A method for characterizing the static safety margin of power systems based on truncated polynomial approximation.

Abstract

This invention belongs to the field of communication equipment security protection technology, and discloses a method for characterizing the static safety margin of power systems based on the truncated polynomial approximation method. This method first maps the load growth factor to complex-domain embedded variables, establishing a fully embedded power flow model; then, it expands the system state variables into high-order truncated polynomials, transforming nonlinear terms into linear convolutions between coefficients through Cauchy products, and solving for the polynomial coefficients using linear recursion; subsequently, it constructs Padé approximation rational functions to achieve analytical extension, directly calculating the high-load operating condition solution exceeding the original series convergence radius; finally, through a multi-stage continuity tracking strategy, it adaptively approximates the voltage collapse critical point, synthesizing the system's static safety margin. This invention abandons the reliance of traditional iterative algorithms on Jacobian matrix inversion and initial value guessing, fundamentally avoiding numerical ill-conditioned problems near the critical point, and achieving rapid characterization of static safety margins with large step size, high precision, and global robustness.

Description

Technical Field

[0001] This invention relates to the field of communication equipment security protection technology, and in particular to a method for characterizing the static security margin of power systems based on the truncated polynomial approximation method. Background Technology

[0002] The static safety margin of a power system is a crucial indicator for measuring the distance between the power grid and the voltage collapse point (critical operating point) under current operating conditions. With the accelerated construction of my country's new power system, the large-scale grid connection of renewable energy sources, and the application of a high proportion of power electronic equipment, the power grid exhibits complex characteristics such as strong nonlinearity, weak inertia, and multi-scale coupling. The system is highly susceptible to approaching extreme operating conditions such as heavy loads or low voltage margins. Therefore, accurately, quickly, and robustly characterizing the static safety margin of the power system is of paramount importance for preventing large-scale blackouts caused by voltage collapse and ensuring the safe operation of the power grid.

[0003] Against this backdrop, current research struggles to accurately and robustly characterize static safety margins under strong nonlinearity and multi-scale coupling characteristics. Consequently, it lacks efficient computational methods to effectively overcome numerical ill-conditioning and global locked-in voltage collapse boundaries when approaching extreme operating conditions. Typically, it relies on numerical iterative algorithms such as the Newton-Raphson method for local linearization search, or uses continuous power flow methods to approximate the voltage through discrete steps using parameterized equations.

[0004] Existing evaluation methods mainly include the Newton-Raphson method based on numerical iteration and the continuous power flow method that introduces parameterized equations. However, these schemes have inherent flaws when dealing with complex operating conditions approaching the critical operating point of the power system, which can be specifically described as follows:

[0005] Lack of global robustness: The Newton-Raphson method is essentially a local search algorithm, and its convergence strictly depends on the nonsingularity of the Jacobian matrix and the selection of initial values. When the system operates in a heavily loaded region or near the voltage collapse point, the Jacobian matrix of the power flow equations tends to be singular, causing the iterative process to easily diverge or get trapped in erroneous local optima. Furthermore, the Newton-Raphson method is highly sensitive to initial values; inappropriate initial value guesses may trigger chaotic phenomena in the iterative process, making it difficult to meet the reliability requirements of online safety assessment.

[0006] Efficiency limitations: Although the continuous power flow method alleviates some singularity problems, its core computational framework still relies on the "tangent prediction-Newton correction" model. Its "correction" step still depends on nonlinear iteration. In highly nonlinear regions such as the "nose point" of the PV curve, to ensure convergence of the correction step, extremely small step sizes must be used for intensive computation, leading to a significant increase in computational load. Secondly, at each discrete step entry point, iterative solutions to the nonlinear equations and updates and decompositions of the Jacobian matrix still need to be repeated, limiting computational efficiency.

[0007] Limitations of step size: The continuous power flow method uses traditional low-order tangent prediction, which makes it difficult to capture the high-order nonlinear characteristics of the system. Step size control often relies on experience and lacks adaptability. Summary of the Invention

[0008] To overcome the technical deficiencies of existing technologies, this invention provides a method for characterizing the static safety margin of power systems based on the truncated polynomial approximation method, comprising the following steps:

[0009] Step S1: Obtain the network topology parameters and current baseline operating status of the power system. This maps the system's load growth parameters to embedded variables in the complex field. ,in This indicates that the load growth parameter in the complex domain can vary freely in the complex plane, and a power flow model of the power system with respect to this embedded variable is established. ;

[0010] Step S2: Expand the system state variables in the power flow model into the embedded variables. The higher-order truncated polynomials are used, and the Cauchy product property of power series is utilized to transform the nonlinear terms in the power flow equations into discrete linear convolution operations between the coefficients of the polynomials.

[0011] Step S3: Based on the discrete linear convolution operation, derive and solve the linear recursive equations for the polynomial coefficients, and obtain the polynomial coefficients of each order in sequence to obtain the polynomial coefficient sequence.

[0012] Step S4: Based on the polynomial coefficient sequence obtained in Step S3, construct the Padé approximation rational function, perform analytic continuation on the truncated polynomial, and calculate the rational function in... The value at =1 is used to obtain an effective solution for the system state under the target load condition;

[0013] Step S5: Perform numerical convergence verification and physical steady-state discrimination on the effective solution of the system state under the target load condition obtained in step S4 to confirm whether the current operating condition is within the static safety domain or to identify whether the system is approaching the voltage collapse critical point.

[0014] Step S6: Use a multi-stage connection strategy to perform full-domain tracking. Use the endpoint state obtained by successful parsing and extension in the current stage as the new initial value of the next stage. Repeat steps S2 to S5 until the system reaches the voltage collapse critical point. Accumulate the load growth of each stage and synthesize the static safety margin of the power system.

[0015] Preferably, in step S1, establishing the power system power flow model specifically involves:

[0016] By introducing the embedded variables The steady-state power flow equations of the power system Transform into embedded variables holomorphic embedding equations ;

[0017] In the above formula For elements of the generalized admittance matrix, Let be the complex power conjugate of node i. For the conjugate of the voltage at node i, The standard notation in the field of power flow calculation for nodes The complex voltage; where It represents the system state variable; it represents the complex voltage of all nodes in the power system as a function of the system state. The trajectory of change;

[0018] Among them, when When =0, the model corresponds to the baseline operating state ( When α=1, the model corresponds to the target load condition to be determined.

[0019] Preferably, in step S2, based on the properties of holomorphic functions, the system state variables are expanded in the holomorphic domain as... power series ,

[0020] To enable numerical computation, it is truncated into an Nth-order polynomial, where N ranges from 15 to 25.

[0021] Preferably, in step S2, converting the nonlinear term into a linear convolution operation specifically involves: for nonlinear multiplication operations... , This represents the voltage at a certain node. The nth order coefficient of its power series expansion Represented as ; Represented as a product function The nth coefficient, The nonlinear terms in the power flow equations It means The Order coefficient; This represents a function. The Order coefficient.

[0022] Preferably, in step S3, the linear recursive equation is:

[0023] ;

[0024] In the above formula, the first order coefficient The calculation depends only on the previous Known coefficients of order and the network parameter matrix; in the above formula The constant coefficient matrix corresponds to the system's admittance matrix. This is the residual term containing the convolution of low-order coefficients; by solving this system of linear equations sequentially, all high-order coefficients are obtained recursively. .

[0025] Preferably, step S4 specifically involves operating based on the polynomial coefficient sequence obtained in step S3. The Padé approximation rational function of order is of the form: ,in and These are L-order and M-order polynomials, respectively;

[0026] in The approximation objective function It means The Padé approximation of a rational function of order is... Approximate; This represents the numerator polynomial of the Padé approximation rational function, which is a polynomial in terms of embedded variables. The Lth degree polynomial. This represents the denominator polynomial of the Padé approximation rational function, which is a polynomial in terms of embedded variables. of Polynomial of degree 1;

[0027] By leveraging the analytic continuation capability of the Padé approximation, the convergence radius limitation of the power series corresponding to the truncated polynomial is overcome, and mathematical singularities on the complex plane of the embedded variables are bypassed, to calculate an efficient solution that exceeds the original series convergence radius. This enables large-step global tracking.

[0028] Preferably, in step S5, the numerical convergence verification is performed by calculating the infinite norm error of the power imbalance. Achieve; if the infinite norm error Less than the preset tolerance If the numerical convergence is achieved, then the current operating point is located within the static safety domain.

[0029] Preferably, in step S5, the method for identifying the voltage collapse critical point includes: if the effective extension step size is less than the preset step size tolerance or the eigenvalue of the Jacobian matrix approaches 0, it indicates that the system is approaching a singular or critical state, and then the system is determined to have reached the voltage collapse critical point.

[0030] Preferably, in step S6, the multi-stage continuation strategy specifically includes:

[0031] If the current stage successfully resolves and extends to the target state If the value is 1, then the endpoint state is updated to the baseline initial value for the next stage. ), reset the fully pure embedding equation and repeat steps S2 to S5;

[0032] If the system is detected to have reached the voltage collapse threshold, the calculation process is terminated.

[0033] The beneficial effects of this invention are:

[0034] 1. This invention is designed for large-scale power grid online safety assessment scenarios, and realizes the automated characterization of static safety margin with "zero initial value dependence". This method does not require relying on good initial value guesses, nor does it require manually setting complex step size control parameters, which greatly reduces the complexity of system assessment and the cost of manual intervention, and helps to build a lightweight and standardized power grid safety early warning platform; it also ensures the robustness and flexibility of the system.

[0035] 2. This invention proposes a method for characterizing the static safety margin of a power system based on truncated polynomial approximation. First, a power flow equation based on holomorphic embedding is constructed. Then, a high-order truncated polynomial is used to transform the nonlinear terms in the power flow equation into linear convolution operations within the coefficient domain, thus mechanistically avoiding the numerical ill-conditioned problem near the critical point in existing numerical iterative algorithms. Subsequently, Padé approximation techniques are used to construct rational functions for analytical extension, and a multi-stage succession strategy is employed to achieve large-step global tracking of the system state. This method can guarantee the numerical robustness and physical accuracy of the static safety margin assessment under extreme conditions approaching the voltage collapse point, and achieves a fast and reliable characterization of the entire PV curve at the cost of non-iterative deterministic computation, meeting the real-time and high-confidence requirements of large-scale power grid online safety assessment.

[0036] 3. Compared with existing numerical iterative methods, this invention has a faster solution speed and a wider convergence region. Especially under ill-conditioned conditions such as heavy loads that cause the Jacobian matrix to approach singularity, this method relies on deterministic algebraic recursion and linear solution to avoid repeated matrix decomposition and the risk of iterative divergence. Its computational efficiency is significantly better than the traditional continuous power flow method, and it can meet the stringent timeliness requirements of online scheduling.

[0037] 4. The computational framework based on the truncated polynomial approximation method proposed in this invention has a certain degree of universality. It can be extended to model any physical system described by nonlinear algebraic equations and requiring the solution of parameter margins under critical conditions. As long as the equations satisfy the holomorphism condition, robust solutions can be achieved using the "linear convolution + analytic extension" idea of ​​this method. Attached Figure Description

[0038] One or more embodiments are illustrated by way of example with reference numerals in the accompanying drawings. These illustrations do not constitute a limitation on the embodiments. Elements with the same reference numerals in the drawings are denoted as similar elements. Unless otherwise stated, the figures in the drawings are not to be limited by scale.

[0039] Figure 1 This is a schematic diagram of the method flow of the present invention;

[0040] Figure 2 This is a diagram showing the static security domain characterization results of the present invention on the IEEE 39-node system. Detailed Implementation

[0041] To make the objectives, technical solutions, and advantages of this invention clearer, the various embodiments of this invention will be described in detail below with reference to the accompanying drawings. However, those skilled in the art will understand that many technical details have been provided in the various embodiments of this invention to facilitate a better understanding of this application. However, the technical solutions claimed in the claims of this application can be implemented even without these technical details and with various variations and modifications based on the following embodiments.

[0042] like Figures 1 to 2 As shown, this embodiment provides a method for characterizing the static safety margin of a power system based on the truncated polynomial approximation method. This method addresses the safety margin characterization problem of large-scale power systems approaching the voltage collapse critical point. It abandons the computational paradigm of existing numerical iterative algorithms that rely on initial value guessing and Jacobian matrix inversion. Based on the power flow model of the power system in complex analysis, it designs a non-iterative solution strategy based on linear recursive convolution and Padé approximation analytical extension. Using the load growth factor as the embedded variable, the nonlinear power flow equation is transformed into a problem of solving for the coefficients of a power series with respect to the embedded variable. Through multi-stage analytical extension, it achieves a large-step, high-precision, and globally robust static safety margin (SSR) characterization. Specifically, it includes the following steps:

[0043] Step S1: Obtain the network topology parameters and current baseline operating status of the power system. This maps the system's load growth parameters to embedded variables in the complex field. ,in This means that the load growth parameter is guaranteed to vary freely in the complex plane in the complex domain, and a power flow model of the power system with respect to this embedded variable is established;

[0044] Step S2: Expand the system state variables in the power flow model into the embedded variables. The higher-order truncated polynomials are used, and the Cauchy product property of power series is utilized to transform the nonlinear terms in the power flow equations into discrete linear convolution operations between the coefficients of the polynomials.

[0045] Step S3: Based on the discrete linear convolution operation, derive and solve the linear recursive equations for the polynomial coefficients, and obtain the polynomial coefficients of each order in sequence to obtain the polynomial coefficient sequence.

[0046] Step S4: Based on the polynomial coefficient sequence obtained in Step S3, construct the Padé approximation rational function, perform analytic continuation on the truncated polynomial, and calculate the rational function in... The value at =1 is used to obtain an effective solution for the system state under the target load condition;

[0047] Step S5: Perform numerical convergence verification and physical steady-state discrimination on the effective solution of the system state under the target load condition obtained in step S4 to confirm whether the current operating condition is within the static safety domain or to identify whether the system is approaching the voltage collapse critical point.

[0048] Step S6: Use a multi-stage continuity strategy for full-domain tracking. Use the endpoint state obtained by successful parsing and extension in the current stage as the new initial value of the next stage. Repeat steps S2 to S5 until the system reaches the voltage collapse critical point. Accumulate the load growth of each stage and synthesize the static safety margin of the power system. The final output result can be used to draw PV curves or as a safety constraint boundary for grid dispatching and operation, providing a high-precision quantitative indicator for preventing large-scale power outage accidents.

[0049] The core of this invention lies in using the determinism of algebraic operations to avoid the uncertainty of iterative algorithms. As long as a physical solution exists, this method can find the solution through analytical continuation; if there is no physical solution (collapse), this method can provide a clear numerical divergence signal, thereby avoiding "false convergence" or "spurious divergence".

[0050] Specifically, in step S1, establishing the power system power flow model involves:

[0051] By introducing the embedded variables The steady-state power flow equations of the power system Transform into embedded variables holomorphic embedding equations ;

[0052] In the above formula For elements of the generalized admittance matrix, Let be the complex power conjugate of node i. For the conjugate of the voltage at node i, The standard notation in the field of power flow calculation for nodes The complex voltage; where It represents the system state variable; it represents the complex voltage of all nodes in the power system as a function of the system state. The trajectory of change.

[0053] Among them, when When =0, the model corresponds to the baseline operating state ( When α=1, the model corresponds to the target load condition to be determined. This invention addresses complex operating conditions in power systems approaching voltage collapse points and establishes power flow equations based on fully embedded variables. By mapping load growth factors to continuously varying embedded variables and uniformly transforming nonlinear terms in the power flow equations into linear convolution operations within the series coefficient domain, the modeling mechanism avoids the numerical ill-conditioned problem near singular points of the Jacobian matrix in traditional iterative algorithms.

[0054] In step S2, based on the properties of holomorphic functions, the system state variables are expanded in the holomorphic domain as follows: power series ,

[0055] To enable numerical computation, the system is truncated into an Nth-order polynomial, where N ranges from 15 to 25. This invention proposes a non-iterative solution architecture based on "truncated polynomial approximation + Padé analytic extension". Utilizing the properties of holomorphic functions, the state variables are constructed as high-order power series, and Padé approximation is used to construct rational functions to bypass singularities on the convergence boundary of the original series. This allows the algorithm to directly calculate the system state under the target high-load condition with large step sizes, eliminating the cumbersome "prediction-correction" iterative loop in the continuous power flow method.

[0056] In step S2, converting the nonlinear term into a linear convolution operation specifically involves: for nonlinear multiplication operations... , This represents the voltage at a certain node. The nth order coefficient of its power series expansion Represented as , Represented as a product function The nth coefficient, The nonlinear terms in the power flow equations It means The Order coefficient; This represents a function. The Order coefficient.

[0057] In step S3, the linear recursive equation is:

[0058] ;

[0059] In the above formula, the first order coefficient The calculation depends only on the previous Known coefficients of order and the network parameter matrix; in the above formula The constant coefficient matrix corresponds to the system's admittance matrix. This is the residual term containing the convolution of low-order coefficients; by solving this system of linear equations sequentially, all high-order coefficients are obtained recursively. .

[0060] The specific operation in step S4 is based on the polynomial coefficient sequence obtained in step S3. The Padé approximation rational function of order is of the form: ,in and These are L-order and M-order polynomials, respectively;

[0061] in The approximation objective function It means The Padé approximation of a rational function of order is... Approximate; This represents the numerator polynomial of the Padé approximation rational function, which is a polynomial in terms of embedded variables. The Lth degree polynomial. This represents the denominator polynomial of the Padé approximation rational function, which is a polynomial in terms of embedded variables. of Polynomial of degree.

[0062] By leveraging the analytic continuation capability of the Padé approximation, the convergence radius limitation of the power series corresponding to the truncated polynomial is overcome, and mathematical singularities on the complex plane of the embedded variables are bypassed, to calculate an efficient solution that exceeds the original series convergence radius. This enables large-step global tracking.

[0063] In step S5, the numerical convergence verification is performed by calculating the infinite norm error of the power imbalance. Achieve; if the infinite norm error Less than the preset tolerance If the numerical convergence is achieved, then the current operating point is located within the static safety domain.

[0064] In step S5, the method for identifying the voltage collapse critical point includes: if the effective extension step size is less than the preset step size tolerance or the eigenvalue of the Jacobian matrix approaches 0, it indicates that the system is close to a singular or critical state, and then it is determined that the system has reached the voltage collapse critical point.

[0065] In step S6, the multi-stage continuity strategy specifically includes:

[0066] If the current stage successfully resolves and extends to the target state If the value is 1, then the endpoint state is updated to the baseline initial value for the next stage. ), reset the fully pure embedding equation and repeat steps S2 to S5;

[0067] If the system is detected to have reached the voltage collapse threshold, the calculation process is terminated.

[0068] In a specific implementation, the IEEE 39-bus system (New England system) was selected as a test case. This system includes 10 generators, 39 buses, and 46 branches. The proposed static security margin characterization method for power systems based on truncated polynomial approximation was applied to characterize the static security domain of the system. This embodiment aims to verify the convergence, computational efficiency, and robustness of the invention when dealing with large-scale power fluctuations and approaching voltage collapse boundaries. Key loads or generator nodes in the system were selected as variables. In this embodiment, it is assumed that the active power injection of bus 3 and bus 4 has a very large range of variation, thus constructing a two-dimensional parameter space. By sampling 10,000 independent operating condition samples, the static security domain of the system was visualized. The results of the embodiment are as follows. Figure 2 As shown.

[0069] This invention employs a "multi-stage succession tracking" strategy. A succession calculation mechanism based on state updates is designed, where the endpoint of the current stage's analytical extension is used as the new initial reference value for the next stage's series expansion. This strategy can adaptively evolve from the ground state to the voltage collapse critical point within a very small number of stages, achieving full-domain locking of the static safety margin while ensuring extremely high computational accuracy.

[0070] This invention addresses large-scale power grid online security assessment scenarios, achieving automated characterization of static security margins with "zero initial value dependence." This method eliminates the need for reliable initial value guesses and the manual setting of complex step-size control parameters, significantly reducing the complexity of system assessments and the cost of manual intervention. This facilitates the construction of a lightweight, standardized power grid security early warning platform, ensuring the system's robustness and flexibility.

[0071] This invention offers faster solution speed and a wider convergence region compared to existing numerical iterative methods. Especially under ill-conditioned conditions such as heavy loads that cause the Jacobian matrix to approach singularity, this method relies on deterministic algebraic recursion and linear solution, avoiding repeated matrix decomposition and the risk of iterative divergence. Its computational efficiency is significantly better than traditional continuous power flow methods, meeting the stringent timeliness requirements of online scheduling.

[0072] The computational framework based on the truncated polynomial approximation method proposed in this invention has a certain degree of universality. It can be extended to model any physical system described by nonlinear algebraic equations and requiring the solution of parameter margins under critical conditions. As long as the equations satisfy the holomorphism condition, robust solutions can be achieved using the "linear convolution + analytic extension" idea of ​​this method.

[0073] This invention proposes a method for characterizing the static safety margin of power systems based on truncated polynomial approximation. First, a power flow equation based on holomorphic embedding is constructed. Then, a high-order truncated polynomial is used to transform the nonlinear terms in the power flow equation into linear convolution operations within the coefficient domain, thus mechanistically avoiding the numerical ill-conditioned problem near the critical point in existing numerical iterative algorithms. Subsequently, Padé approximation techniques are used to construct rational functions for analytical extension, and a multi-stage succession strategy is employed to achieve large-step global tracking of the system state. This method can guarantee the numerical robustness and physical accuracy of static safety margin assessment under extreme conditions approaching voltage collapse points, and achieves a fast and reliable characterization of the entire PV curve at the cost of non-iterative deterministic computation, meeting the real-time and high-confidence requirements of large-scale power grid online safety assessment.

[0074] The effects of this invention are as follows: Figure 2 As shown: Appendix Figure 2 This paper presents the static security domain characterization results of the proposed method under a large-scale parameter scan of the IEEE 39-bus system. The boundaries generated by the proposed method are clear and smooth, and no outliers caused by computational misconvaction are observed. This indicates that as the system approaches the voltage collapse critical point, the proposed method can effectively overcome numerical instability by virtue of the mathematical properties of the analytic function, demonstrating extremely high global robustness. As evaluation data, these results can provide rigorous and robust security boundaries for power grid dispatching, and provide high-precision quantitative support for preventing large-scale power outages caused by voltage collapse.

[0075] This invention establishes a linear recursive solution framework based on Cauchy products, transforming nonlinear operators (such as constant power loads) in power flow equations into linear convolution operations between series coefficients. This step converts the solution of nonlinear algebraic equations into a deterministic recursive system of linear equations, fundamentally eliminating the high dependence on initial value guessing and the risk of divergence near singular points of the Jacobian matrix in iterative algorithms such as the Newton-Raphson method. This ensures that the algorithm possesses solvable and convergent numerical stability under arbitrary heavy load conditions, supporting the automation and lightweighting of the evaluation process.

[0076] This invention introduces the analytical continuation technique of Padé approximation, using rational functions to reconstruct the original series. This allows the algorithm to "bypass" the singularities on the convergence boundary of the power series and calculate effective solutions exceeding the convergence radius of the original series. This mechanism enables the method to maintain large step size computational capabilities even in strongly nonlinear regions such as the "nose point" and lower half of the PV curve, avoiding the efficiency bottleneck of the continuous power flow method, which is forced to use extremely small step sizes to ensure convergence. This significantly improves the computational speed of global tracking.

[0077] This invention employs a multi-stage successive tracking and dual steady-state discrimination strategy, utilizing the pole distribution of the analytical function and the eigenvalues ​​of the Jacobian matrix to jointly verify the system state. This strategy enables the algorithm to accurately distinguish between "numerical algorithm failure" and "physical system collapse," achieving precise locking of the voltage collapse critical point. It ensures that the output static safety margin index has strict physical meaning, balancing the efficiency of online calculation with the reliability of engineering applications, and improving the safety and economy of power grid operation.

[0078] Those skilled in the art will understand that the above embodiments are specific examples of implementing the present invention, and in practical applications, various changes in form and detail may be made without departing from the spirit and scope of the present invention.

Claims

1. A method for characterizing the static security margin of a power system based on the truncated polynomial approximation method, characterized in that, Includes the following steps: Step S1: Obtain the network topology parameters and current baseline operating status of the power system. Mapping the system's load growth parameters to embedded variables in the complex field ,in This means that the load growth parameter is guaranteed to vary freely in the complex plane in the complex domain, and a power flow model of the power system with respect to this embedded variable is established; Step S2: Expand the system state variables in the power flow model into the embedded variables. The higher-order truncated polynomials are used, and the Cauchy product property of power series is utilized to transform the nonlinear terms in the power flow equations into discrete linear convolution operations between polynomial coefficients. Step S3: Based on the discrete linear convolution operation, derive and solve the linear recursive equations for the polynomial coefficients, and obtain the polynomial coefficients of each order in sequence to obtain the polynomial coefficient sequence. Step S4: Based on the polynomial coefficient sequence obtained in Step S3, construct the Padé approximation rational function, perform analytic continuation on the truncated polynomial, and calculate the rational function in... The value at =1 yields an effective solution for the system state under the target load condition; Step S5: Perform numerical convergence verification and physical steady-state discrimination on the effective solution of the system state under the target load condition obtained in step S4 to confirm whether the current operating condition is within the static safety domain or to identify whether the system is approaching the voltage collapse critical point. Step S6: Use a multi-stage connection strategy to perform full-domain tracking. Use the endpoint state obtained by successful parsing and extension in the current stage as the new initial value of the next stage. Repeat steps S2 to S5 until the system reaches the voltage collapse critical point. Accumulate the load growth of each stage and synthesize the static safety margin of the power system.

2. The method for characterizing the static safety margin of a power system based on the truncated polynomial approximation method according to claim 1, characterized in that: In step S1, establishing the power system power flow model specifically involves: By introducing the embedded variables The steady-state power flow equations of the power system Transform into embedded variables holomorphic embedding equations ; In the above formula For elements of the generalized admittance matrix, Let be the complex power conjugate of node i. For the conjugate of the voltage at node i, The standard notation in the field of power flow calculation for nodes The complex voltage; where It represents the system state variable; it represents the complex voltage of all nodes in the power system as a function of the system state. The trajectory of change; Among them, when When =0, the model corresponds to the baseline operating state. When α=1, the model corresponds to the target load condition to be determined.

3. The method for characterizing the static safety margin of a power system based on the truncated polynomial approximation method according to claim 2, characterized in that: In step S2, based on the properties of holomorphic functions, the system state variables are expanded in the holomorphic domain as follows: power series , To enable numerical computation, it is truncated into an Nth-order polynomial, where N ranges from 15 to 25.

4. The method for characterizing the static safety margin of a power system based on the truncated polynomial approximation method according to claim 3, characterized in that: In step S2, converting the nonlinear term into a linear convolution operation specifically involves: for nonlinear multiplication operations... , This represents the voltage at a certain node. The nth order coefficient of its power series expansion Represented as , Represented as a product function The nth coefficient, The nonlinear terms in the power flow equations It means The Order coefficient; This represents a function. The Order coefficient.

5. The method for characterizing the static safety margin of a power system based on the truncated polynomial approximation method according to claim 1, characterized in that: In step S3, the linear recursive equation is: ； In the above formula, the first order coefficient The calculation depends only on the previous Known coefficients of order and the network parameter matrix; in the above formula The constant coefficient matrix corresponds to the system's admittance matrix. The residual term contains the convolution of low-order coefficients; all high-order coefficients are obtained by recursively solving the system of linear equations. .

6. The method for characterizing the static security margin of a power system based on the truncated polynomial approximation method according to claim 4, characterized in that: The specific operation in step S4 is based on the polynomial coefficient sequence obtained in step S3. The Padé approximation rational function of order is of the form: ,in and These are polynomials of order L and order M, respectively; in The approximation objective function It means The Padé approximation of a rational function of order is... Approximate; This represents the numerator polynomial of the Padé approximation rational function, which is a polynomial in terms of embedded variables. The Lth degree polynomial. This represents the denominator polynomial of the Padé approximation rational function, which is a polynomial in terms of embedded variables. of Polynomial of degree 1; By leveraging the analytic continuation capabilities of the Padé approximation, we can overcome the convergence radius limitation of the power series corresponding to the truncated polynomial and bypass mathematical singularities on the complex plane with embedded variables, thus calculating efficient solutions that exceed the original series' convergence radius. This enables large-step global tracking.

7. The method for characterizing the static security margin of a power system based on the truncated polynomial approximation method according to claim 6, characterized in that: In step S5, the numerical convergence verification is performed by calculating the infinite norm error of the power imbalance. Achieve; if the infinite norm error Less than the preset tolerance If the numerical convergence is achieved, then the current operating point is located within the static safety domain.

8. The method for characterizing the static security margin of a power system based on the truncated polynomial approximation method according to claim 7, characterized in that: In step S5, the method for identifying the voltage collapse critical point includes: if the effective extension step size is less than the preset step size tolerance or the eigenvalue of the Jacobian matrix approaches 0, it indicates that the system is close to a singular or critical state, and then it is determined that the system has reached the voltage collapse critical point.

9. The method for characterizing the static safety margin of a power system based on the truncated polynomial approximation method according to claim 1, characterized in that: In step S6, the multi-stage continuity strategy specifically includes: If the current stage successfully resolves and extends to the target state If the value is 1, then the endpoint state is updated to the baseline initial value for the next stage. Reset the fully pure embedding equation and repeat steps S2 to S5; If the system is detected to have reached the voltage collapse threshold, the calculation process is terminated.

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