111] Furthermore, while existing improvement methods (such as those based on sensitivity analysis and machine learning surrogate models) can partially improve computation speed, they still have shortcomings in terms of boundary accuracy and robustness. Therefore, this invention proposes a fast calculation method for the static voltage stability domain boundary that balances efficiency, robustness, and adaptability to support the safe and stable operation of new power systems.

[0112] To address the aforementioned problem 1, this embodiment of the invention uses an innovative algorithm to shorten the computation time while ensuring accuracy, thus solving the defects of large computational load and long computation time in CPF.

[0113] To address the aforementioned problem 2, this embodiment of the invention improves the success performance of boundary tracking through intelligent prediction and dynamic correction mechanisms, thus solving the technical challenge of easy divergence in traditional methods under high-proportion renewable energy access scenarios.

[0114] To address the aforementioned problem 3, the algorithm proposed in this embodiment of the invention can adapt to the static voltage stability under high-penetration renewable energy access scenarios, and can solve the shortcomings of traditional methods in dealing with random fluctuations in renewable energy output.

[0115] As can be seen, this invention specifically addresses the technical challenges brought about by the high proportion of renewable energy integration in new power systems, focusing on solving key technical problems in existing methods in terms of computational efficiency, convergence, and adaptability, and providing a reliable means for rapid stability domain assessment for safe power grid operation.

[0116] This invention proposes a rapid construction technique for the static voltage stability domain boundary of a new energy power system, and innovatively improves upon existing methods to address issues such as low computational efficiency and insufficient accuracy. Currently, traditional static voltage stability domain boundary calculation methods mainly rely on the continuous power flow method, which suffers from drawbacks such as large computational load and poor convergence, making it difficult to meet the needs of large-scale power grid online analysis. The advantages of this technique are reflected in: (1) analyzing the failure mechanism of the boundary tracking method and identifying the key factors for failure measures under complex operating conditions; (2) introducing curve extrapolation technology to predict the possible positions of subsequent boundary points based on known boundary point information, thereby improving the continuity of boundary tracking; and (3) employing correction and conversion technology to dynamically correct the prediction results, improving the accuracy and robustness of boundary tracking and avoiding boundary tracking failure. Compared with existing technologies, this method can improve the accuracy and robustness of boundary tracking, and is particularly suitable for real-time voltage stability assessment of power grids with a high proportion of new energy, providing an efficient analysis tool for the safe operation of smart grids.

[0117] Furthermore, the rapid construction technology for the static voltage stability domain boundary of new energy power systems proposed in this invention has broad application prospects in the planning, operation, and control of power grids with a high proportion of new energy. Currently, with the large-scale grid connection of fluctuating power sources such as wind power and photovoltaics, the operating conditions of the power grid are becoming increasingly complex, and traditional voltage stability analysis methods are no longer sufficient to meet real-time requirements. With the accelerated advancement of the construction of new power systems, this technology is expected to be widely applied in the industry: on the one hand, it can be integrated into the intelligent decision-making platform of dispatch centers at all levels to provide real-time stability margin assessment for power grids with a high proportion of renewable energy; on the other hand, it can be embedded in the grid connection control system of new energy power plants. In addition, this technology can also be extended to emerging fields such as integrated energy systems and microgrid clusters, providing key technical support for building a clean, low-carbon, safe, and efficient energy system.

[0118] Example 2: Based on the same inventive concept, this invention also provides a calculation system for the boundary of the static voltage stability domain of a power system, as shown in the schematic diagram below. Figure 12 As shown, it includes: The convex hull modeling module is used to construct a convex hull model that considers the uncertainty of new energy power output based on the active power data and reactive power data of the new energy power system under the inverter operation constraints. The convex hull model limits the feasible domain of new energy power output. The curve extrapolation module is used to perform curve extrapolation prediction based on known boundary points and convex hull models on the boundary of the static voltage stability domain, using cubic spline interpolation or local principal component direction prediction method to obtain predicted boundary points. The correction module is used to correct the predicted boundary points based on the convex hull model and using a correction algorithm that takes into account the circular arc correction strategy, so as to obtain the corrected boundary points. The boundary tracking module is used to take the corrected boundary points as new known boundary points and re-perform curve extrapolation prediction and correction according to the step size control strategy until all boundary points on the static voltage stability domain boundary are tracked.

[0119] In one specific implementation, the convex hull modeling module includes: The point set calculation unit is used to calculate the new energy output capacity boundary based on the active power data and reactive power data of the new energy power system under inverter operation constraints, and to form a point set by using the boundary points on the new energy output capacity boundary as known boundary points on the static voltage stability domain boundary. The convex hull calculation unit is used to consider the uncertainty of new energy output, perform convex hull calculation on the point set, and obtain the convex hull model that limits the feasible domain of new energy output. Inverter operating constraints include the inverter's apparent power limit and power factor angle limit.

[0120] In one specific implementation, the convex hull model satisfies the following formula:

[0121] in, This is a convex hull model, i.e., the feasible region for new energy output. conv denotes convex hull calculation. This represents the active power data for the i-th sampling point. These are the lower and upper limits of the active power boundary. For the reactive power data of the i-th sampling point, Indicates the control mode at time t. mode The determined mapping relationship, This represents the voltage at the grid connection point of the new energy source at time t. S max This represents the upper limit of the apparent power of the inverter. The inverter's operating constraints satisfy the following formula:

[0122] in, P The output active power of the inverter. Q The output reactive power of the inverter. S max This is the upper limit of the apparent power of the inverter. This is the operating power factor angle of the inverter.

[0123] In one specific implementation, the curve extrapolation module includes: The cubic spline interpolation function construction unit is used to sort the known boundary points on the boundary of the static voltage stability domain according to the time step to form a boundary point sequence; based on the active power data and reactive power data in the boundary point sequence, the cubic spline interpolation function and the continuity conditions of each spline coefficient in the cubic spline interpolation function are constructed. The tridiagonal linear equation system construction unit is used to establish a tridiagonal linear equation system about each spline coefficient based on the cubic spline interpolation function and the continuity condition of each spline coefficient. The boundary point prediction unit is used to solve the tridiagonal linear equation system using the chasing method to obtain the spline coefficients; based on the spline coefficients, curve extrapolation prediction is performed for the next time step to obtain the predicted boundary points for the next time step.

[0124] In one specific implementation, the cubic spline interpolation function satisfies the following formula:

[0125] in, This represents the active power or reactive power data at the i-th boundary point. These are continuous parameters used to parameterize the boundary of the stability region; These are the continuous parameter values ​​corresponding to the i-th known boundary point; The spline coefficients of the function value represent the active power data or reactive power data of the i-th known boundary point. The spline coefficients are the first derivative coefficients, representing the slope of the boundary trajectory at the i-th known boundary point; The spline coefficients are the coefficients of the second derivative, representing the curvature of the boundary trajectory at the i-th known boundary point; The spline coefficients are the coefficients of the third derivative, representing the smoothness of the boundary trajectory at the i-th known boundary point; The continuity conditions for each spline coefficient include the function value continuity condition, the first derivative continuity condition, the second derivative continuity condition, and the boundary conditions. The function value continuity condition satisfies the following formula: ,in, This represents the active power or reactive power data at the i-th boundary point. For continuous parameters; x i This represents the active power data or reactive power data of the i-th known boundary point; The continuity condition of the first derivative satisfies the following formula: ,in, This represents the slope corresponding to the i-th boundary point; This represents the slope corresponding to the (i+1)th boundary point. These are the continuous parameter values ​​corresponding to the (i+1)th boundary point; The condition for continuity of the second derivative satisfies the following formula: ,in, This represents the curvature corresponding to the i-th boundary point; This represents the curvature corresponding to the (i+1)th boundary point. These are the continuous parameter values ​​corresponding to the (i+1)th boundary point; The boundary conditions satisfy the formula: ,in, This represents the curvature corresponding to the first boundary point; This represents the curvature corresponding to the (n-1)th boundary point. These are the continuous parameter values ​​corresponding to the first boundary point. These are the continuous parameter values ​​corresponding to the nth boundary point.

[0126] In one specific implementation, the spline coefficients satisfy the following formula:

[0127] in, The spline coefficients of the function value represent the active power data or reactive power data of the i-th known boundary point. The spline coefficients are the first derivative coefficients, representing the slope of the boundary trajectory at the i-th known boundary point; , Let be the second derivatives corresponding to the i-th and (i+1)-th boundary points, and let represent the curvature of the boundary trajectory at the i-th known boundary point. x i , x i+1 Represents the physical quantity values ​​of the i-th and (i+1)-th boundary points; h i This represents the continuous parameter step size corresponding to the i-th boundary point; The predicted boundary points for the next time step satisfy the following formula:

[0128] in, x (t) represents the prediction boundary point at time step t, where t represents the time step. i This represents the time step corresponding to the i-th known boundary point. The spline coefficients of the function value represent the active power data or reactive power data of the i-th known boundary point. The spline coefficients are the first derivative coefficients, representing the slope of the boundary trajectory at the i-th known boundary point; The spline coefficients are the coefficients of the second derivative, representing the curvature of the boundary trajectory at the i-th known boundary point; The spline coefficients are the coefficients of the third derivative, representing the smoothness of the boundary trajectory at the i-th known boundary point.

[0129] In one specific implementation, the curve extrapolation module includes: The neighborhood point set determination unit is used to sort the known boundary points on the boundary of the static voltage stability domain according to the time step to obtain the boundary point sequence; and to determine the neighborhood point set of each boundary point based on each boundary point in the boundary point sequence. The local principal component orientation determination unit is used to calculate the covariance matrix of each boundary point based on the neighborhood point set of the boundary point using the local principal component orientation prediction method; and to perform eigenvalue decomposition on the covariance matrix to obtain the local principal component orientation of the boundary point. The boundary point prediction unit is used to perform curve extrapolation prediction for the next time step along the direction of the local principal components to obtain the predicted boundary points for the next time step.

[0130] In one specific implementation, the covariance matrix satisfies the following formula:

[0131] in, Let i represent the covariance matrix of the i-th boundary point. pLet a point be a neighbor of the i-th boundary point, located in the neighborhood point set. T represents the transpose matrix; The directions of the local principal components satisfy the following formula:

[0132] in, Let i represent the covariance matrix of the i-th boundary point. It is the diagonal matrix of eigenvalues ​​of the i-th boundary point, and the eigenvector of the i-th boundary point is... The columns, where the local principal component directions are defined as .

[0133] In one specific implementation, the correction module is specifically used for: Based on the convex hull model, with the predicted boundary points as the initial values, the Newton-Raphson method is used to iteratively solve the correction algorithm that takes into account the circular arc correction strategy to obtain the correction boundary points. The correction algorithm considering the circular arc correction strategy is a joint algorithm of the circular arc equation and the power grid boundary equation; the correction algorithm considering the circular arc correction strategy satisfies the following formula:

[0134] in, This represents the correction algorithm that takes into account the circular arc correction strategy; These are the boundary equations for the power grid. The equation for a circular arc is... Represents the inner product between vectors. To correct boundary points, This is the boundary convergence point; The equation of a circular arc satisfies the following formula:

[0135] in, Let be the radius of the arc, represent the comprehensive error index, j be the j-th node, j=1,…, and n be the total number of nodes. Represents the corrected state variable of the j-th node. and the state variables before correction Error term, Formula for representing the power flow state of the system Component, m represents the m-th boundary point, Represents the load variable after correction at the j-th node. and the load variable before correction Error term, Represents the continuous parameters after correction at the j-th node. and continuous parameters before correction Error term, Indicates the other parameters after correction of the j-th node. And other parameters before calibration Error term, Represents the inner product between vectors. To correct boundary points, This is the boundary convergence point.

[0136] Example 3: like Figure 13 As shown, the present invention also provides an electronic device, which may be a computer device, a microcontroller device, a smart mobile device, etc. The electronic device in this embodiment may include a processor, a memory, a transceiver component, etc. The memory, processor, and transceiver component are connected via a bus; the memory can be used to store executable programs, and an exemplary executable program may include instructions; the processor is used to execute the instructions stored in the memory. The memory can also be used to store data, which can be accessed and / or modified when instructions are executed.

[0137] The processor may be a Central Processing Unit (CPU), or it may be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing core and control core of the terminal, and it is suitable for implementing one or more instructions. Specifically, it is suitable for loading and executing one or more instructions in the storage medium to implement the corresponding method flow or corresponding function, so as to realize the steps of the calculation method of the static voltage stability domain boundary of a power system in the above embodiments.

[0138] Example 4: Based on the same inventive concept, this invention also provides a readable storage medium, specifically an electronic device readable storage medium (Memory). This readable storage medium is a memory device within an electronic device used to store programs and data. It is understood that the storage medium here can include both built-in storage media within the electronic device and extended storage media supported by the electronic device. The storage medium provides storage space, which stores the terminal's operating system. Furthermore, this storage space also stores one or more instructions suitable for loading and execution by a processor. These instructions can be one or more executable programs (including program code). It should be noted that the storage medium here can be high-speed RAM or non-volatile memory, such as at least one disk storage device. Loading and executing one or more instructions stored in the storage medium by the processor can implement the steps of the method for calculating the boundary of the static voltage stability domain of a power system in the above embodiments.

[0139] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0140] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0141] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1The function specified in one or more boxes.

[0142] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0143] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit its scope of protection. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that after reading the present invention, they can still make various changes, modifications or equivalent substitutions to the specific implementation methods of the application, but these changes, modifications or equivalent substitutions are all within the scope of protection of the claims pending approval.

Claims

1. A method for calculating the boundary of the static voltage stability domain of a power system, characterized in that, include: Based on the active power data and reactive power data of the new energy power system under the inverter operation constraints, a convex hull model considering the uncertainty of new energy output is constructed. The convex hull model limits the feasible domain of new energy output. Based on the known boundary points on the boundary of the static voltage stability domain and the convex hull model, the curve extrapolation prediction is performed using cubic spline interpolation or local principal component direction prediction method to obtain the predicted boundary points. Based on the convex hull model, the predicted boundary points are corrected using a correction algorithm that takes into account the arc correction strategy, and the corrected boundary points are obtained. The corrected boundary points are used as new known boundary points, and the curve extrapolation prediction and correction are performed again according to the step size control strategy until all boundary points on the static voltage stability domain boundary are tracked.

2. The method as described in claim 1, characterized in that, The aforementioned convex hull model, constructed based on active and reactive power data of the new energy power system under inverter operation constraints, considers the uncertainty of new energy output and includes: Based on the active power data and reactive power data of the new energy power system under inverter operation constraints, the boundary of the new energy output capacity is calculated, and the boundary points on the boundary of the new energy output capacity are used as known boundary points on the boundary of the static voltage stability domain to form a point set. Considering the uncertainty of new energy output, convex hull calculation is performed on the point set to obtain a convex hull model that limits the feasible region of new energy output; The inverter operating constraints include the inverter's apparent power limit and power factor angle limit.

3. The method as described in claim 2, characterized in that, The convex hull model satisfies the following formula: in, This is a convex hull model, i.e., the feasible region for new energy output. conv denotes convex hull calculation. This represents the active power data for the i-th sampling point. These are the lower and upper limits of the active power boundary. For the reactive power data of the i-th sampling point, The control mode at time t is indicated by the control mode. mode The determined mapping relationship, This represents the voltage at the new energy grid connection point at time t. S max This represents the upper limit of the apparent power of the inverter. The inverter operating constraints satisfy the following formula: in, P The output active power of the inverter. Q The output reactive power of the inverter. S max This is the upper limit of the apparent power of the inverter. This is the power factor angle of the inverter.

4. The method as described in claim 1, characterized in that, Based on the known boundary points on the static voltage stability domain boundary and the convex hull model, cubic spline interpolation is used to perform curve extrapolation prediction to obtain the predicted boundary points, including: The known boundary points on the boundary of the static voltage stability domain are sorted according to time steps to form a boundary point sequence; Based on the active power data and reactive power data in the boundary point sequence, a cubic spline interpolation function and the continuity conditions of each spline coefficient in the cubic spline interpolation function are constructed. Based on the cubic spline interpolation function and the continuity condition of each spline coefficient, a tridiagonal linear equation system is established for each spline coefficient. The tridiagonal linear equations are solved using the chasing method to obtain the spline coefficients. Based on the spline coefficients, curve extrapolation prediction is performed for the next time step to obtain the prediction boundary points for the next time step.

5. The method as described in claim 4, characterized in that, The cubic spline interpolation function satisfies the following formula: in, This represents the active power or reactive power data at the i-th boundary point. These are continuous parameters used to parameterize the boundary of the stability region; These are the continuous parameter values ​​corresponding to the i-th known boundary point; The spline coefficients of the function value represent the active power data or reactive power data of the i-th known boundary point. The spline coefficients are the first derivative coefficients, representing the slope of the boundary trajectory at the i-th known boundary point; The spline coefficients are the coefficients of the second derivative, representing the curvature of the boundary trajectory at the i-th known boundary point; The spline coefficients are the coefficients of the third derivative, representing the smoothness of the boundary trajectory at the i-th known boundary point; The continuity conditions for each spline coefficient include the function value continuity condition, the first derivative continuity condition, the second derivative continuity condition, and the boundary conditions. The condition for the continuity of the function value satisfies the following formula: ,in, This represents the active power or reactive power data at the i-th boundary point. For continuous parameters; x i This represents the active power data or reactive power data of the i-th known boundary point; The condition for the continuity of the first derivative satisfies the following formula: ,in, This represents the slope corresponding to the i-th boundary point; This represents the slope corresponding to the (i+1)th boundary point. These are the continuous parameter values ​​corresponding to the (i+1)th boundary point; The continuity condition of the second derivative satisfies the following formula: ,in, This represents the curvature corresponding to the i-th boundary point; This represents the curvature corresponding to the (i+1)th boundary point. These are the continuous parameter values ​​corresponding to the (i+1)th boundary point; The boundary conditions satisfy the formula: ,in, This represents the curvature corresponding to the first boundary point; This represents the curvature corresponding to the (n-1)th boundary point. These are the continuous parameter values ​​corresponding to the first boundary point. These are the continuous parameter values ​​corresponding to the nth boundary point.

6. The method as described in claim 5, characterized in that, The spline coefficients described above satisfy the following formula: in, The spline coefficients of the function value represent the active power data or reactive power data of the i-th known boundary point. The spline coefficients are the first derivative coefficients, representing the slope of the boundary trajectory at the i-th known boundary point; , Let be the second derivatives corresponding to the i-th and (i+1)-th boundary points, and let represent the curvature of the boundary trajectory at the i-th known boundary point. x i , x i+1 Represents the physical quantity values ​​of the i-th and (i+1)-th boundary points; h i This represents the continuous parameter step size corresponding to the i-th boundary point; The predicted boundary points for the next time step satisfy the following formula: in, x (t) represents the prediction boundary point at time step t, where t represents the time step. i This represents the time step corresponding to the i-th known boundary point. The spline coefficients of the function value represent the active power data or reactive power data of the i-th known boundary point. The spline coefficients are the first derivative coefficients, representing the slope of the boundary trajectory at the i-th known boundary point; The spline coefficients are the coefficients of the second derivative, representing the curvature of the boundary trajectory at the i-th known boundary point; The spline coefficients are the coefficients of the third derivative, representing the smoothness of the boundary trajectory at the i-th known boundary point.

7. The method as described in claim 1, characterized in that, Based on the known boundary points on the static voltage stability domain boundary and the convex hull model, the local principal component direction prediction method is used to perform curve extrapolation prediction to obtain the predicted boundary points, including: The known boundary points on the static voltage stability domain boundary are sorted according to time steps to obtain the boundary point sequence; Based on each boundary point in the boundary point sequence, determine the neighborhood point set of each boundary point; Based on each boundary point, the covariance matrix of the boundary point is calculated using the local principal component direction prediction method according to the neighborhood point set of the boundary point; the covariance matrix is ​​decomposed into eigenvalues ​​to obtain the local principal component direction of the boundary point; and curve extrapolation prediction is performed along the local principal component direction for the next time step to obtain the predicted boundary point of the next time step.

8. The method as described in claim 7, characterized in that, The covariance matrix satisfies the following formula: in, Let i represent the covariance matrix of the i-th boundary point. p Let a point be a neighbor of the i-th boundary point, located in the neighborhood point set. T represents the transpose matrix; The directions of the local principal components satisfy the following formula: in, Let i represent the covariance matrix of the i-th boundary point. It is the diagonal matrix of eigenvalues ​​of the i-th boundary point, and the eigenvector of the i-th boundary point is... The columns, where the local principal component directions are defined as .

9. The method as described in claim 1, characterized in that, The step of correcting the predicted boundary points based on the convex hull model using a correction algorithm that takes into account the arc correction strategy, to obtain corrected boundary points, includes: Based on the convex hull model, with the predicted boundary points as initial values, the Newton-Raphson method is used to iteratively solve the correction algorithm that takes into account the circular arc correction strategy to obtain the correction boundary points. The correction algorithm considering the circular arc correction strategy is a joint algorithm of the circular arc equation and the power grid boundary equation; the correction algorithm considering the circular arc correction strategy satisfies the following formula: in, This represents the correction algorithm that takes into account the circular arc correction strategy; These are the boundary equations for the power grid. The equation for a circular arc is... Represents the inner product between vectors. To correct boundary points, This is the boundary convergence point; The equation of the circular arc satisfies the following formula: in, Let be the radius of the arc, represent the comprehensive error index, j be the j-th node, j=1,…, and n be the total number of nodes. Represents the corrected state variable of the j-th node. and the state variables before correction Error term, Formula for representing the power flow state of the system Component, m represents the m-th boundary point, Represents the load variable after correction at the j-th node. and the load variable before correction Error term, Represents the continuous parameters after correction at the j-th node. and continuous parameters before correction Error term, Indicates the other parameters after correction of the j-th node. And other parameters before calibration Error term, Represents the inner product between vectors. To correct boundary points, This is the boundary convergence point.

10. A calculation system for the boundary of the static voltage stability domain of a power system, characterized in that, include: The convex hull modeling module is used to construct a convex hull model that considers the uncertainty of new energy output based on the active power data and reactive power data of the new energy power system under the inverter operation constraints. The convex hull model defines the feasible domain of new energy output. The curve extrapolation module is used to perform curve extrapolation prediction based on the known boundary points on the boundary of the static voltage stability domain and the convex hull model, using cubic spline interpolation technology or local principal component direction prediction method, to obtain the predicted boundary points. The correction module is used to correct the predicted boundary points based on the convex hull model using a correction algorithm that takes into account the circular arc correction strategy, so as to obtain the corrected boundary points. The boundary tracking module is used to take the corrected boundary point as a new known boundary point and re-perform curve extrapolation prediction and correction according to the step size control strategy until all boundary points on the static voltage stability domain boundary are tracked.

11. The system as claimed in claim 10, characterized in that, The convex hull modeling module includes: The point set calculation unit is used to calculate the new energy output capacity boundary based on the active power data and reactive power data of the new energy power system under inverter operation constraints, and to form a point set by using the boundary points on the new energy output capacity boundary as known boundary points on the static voltage stability domain boundary. A convex hull calculation unit is used to consider the uncertainty of new energy output, perform convex hull calculation on the point set, and obtain a convex hull model that limits the feasible domain of new energy output. The inverter operating constraints include the inverter's apparent power limit and power factor angle limit.

12. The system as claimed in claim 11, characterized in that, The convex hull model satisfies the following formula: in, This is a convex hull model, i.e., the feasible region for new energy output. conv denotes convex hull calculation. This represents the active power data for the i-th sampling point. These are the lower and upper limits of the active power boundary. For the reactive power data of the i-th sampling point, The control mode at time t is indicated by the control mode. mode The determined mapping relationship, This represents the voltage at the new energy grid connection point at time t. S max This represents the upper limit of the apparent power of the inverter. The inverter operating constraints satisfy the following formula: in, P The output active power of the inverter. Q The output reactive power of the inverter. S max This is the upper limit of the apparent power of the inverter. This is the power factor angle of the inverter.

13. The system as described in claim 10, characterized in that, The curve extrapolation module includes: A cubic spline interpolation function construction unit is used to sort the known boundary points on the boundary of the static voltage stability domain according to the time step to form a boundary point sequence; based on the active power data and reactive power data in the boundary point sequence, a cubic spline interpolation function and the continuity conditions of each spline coefficient in the cubic spline interpolation function are constructed. The tridiagonal linear equation system construction unit is used to establish a tridiagonal linear equation system about each spline coefficient based on the cubic spline interpolation function and the continuity condition of each spline coefficient. The boundary point prediction unit is used to solve the tridiagonal linear equation system using the chasing method to obtain the spline coefficients; based on the spline coefficients, it performs curve extrapolation prediction for the next time step to obtain the predicted boundary points for the next time step.

14. The system as described in claim 13, characterized in that, The cubic spline interpolation function satisfies the following formula: in, This represents the active power or reactive power data at the i-th boundary point. These are continuous parameters used to parameterize the boundary of the stability region; These are the continuous parameter values ​​corresponding to the i-th known boundary point; The spline coefficients of the function value represent the active power data or reactive power data of the i-th known boundary point. The spline coefficients are the first derivative coefficients, representing the slope of the boundary trajectory at the i-th known boundary point; The spline coefficients are the coefficients of the second derivative, representing the curvature of the boundary trajectory at the i-th known boundary point; The spline coefficients are the coefficients of the third derivative, representing the smoothness of the boundary trajectory at the i-th known boundary point; The continuity conditions for each spline coefficient include the function value continuity condition, the first derivative continuity condition, the second derivative continuity condition, and the boundary conditions. The condition for the continuity of the function value satisfies the following formula: ,in, This represents the active power or reactive power data at the i-th boundary point. For continuous parameters; x i This represents the active power data or reactive power data of the i-th known boundary point; The condition for the continuity of the first derivative satisfies the following formula: ,in, This represents the slope corresponding to the i-th boundary point; This represents the slope corresponding to the (i+1)th boundary point. These are the continuous parameter values ​​corresponding to the (i+1)th boundary point; The continuity condition of the second derivative satisfies the following formula: ,in, This represents the curvature corresponding to the i-th boundary point; This represents the curvature corresponding to the (i+1)th boundary point. These are the continuous parameter values ​​corresponding to the (i+1)th boundary point; The boundary conditions satisfy the formula: ,in, This represents the curvature corresponding to the first boundary point; This represents the curvature corresponding to the (n-1)th boundary point. These are the continuous parameter values ​​corresponding to the first boundary point. These are the continuous parameter values ​​corresponding to the nth boundary point.

15. The system as described in claim 14, characterized in that, The spline coefficients described above satisfy the following formula: in, The spline coefficients of the function value represent the active power data or reactive power data of the i-th known boundary point. The spline coefficients are the first derivative coefficients, representing the slope of the boundary trajectory at the i-th known boundary point; , Let be the second derivatives corresponding to the i-th and (i+1)-th boundary points, and let represent the curvature of the boundary trajectory at the i-th known boundary point. x i , x i+1 Represents the physical quantity values ​​of the i-th and (i+1)-th boundary points; h i This represents the continuous parameter step size corresponding to the i-th boundary point; The predicted boundary points for the next time step satisfy the following formula: in, x (t) represents the prediction boundary point at time step t, where t represents the time step. i This represents the time step corresponding to the i-th known boundary point. The spline coefficients of the function value represent the active power data or reactive power data of the i-th known boundary point. The spline coefficients are the first derivative coefficients, representing the slope of the boundary trajectory at the i-th known boundary point; The spline coefficients are the coefficients of the second derivative, representing the curvature of the boundary trajectory at the i-th known boundary point; The spline coefficients are the coefficients of the third derivative, representing the smoothness of the boundary trajectory at the i-th known boundary point.

16. The system as claimed in claim 10, characterized in that, The curve extrapolation module includes: The neighborhood point set determination unit is used to sort the known boundary points on the boundary of the static voltage stability domain according to the time step to obtain a boundary point sequence; and to determine the neighborhood point set of each boundary point based on each boundary point in the boundary point sequence. The local principal component direction determination unit is used to calculate the covariance matrix of each boundary point based on the neighborhood point set of the boundary point and using the local principal component direction prediction method; and to perform eigenvalue decomposition on the covariance matrix to obtain the local principal component direction of the boundary point. The boundary point prediction unit is used to perform curve extrapolation prediction for the next time step along the direction of the local principal component to obtain the predicted boundary points for the next time step.

17. The system as claimed in claim 16, characterized in that, The covariance matrix satisfies the following formula: in, Let i represent the covariance matrix of the i-th boundary point. p Let a point be a neighbor of the i-th boundary point, located in the neighborhood point set. T represents the transpose matrix; The directions of the local principal components satisfy the following formula: in, Let i represent the covariance matrix of the i-th boundary point. It is the diagonal matrix of eigenvalues ​​of the i-th boundary point, and the eigenvector of the i-th boundary point is... The columns, where the local principal component directions are defined as .

18. The system as claimed in claim 10, characterized in that, The correction module is specifically used for: Based on the convex hull model, with the predicted boundary points as initial values, the Newton-Raphson method is used to iteratively solve the correction algorithm that takes into account the circular arc correction strategy to obtain the correction boundary points. The correction algorithm considering the circular arc correction strategy is a joint algorithm of the circular arc equation and the power grid boundary equation; the correction algorithm considering the circular arc correction strategy satisfies the following formula: in, This represents the correction algorithm that takes into account the circular arc correction strategy; These are the boundary equations for the power grid. The equation for a circular arc is... Represents the inner product between vectors. To correct boundary points, This is the boundary convergence point; The equation of the circular arc satisfies the following formula: in, Let be the radius of the arc, represent the comprehensive error index, j be the j-th node, j=1,…, and n be the total number of nodes. Represents the corrected state variable of the j-th node. and the state variables before correction Error term, Formula for representing the power flow state of the system Component, m represents the m-th boundary point, Represents the load variable after correction at the j-th node. and the load variable before correction Error term, Represents the continuous parameters after correction at the j-th node. and continuous parameters before correction Error term, Indicates the other parameters after correction of the j-th node. And other parameters before calibration Error term, Represents the inner product between vectors. To correct boundary points, This is the boundary convergence point.

19. An electronic device, characterized in that, include: At least one processor and memory; The memory and processor are connected via a bus; The memory is used to store one or more programs; When the one or more programs are executed by the at least one processor, the method for calculating the boundary of the static voltage stability domain of a power system as described in any one of claims 1 to 9 is implemented.

20. A readable storage medium, characterized in that, It contains an executable program, which, when executed, implements the method for calculating the boundary of the static voltage stability domain of a power system as described in any one of claims 1 to 9.

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