Power system transient voltage prediction method, risk analysis method and system

Abstract

The invention discloses a transient voltage prediction method, a risk analysis method and a risk analysis system for an electric power system, relates to the technical field of stability analysis of the electric power system, and solves the problems of insufficient prediction precision and generalization ability in the prior art. According to the technical scheme, a voltage signal of a current time sequence of a power system is obtained; selecting an optimal observation function from a primary function space corresponding to the voltage signal of the current time sequence according to a predetermined optimal weight of the observation function combination; and estimating an optimal Koopman operator according to the optimal observation function, and predicting a trajectory curve of the future time sequence transient voltage of the power system in combination with the optimal observation function and the optimal Koopman operator.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of power system stability analysis, more particularly, it relates to a power system transient voltage prediction method, a risk analysis method and system. BACKGROUND

[0002] With high proportion of renewable energy access to the power grid, the dynamic characteristics of the power system become more complex, especially the problem of transient voltage stability. Renewable energy generation has the characteristics of intermittency and randomness, and its output fluctuation will lead to frequent changes in the voltage of the power grid. At the same time, new energy devices such as wind power and photovoltaic are mostly connected to the power grid through power electronic converters, which lack the inertia and voltage support capability of traditional synchronous generators, further weakening the voltage regulation capability of the system. When the system is subjected to large disturbances such as short-circuit faults and sudden changes in new energy power, the voltage may quickly drop and be difficult to recover, and if the transient voltage is unstable, it will cause a large amount of load loss and equipment damage, and even cause a chain of faults to cause a large area blackout, which seriously threatens the safe and stable operation of the power system. Therefore, accurately predicting the transient voltage trajectory and quantifying the stability margin is crucial for early risk identification and the adoption of preventive measures, and is a key technical requirement for ensuring the safe and reliable power supply of high-proportion new energy power grids.

[0003] The existing voltage stability analysis method usually relies on traditional physical models and numerical simulation, but these methods have problems of low calculation efficiency and insufficient accuracy in power grids with high proportion of new energy access due to the strong nonlinearity and time-varying characteristics of the system. In addition, the existing methods are mostly point predictions, which cannot provide complete voltage trajectory prediction, and there is no complete solution from stability margin to risk level warning.

[0004] Specifically, the traditional transient voltage analysis method mainly includes two categories: physical model simulation method and data-driven method. The former mainly includes numerical time domain simulation method and direct method, which can complete the basic analysis, but relies on accurate system parameters, has low calculation efficiency and insufficient adaptability when facing strong nonlinear systems, and is difficult to meet the timeliness requirements of online applications; the latter mainly includes machine learning and deep learning, which to some extent solves the problems existing in the physical model simulation method and improves the prediction speed, but has problems of unbalanced sample distribution and weak generalization ability, and mostly focuses on short-term "point" prediction, which cannot completely depict the dynamic evolution process of the voltage trajectory, and does not form an integrated framework from prediction to quantitative evaluation to risk warning, resulting in a disconnection between stability evaluation and risk warning, making it difficult to support accurate decision-making by operation personnel. SUMMARY

[0005] The purpose of the present application is to provide a power system transient voltage prediction method, a risk analysis method and system, which solves the problem of insufficient prediction accuracy and generalization ability in the prior art.

[0006] The above technical objective of the present application is achieved by the following technical solutions:

[0007] In a first aspect, the present application provides a power system transient voltage prediction method, the method comprising:

[0008] obtaining a voltage signal of a current time sequence of the power system;

[0009] selecting an optimal observation function from a basis function space corresponding to the voltage signal of the current time sequence according to an optimal weight of an observation function combination determined in advance; wherein the optimal weight of the observation function combination is determined as follows: obtaining a voltage signal of a historical time sequence of the power system and a state actual measurement result; decomposing the voltage signal of the historical time sequence based on an empirical mode decomposition method to obtain an intrinsic mode component; analyzing a time-frequency characteristic of the intrinsic mode component to analyze an observation function space used for approximating a transient voltage dynamic characteristic; solving a Koopman operator based on the observation function in the observation function space, and calculating a variance of an eigenvalue decomposed by the Koopman operator; predicting a state of the power system according to the observation function and the Koopman operator to obtain a state prediction result, and calculating a prediction residual according to the state prediction result and the state actual measurement result; dynamically adjusting the weight of the observation function combination in the observation space by a gradient descent method until a sum function of the variance and the prediction residual reaches a minimum value, to obtain the optimal weight of the observation function combination;

[0010] estimating an optimal Koopman operator according to the optimal observation function, and predicting a trajectory curve of a transient voltage of a future time sequence of the power system in combination with the optimal observation function and the optimal Koopman operator.

[0011] In an implementation scheme, the basis function space includes three basis functions of a polynomial basis function, a Gaussian radial basis function and a trigonometric function basis function.

[0012] In an implementation scheme, an expression of the sum function is: wherein, is the weight of the observation function combination, is a variance operation, is an eigenvalue of the Koopman operator, is a state prediction result obtained by predicting the state of the power system according to the observation function and the Koopman operator, is a state actual result of the power system.

[0013] In an implementation scheme, while estimating the optimal Koopman operator according to the optimal observation function, the method further comprises:

[0014] if the rate of change of the amplitude of the voltage signal of the current time sequence is greater than the rate of change threshold, re-estimating the optimal Koopman operator based on the optimal observation function;

[0015] if the similarity between the extracted Koopman mode and the historical typical mode is lower than the similarity threshold, re-estimating the optimal Koopman operator based on the optimal observation function.

[0016] In an implementation scheme, the method further comprises:

[0017] obtaining the actual measurement result of the state of the future time sequence of the power system;

[0018] determining the deviation of the actual measurement result of the state of the future time sequence from the predicted result of the state of the future time sequence;

[0019] dynamically correcting the predicted result of the state of the next time sequence of the future time sequence according to the deviation.

[0020] In an implementation scheme, the expression for dynamically correcting the predicted result of the state of the next time sequence of the future time sequence according to the deviation is: wherein, is the predicted result of the state of the future time sequence of the power system, is the predicted result of the state of the next time sequence of the future time sequence of the power system, is the actual measurement result of the state of the future time sequence of the power system, is a dynamic weight, is a Koopman operator.

[0021] In a second aspect of the present application, a power system transient voltage risk analysis method is provided, the method comprising:

[0022] obtaining a trajectory curve of the transient voltage of the future time sequence of the power system; wherein the trajectory curve of the transient voltage of the future time sequence of the power system is obtained based on the power system transient voltage prediction method provided in the first aspect of the present application;

[0023] calculating a transient voltage stability quantitative index of any bus node according to the trajectory curve;

[0024] taking the maximum value of the transient voltage stability quantitative index as the stability margin of the transient voltage of the power system;

[0025] comparing the stability margin with a preset margin threshold interval to determine the stability analysis result of the transient voltage of the power system.

[0026] In an implementation scheme, the method further comprises:

[0027] construct a risk function with a segmented exponential function characteristic; wherein the value range of the segmented exponential function corresponds to the margin threshold interval;

[0028] In combination with the stable margin and the risk function, the risk value of the power system instability is determined.

[0029] The risk value is discretized to determine the risk level of the power system instability.

[0030] In a third aspect of the present application, a power system transient voltage prediction system is provided, which comprises:

[0031] A voltage signal acquisition module is configured to acquire the voltage signal of the current time sequence of the power system.

[0032] An observation function selection module is configured to select an optimal observation function from the basis function space corresponding to the voltage signal of the current time sequence according to the optimal weight of the observation function combination determined in advance; wherein the optimal weight of the observation function combination is determined as follows: the voltage signal and the state actual measurement result of the historical time sequence of the power system are acquired; the voltage signal of the historical time sequence is decomposed based on the empirical mode decomposition method to obtain the intrinsic mode component; the observation function space used to approximate the dynamic characteristics of the transient voltage is analyzed based on the time-frequency characteristics of the intrinsic mode component; the Koopman operator is solved based on the observation function in the observation function space, and the variance of the eigenvalue decomposed by the Koopman operator is calculated; the state of the power system is predicted based on the observation function and the Koopman operator to obtain the state prediction result, and the prediction residual is calculated based on the state prediction result and the state actual measurement result; the weight of the observation function combination in the observation space is dynamically adjusted by the gradient descent method until the sum function of the variance and the prediction residual reaches a minimum value, thereby obtaining the optimal weight of the observation function combination.

[0033] A transient voltage prediction module is configured to estimate the optimal Koopman operator based on the optimal observation function, and predict the trajectory curve of the transient voltage of the future time sequence of the power system in combination with the optimal observation function and the optimal Koopman operator.

[0034] In a fourth aspect of the present application, a power system transient voltage risk analysis system is provided, which comprises:

[0035] A trajectory curve acquisition module is configured to acquire the trajectory curve of the transient voltage of the future time sequence of the power system; wherein the trajectory curve of the transient voltage of the future time sequence of the power system is predicted based on the power system transient voltage prediction system provided in the third aspect of the present application.

[0036] A quantitative index calculation module is configured to calculate the transient voltage stability quantitative index of any bus node according to the trajectory curve.

[0037] A stability margin determination module is configured to take the maximum value of the transient voltage stability quantitative index as the stability margin of the power system transient voltage.

[0038] An analysis module is configured to compare the stability margin with a preset margin threshold interval to determine the stability analysis result of the power system transient voltage.

[0039] Compared with the prior art, the present application has the following beneficial effects:

[0040] 1、Traditional Koopman theory maps the evolution of a nonlinear dynamical system into an infinite-dimensional linear operator space, and through the spectral analysis of Koopman operator, the dominant mode of the system can be extracted using only short-term measurement data, and fast trajectory prediction can be realized. Although the traditional Koopman theory can realize the trajectory prediction of the nonlinear system, when it is applied to the complex power system, there are still problems such as insufficient adaptability of the base function, tracking lag of the time-varying characteristics, and accumulation of multi-source errors, so that the traditional Koopman method has the problems of weak generalization ability, dynamic tracking lag and error accumulation. Therefore, the first aspect of the present application provides a power system transient voltage prediction method, which solves the problems of weak generalization ability, dynamic tracking lag and error accumulation of the traditional Koopman method through base function adaptive optimization, operator dynamic updating and multi-stage error correction, and improves the transient voltage trajectory prediction accuracy and long-period characterization ability. First, in the base function optimization link, the voltage signal of the historical time sequence is processed by using empirical mode decomposition, and a observation function space covering polynomial, Gaussian radial basis function and trigonometric function is initialized in a multi-scale feature guided manner, so as to ensure that the dynamic characteristics such as slow change, high-frequency oscillation and periodic fluctuation of the voltage can be covered; further, an adaptability evaluation function taking the minimum of the eigenvalue stability variance of the Koopman operator and the prediction residual as the target is constructed, and the gradient descent method is used to dynamically adjust the combination weight of each base function, so that the observation space can adaptively match the nonlinear characteristics of the power system at present. Secondly, in the operator dynamic updating link, in order to overcome the response lag problem of the traditional method, a multi-source triggering mechanism is designed, which not only adaptively adjusts the data window width used to estimate the Koopman operator according to the dynamic change rate of the system, but also introduces two instant restart conditions of measurement data mutation triggering (when the voltage change rate exceeds the threshold) and Koopman mode deviation triggering (when the cosine similarity of the real-time extracted mode and the historical typical mode is lower than the threshold), so as to shorten the Koopman operator update delay to within 10 milliseconds, and significantly enhance the tracking ability of the fast time-varying process of the power system. Finally, in the error correction link, the rolling optimization idea of model predictive control is introduced in the trajectory prediction stage, and the deviation between the latest measurement value and the prediction value is used to form a dynamic correction term, which is fed back to the subsequent prediction, so as to effectively suppress the error accumulation in long-term prediction, and accurately depict the prediction trajectory curve of the transient voltage in the future period of time.

[0041] 2、Traditional binary classification mode can only give stable or unstable conclusion, cannot quantify the stability degree of system, and is difficult to give early warning to the fragile bus node in critical state, therefore, the second aspect of the present application provides a kind of power system transient voltage risk analysis, effective criterion that can quantify stability degree is extracted from predicted transient voltage trajectory curve, that is, transient voltage stability quantization index is used to define the distance between current state and instability boundary, which can quantize the stability degree of node and system continuously, avoid misjudgment caused by single threshold or fixed criterion, and accurately locate the weak bus node of system, convert continuous stability margin index into intuitive discrete risk level, form a closed-loop logic of "prediction-quantization-early warning". The operator can directly match the prevention and control strategy according to the risk level, compared with the traditional early warning mode lacking grading mechanism, it can more efficiently support decision-making and enhance the ability of power grid to actively identify and prevent transient voltage risk. BRIEF DESCRIPTION OF DRAWINGS

[0042] The drawings described herein are used to provide further understanding of the embodiments of the present application, form a part of the present application, and do not constitute a limitation on the embodiments of the present application. In the drawings:

[0043] Figure 1 A flowchart of a power system transient voltage prediction method provided by the embodiments of the present application is shown in the figure.

[0044] Figure 2 A relationship diagram of risk value and stability margin provided by the embodiments of the present application is shown in the figure. DETAILED DESCRIPTION

[0045] In order to make the purpose, technical scheme and advantages of the present application more clear, the present application is further described in detail below in combination with embodiments and drawings, the illustrative embodiments of the present application and the description thereof are only used to explain the present application, and do not constitute a limitation on the present application.

[0046] It should be noted that the term "include" or "may include" used in various embodiments of the present application indicates the existence of the claimed function, operation or element, and does not limit the addition of one or more functions, operations or elements. In addition, as used in various embodiments of the present application, the terms "include", "have" and their synonyms only mean to indicate specific features, numbers, steps, operations, elements, components or combinations of the foregoing, and should not be understood as first excluding the existence or addition of one or more other features, numbers, steps, operations, elements, components or combinations of the foregoing.

[0047] It should be understood that terms such as "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0048] Figure 1 This is a flowchart illustrating a power system transient voltage prediction method provided in an embodiment of the present invention, as shown below. Figure 1 As shown, the method includes:

[0049] S101, acquire the voltage signal of the current timing of the power system.

[0050] In this embodiment, the method of obtaining the voltage signal is common knowledge in the technical field, and will not be described in detail here.

[0051] S102, based on the pre-determined optimal weights of the observation function combination, the optimal observation function is selected from the basis function space corresponding to the voltage signal of the current time series. The process for determining the optimal weights of the observation function combination is as follows: Obtain the voltage signal and actual state measurement results of the power system's historical time series; decompose the historical time series voltage signal using the empirical mode decomposition method to obtain intrinsic mode components; analyze the time-frequency characteristics of the intrinsic mode components to determine the observation function space used to approximate the dynamic characteristics of the transient voltage; solve for the Koopman operator based on the observation functions in the observation function space and calculate the variance of the eigenvalues ​​decomposed by the Koopman operator; predict the power system state based on the observation functions and the Koopman operator to obtain the state prediction result, and calculate the prediction residual based on the state prediction result and the actual state measurement results; dynamically adjust the weights of the observation function combination in the observation space using the gradient descent method until the sum of the variance and the prediction residual reaches its minimum value, thus obtaining the optimal weights of the observation function combination.

[0052] In this embodiment, the traditional Koopman theory is expressed as follows: Koopman theory maps the evolution of a nonlinear dynamic system to an infinite-dimensional linear operator space. Through spectral analysis of the Koopman operators, the dominant modes of the system can be extracted using only short-time measurement data, enabling rapid trajectory prediction. Specifically, the system's state equation is assumed to be: (1), where, For the system in the first A state vector at discrete moments. For the system in the first The state vector at each discrete moment, i.e., the next moment. is the state transition function, describing how to map the state at the current time to the state at the next time.

[0053] Koopman operator is able to map the state of a nonlinear system to its linearized representation , i.e.

[0054] (2).

[0055] In prediction, the Koopman operator can linearly propagate the state by iteration: (3), where is the state vector of the system at the discrete time, is the power of the Koopman operator, representing the linear evolution described by applying the Koopman operator n times successively to the observed state.

[0056] Although the above traditional Koopman theory can realize trajectory prediction of nonlinear systems, when applied to complex power systems, there are still problems such as insufficient adaptability of basis functions, tracking lag of time-varying characteristics, and accumulation of multi-source errors. In view of the above three problems, the following three improvement measures are proposed:

[0057] In the basis function optimization link, first, the empirical mode decomposition (EMD) is used to process the voltage signal, and a basis function space covering polynomial, Gaussian radial basis function and trigonometric function is initialized in a multi-scale feature guided manner, to ensure that the slow change, high frequency oscillation and periodic fluctuation and other dynamic characteristics of the voltage can be covered; further, an adaptability evaluation function is constructed with the stability of the Koopman operator eigenvalue and the minimization of the prediction residual as the target, and the combination weight of each basis function is dynamically adjusted by the gradient descent method, so that the observation space can adaptively match the current nonlinear characteristics of the system. Specifically, the voltage signal can be expressed as:

[0058] (4), where is the voltage signal, is the th intrinsic mode function, is the number of decomposed intrinsic mode functions, which is determined by the complexity of the original voltage signal and the result of empirical mode decomposition, is the residual term. Based on the time-frequency characteristics of the IMF component, three types of basis function spaces are initialized:

[0059] 1) Polynomial basis function, used to adapt to the slow trend of the voltage.

[0060] 2) Gaussian radial basis function (RBF), which fits the high-frequency oscillation of the voltage.

[0061] 3) Trigonometric basis function, which fits the periodic fluctuation of the voltage.

[0062] This EMD-based basis function initialization strategy ensures that the function space (denoted as the observation function mentioned in equation (2) and equation (3)) has the ability to cover the main dynamic characteristics of the system, laying the foundation for subsequent high-precision Koopman operator solving.

[0063] Then an optimization process is constructed to minimize the stability variance of the eigenvalues after Koopman operator spectral decomposition + prediction residual, and the combination weight of the basis function is dynamically adjusted by gradient descent method. The objective function of this optimization process is: (5), where is the weight of the observation function combination, is the variance operation, is the eigenvalue of the Koopman operator, is the state prediction result obtained by predicting the power system state according to the observation function and the Koopman operator, is the actual result of the state of the power system.

[0064] The contribution of EMD decomposition to the accuracy of the final prediction value is realized through this optimization process: the basis function space with clear physical meaning generated by EMD guidance provides a high-quality initial value close to the global optimum for the optimization problem of equation (5). By solving this problem by gradient descent method, we finally obtain a set of optimal basis function weights (i.e. the optimization result of equation (5)), which defines an optimal observation function This observation function can achieve the following two specific benefits.

[0065] Guides to solve an optimal Koopman operator that is both stable and accurate.

[0066] When performing linear prediction in the state space , the true evolution of the system can be restored to the greatest extent.

[0067] S103, estimate the optimal Koopman operator according to the optimal observation function, and predict the trajectory curve of the future time series transient voltage of the power system combining the optimal observation function and the optimal Koopman operator.

[0068] In this embodiment, the specific implementation process of estimating the optimal Koopman operator using the optimal observation function is common knowledge in the technical field; therefore, this embodiment will not provide further description. Secondly, regarding the process of predicting the trajectory curve of the future time-series transient voltage of the power system by combining the optimal observation function and the optimal Koopman operator, it can be implemented using the linear prediction method in the state space described above; this embodiment will not provide further description.

[0069] In some embodiments, while estimating the optimal Koopman operator based on the optimal observation function, the method further includes:

[0070] If the rate of change of the amplitude of the voltage signal in the current time series is greater than the rate of change threshold, the optimal Koopman operator is re-estimated based on the optimal observation function;

[0071] If the similarity between the extracted Koopman pattern and the historical typical pattern is lower than the similarity threshold, the optimal Koopman operator is re-estimated based on the optimal observation function.

[0072] Specifically, the traditional Koopman theory defines the dynamic rate of change of a system. This is achieved by calculating the sum of the absolute values ​​of the voltage change slopes of adjacent measurement data: (6).

[0073] according to Adjust the value of the sliding window width. : (7), among which, It is the threshold of the system's dynamic rate of change.

[0074] Based on the traditional recursive sliding window timed update, two types of triggering conditions are added: First, measurement data mutation triggering: when the rate of change of voltage amplitude exceeds the rate of change threshold (such as 0.05 pu / ms, 0.06 pu / ms, etc.), operator re-estimation is immediately initiated. Second, Koopman pattern deviation triggering: when the similarity between the extracted Koopman pattern and the historical typical pattern is lower than the similarity threshold (such as 0.85, 0.86, etc.), operator re-estimation is immediately initiated.

[0075] In some embodiments, the method further includes: acquiring actual measurement results of the state of the power system in future time series; determining the deviation between the actual measurement results of the state in future time series and the state prediction results of future time series; and dynamically correcting the state prediction results of the next time series based on the deviation.

[0076] Specifically, in the error correction link, the deviation compensation model based on the operator spectrum characteristics is constructed to correct the attenuation and oscillation frequency deviation of the eigenvalue in advance; and the rolling optimization idea of model predictive control is introduced in the trajectory prediction stage, and the deviation between the latest measurement value and the predicted value is used to form a dynamic correction term, which is fed back to the subsequent prediction, thereby effectively suppressing the error accumulation in long-term prediction. Finally, the prediction model outputs a high-precision transient voltage prediction trajectory in the future period. Specifically, based on the Koopman operator spectrum characteristic analysis, the dynamic correction term is introduced, and the rolling optimization idea of predictive control is adopted, so that the expression for dynamically correcting the state prediction result of the next time sequence according to the deviation of the future time sequence is determined as:

[0077] (8), wherein, wherein, is the state prediction result of the future time sequence of the power system, is the state prediction result of the next time sequence of the future time sequence of the power system, is the actual measurement result of the state of the future time sequence of the power system, is a dynamic weight, is the Koopman operator.

[0078] The embodiment feeds back the difference between the actual measurement value and the predicted value to adjust the next step of prediction, thereby ensuring the accuracy of long-term prediction.

[0079] In combination with the above-described embodiments, the improved Koopman model of the present application can more accurately capture the dynamic evolution characteristics of transient voltage through the adaptive optimization of basis functions, dynamic updating of operators and multi-stage error correction mechanism. Compared with the traditional Koopman method, the prediction accuracy of the trajectory can be effectively improved, and the adaptive ability to the complex variable characteristics of the strong nonlinear system is stronger.

[0080] The online prediction method based on improved Koopman theory described above can accurately depict the transient voltage trajectory of a system after a disturbance. However, describing the dynamic trajectory is insufficient for a comprehensive assessment of stability. Further, rapid determination of transient voltage stability is crucial for ensuring the safe operation of the power system. However, traditional binary classification methods can only provide a conclusion of "stable" or "instable," failing to quantify the system's stability and making it difficult to provide early warnings for vulnerable bus nodes in critical states. Therefore, it is urgent to extract effective criteria for quantifying stability from trajectory information. This invention also provides a method for analyzing the transient voltage risk of a power system, comprising: acquiring the trajectory curve of the future time-series transient voltage of the power system; wherein the trajectory curve of the future time-series transient voltage of the power system is predicted based on a power system transient voltage prediction method described above; calculating a transient voltage stability quantification index for any bus node based on the trajectory curve; taking the maximum value of the transient voltage stability quantification index as the stability margin of the power system transient voltage; and comparing the stability margin with a preset margin threshold range to determine the stability analysis result of the power system transient voltage.

[0081] At the bus node level, for any bus node in the system Its transient voltage stability quantification index The definition is as follows:

[0082] (9), among which, It is the fault clearing moment, that is, the starting point of the transient process. This is the end point of the delayed recovery feature. This is the end point of the sustained low voltage characteristic. It is a node The rated reference value of the voltage. It is a node At any moment voltage amplitude, These are weighting coefficients, and their values ​​are determined according to the following rules:

[0083] (10) Where S is a function consisting of several parameters, and its explicit expression is:

[0084] (11), among which, This is the lower limit of DC current. This is the lower limit of DC voltage. Where is the upper limit of DC voltage, and T is the fault duration. denoted as voltage drop depth, and b is a constant term used for adjustment.

[0085] At the system level, define the system transient voltage stability margin. The maximum indicator value among all monitored nodes is:

[0086] (12), where a is the calculated number of node buses.

[0087] By setting a margin threshold interval, the system state can be classified into three levels in detail as follows:

[0088] 1) Stable zone , the stability margin is sufficient, and the instability is extremely low.

[0089] 2) Warning zone , the system stability margin decreases, there is a potential risk of instability, and attention should be paid.

[0090] 3) Instability zone , the system has lost transient voltage stability, and control measures should be taken immediately.

[0091] At the same time, by analyzing the of each bus node, the weak nodes in the system can be clearly identified, that is the node with the maximum value or close to 1, providing a target for precise prevention and control.

[0092] In some embodiments, the method further comprises: constructing a risk function with a segmented exponential function characteristic; wherein the value range of the segmented exponential function corresponds to the margin threshold interval; combining the stability margin and the risk function to determine the risk value of power system instability; discretizing the risk value to determine the risk level of power system instability.

[0093] Specifically, in actual power engineering operation scenarios, operation personnel not only need to obtain the specific quantitative value of the margin, but also need to clearly understand the transient voltage instability risk degree corresponding to the margin, and what level of response measures should be taken according to the risk degree. It is the key technology to achieve active safety defense of transient voltage to accurately convert the continuous transient voltage stability margin, which is a physical quantity, into discrete and operable decision instructions (i.e. risk level). Based on this, this step focuses on the connection between "transient voltage quantitative evaluation" and "operation decision guidance", and constructs a complete and scientific transient voltage risk quantitative and graded warning system.

[0094] First, define a risk function that satisfies the following mathematical characteristics :

[0095] (13), where is the first and second derivatives of the risk function with respect to the margin indicator . The rule of this function is that the risk value R increases with the margin indicator The increase of the risk value R, i.e., the deterioration of the stability, is accelerated, and the risk value R increases at a higher rate. The mathematical expression of the risk function with the segmented exponential function characteristics is derived and constructed Figure 2 , and the function relationship is shown in the accompanying .

[0096] (14), and then the voltage stability condition is divided into three regions:

[0097] 1) completely stable region , the risk value R is 0, and the system has no risk of instability.

[0098] 2) risk transition region , the risk value R increases from 0 to 3 at a nonlinear rate. The exponential form ensures the sharp change of the risk near the critical point.

[0099] 3) completely unstable region , the risk value R is always the maximum value 3, which represents that the system has lost control.

[0100] In order to realize efficient and intuitive decision support, the continuous risk value R is divided into five discrete risk levels :

[0101] (15), in formula (15), when , the system is in a super stable state and has no risk of transient voltage instability; when , the system is in a good running state and has a small risk of transient voltage instability; when , the system is in a general running state and has a certain risk of transient voltage instability; when , the system is in a state close to instability and has a great risk of instability; and when , the system is in an unstable state and needs to take corresponding control measures immediately.

[0102] The embodiment of the application also provides a power system transient voltage prediction system, and the system comprises:

[0103] a voltage signal acquisition module, configured to acquire a voltage signal of a current time sequence of the power system;

[0104] ​The observation function selection module is configured to select an optimal observation function from a basis function space corresponding to a current time sequence voltage signal according to optimal weights of a predetermined observation function combination; wherein the optimal weights of the observation function combination are determined as follows: obtaining historical time sequence voltage signals and state actual measurement results of the power system; decomposing the historical time sequence voltage signals based on an empirical mode decomposition method to obtain intrinsic mode components; analyzing a time-frequency characteristic of the intrinsic mode components to obtain an observation function space for approximating transient voltage dynamic characteristics; solving a Koopman operator based on the observation functions in the observation function space and calculating variances of eigenvalues decomposed by the Koopman operator; predicting the state of the power system according to the observation functions and the Koopman operator to obtain state prediction results, and calculating prediction residuals according to the state prediction results and the state actual measurement results; dynamically adjusting the weights of the observation function combination in the observation space by a gradient descent method until a sum function of the variances and the prediction residuals reaches a minimum value to obtain the optimal weights of the observation function combination;

[0105] The transient voltage prediction module is configured to estimate an optimal Koopman operator according to the optimal observation function, and predict a trajectory curve of a future time sequence transient voltage of the power system in combination with the optimal observation function and the optimal Koopman operator.

[0106] It should be noted that the power system transient voltage prediction system provided by the embodiment of the present application is a scheme belonging to the same inventive concept as the power system transient voltage prediction method described in the above embodiment, and therefore, the implementation process of each module included in the power system transient voltage prediction system is not described in detail.

[0107] Correspondingly, the traditional Koopman theory maps the evolution of a nonlinear dynamic system to an infinite-dimensional linear operator space, and through spectral analysis of the Koopman operator, the dominant mode of the system can be extracted using only short-term measurement data, and fast trajectory prediction can be achieved. Although the traditional Koopman theory can realize trajectory prediction of a nonlinear system, when applied to a complex power system, there are still problems such as insufficient adaptability of basis functions, tracking lag of time-varying characteristics, and accumulation of multi-source errors, thereby the traditional Koopman method has weak generalization ability, dynamic tracking lag, and error accumulation. To solve the problems of weak generalization ability, dynamic tracking lag, and error accumulation of the traditional Koopman method, the first aspect of the present application provides a power system transient voltage prediction method, which optimizes the basis function adaptively, dynamically updates the operator, and corrects the multi-stage error, thereby improving the trajectory prediction accuracy and long-period characterization ability of the transient voltage. First, in the basis function optimization link, the historical time series voltage signal is processed by using empirical mode decomposition, and a multi-scale feature guided mode is used to initialize an observation function space covering polynomial, Gaussian radial basis function and trigonometric function, so as to ensure that the dynamic characteristics of the voltage such as slow change, high-frequency oscillation and periodic fluctuation can be covered; further, an adaptability evaluation function is constructed with the minimum prediction residual and the stability variance of the eigenvalue of the Koopman operator as the target, and the gradient descent method is used to dynamically adjust the combination weight of each basis function, so that the observation space can adaptively match the current nonlinear characteristics of the power system. Secondly, in the operator dynamic updating link, in order to overcome the response lag of the traditional method, a multi-source triggering mechanism is designed, which not only adaptively adjusts the data window width for estimating the Koopman operator according to the dynamic change rate of the system, but also introduces two instant restart conditions of measurement data mutation triggering (when the voltage change rate exceeds the threshold) and Koopman mode deviation triggering (when the cosine similarity between the real-time extracted mode and the historical typical mode is lower than the threshold), thereby shortening the Koopman operator update delay to within 10 milliseconds, and significantly enhancing the tracking ability of the fast time-varying process of the power system. Finally, in the error correction link, the rolling optimization idea of model predictive control is introduced in the trajectory prediction stage, and the deviation between the latest measurement value and the prediction value is used to form a dynamic correction term, which is fed back to the subsequent prediction, thereby effectively suppressing the error accumulation in long-term prediction, and accurately depicting the prediction trajectory curve of the transient voltage in the future period.

[0108] The embodiment of the present application also provides a power system transient voltage risk analysis system, which comprises:

[0109] A trajectory curve acquisition module is configured to acquire a trajectory curve of future time series transient voltage of a power system, wherein the trajectory curve of future time series transient voltage of the power system is predicted based on the power system transient voltage prediction system provided in the third aspect of the present application.

[0110] a quantitative index calculation module configured to calculate a transient voltage stability quantitative index of any bus node according to the trajectory curve;

[0111] a stability margin determination module configured to take the maximum value of the transient voltage stability quantitative index as a stability margin of the transient voltage of the power system;

[0112] an analysis module configured to compare the stability margin with a preset margin threshold interval to determine a stability analysis result of the transient voltage of the power system.

[0113] It should be noted that the power system transient voltage risk analysis system provided by the embodiment of the present application is a scheme belonging to the same inventive concept as the power system transient voltage risk analysis method described in the above embodiment, and therefore, the embodiment does not make a detailed description of the implementation process of each module included in the power system transient voltage risk analysis system.

[0114] Accordingly, the traditional binary classification discrimination mode can only give a conclusion of stability or instability, cannot quantify the stability degree of the system, and is difficult to give a warning for the vulnerable bus node in a critical state, and therefore, the second aspect of the present application provides a power system transient voltage risk analysis method for extracting an effective criterion capable of quantifying the stability degree from the predicted transient voltage trajectory curve, i.e., using the transient voltage stability quantitative index to define the distance between the current state and the instability boundary, which can quantize the stability degree of the node and the system continuously, avoid misjudgment caused by a single threshold or fixed criterion, accurately locate the weak bus node of the system, convert the continuous stability margin index into an intuitive discrete risk level, and form a closed-loop logic of "prediction-quantification-warning". The operation personnel can directly match the prevention and control strategy according to the risk level, compared with the traditional warning mode lacking a grading mechanism, can more efficiently support decision-making, and enhance the ability of the power grid to actively identify and prevent the transient voltage risk.

[0115] The above specific embodiments further specifically describe the purposes, technical solutions and beneficial effects of the present application, and it should be understood that the above description is only a specific embodiment of the present application and is not used to limit the protection scope of the present application, and any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application should be included in the protection scope of the present application.

Claims

1. A method for predicting transient voltage in a power system, characterized in that, The methods include: Obtain the voltage signal of the power system at the current time sequence; Based on the predetermined optimal weights of the observation function combination, the optimal observation function is selected from the basis function space corresponding to the voltage signal of the current time series. The process of determining the optimal weights of the observation function combination is as follows: obtain the voltage signal and actual state measurement results of the power system in the historical time series; decompose the voltage signal of the historical time series based on the empirical mode decomposition method to obtain the intrinsic mode components; analyze the time-frequency characteristics of the intrinsic mode components to determine the observation function space used to approximate the dynamic characteristics of the transient voltage. The Koopman operator is derived from the observation functions in the observation function space, and the variance of the eigenvalues ​​decomposed by the Koopman operator is calculated. The state of the power system is predicted based on the observation functions and the Koopman operator, and the state prediction result is obtained. The prediction residual is calculated based on the state prediction result and the actual state measurement result. The weights of the combination of observation functions in the observation space are dynamically adjusted by the gradient descent method until the sum of the variance and the prediction residual reaches the minimum value, thus obtaining the optimal weights of the combination of observation functions. The optimal Koopman operator is estimated based on the optimal observation function, and the trajectory curve of the future time-series transient voltage of the power system is predicted by combining the optimal observation function and the optimal Koopman operator.

2. The method for predicting transient voltage in a power system according to claim 1, characterized in that, The basis function space includes three types of basis functions: polynomial basis functions, Gaussian radial basis functions, and trigonometric basis functions.

3. The method for predicting transient voltage in a power system according to claim 1, characterized in that, The expression for the summation function is: ,in, The weights of the observation function combination, For variance calculation, These are the eigenvalues ​​of the Koopman operator. The state prediction results are obtained by predicting the power system state based on the observation function and the Koopman operator. This represents the actual state of the power system.

4. The method for predicting transient voltage in a power system according to claim 1, characterized in that, While estimating the optimal Koopman operator based on the optimal observation function, the method also includes: If the rate of change of the amplitude of the voltage signal in the current time series is greater than the rate of change threshold, the optimal Koopman operator is re-estimated based on the optimal observation function; If the similarity between the extracted Koopman pattern and the historical typical pattern is lower than the similarity threshold, the optimal Koopman operator is re-estimated based on the optimal observation function.

5. A method for predicting transient voltage in a power system according to any one of claims 1 to 4, characterized in that, The method further includes: Obtain actual measurement results of the future time-series state of the power system; Determine the deviation between the actual measured state of the future time series and the predicted state of the future time series; The state prediction results of the next time series in the future time series are dynamically corrected based on the deviation.

6. The method for predicting transient voltage in a power system according to claim 5, characterized in that, The expression for dynamically correcting the state prediction result of the next time series based on the deviation is as follows: ,in, This is a prediction of the future time-series state of the power system. This refers to the state prediction results for the next time series of the power system in the future time series. It is the actual measurement result of the future time sequence state of the power system. For dynamic weights, This is the Koopman operator.

7. A method for analyzing transient voltage risks in a power system, characterized in that, The methods include: The trajectory curve of the future time-series transient voltage of the power system is obtained; wherein the trajectory curve of the future time-series transient voltage of the power system is predicted based on a power system transient voltage prediction method as described in any one of claims 1 to 6; The transient voltage stability quantification index of any bus node is calculated based on the trajectory curve. The maximum value of the transient voltage stability quantification index is taken as the stability margin of the power system transient voltage. The stability margin is compared with the preset margin threshold range to determine the stability analysis results of the power system transient voltage.

8. The method for transient voltage risk analysis in a power system according to claim 7, characterized in that, The method further includes: Construct a risk function with piecewise exponential function characteristics; wherein the range of values ​​of the piecewise exponential function corresponds to the margin threshold interval; By combining stability margin and risk function, the risk value of power system instability is determined; Discretize the risk values ​​to determine the risk level of power system instability.

9. A power system transient voltage prediction system, characterized in that, The system includes: The voltage signal acquisition module is used to acquire the voltage signal of the power system at the current time. The observation function selection module is used to select the optimal observation function from the basis function space corresponding to the voltage signal of the current time series based on the optimal weights of the pre-determined combination of observation functions. The process of determining the optimal weights of the observation function combination is as follows: Obtain the voltage signal and actual state measurement results of the power system's historical time series; decompose the historical time series voltage signal using the empirical mode decomposition method to obtain intrinsic mode components; analyze the time-frequency characteristics of the intrinsic mode components to determine the observation function space used to approximate the dynamic characteristics of the transient voltage; solve for the Koopman operator based on the observation functions in the observation function space and calculate the variance of the eigenvalues ​​decomposed by the Koopman operator; predict the power system state based on the observation functions and the Koopman operator to obtain the state prediction result, and calculate the prediction residual based on the state prediction result and the actual state measurement results; dynamically adjust the weights of the observation function combination in the observation space using the gradient descent method until the sum of the variance and the prediction residual reaches its minimum value, thus obtaining the optimal weights of the observation function combination. The transient voltage prediction module is used to estimate the optimal Koopman operator based on the optimal observation function, and combine the optimal observation function and the optimal Koopman operator to predict the trajectory curve of the future time-series transient voltage of the power system.

10. A power system transient voltage risk analysis system, characterized in that, The system includes: The trajectory curve acquisition module is used to acquire the trajectory curve of the future time-series transient voltage of the power system; wherein, the trajectory curve of the future time-series transient voltage of the power system is obtained based on the prediction of the power system transient voltage prediction system as described in claim 9; The quantitative index calculation module is used to calculate the transient voltage stability quantitative index of any bus node based on the trajectory curve. The stability margin determination module is used to take the maximum value of the transient voltage stability quantification index as the stability margin of the power system transient voltage. The analysis module is used to compare the stability margin with a preset margin threshold range to determine the stability analysis results of the power system transient voltage.

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