Static stability margin tail risk prediction method and device for power system and medium

Abstract

The application discloses a kind of static stability margin tail risk prediction method, device and medium of power system, belong to risk prediction technical field.Its method includes: using quantile regression model to carry out multi-quantile prediction to wind power, photovoltaic and other new energy output, obtains the cumulative distribution function of each new energy node output;Further, the discrete probability density function of new energy output is constructed by discretization and difference method, to avoid the modeling error caused by continuous distribution assumption;On this basis, combined with thermal power output configuration and static stability margin based on converter dynamic parameters, the mapping relationship between new energy random injection and system static stability margin is established, to realize the quantitative prediction of stability margin probability distribution and its tail risk.The application can accurately reflect the distribution characteristics of receiving-end power system static stability margin in the sense of probability, especially the stability margin change law under low-probability, high-risk working condition.

Description

Technical Field

[0001] This invention relates to the field of risk prediction technology, and in particular to a method, apparatus and medium for predicting the tail risk of static stability margin in power systems. Background Technology

[0002] As the penetration rate of renewable energy generation in receiving-end power systems continues to increase, the randomness and volatility of renewable energy output, represented by wind and solar power, have significantly increased. Under conditions of high renewable energy integration, receiving-end power systems face more complex static stability problems. Especially in scenarios where large-scale renewable energy is integrated via power electronic interfaces, the system's static stability margin exhibits significant uncertainty, and its changes are influenced by multiple factors, including the distribution of renewable energy output, the configuration of thermal power output, and converter control parameters.

[0003] Existing research methods for static stability problems in receiving-end power systems mostly employ deterministic analysis or margin assessment based on typical operating conditions, typically using stability margin under a single or limited number of scenarios as the evaluation index. While these methods are applicable to situations with low renewable energy penetration, they struggle to accurately reflect the probabilistic distribution characteristics of stability margin under conditions of highly random renewable energy output, particularly failing to characterize low-probability but high-risk tail events in stability margin.

[0004] In recent years, some studies have begun to introduce probabilistic power flow or Monte Carlo simulation methods to stochastically model the uncertainty of renewable energy output and evaluate the statistical characteristics of system stability margin. However, these methods typically rely on prior assumptions about the probability distribution of renewable energy output, such as normal or empirical distribution models, making it difficult to fully utilize multi-source historical data and operational status information. Furthermore, Monte Carlo simulations are computationally intensive and have low efficiency under multi-node, high-dimensional random injection conditions, making it difficult to meet the real-time and scalability requirements of engineering applications.

[0005] Furthermore, existing technologies primarily focus on the expected or mean level analysis of stability margins, paying insufficient attention to the probabilistic characteristics of the tails of the stability margin distribution, and lacking quantitative prediction methods for static stability risks under low-probability extreme operating conditions. Given the complex structure and variable operating modes of receiving-end power systems, these shortcomings limit the engineering applicability and risk assessment capabilities of existing technologies in scenarios with high penetration of renewable energy. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method, device and medium for predicting the tail risk of static stability margin of a power system, which can accurately reflect the distribution characteristics of the static stability margin of the receiving-end power system in a probabilistic sense, especially the stability margin change law under low probability and high risk conditions.

[0007] To achieve the above objectives, the present invention is implemented using the following technical solution:

[0008] On the one hand, the present invention provides a method for predicting the tail risk of static stability margin in a power system, comprising:

[0009] The multi-source feature vectors are input into a pre-built quantile regression model, the node quantile prediction results are output, and physical constraints are applied to the node quantile prediction results to obtain the node corrected quantile prediction results.

[0010] The node cumulative distribution function is reconstructed based on the node correction quantile prediction results. The node discrete probability density function is calculated based on the node cumulative distribution function. The generated node joint injection scene auxiliary vector is mapped through the node discrete probability density function to obtain the random injection tensor.

[0011] The endpoints of the branches are renumbered to obtain a new set of branches. An susceptance matrix is ​​constructed based on the new set of branches. The reference bus is removed from the set of buses to obtain the remaining set of buses. The order of the susceptance matrix is ​​reduced based on the remaining set of buses to obtain a submatrix.

[0012] The remaining bus set is divided into a grid-connected bus set and a passive bus set. The sub-matrix is ​​then divided into blocks and eliminated according to this division to obtain the equivalent coupling matrix of the grid-connected bus.

[0013] The scenario-based generalized short-circuit ratio and scenario-based participation factor are calculated based on the random injection tensor and the equivalent coupling matrix. The pre-constructed single-machine admittance matrix is ​​weighted according to the scenario-based participation factor, and the system characteristic equation is constructed based on the weighting result.

[0014] The system characteristic equation is solved based on the preset candidate scenario-based critical short-circuit ratio sequence to generate a root set. The scenario-based critical short-circuit ratio is obtained based on the root set and the critical stability criterion. The stability margin is calculated based on the scenario-based generalized short-circuit ratio and the scenario-based critical short-circuit ratio. The static stability margin tail risk prediction result of the power system is generated based on the stability margin.

[0015] Optionally, the construction of the quantile regression model includes:

[0016] A training set is constructed based on the multi-source feature vectors and renewable energy injection power at historical moments. ;in, Represents a node At a historical moment Multi-source feature vectors; Represents a node At a historical moment The power of new energy injection; Represents a set of historical moments; Representing nodes respectively At a historical moment Meteorological forecast feature vector, historical operation feature vector, and time tag feature;

[0017] A quantile regression model at the quantile level is constructed and trained using the CatBoost algorithm to obtain the constructed and trained quantile regression model; the quantile loss function of the quantile regression model is then defined. ;in, Indicates quantile level Lower historical samples and model predictions The quantile loss function.

[0018] Optionally, physical constraints are applied to the node quantile prediction results to obtain node modified quantile prediction results, including:

[0019] Node quantile prediction results ;

[0020] Apply quantile monotonicity constraints to the nodal quantile prediction results and output boundary constraints The node-corrected quantile prediction results are obtained. ;

[0021] in, They represent quantile levels respectively. quantile level quantile level quantile level Next node At any moment The node quantile prediction results; Represents a node At any moment Multi-source feature vectors; Indicates quantile level Next node Quantile regression model; Represents a node The corresponding wind power or photovoltaic installed capacity.

[0022] Optionally, the node cumulative distribution function is expressed as:

[0023] ;

[0024] in, Represents a node In the power injection of new energy The node cumulative distribution function; They represent quantile levels. quantile level quantile level quantile level Next node The node quantile prediction results;

[0025] The formula for calculating the discrete probability density function of the node is:

[0026] ;

[0027] ;

[0028] in, Represents a node In the The node probability density function for discrete power points; Representing nodes respectively In the Discrete power points, nodes In the The node cumulative distribution function at discrete power points; Represents a node In the Discrete probability density function of nodes at discrete power points; Indicates at node New energy injection power range Inner step length The number of discrete power points obtained from the division; Represents a node The corresponding wind power or photovoltaic installed capacity.

[0029] Optionally, the generated node joint injection scene auxiliary vector is mapped using the node discrete probability density function to obtain a random injection tensor, including:

[0030] Based on the node discrete probability density function Calculate the probability of node occurrence ;

[0031] The generated nodes are jointly injected into the scene auxiliary vector. Probability of occurrence through nodes Perform mapping to obtain a randomly injected tensor. ;

[0032] in, Represents a node In the Discrete probability density function at discrete power points; Represents a node At any moment No. The probability of node occurrence at a discrete power point; Represents a node At any moment Scene The nodes below jointly inject scene auxiliary vectors; Represents a node At any moment Scene Randomly injected tensors; Represents a node At any moment The Discrete power points; This indicates taking the minimum value; Indicates at node New energy injection power range Inner step length The number of discrete power points obtained from the division; Represents a node The corresponding wind power or photovoltaic installed capacity.

[0033] Optionally, the endpoints of the branches can be renumbered to obtain a new set of branches, including:

[0034] Traverse the branches, renumber the endpoints of the branches based on the original node array and the target node array, and obtain a new set of branches. The renumbering rule is as follows:

[0035] ;

[0036] in, Representing branch roads The starting point and the ending point; These represent the nodes in the original node array and the nodes in the target node array, respectively. This represents the set of new branch paths.

[0037] Optionally, the susceptance matrix is ​​constructed based on the new branch set, including:

[0038] Use the endpoint codes of each branch in the new branch set as the row and column indices of the susceptance matrix;

[0039] If the branches in the new branch set Reactance Then the susceptance matrix OK List, OK The elements of the column are set to ;

[0040] If the branches in the new branch set Reactance Then the susceptance matrix OK List, OK The elements of the column are set to the minimum reactance threshold;

[0041] Set the diagonal elements of the susceptance matrix to ;

[0042] in, Representing branch roads The starting point and the ending point; Representing the susceptance matrix OK Column elements, susceptance matrix OK Column elements; Indicates the number of busbars.

[0043] Optionally, the submatrix is ​​represented as:

[0044] ;

[0045] The equivalent coupling matrix is ​​represented as follows:

[0046] ;

[0047] in, Represents a submatrix; Represents the susceptance matrix; Represents the set of remaining busbars; Represents the real number field; Indicates the number of busbars; Represents an equivalence coupling matrix; Represents the coupling matrix of the grid-connected bus; Represents the coupling matrix of a passive bus; These represent the coupling matrices between the grid-connected network and the passive network, and the coupling matrix between the passive network and the grid-connected network, respectively.

[0048] Optionally, the scenario-based generalized short-circuit ratio and scenario-based participation factor are calculated based on the randomly injected tensor and the equivalent coupling matrix, including:

[0049] Construct a scenario-based active diagonal matrix based on the randomly injected tensor. The short-circuit ratio matrix is ​​calculated based on the equivalent coupling matrix and the scenario-specific active power diagonal matrix. ;

[0050] Short-circuit ratio matrix The minimum eigenvalue is used as the scenario-based generalized short-circuit ratio. According to the scenario-based generalized short-circuit ratio Calculate contextualized participation factors ;

[0051] in, Indicates at time Scene The following is a scenario-based active diagonal matrix; Indicates the diagonalization operation; Representing node 1, node 2, and node respectively. At any moment Scene Randomly injected tensors; Indicates at time Scene The short-circuit ratio matrix below; Represents an equivalence coupling matrix; Indicates at time Scene The following is a scenario-specific generalized short-circuit ratio; Represents a node At any moment Scene Contextualized participation factors; Representing nodes respectively At any moment Scene The right and left eigenvectors of the generalized short-circuit ratio in the contextualized model.

[0052] Optionally, the construction of the single-machine admittance matrix includes:

[0053] ;

[0054] ;

[0055] ;

[0056] ;

[0057] in, Representing Laplace variables respectively The PI controllers for the power outer loop, the current inner loop, and the phase-locked loop are all included. Representing Laplace variables Power filtering under; These represent the proportional coefficient and integral coefficient of the power outer loop, respectively; These represent the proportional coefficient and integral coefficient of the inner current loop, respectively. These represent the proportional coefficient and integral coefficient of the phase-locked loop, respectively. Representing Laplace variables respectively The first admittance matrix element and the second admittance matrix element; Indicates the grid-connected filter inductor; Representing Laplace variables Next node The single-machine admittance matrix.

[0058] Optionally, the construction of the system characteristic equation includes:

[0059] ;

[0060] ;

[0061] ;

[0062] in, Representing Laplace variables Total admittance below; Represents a node At any moment Scene Contextualized participation factors; Representing Laplace variables Next node The single-machine admittance matrix; Indicates the number of nodes; Representing Laplace variables The system disturbance model is as follows; Indicates the rated angular velocity; A factor representing the influence of the system's equivalent damping or resistance / reactance; Indicates at time Scene Candidate scenario-based critical short-circuit ratio; This indicates the calculation of determinants.

[0063] Optionally, the scenario-specific critical short-circuit ratio is obtained based on the root set and critical stability criterion. The stability margin is then calculated based on the scenario-specific generalized short-circuit ratio and the scenario-specific critical short-circuit ratio, including:

[0064] The candidate scenario-specific critical short-circuit ratio corresponding to the root that satisfies the critical stability criterion is taken as the scenario-specific critical short-circuit ratio. The critical stability criterion is expressed as:

[0065] ;

[0066] in, Indicates at time Scene Next The candidate scenario-based critical short-circuit ratio corresponds to the first The real part of each root; Represents positive numbers; These represent taking the minimum value and taking the maximum value, respectively.

[0067] The stability margin is expressed as:

[0068] ;

[0069] in, Indicates at time Scene The stability margin below; Indicates at time Scene The following is a scenario-specific generalized short-circuit ratio; Indicates at time Scene The critical short-circuit ratio in the given scenario.

[0070] Optionally, the static stability margin tail risk prediction results of the power system are generated based on the stability margin, including:

[0071] Based on stability margin First sample quantile estimate for calculating tail stability margin Second sample quantile estimation and stability margin range ;

[0072] Based on the scenario-based generalized short-circuit ratio, scenario-based critical short-circuit ratio, stability margin, first sample quantile estimate of tail stability margin, second sample quantile estimate of tail stability margin, and stability margin interval, the static stability margin tail risk prediction result of the power system is generated.

[0073] in, Indicates at time Scene The stability margin below; Indicates at time Confidence parameters First sample quantile estimate of lower tail stability margin; Indicates at time Scene The stability margin below; Indicates the number of scenes; This indicates the rounding up operation; Indicates at time Confidence parameters Second sample quantile estimation of lower tail stability margin; Indicates at time Confidence parameters The stability margin range below; They represent the times at time 1 and 2 respectively. Scene At any moment Scene The stability margin below.

[0074] Secondly, the present invention provides a device for predicting the tail risk of static stability margin in a power system, comprising:

[0075] The quantile prediction module is used to: input multi-source feature vectors into a pre-built quantile regression model, output node quantile prediction results, apply physical constraints to the node quantile prediction results, and obtain node corrected quantile prediction results.

[0076] The tensor calculation module is used to: reconstruct the node cumulative distribution function based on the node correction quantile prediction results; calculate the node discrete probability density function based on the node cumulative distribution function; and map the generated node joint injection scene auxiliary vector through the node discrete probability density function to obtain the random injection tensor.

[0077] The matrix construction module is used to: renumber the branch endpoints to obtain a new branch set; construct the susceptance matrix based on the new branch set; remove the reference bus from the bus set to obtain the remaining bus set; and reduce the order of the susceptance matrix based on the remaining bus set to obtain a submatrix.

[0078] The matrix elimination module is used to: divide the remaining bus set into a grid-connected bus set and a passive bus set, and perform block elimination on the sub-matrix according to this division to obtain the equivalent coupling matrix of the grid-connected bus;

[0079] The equation construction module is used to: calculate the scenario-based generalized short-circuit ratio and scenario-based participation factor based on the randomly injected tensor and the equivalent coupling matrix; weight the pre-constructed single-machine admittance matrix according to the scenario-based participation factor; and construct the system characteristic equation based on the weighting result.

[0080] The risk prediction module is used to: solve the system characteristic equations based on the preset candidate scenario-based critical short-circuit ratio sequence, generate a root set, obtain the scenario-based critical short-circuit ratio based on the root set and critical stability criterion, calculate the stability margin based on the scenario-based generalized short-circuit ratio and the scenario-based critical short-circuit ratio, and generate the static stability margin tail risk prediction result of the power system based on the stability margin.

[0081] Thirdly, the present invention provides a computer-readable storage medium having a computer program / instruction stored thereon, which, when executed by a processor, implements the steps of the static stability margin tail risk prediction method for power systems described in the first aspect.

[0082] Compared with the prior art, the beneficial effects achieved by the present invention are as follows:

[0083] This invention constructs a probabilistic prediction model for multi-node renewable energy output through a data-driven approach, without relying on prior assumptions about the probability distribution of renewable energy output. Based on this model, it enables risk prediction of the static stability margin of the receiving-end power system, focusing on characterizing the tail risk characteristics of the stability margin in the low-probability region. This provides a quantitative basis for system planning, operation control, and risk defense. While ensuring computational efficiency, it accurately reflects the probabilistic distribution characteristics of the static stability margin of the receiving-end power system, especially the stability margin variation pattern under low-probability, high-risk operating conditions, thereby improving the risk perception and assessment capabilities of the receiving-end power system under conditions of high renewable energy penetration. Attached Figure Description

[0084] Figure 1 This is a flowchart illustrating one embodiment of the static stability margin tail risk prediction method for power systems according to the present invention.

[0085] Figure 2 This is a schematic diagram of the wind and solar power output curves for four scenes at different times, randomly generated in one embodiment of the present invention.

[0086] Figure 3 This is a stability margin heatmap of one embodiment of the present invention;

[0087] Figure 4 This is a schematic diagram of gSCR curves for three typical scenarios in one embodiment of the present invention;

[0088] Figure 5 This is a schematic diagram of the lower bound of the stability margin protection in one embodiment of the present invention;

[0089] Figure 6 This is a schematic diagram illustrating the lower tail risk of stability margin in one embodiment of the present invention.

[0090] Figure 7 This is a schematic diagram illustrating the stability margin out-of-bounds probability in one embodiment of the present invention. Detailed Implementation

[0091] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments of the present invention and the specific features in the embodiments are detailed descriptions of the technical solution of the present invention, rather than limitations thereof. In the absence of conflict, the embodiments of the present invention and the technical features in the embodiments can be combined with each other.

[0092] The term "and / or" simply describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A alone, A and B simultaneously, or B alone. Additionally, the character " / " generally indicates that the preceding and following related objects have an "or" relationship.

[0093] Example 1: This example introduces a method for predicting the tail risk of static stability margin in a power system.

[0094] The first stage is the probabilistic modeling stage of multi-node renewable energy injection power:

[0095] Based on historical operating data and multi-source meteorological information, a probabilistic prediction model with operating status and meteorological characteristics as conditional variables is constructed for each new energy access node in the receiving-end power system. The cumulative distribution function of the injected power of new energy is obtained through dense quantile regression, and the discrete probability density function of the output of new energy is further constructed.

[0096] The second stage is the static stability margin probability mapping and tail risk assessment stage:

[0097] Based on the discrete probability density function of the above-mentioned new energy output, and combined with the thermal power output configuration and converter dynamic parameters, a mapping relationship between the injected power of new energy and the static stability margin of the system is established. The probability distribution of the stability margin is obtained through discrete probability calculation method, and the tail risk of stability margin in the low probability region is quantitatively predicted.

[0098] In receiving-end power systems, new energy sources such as wind power and photovoltaics are typically connected to the grid in the form of multiple access nodes and multiple power units, and their output exhibits significant time-varying, stochastic, and spatial heterogeneity. Point predictions of a single node or a single curve are insufficient to reflect the impact of new energy output on the system's static stability margin under extreme weather conditions and low-probability, high-impact scenarios.

[0099] Therefore, before the static stability margin assessment, this embodiment meticulously characterizes the power uncertainty of each node in the future time period, providing an input distribution basis for the subsequent tail stability margin risk calculation. Unlike the prediction method that only outputs the mean or confidence interval, it uses dense quantiles as a unified intermediate representation. Without pre-setting the probability distribution form, it constructs the conditional probability distribution of wind and solar power output for each node and further reconstructs the probability density function, providing a continuous distribution input for system-level risk assessment.

[0100] The method includes the following steps:

[0101] Step 1: Multi-source data reading and feature construction, specifically:

[0102] Assume the set of grid-connected buses for new energy sources in the receiving-end power system. That is, a set of nodes. ,node exist The power of new energy injection at any given time is In engineering implementation, the power injected by new energy sources is formed by the superposition of the output of grid-connected wind farms and photovoltaic power plants, which can be expressed as: ;in, Represents a node exist Wind power output is constant; Represents a node exist At any given moment, photovoltaic power output is positive. If a node is connected to only one type of renewable energy source, then the other power output can be considered zero.

[0103] To characterize the sources of uncertainty in new energy power output, this study examines each new energy source connection bus node. Construct a multi-source feature vector composed of meteorological forecast information, historical operating status, and time labels. ,in, Represents a node At any moment The meteorological forecast feature vector is used to characterize the external environmental conditions affecting the output of new energy sources, including but not limited to wind speed, wind direction, ambient temperature, air pressure, air density, total solar irradiance, and diffuse irradiance. In engineering implementation, meteorological forecast data can come from one or more numerical weather prediction sources. This embodiment does not limit the specific source of meteorological data or the type of prediction model. Meteorological forecast information from different sources can be directly concatenated into a unified feature vector, or filtered through feature selection methods. Represents a node At any moment The historical operating feature vector is used to characterize the time correlation and inertia characteristics of new energy output, including but not limited to the active power output value, power change rate, mean and variance within the sliding time window at historical moments. Represents a node At any moment The time-stamping features are used to reflect the periodic patterns of new energy output, including time index, day type (working day or non-working day) and seasonal information.

[0104] By constructing the above-mentioned multi-source features, the model can simultaneously perceive meteorological changes, historical operating status, and time patterns, thereby improving the stability and engineering applicability of probabilistic predictions.

[0105] Step 2: CatBoost Dense Quantile Regression, specifically:

[0106] After obtaining the multi-source feature vectors of each new energy node in the receiving-end power system, in order to characterize the conditional distribution characteristics of the injected power at different confidence levels, a dense quantile regression method based on the CatBoost algorithm is used to perform probabilistic prediction modeling of the wind power and photovoltaic output of each node.

[0107] A training set is constructed based on the multi-source feature vectors and renewable energy injection power at historical moments. ;in, Represents a node At a historical moment Multi-source feature vectors; Represents a node At a historical moment The power of new energy injection; Represents a set of historical moments; Representing nodes respectively At a historical moment The meteorological forecast feature vector, historical operation feature vector, and time tag feature.

[0108] The modeling goal of this step is not to predict a single power expectation value, but to directly learn the response of the power random variable at different quantile levels under given feature conditions, thereby providing discrete quantile support for subsequent probability distribution reconstruction.

[0109] Based on the requirements for tail uncertainty in the stability margin assessment of the receiving-end system, the quantile set is defined as follows: ;in, This indicates the quantile level. The quantile points are encrypted in the high confidence interval to enhance the ability to characterize low-probability, high-risk output intervals.

[0110] Construct any quantile level quantile regression model The quantile regression model is trained using the Categorical Boosting (CatBoost) algorithm, resulting in the constructed and trained quantile regression model; the quantile loss function of the quantile regression model. ;in, Indicates quantile level Lower historical samples and model predictions quantile loss function; Indicates quantile level Next node The quantile regression model.

[0111] Step 3: Quantile consistency and physical constraints, specifically:

[0112] After completing the quantile regression model training, the multi-source feature vectors are input into the pre-trained quantile regression model, which outputs the node quantile prediction results. At any moment Multi-source feature vectors Each quantile regression model is called separately to obtain the nodes. At any moment Node quantile prediction results .

[0113] To ensure the probabilistic consistency and physical rationality of the nodal quantile prediction results, quantile monotonicity constraints are imposed on the nodal quantile prediction results. and output boundary constraints The node-corrected quantile prediction results are obtained. When the node quantile prediction results show quantile overlap, the results are corrected by sorting or minimum adjustment to ensure the monotonicity of the quantile function. When the node quantile prediction results exceed the above physical boundaries, they are corrected by boundary pruning.

[0114] in, They represent quantile levels. quantile level quantile level quantile level Next node At any moment The node quantile prediction results; Represents a node The corresponding wind power or photovoltaic installed capacity.

[0115] Step 4: Reconstruct the probability distribution based on the quantile prediction results, specifically:

[0116] The node-corrected quantile prediction results have been obtained. .

[0117] Using the aforementioned discrete quantiles, the cumulative distribution function of the nodes is reconstructed through piecewise interpolation.

[0118] node In the power injection of new energy The node cumulative distribution function is expressed as:

[0119] ;

[0120] in, Represents a node In the power injection of new energy The node cumulative distribution function; They represent quantile levels. quantile level quantile level quantile level Next node The node quantile prediction results;

[0121] When the injected power of new energy is between two adjacent quantile prediction results, its node cumulative distribution function is calculated by linear interpolation of the corresponding quantile interval; when the injected power of new energy is less than the minimum quantile prediction result, the node cumulative distribution function is zero; when the injected power of new energy is greater than the maximum quantile prediction result, the node cumulative distribution function is one.

[0122] Using quantile prediction results as constraint nodes, without assuming the specific form of the probability distribution function, it can effectively characterize the asymmetry and cutoff characteristics of the distribution of new energy power output.

[0123] Step 5: Generate a joint scenario for multi-node renewable energy injection power, specifically as follows:

[0124] After obtaining the node cumulative distribution function, in order to facilitate the subsequent calculation of stability margin probability, the node discrete probability density function is further solved in the discrete power space.

[0125] First, connect the grid-connected bus nodes. New energy injection power range According to fixed step size Discretize to obtain nodes Discrete power point set At this point, the cumulative distribution function of the nodes is also discretized, where, Represents a node The Discrete power points, To show the node The number of discrete power points; Represents a node The corresponding wind power or photovoltaic installed capacity.

[0126] Based on the node cumulative distribution function, the probability density function is approximated using the difference method:

[0127] ;

[0128] To ensure that the obtained probability density function satisfies probability normalization, the probability density function is normalized to obtain the discrete probability density function of the node:

[0129] ;

[0130] in, Represents a node In the The node probability density function for discrete power points; Representing nodes respectively In the Discrete power points, nodes In the The node cumulative distribution function at discrete power points; Represents a node In the The node discrete probability density function for a discrete power point.

[0131] According to the node In the Discrete probability density function of nodes at discrete power points compute nodes In the Discrete power points The probability of the following nodes occurring By performing the above modeling process on all new energy nodes in the receiving system, a joint stochastic description of the new energy injection power of multiple nodes can be obtained. This description does not depend on specific probability distribution assumptions and can be directly used as input conditions for subsequent static stability margin calculation and tail risk analysis.

[0132] The uncertainty of new energy output is fully characterized by discrete probability density functions. To transform the discrete probability density functions of each node into the stochastic injection tensors required for system-level stability margin assessment, a time set is used... Scene collection Grid-connected busbar assembly The multi-node joint injection scene is generated and organized as a 3D tensor input; among which, Indicates the amount of time; Indicates the number of scenes.

[0133] node At any moment Discrete power point set Probability of occurrence with the corresponding node ,satisfy ;in, Representing time respectively node The first discrete power point, the second discrete power point, the... Discrete power points; Representing time respectively node At the first discrete power point, the second discrete power point, and the third discrete power point The probability of node occurrence at a discrete power point.

[0134] node At any moment Scene The following nodes jointly inject scene auxiliary vectors If the independence assumption is adopted, then Independent and subordinating If correlation is considered, then a correlation Gaussian vector should be generated first. and order ;in, node At any moment Scene The Gaussian vector below; for Uniform distribution within the range; It follows a zero-mean multivariate normal distribution, where 0 is a vector of all zeros matching the node dimension. For a moment The covariance matrix of the power output of the new energy nodes is used to characterize the linear correlation between the power outputs of multiple nodes; This is the cumulative distribution function of the standard normal distribution.

[0135] Will By probability of occurrence Perform mapping to obtain nodes At any moment Scene Randomly injected tensors ;

[0136] in, Represents a node At any moment The Discrete power points; This indicates taking the minimum value.

[0137] Step Six: System Network Model Construction and Consistency Processing, specifically:

[0138] Read busbar and branch data to obtain the busbar set. and branch set and the starting point of each branch road End of branch road Branch resistance Branch reactor To ensure consistency of data from different sources, a unified baseline capacity S should be established. base With reference voltage U base The branch resistance and branch reactance should be converted to a unified per-unit system. If the original data contains multiple voltage levels, equivalent or partitioned processing should be completed in advance. Representing branch roads The starting point, the ending point, the resistance, and the reactance.

[0139] The number of converters is the number of nodes. Number of busbars Number of branch roads Map the grid-connected objects to the grid-connected bus set .

[0140] To meet the engineering requirements of increasing the grid bus numbering from 1 and decreasing the numbering of infinite nodes from 69, node renumbering is achieved through branch endpoint number exchange:

[0141] Given the original node array node1 and the target node array node2 to be swapped, where node1 represents the number of the network converter and the infinite node in the original network, and node2 represents the number of the new node to be swapped, this mapping can be obtained by engineers based on the network topology configuration.

[0142] Swap each pair in the two arrays in turn, traverse the branches, renumber the endpoints of all branches, and obtain a new set of branches. To avoid conflicts between a single swap and subsequent swaps, this invention employs a pair-by-pair scanning and column-by-column replacement method to ensure consistency between the swap result and the project code. The renumbering rule is as follows:

[0143] ;

[0144] in, These represent the nodes in the original node array and the nodes in the target node array, respectively. This represents the set of new branch paths.

[0145] To ensure the swap is correct, the output information will be verified (e.g., a list of the first few branches after the swap). And check whether the set of grid-connected buses has become {1,2,…,n}. g At the same time, ensure that the reference infinite bus number is not swapped into the grid connection point set of the grid-connected converter; check whether there are zero reactance or duplicate branches in the branch; check whether the grid connection capacity is positive; if there is data that does not meet the conditions, output an alarm and terminate.

[0146] Construct the susceptance matrix based on the new branch set. :

[0147] Use the endpoint codes of each branch in the new branch set as the row and column indices of the susceptance matrix;

[0148] If the branches in the new branch set Reactance Then the susceptance matrix OK List, OK The elements of the column are set to ;

[0149] If the branches in the new branch set Reactance Then the susceptance matrix OK List, OK The elements of the column are set to the minimum reactance threshold; this avoids the matrix from being unable to be inverted.

[0150] Set the diagonal elements of the susceptance matrix to The diagonal elements are constructed with the row sum being zero, which ensures the consistency of the Laplace structure of the electric susceptance matrix and provides a basis for reversibility after choosing an infinite bus.

[0151] in, Representing the susceptance matrix OK Column elements, susceptance matrix OK The elements of the column.

[0152] Step 7: Selection of the infinite bus and Krone elimination, specifically:

[0153] If there is a clearly defined external power grid equivalent access point, then that point is selected as the infinite busbar; if there is a strong grid support point for the thermal power unit / synchronous machine, then that point is selected as the infinite busbar.

[0154] Remove the reference bus from the bus set. Obtain the set of remaining busbars According to the set of remaining busbars susceptance matrix Reduce the order to obtain the submatrix :

[0155] ;

[0156] Set up the remaining busbars Divided into grid-connected bus sets and passive busbar assembly Based on this division, the submatrix is ​​divided into blocks and eliminated to obtain the equivalent coupling matrix of the grid-connected bus. :

[0157] ;

[0158] in, Represents the susceptance matrix; Represents the real number field; Represents the coupling matrix of the grid-connected bus; Represents the coupling matrix of a passive bus; These represent the coupling matrices between the grid-connected network and the passive network, and the coupling matrix between the passive network and the grid-connected network, respectively.

[0159] Step 8: Calculate the generalized short-circuit ratio based on the specific scenario, as follows:

[0160] Based on the randomly injected tensor Constructing a scenario-based active diagonal matrix According to the equivalence coupling matrix Calculate the short-circuit ratio matrix using the scenario-specific active power diagonal matrix. ;

[0161] Short-circuit ratio matrix The minimum eigenvalue is used as the scenario-based generalized short-circuit ratio. When multiple machines are coupled, the mode corresponding to the smallest eigenvalue is the weakest short-circuit coupling mode, which has the smallest stability margin and preferentially determines the critical stability condition of the system.

[0162] Based on the scenario-specific generalized short-circuit ratio Calculate contextualized participation factors ;

[0163] in, Indicates at time Scene The following is a scenario-based active diagonal matrix; Indicates the diagonalization operation; Representing node 1, node 2, and node respectively. At any moment Scene Randomly injected tensors; Indicates at time Scene The short-circuit ratio matrix below; Indicates at time Scene The following is a scenario-specific generalized short-circuit ratio; Represents a node At any moment Scene Contextualized participation factors; Representing nodes respectively At any moment Scene The right and left eigenvectors of the generalized short-circuit ratio in the contextualized model.

[0164] Step Nine: Construct the equivalent model of the grid converter, specifically as follows:

[0165] Define the control loop transfer function and the Laplace variable. The power outer loop proportional-integral (PI) controller PI controller with current inner loop PI controller with phase-locked loop They are respectively:

[0166] ;

[0167] Laplace variable The power filtering stage below The grid-connected filter inductor is .

[0168] In Laplace variables Under the typical setting of zeroing the outer reactive power loop, the admittance matrix elements are:

[0169] ;

[0170] ;

[0171] The single-machine admittance matrix is:

[0172] ;

[0173] in, These represent the proportional coefficient and integral coefficient of the power outer loop, respectively; These represent the proportional coefficient and integral coefficient of the inner current loop, respectively. These represent the proportional coefficient and integral coefficient of the phase-locked loop, respectively. Representing Laplace variables respectively The first admittance matrix element and the second admittance matrix element; Representing Laplace variables Next node The single-machine admittance matrix.

[0174] In engineering, if it is necessary to consider the cross-coupling of the direct axis and the quadrature axis, filter capacitors, etc., the matrix can be expanded to include off-diagonal elements to ensure that the parameters of all PI controllers are within a physically reasonable range; otherwise, the default parameters are used and an alarm is triggered.

[0175] The total admittance is obtained by weighting the single-machine admittance matrix according to the scenario-based participation factors:

[0176] ;

[0177] Assuming all converters have the same control parameters, ;

[0178] The system disturbance model is as follows:

[0179] ;

[0180] Total admittance combined with system disturbance model Construct the characteristic equation of the system:

[0181] ;

[0182] in, Representing Laplace variables Total admittance below; Representing Laplace variables The system disturbance model is as follows; Indicates the rated angular velocity; A factor representing the influence of the system's equivalent damping or resistance / reactance; Indicates at time Scene Candidate scenario-based critical short-circuit ratio; This indicates the calculation of determinants.

[0183] Step 10: Calculate the critical stability margin and construct a stability margin sample, specifically as follows:

[0184] Set scan step size (like Generate a candidate scenario-based critical short-circuit ratio sequence. ;in, Indicates at time Scene The first candidate scenario-based critical short-circuit ratio sequence One candidate scenario-based critical short-circuit ratio; This represents the number of candidate scenario-based critical short-circuit ratios in the candidate scenario-based critical short-circuit ratio sequence.

[0185] For each candidate scenario, a critical short-circuit ratio is defined. Solve the characteristic equation of the system to generate the root set. The candidate scenario-based critical short-circuit ratio corresponding to the root that satisfies the critical stability criterion is taken as the scenario-based critical short-circuit ratio.

[0186] The real part of the root is The critical stability criterion is expressed as:

[0187] ;

[0188] in, Indicates at time Scene Next The candidate scenario-based critical short-circuit ratio corresponds to the first One root; Indicates at time Scene Next The candidate scenario-based critical short-circuit ratio corresponds to the first The real part of each root; Represents small positive numbers close to zero (e.g.) ); These represent taking the minimum value and taking the maximum value, respectively.

[0189] If there exists a pair or a single root that is close to the imaginary axis but remains in the left half-plane, the system is near the critical stability boundary. The corresponding candidate scenario-based critical short-circuit ratio is then called the scenario-based critical short-circuit ratio. When the critical stability criterion is met for the first time, the candidate scenario-based critical short-circuit ratio at this time is recorded as the scenario-based critical short-circuit ratio. And stop scanning. To improve efficiency, if the candidate scenario-based critical short-circuit ratio is greater than the scenario-based generalized short-circuit ratio, the process can be terminated early and a positive stability margin can be indicated. Indicates at time Scene The critical short-circuit ratio in the given scenario.

[0190] Based on the scenario-specific generalized short-circuit ratio and scenario-based critical short-circuit ratio Calculate the stability margin at time 10:00. Scene stability margin .

[0191] At any moment Scene relative stability margin This yields the relatively stable margin for each scenario and time period.

[0192] It can characterize the safety margin of the system from the small disturbance synchronous instability boundary under the driving force of active power output uncertainty, and provide input for subsequent tail risk measurement and stability margin interval calculation.

[0193] For stability margin Sort in ascending order to get .

[0194] Based on stability margin First sample quantile estimate for calculating tail stability margin Second sample quantile estimation and stability margin range ;

[0195] First Sample Quantile Estimation Corresponding to the most unfavorable confidence parameter The boundary margin of a scaled scenario is reflected at time... Below, the margin is distributed as a safety margin at the tail boundary, when When <0, it indicates the existence of at least a confidence parameter. The proportional scene samples cause the stability margin to exceed or approach the limit, satisfying the boundary triggering conditions of the engineering alarm.

[0196] Second sample quantile estimation Corresponding to the most unfavorable confidence parameter The margins of proportional scenarios are averaged to characterize the overall severity of tail risk. It only reflects the difference in boundaries. It can reflect the contribution of extreme samples within the tail to the risk intensity, thus providing more stable risk quantification results even when there are a few extremely adverse scenarios. In engineering applications, Used for boundary triggering. Used for tail risk intensity classification and governance strength assessment.

[0197] Stability margin range Used to describe at time The stability margin random variable is defined as the range of values ​​it can take in a high-probability context. The lower bound of the interval represents the minimum margin level that can still be obtained after excluding extremely low-probability extreme scenarios, while the upper bound represents the maximum margin level that can still be obtained after excluding extremely low-probability extremely favorable scenarios. The interval width is used to characterize the strength of the impact of active power output uncertainty on stability margin fluctuations, and the sign of the lower bound is used to determine whether there is a risk of stability margin overflow in a high-probability context.

[0198] For the entire set of time points Repeat the above steps to form the first sample quantile estimation sequence, the second sample quantile estimation sequence, and the stability margin interval sequence of the tail stability margin that vary over time.

[0199] Based on the scenario-based generalized short-circuit ratio, scenario-based critical short-circuit ratio, stability margin, first sample quantile estimate of tail stability margin, second sample quantile estimate of tail stability margin, and stability margin interval, the tail risk prediction result of the static stability margin of the power system is generated.

[0200] in, Indicates at time Confidence parameters First sample quantile estimate of lower tail stability margin; Indicates at time Scene The stability margin below; This indicates the rounding up operation; Indicates at time Confidence parameters Second sample quantile estimation of lower tail stability margin; Indicates at time Confidence parameters The stability margin range below; They represent the times at time 1 and 2 respectively. Scene At any moment Scene The stability margin below.

[0201] Example 2, based on Example 1, introduces an experimental example of a method for predicting the tail risk of static stability margin in a power system:

[0202] Figure 2 It showcases the scenic power of five typical scenes. Figures 3-7 Table 1 shows the stability margin assessment results obtained based on the prediction results.

[0203] Table 1

[0204] Hour Mean margin median margin Lower bound of margin interval upper bound of margin interval Margin one-sided lower bound First Sample Quantile Estimation Second sample quantile estimation Outbound probability 1 1.0613 0.8455 0.53199 2.1800 0.5762 0.5319 0.5064 0 2 1.3111 0.9031 0.52249 3.8376 0.5783 0.5224 0.5080 0 3 1.1137 0.9070 0.52641 2.2468 0.5901 0.5264 0.5105 0 4 1.1295 0.9164 0.53432 2.4125 0.6105 0.5343 0.4970 0 5 1.4569 0.8882 0.49104 5.1838 0.5119 0.4910 0.4759 0 6 1.3116 0.8176 0.39622 5.0277 0.4775 0.3962 0.3798 0 7 0.8123 0.5645 0.15189 2.0899 0.2146 0.1518 0.0827 0 8 0.7177 0.5413 -0.0803 1.6829 0.0255 -0.0803 -0.0985 0.07 9 0.5263 0.4326 -0.0116 1.2620 0.0235 -0.0116 -0.0870 0.06 10 0.3527 0.2746 -0.1075 0.9977 -0.0496 -0.1075 -0.1950 0.15 11 0.2715 0.2262 -0.1146 0.8198 -0.0250 -0.1146 -0.1652 0.14 12 0.3924 0.2961 -0.0382 1.2335 -0.0191 -0.0382 -0.0724 0.14 13 0.5286 0.41701 -0.0421 1.3659 0.0034 -0.0421 -0.0965 0.08 14 0.8677 0.70152 0.1454 2.0317 0.2416 0.1454 0.1048 0 15 1.8186 1.428 0.3718 4.5218 0.5728 0.3718 0.2734 0 16 4.4301 3.3588 1.2923 9.0782 1.4707 1.2923 1.1632 0 17 8.0503 5.0788 1.4935 22.181 2.0384 1.4935 1.2385 0 18 5.6245 3.9372 1.0893 19.691 1.4610 1.0893 0.8262 0 19 6.9170 3.5191 0.8080 12.136 1.2670 0.8080 0.7064 0 20 6.2321 4.1458 1.2726 18.715 1.7957 1.2726 0.9702 0 21 7.4247 5.5614 1.2971 13.795 2.1019 1.2971 1.0248 0 22 22.817 7.5945 2.8243 72.478 3.8514 2.8243 2.2376 0 23 26.077 11.238 3.6997 119.14 4.3851 3.6997 2.8736 0 24 42.884 16.628 4.9534 250.3 5.7856 4.9534 3.1642 0

[0205] The wind and solar forecast results show the power variation trend and fluctuation characteristics of the system at different times. Combined with the calculated generalized short-circuit ratio and stability margin tail risk, the weak periods of system stability can be clearly identified.

[0206] like Figures 2-7 As shown, the experimental process in this paper mainly includes three stages: wind and solar power output scenario generation, scenario-based generalized short-circuit ratio calculation, and stability margin risk assessment. First, new energy power output scenarios are constructed based on wind and solar power prediction results; then, the scenario-based generalized short-circuit ratio and stability margin indicators for each time period are calculated; finally, the out-of-bounds probability, ... and A comprehensive analysis of the system's static stability level was conducted using equal risk parameters. Experimental results show that during periods of higher predicted wind and solar power output but relatively weaker conventional system support capabilities, the generalized short-circuit ratio decreases significantly, and the stability margin narrows accordingly. This indicates that the system is closer to the stability boundary at this time, belonging to a vulnerable operating range that requires close attention. Table 1 shows that the stability indicators for periods 8-13 are relatively poor, with some periods exhibiting... , Furthermore, the lower bound index further decreased, and the probability of exceeding the limit increased, indicating that static stability risks are more likely to occur during these periods; while the overall stability margin is higher during other periods, and the system operates relatively safely. In addition, the calculated scenario-based critical short-circuit ratio... The value is 1.4533, which can be considered as the lower limit for system stability. When the actual stability margin is higher than this value, the system is in a stable state. Overall, this method effectively connects "new energy power prediction" to "system stability early warning," providing a basis for dispatchers to identify potential weak periods and formulate control measures in advance during the day-ahead phase.

[0207] Example 3: This example introduces a device for predicting the tail risk of static stability margin in a power system, comprising:

[0208] The quantile prediction module is used to: input multi-source feature vectors into a pre-built quantile regression model, output node quantile prediction results, apply physical constraints to the node quantile prediction results, and obtain node corrected quantile prediction results.

[0209] The tensor calculation module is used to: reconstruct the node cumulative distribution function based on the node correction quantile prediction results; calculate the node discrete probability density function based on the node cumulative distribution function; and map the generated node joint injection scene auxiliary vector through the node discrete probability density function to obtain the random injection tensor.

[0210] The matrix construction module is used to: renumber the branch endpoints to obtain a new branch set; construct the susceptance matrix based on the new branch set; remove the reference bus from the bus set to obtain the remaining bus set; and reduce the order of the susceptance matrix based on the remaining bus set to obtain a submatrix.

[0211] The matrix elimination module is used to: divide the remaining bus set into a grid-connected bus set and a passive bus set, and perform block elimination on the sub-matrix according to this division to obtain the equivalent coupling matrix of the grid-connected bus;

[0212] The equation construction module is used to: calculate the scenario-based generalized short-circuit ratio and scenario-based participation factor based on the randomly injected tensor and the equivalent coupling matrix; weight the pre-constructed single-machine admittance matrix according to the scenario-based participation factor; and construct the system characteristic equation based on the weighting result.

[0213] The risk prediction module is used to: solve the system characteristic equations based on the preset candidate scenario-based critical short-circuit ratio sequence, generate a root set, obtain the scenario-based critical short-circuit ratio based on the root set and critical stability criterion, calculate the stability margin based on the scenario-based generalized short-circuit ratio and the scenario-based critical short-circuit ratio, and generate the static stability margin tail risk prediction result of the power system based on the stability margin.

[0214] The specific functions of each module described above are explained in the relevant content of Embodiment 1 or 2, and will not be repeated here.

[0215] Example 4: This example introduces a computer-readable storage medium storing a computer program / instruction, which, when executed by a processor, implements the steps of the static stability margin tail risk prediction method for power systems described in Example 1 or 2.

[0216] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0217] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. 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... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0218] 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.

[0219] 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.

[0220] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A method for predicting the tail risk of static stability margin in a power system, characterized in that, include: The multi-source feature vectors are input into a pre-built quantile regression model, the node quantile prediction results are output, and physical constraints are applied to the node quantile prediction results to obtain the node corrected quantile prediction results. The node cumulative distribution function is reconstructed based on the node correction quantile prediction results. The node discrete probability density function is calculated based on the node cumulative distribution function. The generated node joint injection scene auxiliary vector is mapped through the node discrete probability density function to obtain the random injection tensor. The endpoints of the branches are renumbered to obtain a new set of branches. An susceptance matrix is ​​constructed based on the new set of branches. The reference bus is removed from the set of buses to obtain the remaining set of buses. The order of the susceptance matrix is ​​reduced based on the remaining set of buses to obtain a submatrix. The remaining bus set is divided into a grid-connected bus set and a passive bus set. The sub-matrix is ​​then divided into blocks and eliminated according to this division to obtain the equivalent coupling matrix of the grid-connected bus. The scenario-based generalized short-circuit ratio and scenario-based participation factor are calculated based on the random injection tensor and the equivalent coupling matrix. The pre-constructed single-machine admittance matrix is ​​weighted according to the scenario-based participation factor, and the system characteristic equation is constructed based on the weighting result. The system characteristic equation is solved based on the preset candidate scenario-based critical short-circuit ratio sequence to generate a root set. The scenario-based critical short-circuit ratio is obtained based on the root set and the critical stability criterion. The stability margin is calculated based on the scenario-based generalized short-circuit ratio and the scenario-based critical short-circuit ratio. The static stability margin tail risk prediction result of the power system is generated based on the stability margin. The scenario-based generalized short-circuit ratio and scenario-based participation factor are calculated based on the random injection tensor and the equivalent coupling matrix, including: Construct a scenario-based active diagonal matrix based on the randomly injected tensor. The short-circuit ratio matrix is ​​calculated based on the equivalent coupling matrix and the scenario-specific active power diagonal matrix. ; Short-circuit ratio matrix The minimum eigenvalue is used as the scenario-based generalized short-circuit ratio. According to the scenario-based generalized short-circuit ratio Calculate contextualized participation factors ; in, Indicates at time Scene The scenario-specific active diagonal matrix; Indicates the diagonalization operation; Representing node 1, node 2, and node respectively. At any moment Scene Randomly injected tensors; Indicates at time Scene The short-circuit ratio matrix below; Represents an equivalence coupling matrix; Indicates at time Scene The following is a scenario-specific generalized short-circuit ratio; Represents a node At any moment Scene Contextualized participation factors; Representing nodes respectively At any moment Scene The right and left eigenvectors of the generalized short-circuit ratio in the contextualized model.

2. The method for predicting the tail risk of static stability margin in a power system according to claim 1, characterized in that, The construction of the quantile regression model includes: A training set is constructed based on the multi-source feature vectors and renewable energy injection power at historical moments. , ;in, Represents a node At a historical moment Multi-source feature vectors ; Represents a node At a historical moment The power of new energy injection; Represents a set of historical moments; Representing nodes respectively At a historical moment Meteorological forecast feature vector, historical operation feature vector, and time tag feature; A quantile regression model at the quantile level is constructed and trained using the CatBoost algorithm to obtain the constructed and trained quantile regression model; the quantile loss function of the quantile regression model is then defined. ;in, Indicates quantile level Lower historical samples and model predictions The quantile loss function.

3. The method for predicting the tail risk of static stability margin in a power system according to claim 1, characterized in that, Physical constraints are applied to the node quantile prediction results to obtain the node corrected quantile prediction results, including: Node quantile prediction results ; Apply quantile monotonicity constraints to the nodal quantile prediction results and output boundary constraints The node-corrected quantile prediction results are obtained. ; in, They represent quantile levels respectively. quantile level quantile level quantile level Next node At any moment The node quantile prediction results; Represents a node At any moment Multi-source feature vectors; Indicates quantile level Next node Quantile regression model; Represents a node The corresponding wind power or photovoltaic installed capacity.

4. The method for predicting the tail risk of static stability margin in a power system according to claim 1, characterized in that, The node cumulative distribution function is expressed as: ； in, Represents a node In the power injection of new energy The node cumulative distribution function; They represent quantile levels respectively. quantile level quantile level quantile level Next node The node quantile prediction results; The formula for calculating the discrete probability density function of the node is: ； ； in, Represents a node In the The node probability density function for discrete power points; Representing nodes respectively In the Discrete power points, nodes In the The node cumulative distribution function at discrete power points; Represents a node In the Discrete probability density function of nodes at discrete power points; Indicates at node New energy injection power range Inner step length The number of discrete power points obtained from the division; Represents a node The corresponding wind power or photovoltaic installed capacity.

5. The method for predicting the tail risk of static stability margin in a power system according to claim 1, characterized in that, The generated node joint injection scene auxiliary vector is mapped through the node discrete probability density function to obtain a random injection tensor, including: Based on the node discrete probability density function Calculate the probability of node occurrence , ; The generated nodes are jointly injected into the scene auxiliary vector. Probability of occurrence through nodes Mapping is performed to obtain a randomly injected tensor. , ; in, Represents a node In the Discrete probability density function at discrete power points; Represents a node At any moment No. The probability of node occurrence at a discrete power point; Represents a node At any moment Scene The nodes below jointly inject scene auxiliary vectors; Represents a node At any moment Scene Randomly injected tensors; Represents a node At any moment The Discrete power points; This indicates taking the minimum value; Indicates at node New energy injection power range Inner step length The number of discrete power points obtained from the division; Represents a node The corresponding wind power or photovoltaic installed capacity.

6. The method for predicting the tail risk of static stability margin in a power system according to claim 1, characterized in that, Renumbering the endpoints of the branches yields a new set of branches, including: Traverse the branches, renumber the endpoints of the branches based on the original node array and the target node array, and obtain a new set of branches. The renumbering rule is as follows: ； in, Representing branch roads The starting point and the ending point; These represent the nodes in the original node array and the nodes in the target node array, respectively. This represents the set of new branch paths.

7. The method for predicting the tail risk of static stability margin in a power system according to claim 1, characterized in that, Construct the susceptance matrix based on the new branch set, including: Use the endpoint codes of each branch in the new branch set as the row and column indices of the susceptance matrix; If the branches in the new branch set Reactance Then the susceptance matrix OK List, OK The elements of the column are set to ; If the branches in the new branch set Reactance Then the susceptance matrix OK List, OK The elements of the column are set to the minimum reactance threshold; Set the diagonal elements of the susceptance matrix to ; in, Representing branch roads The starting point and the ending point; Representing the susceptance matrix OK Column elements, susceptance matrix OK Column elements; Indicates the number of busbars.

8. The method for predicting the tail risk of static stability margin in a power system according to claim 1, characterized in that, The submatrix is ​​represented as follows: ； The equivalent coupling matrix is ​​represented as follows: ； in, Represents a submatrix; Represents the susceptance matrix; Represents the set of remaining busbars; Represents the real number field; Indicates the number of busbars; Represents an equivalence coupling matrix; Represents the coupling matrix of the grid-connected bus; Represents the coupling matrix of a passive bus; These represent the coupling matrices between the grid-connected network and the passive network, and the coupling matrix between the passive network and the grid-connected network, respectively.

9. The method for predicting the tail risk of static stability margin in a power system according to claim 1, characterized in that, The construction of the single-machine admittance matrix includes: ； ； ； ； in, Representing Laplace variables respectively The PI controllers for the power outer loop, the current inner loop, and the phase-locked loop are all included. Representing Laplace variables Power filtering under; These represent the proportional coefficient and integral coefficient of the power outer loop, respectively; These represent the proportional coefficient and integral coefficient of the inner current loop, respectively. These represent the proportional coefficient and integral coefficient of the phase-locked loop, respectively. Representing Laplace variables respectively The first admittance matrix element and the second admittance matrix element; Indicates the grid-connected filter inductor; Representing Laplace variables Next node The single-machine admittance matrix.

10. The method for predicting the tail risk of static stability margin in a power system according to claim 1, characterized in that, The construction of the system characteristic equation includes: ； ； ； in, Representing Laplace variables Total admittance below; Represents a node At any moment Scene Contextualized participation factors; Representing Laplace variables Next node The single-machine admittance matrix; Indicates the number of nodes; Representing Laplace variables The system disturbance model is as follows; Indicates the rated angular velocity; A factor representing the influence of the system's equivalent damping or resistance / reactance; Indicates at time Scene Candidate scenario-based critical short-circuit ratio; This indicates the calculation of determinants.

11. The method for predicting the tail risk of static stability margin in a power system according to claim 1, characterized in that, The scenario-specific critical short-circuit ratio is obtained based on the root set and critical stability criterion. The stability margin is calculated based on the scenario-specific generalized short-circuit ratio and the scenario-specific critical short-circuit ratio, including: The candidate scenario-specific critical short-circuit ratio corresponding to the root that satisfies the critical stability criterion is taken as the scenario-specific critical short-circuit ratio. The critical stability criterion is expressed as: ； in, Indicates at time Scene Next The candidate scenario-based critical short-circuit ratio corresponds to the first The real part of each root; Represents positive numbers; These represent taking the minimum value and taking the maximum value, respectively. The stability margin is expressed as: ； in, Indicates at time Scene The stability margin below; Indicates at time Scene The following is a scenario-specific generalized short-circuit ratio; Indicates at time Scene The critical short-circuit ratio in the given scenario.

12. The method for predicting the tail risk of static stability margin in a power system according to claim 1, characterized in that, Based on the stability margin, the static stability margin tail risk prediction results of the power system are generated, including: Based on stability margin First sample quantile estimate for calculating tail stability margin Second sample quantile estimation and stability margin range , , , ; Based on the scenario-based generalized short-circuit ratio, scenario-based critical short-circuit ratio, stability margin, first sample quantile estimate of tail stability margin, second sample quantile estimate of tail stability margin, and stability margin interval, the static stability margin tail risk prediction result of the power system is generated. in, Indicates at time Scene The stability margin below; Indicates at time Confidence parameters First sample quantile estimate of lower tail stability margin; Indicates at time Scene The stability margin below; Indicates the number of scenes; This indicates the rounding up operation; Indicates at time Confidence parameters Second sample quantile estimation of lower tail stability margin; Indicates at time Confidence parameters The stability margin range below; They represent the times at time 1 and 2 respectively. Scene At any moment Scene The stability margin below.

13. A device for predicting the tail risk of static stability margin in a power system, characterized in that, For performing the method according to any one of claims 1-12, comprising: The quantile prediction module is used to input multi-source feature vectors into a pre-built quantile regression model, output node quantile prediction results, apply physical constraints to the node quantile prediction results, and obtain node corrected quantile prediction results. The tensor calculation module is used to reconstruct the node cumulative distribution function based on the node correction quantile prediction results, calculate the node discrete probability density function based on the node cumulative distribution function, and map the generated node joint injection scene auxiliary vector through the node discrete probability density function to obtain the random injection tensor. The matrix construction module is used to renumber the branch endpoints to obtain a new branch set, construct the susceptance matrix based on the new branch set, remove the reference bus from the bus set to obtain the remaining bus set, and reduce the order of the susceptance matrix based on the remaining bus set to obtain a submatrix. The matrix elimination module is used to divide the remaining bus set into a grid-connected bus set and a passive bus set. According to this division, the sub-matrix is ​​divided into blocks and eliminated to obtain the equivalent coupling matrix of the grid-connected bus. The equation construction module is used to calculate the scenario-based generalized short-circuit ratio and scenario-based participation factor based on the randomly injected tensor and the equivalent coupling matrix. It weights the pre-constructed single-machine admittance matrix according to the scenario-based participation factor and constructs the system characteristic equation based on the weighting result. The risk prediction module is used to solve the system characteristic equations based on the preset candidate scenario-based critical short-circuit ratio sequence, generate a root set, obtain the scenario-based critical short-circuit ratio based on the root set and critical stability criterion, calculate the stability margin based on the scenario-based generalized short-circuit ratio and the scenario-based critical short-circuit ratio, and generate the static stability margin tail risk prediction result of the power system based on the stability margin.

14. A computer-readable storage medium having a computer program / instructions stored thereon, characterized in that, When the computer program / instruction is executed by the processor, it implements the steps of the static stability margin tail risk prediction method for the power system as described in any one of claims 1-12.

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