Galerkin method-based power grid cross-time scale voltage stability analysis method and system

Abstract

The invention relates to the technical field of power system optimization, in particular to a power grid cross-time scale voltage stability analysis method and system based on a Galerkin method, and the method comprises the steps: improving a transient voltage stability index, carrying out the approximation of the improved transient voltage stability index, and constructing a transient stability boundary function; determining the number of primary functions; determining a polynomial approximation function through the number of the primary functions; obtaining a simplified system equation under the condition of no discrete switching event; applying a Galerkin method to obtain a continuous polynomial approximate expression; according to a continuous polynomial approximate expression and the trigger condition function, obtaining a system state after a discrete event occurs; taking the jumped system state as a new initial condition, and obtaining a continuous polynomial approximate expression after a discrete event occurs; and then a polynomial approximation result is used for model prediction control, and full-time-scale stable risk quantification is realized. According to the invention, the accuracy of power grid cross-time scale voltage stability analysis is improved.

Description

Technical Field

[0001] This invention relates to the field of power system optimization technology, and in particular to a method and system for analyzing voltage stability of power grids across time scales based on the Galerkin method. Background Technology

[0002] The integration of a high proportion of renewable energy into the power grid has become an inevitable trend, especially in power grids in Northwest my country, where renewable energy is gradually becoming the main power source. However, this transformation has brought unprecedented technical challenges: the strong volatility and uncertainty of renewable energy generation seriously threaten the safe and stable operation of the power grid; high-power DC faults and other factors have extended stability issues across the entire frequency band, with the complex interaction mechanism between renewable energy, DC, and AC systems, where voltage is the transmission factor, being particularly prominent. Traditional voltage stability analysis methods, such as the continuous power flow method, suffer from high computational complexity and low efficiency, making it difficult to meet the needs of rapid online assessment; while linearization methods (such as the trajectory sensitivity method) lack accuracy when dealing with highly nonlinear power grid dynamic processes. In addition, most existing studies separate transient stability analysis from medium- and long-term stability analysis, lacking a unified assessment framework and failing to effectively characterize the coupled risks of "transient fault triggering - medium- and long-term dynamic evolution." At the same time, the modeling and simulation efficiency of key discrete events in the power system (such as the tap changer of on-load tap changer and the operation of overexcitation limiters) is low, and traditional polynomial approximation methods suffer from insufficient accuracy in identifying stability boundaries due to high parameter sensitivity. These problems severely restrict the accurate analysis and efficient control of voltage stability across time scales in the sending-end power grid with a high proportion of new energy AC / DC hybrid connection. Summary of the Invention

[0003] This invention provides a method and system for analyzing voltage stability across time scales in power grids based on the Galerkin method. It addresses the challenges of traditional methods being unable to efficiently and accurately analyze voltage stability across time scales after a high proportion of new energy sources are connected to the power grid, and the lack of a unified framework to address the risks of transient and medium- to long-term dynamic coupling.

[0004] The objective of this invention can be achieved through the following technical solutions: The first aspect of this invention is to provide a method for analyzing the voltage stability of power grids across time scales based on the Galerkin method, comprising: A dynamic model of the high-proportion AC / DC hybrid power grid at the sending end is established across time scales, denoted as the system equation; The transient voltage stability index is improved to obtain the improved transient voltage stability index; the improved transient voltage stability index is approximated to construct the transient stability boundary function; The system variables are expressed as polynomial functions of control parameters. An orthogonal polynomial basis is selected, and the number of basis functions is determined. The polynomial approximation function is determined by the number of basis functions. Assuming that no discrete switching events occur in the medium to long term, the cross-timescale dynamic model is simplified to a continuous dynamic system, and the simplified model is denoted as the simplified system equation. The Galerkin method is applied to substitute the polynomial approximation function into the simplified system equation to solve for the polynomial approximation expression of the system state variables with respect to the control parameters and time, which is denoted as the continuous polynomial approximation expression. Define the triggering condition function for the discrete switching event; obtain the continuous state at the transition time and the instant before the transition based on the continuous polynomial approximation expression and the triggering condition function; obtain the system state after the discrete event occurs through the system equation based on the continuous state at the transition time and the instant before the transition; use the system state after the transition as the new initial condition, and solve it using the Galerkin method to obtain the continuous polynomial approximation expression after the discrete event occurs. By using the transient stability boundary function and the continuous polynomial approximation expression for model predictive control, stability risk quantification across the entire time scale is achieved.

[0005] Furthermore, the improvement of the transient voltage stability index, to obtain an improved transient voltage stability index, includes:

[0006] In the formula, This indicates the start time when the bus voltage falls below the voltage drop threshold. This indicates the end time when the bus voltage falls below the voltage drop threshold. This represents the adjustment coefficient. This represents the function that takes the maximum value. Indicates the voltage drop threshold. Indicates in arrive Voltage values ​​during the time period between This indicates the improved transient voltage stability index. Represents the integral element with respect to the time variable. It represents 1 second.

[0007] Furthermore, the improved transient voltage stability index is approximated to construct a transient stability boundary function, which is specifically expressed as follows:

[0008] In the formula, This represents the key parameters affecting transient voltage stability. This indicates that, in addition to being selected as a key parameter A vector consisting of all other control parameters besides, Represents a polynomial function; Among them, the key parameter is one that is specially selected from all the control parameters to represent the core influencing factor of stability; The improved transient voltage stability index can be represented by pre-selected polynomial basis functions; where each polynomial basis function is a vector of control parameters. It is composed of independent variables; The goal of the polynomial function is to approximate the true improved TVSI index as accurately as possible, which holds true for any p in the parameter domain D.

[0009] Furthermore, the specific number of basis functions is expressed by the formula:

[0010] In the formula, This indicates the highest total order of the selected polynomial. This represents the dimension of the control parameter vector p. To represent factorial, Indicates the number of basis functions; Indicates from Select from elements The number of combinations of elements.

[0011] Furthermore, by applying the Galerkin method, the polynomial approximation function is substituted into the simplified system equations to obtain a polynomial approximation expression for the system state variables with respect to control parameters and time, denoted as a continuous polynomial approximation expression, which includes: Substituting the polynomial approximation function into the simplified system equations yields the residual equations. By setting the projection of the residuals onto pre-selected polynomial basis functions to zero, a Galerkin equation system with respect to the indeterminate coefficients is constructed. The Galerkin equation system is solved using numerical integration to obtain the solution of the indeterminate coefficients as a function of time. Using the obtained indeterminate coefficients, a polynomial approximation expression for the system state variables with respect to control parameters and time is determined and denoted as a continuous polynomial approximation expression.

[0012] Further, the step of obtaining the continuous state at the transition moment and the instant before the transition based on the continuous polynomial approximation expression and the triggering condition function; and obtaining the system state after the discrete event occurs through system equations based on the continuous state at the transition moment and the instant before the transition, includes: Based on the continuous polynomial approximation expression, a discrete polynomial approximation function is obtained by solving the equation where the triggering condition function equals zero. The discrete polynomial approximation function is used to determine the continuous state at the jump moment and the instant before the jump. At the jump moment, the continuous state at the instant before the jump is substituted into the discrete state jump equation in the system equation to calculate the system state after the discrete event occurs.

[0013] Furthermore, the use of the transient stability boundary function and the continuous polynomial approximation expression for model predictive control achieves full-time-scale stability risk quantification, including: The transient stable boundary function and the continuous polynomial approximation expression are used as analytical constraints or prediction models and embedded into the rolling optimization stage of model predictive control to realize the construction of a transient-medium-long-term collaborative evaluation framework. Specifically, transient scale quantization is performed using the transient stable boundary function, and medium- to long-term scale quantization is performed using the continuous polynomial approximation expression. The model predictive control considers both transient and medium- to long-term scale constraints during optimization, thereby achieving full-time-scale security risk quantification and avoidance from instantaneous to long-term.

[0014] A second aspect of the present invention is to provide a power grid voltage stability analysis system based on the Galerkin method across time scales, comprising: System modeling module: used to establish a dynamic model of the high-proportion AC / DC hybrid power grid at the sending end across time scales, denoted as the system equation; The index improvement and boundary approximation module is used to improve the transient voltage stability index, obtain the improved transient voltage stability index, and approximate the improved transient voltage stability index to construct the transient stability boundary function. The continuous dynamics solution module is used to express system variables as polynomial functions of control parameters, select orthogonal polynomial bases, and determine the number of basis functions; the polynomial approximation function is determined by the number of basis functions; assuming that no discrete switching events occur in the medium to long term, the cross-timescale dynamic model is simplified to a continuous dynamic system, and the simplified model is denoted as the simplified system equation; the Galerkin method is applied to substitute the polynomial approximation function into the simplified system equation to obtain the polynomial approximation expression of the system state variables with respect to control parameters and time, which is denoted as the continuous polynomial approximation expression; Discrete event processing module: used to define the triggering condition function for discrete switch events; obtain the continuous state at the transition time and the instant before the transition based on the continuous polynomial approximation expression and the triggering condition function; obtain the system state after the discrete event occurs through system equations based on the continuous state at the transition time and the instant before the transition; use the system state after the transition as a new initial condition, reuse the Galerkin method to solve, and obtain the continuous polynomial approximation expression after the discrete event occurs. Voltage stability analysis module: used to apply the transient stability boundary function and the continuous polynomial approximation expression to model predictive control, realizing the quantification of stability risk across the entire time scale.

[0015] A third aspect of the present invention is to provide an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the power grid voltage stability analysis method based on the Galerkin method across time scales.

[0016] A fourth aspect of the present invention is to provide a computer-readable storage medium storing a computer program that, when executed by a processor, implements the power grid voltage stability analysis method based on the Galerkin method across time scales.

[0017] Compared with existing technologies, the beneficial effects of this invention are as follows: A cross-timescale dynamic model of a high-proportion AC / DC hybrid power grid at the sending end is established, denoted as the system equation; the transient voltage stability index is improved to obtain an improved transient voltage stability index; the improved transient voltage stability index is approximated to construct a transient stability boundary function; the accuracy of transient stability boundary analysis is improved; system variables are expressed as polynomial functions of control parameters, orthogonal polynomial bases are selected, and the number of basis functions is determined; the polynomial approximation function is determined by the number of basis functions; assuming no discrete switching events occur in the medium to long term, the cross-timescale dynamic model is simplified to a continuous dynamic system, and the simplified model is denoted as the simplified system equation; the Galerkin method is applied to substitute the polynomial approximation function into the simplified system equation to obtain a polynomial approximation expression of the system state variables with respect to control parameters and time, denoted as the continuous polynomial approximation expression, thus improving the accuracy of obtaining the continuous polynomial approximation expression. The accuracy of the data acquisition is improved; the triggering condition function for discrete switching events is defined; based on the continuous polynomial approximation expression and the triggering condition function, the continuous state at the transition moment and the instant before the transition is obtained; based on the continuous state at the transition moment and the instant before the transition, the system state after the discrete event is obtained through system equations; the system state after the transition is used as a new initial condition, and the Galerkin method is reused to solve the problem, obtaining the continuous polynomial approximation expression after the discrete event, thus improving the accuracy of the analysis of the continuous polynomial approximation expression after the discrete event; the transient stability boundary function and the continuous polynomial approximation expression are used for model predictive control, realizing the quantification of stability risks across the entire time scale; this solves the problem that traditional methods cannot efficiently and accurately analyze voltage stability across time scales after a high proportion of new energy sources are connected to the grid, and lack a unified framework to deal with transient and medium-to-long-term dynamic coupling risks, thus improving the accuracy of voltage stability analysis of the power grid across time scales. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 This invention provides a flowchart illustrating the steps of a power grid voltage stability analysis method based on the Galerkin method across time scales. Figure 2 This invention provides a schematic diagram of the module flow of a power grid voltage stability analysis system based on the Galerkin method across time scales. Detailed Implementation

[0020] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0021] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0022] To address the problems existing in the background technology, a method and system for analyzing voltage stability of power grids across time scales based on the Galerkin method have been developed, which has important practical significance.

[0023] like Figure 1 As shown, the first aspect of this invention is to provide a method for analyzing the voltage stability of a power grid across time scales based on the Galerkin method, comprising the following steps: Step S001: Establish a dynamic model across time scales for the high-proportion AC / DC hybrid power grid of new energy sources, denoted as the system equation.

[0024] It should be noted that, in order to achieve efficient and accurate analysis of voltage stability across the entire time scale from transient to medium- and long-term in a high-proportion renewable energy power grid, it is first necessary to integrate the unified mathematical descriptions of state variables (such as generator rotor motion), algebraic variables (such as node voltage), slow dynamic processes (such as overexcitation limiters and on-load tap-changing transformers), and discrete switching events (such as protection device actions) related to fast dynamics in the system through a comprehensive modeling method. This results in the construction of a complete cross-time-scale dynamic model in the form of differential-algebraic-discrete hybrid equations, which is denoted as the original system equations in this analysis. By establishing these system equations, a precise mathematical object and operational basis are provided for subsequent polynomial approximation using the Galerkin method, thereby achieving a global analytical approximation of the dynamic behavior of complex power grids.

[0025] Specifically, the system equations are expressed as follows:

[0026] In the formula, This represents state variables that are related to fast dynamics (such as the motion of the generator rotor, the excitation system, and the regulation of the governor). Represents algebraic variables (such as bus voltage and injected current). Represents state variables related to slow-dynamic components of the power system (such as the state of overexcitation limiters, on-load tap changers, and recoverable loads). This represents discrete state variables (such as the operation of overexcitation limiters) associated with discrete switches in a power system. This refers to control parameters related to medium- and long-term voltage stability (such as load shedding, generator terminal voltage, reactive power of reactive power compensators, etc.). Vectors representing algebraic equations This represents the equilibrium form vector of the differential equations describing fast dynamics. This represents a vector of differential equations describing slow dynamics. Represents the equation vector describing discrete switching events; express The derivative with respect to time, express The derivative with respect to time; the superscript + indicates the instant after the discrete switching event occurs, and the superscript - indicates the instant before the discrete switching event occurs.

[0027] Step S002: Improve the transient voltage stability index to obtain the improved transient voltage stability index; approximate the improved transient voltage stability index to construct the transient stability boundary function.

[0028] It should be noted that, in order to accurately characterize the transient voltage stability critical state and efficiently obtain its stability boundary, a new index more suitable for polynomial approximation is constructed by improving the traditional index based on the duration of voltage drop into a piecewise function that is continuously smooth at the critical point (the original physical meaning is retained on the stable side, and an integral term based on the drop depth is introduced on the unstable side). Then, the improved index is globally polynomially approximated in the parameter space using the Galerkin collocation method, and its approximate value is set to 1 to solve the critical condition. Finally, an explicit analytical function relationship of the transient voltage stability boundary with respect to the control parameters is constructed.

[0029] Specifically, the transient voltage stability index is improved to obtain the improved transient voltage stability index; the improved transient voltage stability index is then approximated to construct the transient stability boundary function.

[0030] The improved transient voltage stability index is specifically expressed by the following formula:

[0031] In the formula, This indicates the start time when the bus voltage falls below the voltage drop threshold. This indicates the end time when the bus voltage falls below the voltage drop threshold. This indicates the adjustment factor (to ensure the TVSI has the smoothest possible performance, an appropriate constant adjustment factor should be used). This represents the function that takes the maximum value. This indicates the voltage drop threshold (0.75pu, where pu stands for per unit). Indicates in arrive Voltage values ​​during the time period between This indicates the improved transient voltage stability index. Represents the integral element with respect to the time variable. It represents 1 second.

[0032] The transient stability boundary function is specifically expressed as follows:

[0033] In the formula, This represents the key parameters affecting transient voltage stability. This indicates that, in addition to being selected as a key parameter A vector consisting of all other control parameters besides, Represents a polynomial function; Among them, the key parameter is one that is specially selected from all the control parameters to represent the core influencing factor of stability; The improved transient voltage stability index can be represented by pre-selected polynomial basis functions; where each polynomial basis function is a vector of control parameters. It is composed of independent variables; The goal of the polynomial function is to approximate the true improved TVSI (Transient Voltage Stability Index) as accurately as possible, which holds true for any p in the parameter domain D.

[0034] Step S003: Express the system variables as polynomial functions of the control parameters, select an orthogonal polynomial basis, and determine the number of basis functions; determine the polynomial approximation function by the number of basis functions; assume that no discrete switching events occur in the medium to long term, simplify the cross-timescale dynamic model into a continuous dynamic system, and denote the simplified model as the simplified system equation; apply the Galerkin method, substitute the polynomial approximation function into the simplified system equation to solve, and obtain the polynomial approximation expression of the system state variables with respect to the control parameters and time, which is denoted as the continuous polynomial approximation expression.

[0035] It should be noted that, in order to efficiently obtain the analytical expression of the dynamic trajectory of the system state variables in the global parameter space, thereby avoiding repeated time-domain simulations for each parameter point, the system variables are represented as an orthogonal polynomial combination of control parameters, and the number of basis functions is determined according to the parameter dimension and the polynomial order to construct the general form of the polynomial approximation function. Furthermore, assuming that there are no discrete events in the medium to long term, the original hybrid dynamic model is simplified into a purely continuous system, and the Galerkin method is applied to substitute the polynomial approximation function into the simplified system equations. The equation system is constructed by forcing the projection of the residuals onto the basis functions to be zero, and finally, the continuous polynomial approximation expression of the system state variables with respect to the control parameters and time is obtained by solving it.

[0036] Specifically, the system variables are expressed as polynomial functions of the control parameters, an orthogonal polynomial basis is selected, and the number of basis functions is determined. The polynomial approximation function is then determined by the number of basis functions. The specific number of basis functions is expressed by the formula:

[0037] In the formula, This indicates the highest total order of the selected polynomial. This represents the dimension of the control parameter vector p. To represent factorial, Indicates the number of basis functions; Indicates from Select from elements The number of combinations of elements.

[0038] Assuming no discrete switching events occur in the medium to long term, the simplified cross-timescale dynamic model is transformed into a continuous dynamic system, denoted as the simplified system equation. Applying the Galerkin method, the polynomial approximation function is substituted into the simplified system equation to obtain a polynomial approximation expression for the system state variables with respect to control parameters and time, denoted as the continuous polynomial approximation expression, which specifically includes: Substituting the polynomial approximation function into the simplified system equations yields the residual equations. By setting the projection of the residuals onto pre-selected polynomial basis functions to zero, a system of Galerkin equations with undetermined coefficients is constructed. The Galerkin equations are solved using numerical integration to obtain solutions with undetermined coefficients varying over time. Using the obtained undetermined coefficients, a polynomial approximation expression for the system state variables with respect to control parameters and time is determined and denoted as a continuous polynomial approximation expression. The Galerkin method is a well-known technique and will not be described in detail here.

[0039] The simplified system equations are specifically expressed as follows:

[0040] In the formula, This represents state variables that are related to fast dynamics (such as the motion of the generator rotor, the excitation system, and the regulation of the governor). Represents algebraic variables (such as bus voltage and injected current). Represents state variables related to slow-dynamic components of the power system (such as the state of overexcitation limiters, on-load tap changers, and recoverable loads). This refers to control parameters related to medium- and long-term voltage stability (such as load shedding, generator terminal voltage, reactive power of reactive power compensators, etc.). Vectors representing algebraic equations Represents a vector of differential equations describing slow dynamics; express The derivative with respect to time.

[0041] Step S004: Define the triggering condition function for the discrete switching event; obtain the continuous state at the transition moment and the instant before the transition based on the continuous polynomial approximation expression and the triggering condition function; obtain the system state after the discrete event occurs through the system equations based on the continuous state at the transition moment and the instant before the transition; use the system state after the transition as the new initial condition, and solve it using the Galerkin method to obtain the continuous polynomial approximation expression after the discrete event occurs; use the transient stability boundary function and the continuous polynomial approximation expression for model predictive control to achieve full-time-scale stability risk quantification.

[0042] It should be noted that, in order to incorporate discrete event dynamics into the global polynomial approximation framework and ultimately achieve collaborative optimization control, the trigger condition function of discrete switches is defined, and the polynomial approximation of the trigger time is solved using existing continuous polynomial approximation expressions, thereby determining the jump time and the system state before the jump. Then, the new system state after the event is calculated according to the discrete state jump rules in the system equations. Subsequently, the Galerkin method is reused with the post-jump state as the initial condition to solve the subsequent continuous dynamics, obtaining a piecewise polynomial expression for the entire process including discrete events. Finally, by embedding the analytical function describing the transient stability boundary and the polynomial expression characterizing the medium- and long-term dynamics into the model predictive control (MPC) algorithm, the rapid quantification and optimized avoidance of transient stability and medium- and long-term voltage evolution risks are achieved simultaneously.

[0043] Specifically, define the triggering condition function for discrete switch events; Based on the continuous polynomial approximation and the triggering condition function, the continuous state at the jump moment and the instant before the jump is obtained; based on the continuous state at the jump moment and the instant before the jump, the system state after the discrete event occurs is obtained through the system equations, specifically including: Based on the continuous polynomial approximation, the discrete polynomial approximation function is obtained by solving the equation where the trigger condition function equals zero. The discrete polynomial approximation function is used to determine the continuous state at the jump moment and the instant before the jump. At the jump moment, the continuous state instant before the jump is substituted into the discrete state jump equation in the system equation to calculate the system state after the discrete event occurs.

[0044] Using the system state after the jump as a new initial condition, the Galerkin method is reused to solve for the continuous polynomial approximation after the discrete event occurs.

[0045] By applying the transient stability boundary function and the continuous polynomial approximation expression to model predictive control, stability risk quantification across the entire time scale is achieved, specifically including: The transient stable boundary function and the continuous polynomial approximation expression are used as analytical constraints or prediction models and embedded into the rolling optimization stage of model predictive control to realize the construction of a transient-medium-long-term collaborative evaluation framework. Among them, transient scale quantization is performed using transient stable boundary functions, and medium- and long-term scale quantization is performed using continuous polynomial approximation expressions; model predictive control considers both transient and medium- and long-term scale constraints during optimization, thereby achieving full-time-scale security risk quantification and avoidance from instantaneous to long-term.

[0046] The specific process of transient stability risk quantification is as follows: When the transient stability boundary function is If the transient stability boundary function is true, then the system is stable; when the transient stability boundary function is true, the system is stable. If this happens, the system becomes unstable.

[0047] The specific process for quantifying medium- and long-term stable risks is as follows: The voltage value is predicted by a continuous polynomial approximation expression. When the difference between the predicted voltage value and the reference safe voltage value is less than the preset safe threshold, the system is stable; when the difference between the predicted voltage value and the reference safe voltage value is greater than or equal to the preset safe threshold, the system is unstable.

[0048] Among them, full-time scale security risk quantification and coordination combines the results of transient stability risk quantification and the results of medium- and long-term stability risk quantification to determine whether the system is stable or unstable.

[0049] This completes the voltage stability analysis.

[0050] like Figure 2 As shown, a second aspect of the present invention is to provide a power grid voltage stability analysis system based on the Galerkin method across time scales, comprising: System Modeling Module 101: Used to establish a cross-timescale dynamic model of a high-proportion AC / DC hybrid power grid at the sending end, denoted as the system equation; Indicator Improvement and Boundary Approximation Module 102: Used to improve the transient voltage stability index, obtain the improved transient voltage stability index; approximate the improved transient voltage stability index, and construct the transient stability boundary function; Continuous dynamics solution module 103: This module is used to express system variables as polynomial functions of control parameters, select orthogonal polynomial bases, and determine the number of basis functions; it determines the polynomial approximation function based on the number of basis functions; assuming that no discrete switching events occur in the medium to long term, it simplifies the cross-timescale dynamic model into a continuous dynamic system, and denotes the simplified model as the simplified system equation; it applies the Galerkin method, substitutes the polynomial approximation function into the simplified system equation, and obtains the polynomial approximation expression of the system state variables with respect to control parameters and time, which is denoted as the continuous polynomial approximation expression; Discrete event processing module 104: used to define the triggering condition function of discrete switch events; obtain the continuous state at the transition time and the instant before the transition based on the continuous polynomial approximation expression and the triggering condition function; obtain the system state after the discrete event occurs through system equations based on the continuous state at the transition time and the instant before the transition; use the system state after the transition as a new initial condition, reuse the Galerkin method to solve, and obtain the continuous polynomial approximation expression after the discrete event occurs. Voltage stability analysis module 105: used to apply the transient stability boundary function and the continuous polynomial approximation expression to model predictive control, thereby realizing the quantification of stability risk across the entire time scale.

[0051] A third aspect of the present invention is to provide an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement a power grid voltage stability analysis method based on the Galerkin method across time scales.

[0052] A fourth aspect of the present invention is to provide a computer-readable storage medium storing a computer program that, when executed by a processor, implements a power grid voltage stability analysis method based on the Galerkin method across time scales.

[0053] 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, optical storage, etc.) containing computer-usable program code.

[0054] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, 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.

[0055] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0056] 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.

[0057] 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 it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the protection scope of the present invention.

Claims

1. A method for analyzing the voltage stability of power grids across time scales based on the Galerkin method, characterized in that, include: A dynamic model of the high-proportion AC / DC hybrid power grid at the sending end is established across time scales, denoted as the system equation; The transient voltage stability index is improved to obtain the improved transient voltage stability index; the improved transient voltage stability index is approximated to construct the transient stability boundary function; The system variables are expressed as polynomial functions of control parameters. An orthogonal polynomial basis is selected, and the number of basis functions is determined. The polynomial approximation function is determined by the number of basis functions. Assuming that no discrete switching events occur in the medium to long term, the cross-timescale dynamic model is simplified to a continuous dynamic system, and the simplified model is denoted as the simplified system equation. The Galerkin method is applied to substitute the polynomial approximation function into the simplified system equation to solve for the polynomial approximation expression of the system state variables with respect to the control parameters and time, which is denoted as the continuous polynomial approximation expression. Define the trigger condition function for discrete switch events; Based on the continuous polynomial approximation and the triggering condition function, the continuous state at the jump time and the instant before the jump is obtained; based on the continuous state at the jump time and the instant before the jump, the system state after the discrete event is obtained through the system equation; the system state after the jump is used as the new initial condition, and the Galerkin method is reused to solve the problem to obtain the continuous polynomial approximation after the discrete event is obtained. By using the transient stability boundary function and the continuous polynomial approximation expression for model predictive control, stability risk quantification across the entire time scale is achieved.

2. The power grid voltage stability analysis method based on the Galerkin method according to claim 1, characterized in that, The improvement to the transient voltage stability index, resulting in an improved transient voltage stability index, includes: In the formula, This indicates the start time when the bus voltage falls below the voltage drop threshold. This indicates the end time when the bus voltage falls below the voltage sag threshold. This represents the adjustment coefficient. This represents the function that takes the maximum value. Indicates the voltage drop threshold. Indicates in arrive Voltage values ​​during the time period between This indicates the improved transient voltage stability index. Represents the integral element with respect to the time variable. It represents 1 second.

3. The power grid voltage stability analysis method based on the Galerkin method according to claim 1, characterized in that, The improved transient voltage stability index is approximated to construct a transient stability boundary function, which is specifically expressed as follows: In the formula, This indicates the key parameters affecting transient voltage stability. This indicates that, in addition to being selected as a key parameter A vector consisting of all other control parameters besides, Represents a polynomial function; Among them, the key parameter is one that is specially selected from all the control parameters to represent the core influencing factor of stability; The improved transient voltage stability index can be represented by pre-selected polynomial basis functions; where each polynomial basis function is a vector of control parameters. It is composed of independent variables; The goal of the polynomial function is to approximate the true improved TVSI index as accurately as possible, which holds true for any p in the parameter domain D.

4. The power grid voltage stability analysis method based on the Galerkin method according to claim 1, characterized in that, The specific number of basis functions is expressed by the formula: In the formula, This indicates the highest total order of the selected polynomial. This represents the dimension of the control parameter vector p. To represent factorial, Indicates the number of basis functions; Indicates from Select from elements The number of combinations of elements.

5. The power grid voltage stability analysis method based on the Galerkin method according to claim 1, characterized in that, The Galerkin method is applied to substitute the polynomial approximation function into the simplified system equations for solving, obtaining a polynomial approximation expression of the system state variables with respect to control parameters and time, denoted as a continuous polynomial approximation expression, including: Substituting the polynomial approximation function into the simplified system equations yields the residual equations. By setting the projection of the residuals onto pre-selected polynomial basis functions to zero, a Galerkin equation system with respect to the indeterminate coefficients is constructed. The Galerkin equation system is solved using numerical integration to obtain the solution of the indeterminate coefficients as a function of time. Using the obtained indeterminate coefficients, a polynomial approximation expression for the system state variables with respect to control parameters and time is determined and denoted as a continuous polynomial approximation expression.

6. The power grid voltage stability analysis method based on the Galerkin method according to claim 1, characterized in that, The process involves obtaining the continuous state at the transition moment and the instant before the transition based on the continuous polynomial approximation expression and the triggering condition function; and obtaining the system state after the discrete event occurs through system equations based on the continuous state at the transition moment and the instant before the transition, including: Based on the continuous polynomial approximation expression, a discrete polynomial approximation function is obtained by solving the equation where the triggering condition function equals zero. The discrete polynomial approximation function is used to determine the continuous state at the jump moment and the instant before the jump. At the jump moment, the continuous state at the instant before the jump is substituted into the discrete state jump equation in the system equation to calculate the system state after the discrete event occurs.

7. The power grid voltage stability analysis method based on the Galerkin method according to claim 1, characterized in that, The method of using the transient stability boundary function and the continuous polynomial approximation expression for model predictive control achieves full-time-scale stability risk quantification, including: The transient stable boundary function and the continuous polynomial approximation expression are used as analytical constraints or prediction models and embedded into the rolling optimization stage of model predictive control to realize the construction of a transient-medium-long-term collaborative evaluation framework. Specifically, transient scale quantization is performed using the transient stable boundary function, and medium- to long-term scale quantization is performed using the continuous polynomial approximation expression. The model predictive control considers both transient and medium- to long-term scale constraints during optimization, thereby achieving full-time-scale security risk quantification and avoidance from instantaneous to long-term.

8. A power grid voltage stability analysis system based on the Galerkin method across time scales, characterized in that, include: System modeling module: used to establish a dynamic model of the high-proportion AC / DC hybrid power grid at the sending end across time scales, denoted as the system equation; The index improvement and boundary approximation module is used to improve the transient voltage stability index, obtain the improved transient voltage stability index, and approximate the improved transient voltage stability index to construct the transient stability boundary function. The continuous dynamics solution module is used to express system variables as polynomial functions of control parameters, select orthogonal polynomial bases, and determine the number of basis functions; the polynomial approximation function is determined by the number of basis functions; assuming that no discrete switching events occur in the medium to long term, the cross-timescale dynamic model is simplified to a continuous dynamic system, and the simplified model is denoted as the simplified system equation; the Galerkin method is applied to substitute the polynomial approximation function into the simplified system equation to obtain the polynomial approximation expression of the system state variables with respect to control parameters and time, which is denoted as the continuous polynomial approximation expression; Discrete event handling module: used to define the triggering condition functions for discrete switch events; Based on the continuous polynomial approximation and the triggering condition function, the continuous state at the jump time and the instant before the jump is obtained; based on the continuous state at the jump time and the instant before the jump, the system state after the discrete event is obtained through the system equation; the system state after the jump is used as the new initial condition, and the Galerkin method is reused to solve the problem to obtain the continuous polynomial approximation after the discrete event is obtained. Voltage stability analysis module: used to apply the transient stability boundary function and the continuous polynomial approximation expression to model predictive control, realizing the quantification of stability risk across the entire time scale.

9. An electronic device, characterized in that, It includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the power grid time-scale voltage stability analysis method based on the Galerkin method according to any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the power grid voltage stability analysis method based on the Galerkin method according to any one of claims 1-7.

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