A data-driven complex power grid harmonic state estimation method and system

Abstract

This invention relates to the field of power system technology, and in particular to a data-driven method and system for estimating the harmonic state of complex power grids. The method includes: acquiring statistical harmonic monitoring data uploaded by a power quality monitoring device, extracting and constructing interval-type harmonic measurement samples; establishing an interval dynamic harmonic state estimation model considering the uncertainty of harmonic state based on the measurement samples, and obtaining the harmonic prediction equation and harmonic measurement equation; establishing an interval fundamental wave state estimation model based on the interval-type fundamental wave measurement value at the initial time, and obtaining the starting value for interval dynamic harmonic state estimation; recursively solving the interval dynamic harmonic state estimation model using an improved extended interval Kalman filter algorithm to obtain the corrected interval state variables; and performing a robust filtering mechanism based on interval constraints to verify the rationality of each actual measurement interval and adaptively adjust its weight in the filter update to obtain a contracted measurement interval.

Description

Technical Field

[0001] This invention relates to the field of power system technology, and in particular to a data-driven method and system for estimating the harmonic state of complex power grids. Background Technology

[0002] With the large-scale integration of distributed energy sources, such as wind power and photovoltaics, and various power electronic converters into power systems, harmonic pollution of the power grid has become increasingly prominent, exhibiting new characteristics of decentralization, wide frequency domain, and strong time-varying properties. Severe harmonic pollution can lead to overheating of power equipment, insulation damage, local resonance in the system, and even malfunction of protection devices, threatening the safe and stable operation of the power grid. Therefore, real-time and accurate understanding of the harmonic distribution across the entire grid, i.e., harmonic state estimation, is of crucial engineering significance for harmonic source tracing, responsibility allocation, and mitigation decisions.

[0003] Currently, research on harmonic state estimation mainly relies on wide-area measurement systems (PMUs). Using synchronized phasor data, traditional nonlinear harmonic state estimation models can be linearized, significantly reducing model complexity and facilitating solutions. However, PMU devices are expensive and typically deployed only at critical substations or power plant nodes, making it difficult to cover the entire transmission and distribution network, often resulting in the system failing to meet observability requirements. In such cases, the estimation model built based on synchronized phasor data is an underdetermined equation with a non-unique solution. The estimation accuracy of these methods is highly dependent on the location and number of measurement points, as well as the sparsity assumption of harmonic source distribution, making it difficult to guarantee stable and reliable performance in complex real-world power grids.

[0004] In contrast, power quality monitoring devices are less expensive, easier to deploy on a large scale on the distribution network side, and can provide massive amounts of monitoring data, making it easier to meet the observability requirements of state estimation. However, they have a key drawback: the data from different monitoring devices are asynchronous. Their harmonic phase angles are all referenced to the fundamental phase angle of the device's local location, and there is no unified time-scale alignment between different devices, making it impossible to construct cross-sectional data at the same moment.

[0005] Directly substituting this asynchronous statistical data into traditional deterministic harmonic state estimation models will produce huge fundamental errors, rendering the estimation results unusable. Current technologies often have to discard the statistical information or simply perform averaging when processing such data, resulting in a significant waste of useful information. Therefore, overcoming the asynchronous nature of the data and fully exploring and effectively utilizing massive amounts of statistical monitoring data for high-precision harmonic state estimation is a pressing technical challenge in the field of power engineering.

[0006] The information disclosed in this background section is intended only to enhance the understanding of the overall background of the present invention and should not be construed as an admission or in any way implying that the information constitutes prior art known to those skilled in the art. Summary of the Invention

[0007] The technical problem to be solved by this invention is to provide a data-driven method and system for estimating the harmonic state of complex power grids, which transforms the inherent uncertainty of asynchronous data into interval numbers for modeling, and achieves high-precision dynamic tracking of the harmonic state through an innovative robust interval Kalman filter framework.

[0008] To achieve the above objectives, the technical solution adopted by this invention is: a data-driven method for estimating the harmonic state of complex power grids, comprising the following steps: Acquire statistical harmonic monitoring data uploaded by power quality monitoring devices, and extract and construct interval-type harmonic measurement samples; Based on the measured samples, an interval dynamic harmonic state estimation model considering the uncertainty of harmonic state is established, and the harmonic prediction equation and harmonic measurement equation are obtained. Based on the initial interval fundamental wave measurement, an interval fundamental wave state estimation model is established to obtain the starting value for interval dynamic harmonic state estimation. An improved extended interval Kalman filter algorithm is used to recursively solve the interval dynamic harmonic state estimation model to obtain the corrected interval state variables. The robust filtering mechanism based on interval constraints verifies the rationality of each actual measurement interval and adaptively adjusts its weight in the filter update to obtain a shrinking measurement interval. The contraction measurement interval is used to participate in the filter update, and the interval harmonic state quantity of each node is output.

[0009] Furthermore, the statistical harmonic monitoring data includes the harmonic voltage amplitude, harmonic voltage phase angle, maximum and minimum values ​​of harmonic active power and harmonic reactive power at each monitoring point within the statistical period.

[0010] Furthermore, the interval-type harmonic measurement sample The vector form is represented as: ; in, Injecting harmonic active power into the nodes Injecting harmonic reactive power into the nodes, For branch harmonic active power, For branch harmonic reactive power, This represents the amplitude of the node harmonic voltage.

[0011] Furthermore, the expressions for the harmonic prediction equation and the harmonic measurement equation are as follows: ; ; in, For based on The state quantity predicted at time step The harmonic state quantities of the time-prior interval include the harmonic voltage amplitude and phase angle of each node; This is the state transition function; This is a nonlinear harmonic measurement function; For prediction error, For measuring noise.

[0012] Furthermore, the interval fundamental state estimation model is as follows: ; in, For the fundamental phase angle at each node, except for the reference node, a possible interval for the phase angle can be solved. ; For nodes The lower and upper limits of the fundamental-wave injected active power; For nodes The lower and upper limits of the fundamental-wave injected reactive power; For nodes and The lower and upper limits of the fundamental active power of the intermediate branches; For nodes and The lower and upper limits of the fundamental reactive power of the intermediate branches; For nodes The lower and upper limits of the fundamental voltage amplitude; Inject power estimates into the nodes; This is an estimate of the branch power; This is the calculated value of the node voltage amplitude; For reference node constraints; By solving the interval fundamental wave state estimation model, the interval values ​​of the fundamental wave phase angle at each node are obtained. .

[0013] Furthermore, obtaining the starting value for interval dynamic harmonic state estimation includes the following steps: The interval values ​​of the fundamental phase angle at each node are solved using linear programming. ; Synchronization processing is performed on the phase angles of asynchronous harmonics to obtain the starting values ​​for interval dynamic harmonic state estimation. The synchronization processing formula is: ; in, The phase angle of the asynchronous harmonics. This represents the phase angle of the harmonics in the synchronized interval.

[0014] Furthermore, the improved extended interval Kalman filter algorithm is used to recursively solve the interval dynamic harmonic state estimation model to obtain the corrected interval state variables; this includes the following steps: according to The posterior interval estimate at time k+1 is used to predict the interval prior state variables and prior error covariance matrix at time k+1. Construct an affine covariance propagation based on interval prior state variables and calculate the deterministic prior error covariance matrix; A linearized approximate expression is constructed for the measurement function based on the affine form of the prior state variables in the interval; An update formula for affine coefficients is constructed based on the Kalman filter framework. The predicted state at time k+1 is updated using the new measurement value to obtain the affine form reconstruction of the corrected interval state variables.

[0015] Furthermore, the corrected interval state variables are reconstructed in affine form as follows: ; in, For the corrected interval harmonic state quantity, the subscript is... Represents harmonics, Indicates the use of After correcting the measured values ​​at time, The final estimate of the state at time step; This is the midpoint value of the corrected state variable interval; For the corrected first Noise symbol variables The coefficient.

[0016] Furthermore, the robust filtering mechanism based on interval constraints performs a rationality check on each actual measurement interval and adaptively adjusts its weight in the filter update to obtain a shrunken measurement interval; this includes the following steps: Obtain the predicted state interval, and calculate the predicted interval of each interval-type fundamental wave measurement value according to the harmonic measurement equation, and verify the rationality of the predicted interval; Based on a smooth weight adjustment strategy, the weights of the interval-type fundamental wave measurements that are deemed unreasonable are updated in the filter update using confidence factors and measurement noise covariance matrix. The measurement interval is shrunk using the predicted interval to obtain the shrunk measurement interval.

[0017] Furthermore, the reasonableness of the predicted interval is verified, including the following steps: If the actual measurement interval With the prediction interval If there is an intersection, the interval-type fundamental wave measurement value corresponding to the predicted interval is considered normal; If there is no intersection, the measured value of the interval type fundamental wave is determined to be unreasonable.

[0018] Furthermore, the smoothing-based weight adjustment strategy updates the weights of the interval-type fundamental wave measurements deemed unreasonable in the filter update using confidence factors and the measurement noise covariance matrix; this includes the following steps: A smooth weighting strategy is adopted, and the confidence factor is defined. For the One measurement quantity: ; in Indicates the interval length; the confidence factor reflects the degree of overlap between the actual measurement interval and the predicted interval, when they completely overlap. When there is no overlap ; Apply the confidence factor to the measurement noise covariance matrix: ; in This is the original measurement noise covariance matrix. This is the adjusted matrix; when the confidence factor At that time, corresponding to the first The noise variance of each measurement is amplified.

[0019] The present invention also provides a data-driven system for estimating the harmonic state of complex power grids, comprising: The data acquisition module is used to acquire statistical harmonic monitoring data uploaded by the power quality monitoring device, and extract and construct interval harmonic measurement samples; The model building module is used to establish an interval dynamic harmonic state estimation model that considers the uncertainty of harmonic state based on the measurement samples, and to obtain the harmonic prediction equation and the harmonic measurement equation. The start-up value calculation module is used to establish an interval fundamental wave state estimation model based on the interval fundamental wave measurement value at the initial time, and obtain the start-up value for interval dynamic harmonic state estimation. The filtering estimation module is used to recursively solve the interval dynamic harmonic state estimation model using an improved extended interval Kalman filter algorithm to obtain the corrected interval state variables. The robust constraint module is used for a robust filtering mechanism based on interval constraints. It performs a rationality check on each actual measurement interval and adaptively adjusts the weights in the filter update to obtain a shrinking measurement interval. The status output module is used to participate in the filter update using the contraction measurement interval and output the interval harmonic status quantity of each node.

[0020] The beneficial effects of this invention are as follows: By introducing the affine covariance propagation method, this invention transforms the interval state variables into affine form, and directly calculates the deterministic covariance matrix from the affine coefficients, avoiding the expansion effect of the interval gain matrix; at the same time, by combining affine arithmetic to preserve the consistency of noise symbol variables in the correction process, the correlation between the variables of the state variables is naturally taken into account; by constructing a robust filtering mechanism based on interval constraints, bad data is identified online by utilizing the degree of overlap between the measurement interval and the prediction interval, and the measurement noise covariance matrix and the measurement interval itself are adaptively adjusted, effectively isolating the interference of abnormal measurement values ​​on the filter update, and ensuring the stability of harmonic state estimation in complex field environments. Attached Figure Description

[0021] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0022] Figure 1 This is a flowchart illustrating the data-driven harmonic state estimation method for complex power grids in an embodiment of the present invention. Figure 2 This is a schematic diagram of the structure of a data-driven complex power grid harmonic state estimation system in an embodiment of the present invention. Detailed Implementation

[0023] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0024] It should be noted that when an element is referred to as being "fixed to" another element, it can be directly attached to the other element or there may be an intervening element. When an element is referred to as being "connected to" another element, it can be directly connected to the other element or there may be an intervening element. The terms "vertical," "horizontal," "left," "right," and similar expressions used herein are for illustrative purposes only and do not represent the only possible implementation.

[0025] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0026] like Figure 1 The data-driven harmonic state estimation method for complex power grids, as shown, includes the following steps: Acquire statistical harmonic monitoring data uploaded by power quality monitoring devices, and extract and construct interval-type harmonic measurement samples; Based on the measurement samples, an interval dynamic harmonic state estimation model considering the uncertainty of harmonic state is established, and the harmonic prediction equation and harmonic measurement equation are obtained. Based on the initial interval fundamental wave measurement, an interval fundamental wave state estimation model is established to obtain the starting value for interval dynamic harmonic state estimation. An improved extended interval Kalman filter algorithm is used to recursively solve the interval dynamic harmonic state estimation model to obtain the corrected interval state variables. The robust filtering mechanism based on interval constraints verifies the rationality of each actual measurement interval and adaptively adjusts its weight in the filter update to obtain a shrinking measurement interval. The shrinking measurement interval is used to participate in the filter update, and the interval harmonic state quantity of each node is output.

[0027] This invention introduces an affine covariance propagation method to transform interval state variables into affine forms, directly calculating the deterministic covariance matrix from the affine coefficients, thus avoiding the expansion effect of the interval gain matrix. Simultaneously, by combining affine arithmetic to preserve the consistency of noise sign variables in the correction process, the correlation between various state variables is naturally taken into account. Furthermore, by constructing a robust filtering mechanism based on interval constraints, bad data is identified online using the overlap between the measurement and prediction intervals, and the measurement noise covariance matrix and the measurement interval itself are adaptively adjusted. This effectively isolates the interference of abnormal measurements on filter updates, ensuring the stability of harmonic state estimation in complex field environments.

[0028] Based on the above embodiments, the statistical harmonic monitoring data includes the maximum and minimum values ​​of harmonic voltage amplitude, harmonic voltage phase angle, harmonic active power, and harmonic reactive power at each monitoring point within the statistical period.

[0029] In this step, by extracting the maximum and minimum values ​​of harmonic voltage amplitude, harmonic voltage phase angle, harmonic active power, and harmonic reactive power within the statistical period of the power quality monitoring device, an interval-type harmonic measurement sample is constructed. This can quantify the inherent uncertainty of statistical monitoring data, solve the problem that asynchronous statistical data cannot be adapted to traditional deterministic harmonic state estimation models, completely preserve the statistical fluctuation information of the data, avoid the waste of effective information, and improve the utilization efficiency of wide-area, low-cost power quality monitoring data.

[0030] Based on the above embodiments, interval-type harmonic measurement samples The vector form is represented as: ; in, Injecting harmonic active power into the nodes Injecting harmonic reactive power into the nodes, For branch harmonic active power, For branch harmonic reactive power, This represents the amplitude of the node harmonic voltage.

[0031] In this step, by integrating the interval quantities of node-injected harmonic active power, node-injected harmonic reactive power, branch harmonic active power, branch harmonic reactive power, and node harmonic voltage amplitude into a standardized vector form of interval harmonic measurement samples, the interval data structure of multiple types of harmonic monitoring quantities can be unified and standardized, fully covering the full-dimensional harmonic measurement information of nodes and branches, adapting to the input requirements of the subsequent interval dynamic harmonic state estimation model, avoiding the adaptation error of multi-source heterogeneous data, and improving the computational efficiency and model solution stability of interval harmonic state estimation.

[0032] Based on the above embodiments, the expressions for the harmonic prediction equation and the harmonic measurement equation are as follows: ; ; in, For based on The state quantity predicted at time step The harmonic state quantities of the time-prior interval include the harmonic voltage amplitude and phase angle of each node; This is the state transition function; This is a nonlinear harmonic measurement function; For prediction error, For measuring noise.

[0033] In this step, by establishing harmonic prediction equations and nonlinear harmonic measurement equations adapted to interval-type harmonic measurement data, a complete interval dynamic harmonic state estimation model is constructed. The mathematical expressions of interval harmonic state quantities, state transition functions, prediction errors, and measurement noise are clearly defined, which can accurately characterize the dynamic change law of harmonic state and the transmission characteristics of interval uncertainty. It adapts to the modeling requirements of asynchronous statistical data, provides a standardized mathematical model foundation for subsequent filtering recursive solutions, and improves the solution stability of the harmonic state estimation model.

[0034] Based on the above embodiments, the harmonic measurement equation The construction process includes: node The equation for the injected harmonic active power is: ; node The equation for injected harmonic reactive power: ; Connecting nodes and Branch harmonic active power equation: ; The harmonic reactive power equations for the branches connecting nodes i and j are as follows: ; in, node With nodes The phase angle difference of the harmonic voltages between them , These are the real and imaginary parts of the harmonic node admittance matrix, respectively. Earth harmonic admittance.

[0035] In this step, by constructing equations for the active and reactive power of harmonics injected at nodes and those for the active and reactive power of harmonics in branches, the parameter correspondences of harmonic phase angle difference, harmonic node admittance matrix, and harmonic admittance to ground are clarified, thus completing the construction of the harmonic measurement equations. This accurately maps the nonlinear coupling relationship between harmonic state quantities and measured quantities in the interval, closely matches the harmonic physical characteristics of power grid nodes and branches, accurately characterizes the harmonic power flow transmission law, and improves the solution accuracy of the harmonic measurement equations.

[0036] Based on the above embodiments, the state transition function Using a random walk model, i.e. System prediction error Follows a normal distribution Measure noise Follows a normal distribution And with the system prediction error They are independent of each other.

[0037] In this step, by using a random walk model as the state transition function, the normal distribution characteristics of the system prediction error and measurement noise, as well as their independent statistical constraints, are clearly defined. This approach can accurately adapt to the time-varying random fluctuation characteristics of the power grid harmonic state, simplify the computational complexity of state recursion, provide a standardized model foundation that conforms to statistical laws for Kalman filter recursion, avoid the fundamental error of mismatch between the state transition model and the actual harmonic dynamic characteristics, and improve the convergence speed, dynamic tracking accuracy, and engineering site adaptability of interval harmonic state estimation.

[0038] Based on the above embodiments, the interval fundamental state estimation model is as follows: ; in, For the fundamental phase angle at each node, except for the reference node, a possible interval for the phase angle can be solved. ; For nodes The lower and upper limits of the fundamental-wave injected active power; For nodes The lower and upper limits of the fundamental-wave injected reactive power; For nodes and The lower and upper limits of the fundamental active power of the intermediate branches; For nodes and The lower and upper limits of the fundamental reactive power of the intermediate branches; For nodes The lower and upper limits of the fundamental voltage amplitude; Inject power estimates into the nodes; This is an estimate of the branch power; This is the calculated value of the node voltage amplitude; For reference node constraints; By solving the interval fundamental wave state estimation model, the interval values ​​of the fundamental wave phase angle at each node are obtained. .

[0039] In this step, by constructing an interval fundamental state estimation model that includes node fundamental injected power, branch power, voltage amplitude interval constraints, and reference node constraints, the interval values ​​of the fundamental phase angle of each node are obtained. This can accurately quantify the uncertainty boundary of the fundamental phase angle, solve the problem of no unified reference benchmark for the phase angle of asynchronous harmonics, provide a reliable benchmark for harmonic phase angle synchronization processing, provide accurate starting values ​​for interval dynamic harmonic state estimation, and improve the initial accuracy of subsequent harmonic state estimation.

[0040] Based on the above embodiments, obtaining the starting value for interval dynamic harmonic state estimation includes the following steps: The interval values ​​of the fundamental phase angle at each node are solved using linear programming. ; Synchronization processing of asynchronous harmonic phase angles is performed based on the fundamental phase angle reference synchronization formula to obtain the starting value for interval dynamic harmonic state estimation. : ; in, The phase angle of the asynchronous harmonics. This represents the phase angle of the harmonics in the synchronized interval.

[0041] In this step, the fundamental phase angle interval values ​​of each node are obtained by solving the interval fundamental state estimation model using linear programming. Based on these values, the asynchronous harmonic phase angles are synchronized to generate the starting values ​​for interval dynamic harmonic state estimation. This solves the problem that the harmonic phase angles lack a unified time scale across the entire network and that asynchronous statistical data cannot be adapted to traditional estimation models, thus improving the initial estimation accuracy of interval harmonic state estimation.

[0042] Based on the above embodiments, an improved extended interval Kalman filter algorithm is used to recursively solve the interval dynamic harmonic state estimation model to obtain the corrected interval state variables; including the following steps: according to The posterior interval estimate at time k+1 is used to predict the interval prior state variables and prior error covariance matrix at time k+1. Construct an affine covariance propagation based on interval prior state variables and calculate the deterministic prior error covariance matrix; A linearized approximate expression is constructed by using the affine form of the measurement function based on the interval prior state variables; An update formula for affine coefficients is constructed based on the Kalman filter framework. The predicted state at time k+1 is updated using the new measurement value to obtain the affine form reconstruction of the corrected interval state variables.

[0043] In this step, an improved extended interval Kalman filter algorithm is used to complete state prediction, affine covariance propagation, affine linearization of the measurement function, and affine coefficient correction and update. The interval dynamic harmonic state estimation model is solved recursively, which can avoid the interval expansion effect of traditional interval filtering, accurately preserve the coupling correlation between state variables, reduce the conservatism of interval estimation results, and improve the engineering practical value of interval harmonic state estimation.

[0044] Based on the above embodiments, an affine covariance propagation based on interval prior state quantities is constructed, and the deterministic prior error covariance matrix is ​​calculated; including the following steps: The interval prior state variables obtained in the prediction process Convert to affine form: ; in The midpoint value of the prior state variable in the interval. For the first Noise symbol variables coefficient, The number of state variables; each noise symbol variable is considered independent, and the transformation is determined by the interval radius, which is defined as: ; The deterministic prior error covariance matrix can be directly calculated from the affine coefficients: ; This matrix serves as a deterministic covariance in subsequent gain calculations, avoiding the expansion effect caused by interval operations.

[0045] In this step, by converting the interval prior state variables obtained in the prediction stage into an affine form containing midpoint values ​​and noise sign variable coefficients, and explicitly defining the interval radius calculation rules, the deterministic prior error covariance matrix is ​​directly calculated based on the affine coefficients and participates in subsequent gain calculations. This avoids the interval expansion and wrapping effects caused by the interval covariance recursion operation in traditional interval Kalman filtering, explicitly preserves the linear correlation between state variables, breaks the bottleneck of interval operation's inability to accurately transmit covariance information, avoids the problem of abnormal amplification of interval width with filter recursion, improves the compactness and accuracy of interval harmonic state estimation results, reduces the conservatism of interval estimation, and provides a standardized deterministic matrix basis for subsequent filter gain calculations, thereby improving the computational efficiency of filter recursion.

[0046] Based on the above embodiments, a linearized approximate expression is constructed for the measurement function based on the affine form of the interval prior state variables; including the following steps: Predict the state variables Represented in affine form: ; in The midpoint value of the state variable. For the first Noise symbol variables coefficient, This represents the number of state variables. This representation is equivalent to the interval form. But through The independence assumption preserves the linear correlation between the components; Measurement function exist Performing a first-order affine expansion at the given point yields a linearized approximate expression: ; The partial derivatives in the formula form the Jacobian matrix. This expansion maps nonlinear measurements to an affine form, where the noise sign variable... It maintains consistency with the fluctuations of state variables, thereby preserving the coupling information between variables.

[0047] In this step, by converting the predicted state variables into an affine form equivalent to the interval form while preserving the linear correlation between components, a first-order affine expansion of the nonlinear measurement function at the midpoint of the state variables is performed. A linearized approximate expression containing the Jacobian matrix is ​​constructed, maintaining consistency between the noise symbol variable and the fluctuation of the state variables, and fully preserving the coupling information between variables. This solves the problems of insufficient preservation of variable correlation in traditional interval Taylor expansion and the tendency of nonlinear mapping to amplify interval conservatism. It accurately characterizes the mapping relationship between the measurement function and the interval state variables, avoids information loss and interval expansion during the linearization process, improves the linearization accuracy of the nonlinear measurement link, provides an accurate affine mapping basis for subsequent filtering correction, further reduces the conservatism of the interval estimation results, and improves the solution accuracy and convergence stability of the interval harmonic state estimation.

[0048] Based on the above embodiments, an update formula for the affine coefficients is constructed using the Kalman filter framework. The predicted state at time k+1 is updated using the new measurement value to obtain the affine form reconstruction of the corrected interval state variables; including the following steps: Determinism is obtained by combining affine covariance propagation. The matrix can be used to calculate the deterministic gain matrix. : ; The affine coefficients of the predicted state are propagated through the gain matrix. The midpoint of the corrected state is updated as follows: ; in Measurement interval The midpoint.

[0049] The corrected affine coefficients (i.e., the coefficients of the noise symbol variable) are updated as follows: ; This formula embodies the core advantage of affine arithmetic: the same noise sign variable. Maintaining consistency between prediction and correction ensures that the correlation between the components of the state variable is naturally accounted for during the update process, avoiding interval expansion. Finally, the corrected interval state variable is reconstructed from an affine form: ; in, For the corrected interval harmonic state quantity, the subscript is... Represents harmonics, Indicates the use of After correcting the measured values ​​at time, The final estimate of the state at time step; This is the midpoint value of the corrected state variable interval; For the corrected first Noise symbol variables The coefficient.

[0050] Through the above-described affine expansion and propagation, this invention improves the extended interval Kalman filter with affine arithmetic. While maintaining computational feasibility, it more accurately preserves the correlation between harmonic variables at each node, further reducing the conservatism of the harmonic interval estimation results.

[0051] In this step, the Kalman gain matrix is ​​calculated using the deterministic matrix obtained from affine covariance propagation. This completes the iterative update of the state midpoint and affine coefficients in the correction stage, maintaining consistency between the noise symbol variables in the prediction and correction stages. Finally, the corrected interval harmonic state variables are reconstructed through affine forms. This approach naturally takes into account the correlation between the components of the state variables during the filtering update process, avoiding the interval expansion problem in the traditional interval Kalman filter correction stage. It breaks through the bottleneck of the drastic increase in conservatism after multiple iterations of interval operations. While ensuring computational feasibility, it accurately preserves the coupling information between harmonic variables at each node, compresses the width of the interval estimation results, and improves the compactness, solution accuracy, and engineering practical value of the interval harmonic state estimation. At the same time, it ensures the convergence stability of the filtering recursion.

[0052] Based on the above embodiments, a robust filtering mechanism based on interval constraints is used to verify the rationality of each actual measurement interval and adaptively adjust its weight in the filter update to obtain a shrunken measurement interval; this includes the following steps: Obtain the predicted state interval, calculate the predicted interval of the fundamental wave measurement value of each interval type according to the harmonic measurement equation, and verify the rationality of the predicted interval; Based on a smooth weight adjustment strategy, the weights of the fundamental wave measurements that are deemed unreasonable in the filtering update are updated using the confidence factor and the measurement noise covariance matrix. The measurement interval is shrunk by using the prediction interval to obtain the shrunk measurement interval.

[0053] In this step, the predicted intervals for each measurement quantity are calculated based on the predicted state interval and the harmonic measurement equation, and the rationality verification of the measured interval is completed. Then, based on the smoothing weight adjustment strategy, the measurement noise covariance matrix and filter update weights of bad data are adaptively adjusted through the confidence factor. Finally, the abnormal measurement interval is shrunk using the predicted interval. This can accurately identify the bad harmonic measurement data in the power grid field online, effectively isolate the interference of outliers on the filter recursion, avoid the inaccuracy of state estimation caused by bad data, and at the same time, it does not amplify the conservatism of the interval estimation in the robustness process, thereby improving the solution accuracy of harmonic state estimation in complex power grid field environments.

[0054] Based on the above embodiments, the predicted state interval is obtained, and the predicted interval of the fundamental wave measurement value of each interval type is calculated according to the harmonic measurement equation. The rationality of the predicted interval is then verified. This includes the following steps: In obtaining the predicted state range Then, the prediction intervals of the fundamental wave measurements for each interval type were calculated based on the harmonic measurement equation. : ; If the actual measurement interval With the prediction interval If there is an intersection, the interval-type fundamental wave measurement value corresponding to the prediction interval is considered normal; If there is no intersection, it is determined to be an unreasonable interval-type fundamental wave measurement value.

[0055] In this step, the predicted intervals of each interval-type measurement value are calculated based on the predicted state interval and the harmonic measurement equation. The rationality of the measurement data is verified by whether there is an intersection between the actual measurement interval and the predicted interval. This method can accurately identify bad harmonic measurement data online, adapt to the inherent characteristics of interval-type statistical monitoring data, and does not require additional complex detection algorithms. It provides a clear basis for subsequent adaptive weight adjustment and measurement interval shrinkage, isolates abnormal data without physical meaning in advance, and improves the accuracy of bad data identification, the anti-interference ability of filtering update, and the on-site adaptation stability of harmonic state estimation.

[0056] Based on the above embodiments, and using a smooth weight adjustment strategy, the weights of the fundamental frequency measurements deemed unreasonable in the filtering update are updated using the confidence factor and the measurement noise covariance matrix; this includes the following steps: A smooth weighting strategy is adopted, and the confidence factor is defined. For the One measurement quantity: ; in Indicates the interval length; the confidence factor reflects the degree of overlap between the actual measured interval and the predicted interval, when they completely overlap. When there is no overlap ; Apply the confidence factor to the measurement noise covariance matrix: ; in This is the original measurement noise covariance matrix. This is the adjusted matrix; when the confidence factor At that time, corresponding to the first The noise variance of each measurement is amplified, thereby automatically reducing the weight of this bad data in subsequent gain calculations.

[0057] In this step, by defining a confidence factor that reflects the degree of overlap between the actual measurement interval and the predicted interval, a smooth weight adjustment strategy is adopted to apply the confidence factor to the measurement noise covariance matrix to complete adaptive correction. This can accurately quantify the reliability of the measurement data, smoothly reduce the weight of bad data in the filter gain calculation, avoid the decrease in model observability caused by hard data removal, isolate outliers from the interference of filter updates, and improve the robustness of harmonic state estimation.

[0058] Based on the above embodiments, the measurement interval is shrunk using the prediction interval to obtain the shrunk measurement interval. The expression is: ; This interval retains the meaningful parts from the actual measurements while eliminating outliers that exceed the physical boundaries. In the subsequent correction process, the shrunken measurement interval is used to replace the original measurement interval for filtering updates.

[0059] In this step, a shrunken measurement interval is constructed by the intersection of the predicted interval and the actual measurement interval. This shrinkage replaces the original measurement interval in the subsequent filtering and correction process. This process can accurately remove abnormal components that exceed the physical boundaries in the measurement interval, fully retain meaningful and effective information in the measured data, further suppress the interference of bad data on harmonic state estimation, avoid outliers from amplifying the conservatism of interval estimation, improve the solution accuracy of harmonic state estimation, and enhance the engineering adaptability in complex power grid field environments.

[0060] like Figure 2 As shown, the present invention also provides a data-driven harmonic state estimation system for complex power grids, comprising: The data acquisition module is used to acquire statistical harmonic monitoring data uploaded by the power quality monitoring device, and extract and construct interval harmonic measurement samples; The model building module is used to establish an interval dynamic harmonic state estimation model that considers the uncertainty of harmonic state based on measurement samples, and to obtain the harmonic prediction equation and the harmonic measurement equation. The start-up value calculation module is used to establish an interval fundamental wave state estimation model based on the interval fundamental wave measurement value at the initial time, and obtain the start-up value for interval dynamic harmonic state estimation. The filtering estimation module is used to recursively solve the interval dynamic harmonic state estimation model using an improved extended interval Kalman filter algorithm to obtain the corrected interval state variables. The robust constraint module is used for a robust filtering mechanism based on interval constraints. It performs a rationality check on each actual measurement interval and adaptively adjusts the weights in the filter update to obtain a shrinking measurement interval. The status output module is used to participate in the filter update using the contracted measurement interval and output the interval harmonic status quantity of each node.

[0061] This system can automate the processing of asynchronous statistical monitoring data of power quality in a wide area and solve the harmonic state in a closed loop. It is adapted to the engineering requirements of dynamic harmonic tracking, low-conservatism interval estimation and robust suppression of bad data in complex power grids, improves the automation level of harmonic state estimation, and provides standardized and highly reliable system support for power grid harmonic management.

[0062] Those skilled in the art should understand that this invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to this invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A data-driven complex power grid harmonic state estimation method, characterized in that, Includes the following steps: Acquire statistical harmonic monitoring data uploaded by power quality monitoring devices, and extract and construct interval-type harmonic measurement samples; Based on the measurement samples, an interval dynamic harmonic state estimation model considering the uncertainty of harmonic state is established, and the harmonic prediction equation and harmonic measurement equation are obtained. The harmonic measurement equation is obtained by adding the nonlinear harmonic measurement function and the measurement noise. Based on the initial interval fundamental wave measurement, an interval fundamental wave state estimation model is established to obtain the starting value for interval dynamic harmonic state estimation. An improved extended interval Kalman filter algorithm is used to recursively solve the interval dynamic harmonic state estimation model to obtain the corrected interval state variables. The robust filtering mechanism based on interval constraints verifies the rationality of each actual measurement interval and adaptively adjusts its weight in the filter update to obtain a shrinking measurement interval. The contraction measurement interval is used to participate in the filter update, and the interval harmonic state quantity of each node is output. The step of recursively solving the interval dynamic harmonic state estimation model using an improved extended interval Kalman filter algorithm to obtain the corrected interval state variables includes the following steps: Based on the posterior interval estimate at time k, predict the interval prior state variables and prior error covariance matrix at time k+1. Construct an affine covariance propagation based on interval prior state variables and calculate the deterministic prior error covariance matrix; A linearized approximate expression is constructed for the harmonic measurement function based on the affine form of the interval prior state quantity; An update formula for affine coefficients is constructed based on the Kalman filter framework. The predicted state at time k+1 is updated using the new measurement value to obtain the affine form reconstruction of the corrected interval state variables. The corrected interval state variables are reconstructed in affine form as follows: ； in, For the corrected interval harmonic state quantity, the subscript is... Represents harmonics, Indicates the use of After correcting the measured values ​​of time, The final estimate of the state at time step; This is the midpoint value of the corrected state variable interval; For the corrected first Noise symbol variables The coefficient.

2. The data-driven complex power grid harmonic state estimation method of claim 1, wherein, The statistical harmonic monitoring data includes the maximum and minimum values ​​of harmonic voltage amplitude, harmonic voltage phase angle, harmonic active power, and harmonic reactive power at each monitoring point within the statistical period.

3. The data-driven complex power grid harmonic state estimation method of claim 2, wherein, The vector form of the interval-type harmonic measurement sample is as follows: ； wherein, injecting harmonic active power for the node, injecting harmonic reactive power for the node, injecting harmonic active power for the branch, injecting harmonic reactive power for the branch, harmonic voltage magnitude for the node.

4. The data-driven complex power grid harmonic state estimation method of claim 1, wherein, The expressions for the harmonic prediction equation and the harmonic measurement equation are as follows: ； ； in, , for The interval harmonic state quantities at each time point include the harmonic voltage amplitude and phase angle at each node; This is the state transition function; This is a nonlinear harmonic measurement function; For prediction error, For measuring noise.

5. The data-driven complex power grid harmonic state estimation method of claim 1, wherein, The interval fundamental state estimation model is as follows: ； in, For the fundamental phase angle at each node, except for the reference node, a possible interval for the phase angle can be solved. ; For nodes The lower and upper limits of the fundamental-wave injected active power; For nodes The lower and upper limits of the fundamental wave injected reactive power; For nodes and The lower and upper limits of the fundamental active power of the intermediate branches; For nodes and The lower and upper limits of the fundamental reactive power of the intermediate branches; For nodes The lower and upper limits of the fundamental voltage amplitude; Inject power estimates into the nodes; This is an estimate of the branch power; This is the calculated value of the node voltage amplitude; By solving the interval fundamental state estimation model, interval values of the fundamental phase angle of each node are obtained .

6. The data-driven complex power grid harmonic state estimation method of claim 1, wherein, The steps for obtaining the starting value for interval dynamic harmonic state estimation include: The linear programming method is used to solve the interval value of the fundamental phase angle of each node ; Synchronization processing is performed on the non-synchronous harmonic phase angle to obtain a starting value of interval dynamic harmonic state estimation and the synchronization processing formula is: ； in, The phase angle of the asynchronous harmonics. This represents the phase angle of the harmonics in the synchronized interval.

7. The data-driven complex power grid harmonic state estimation method of claim 1, wherein, The robust filtering mechanism based on interval constraints verifies the rationality of each actual measurement interval and adaptively adjusts its weights in the filter update to obtain a shrunken measurement interval; it includes the following steps: Obtain the predicted state interval, and calculate the predicted interval of each interval-type fundamental wave measurement value according to the harmonic measurement equation, and verify the rationality of the predicted interval; Based on a smooth weight adjustment strategy, the weights of the interval-type fundamental wave measurements that are deemed unreasonable are updated in the filter update using confidence factors and measurement noise covariance matrix. The measurement interval is shrunk using the predicted interval to obtain the shrunk measurement interval.

8. The data-driven complex power grid harmonic state estimation method of claim 7, wherein, The reasonableness of the predicted interval is verified, including the following steps: If the actual measurement interval With the prediction interval If there is an intersection, the interval-type fundamental wave measurement value corresponding to the predicted interval is considered normal; If there is no intersection, the measured value of the interval type fundamental wave is determined to be unreasonable.

9. The data-driven complex power grid harmonic state estimation method of claim 8, wherein, The smoothing-based weight adjustment strategy updates the weights of the interval-type fundamental wave measurements deemed unreasonable in the filter update using a confidence factor and the measurement noise covariance matrix; it includes the following steps: A smooth weight adjustment strategy is employed to define a confidence factor for the first measured quantity: ； in Indicates the interval length; the confidence factor reflects the degree of overlap between the actual measurement interval and the predicted interval, when they completely overlap. When there is no overlap ; Apply the confidence factor to the measurement noise covariance matrix: ； in This is the original measurement noise covariance matrix. For the adjusted matrix; when When the value is small, the noise variance of the corresponding measurement is amplified.

10. A data-driven complex power grid harmonic state estimation system, characterized in that, The system is applied to the data-driven complex power grid harmonic state estimation method as described in claim 1, and the system comprises: The data acquisition module is used to acquire statistical harmonic monitoring data uploaded by the power quality monitoring device, and extract and construct interval harmonic measurement samples; The model building module is used to establish an interval dynamic harmonic state estimation model considering the uncertainty of harmonic state based on the measurement samples, and to obtain the harmonic prediction equation and the harmonic measurement equation. The harmonic measurement equation is obtained by adding the nonlinear harmonic measurement function and the measurement noise. The start-up value calculation module is used to establish an interval fundamental wave state estimation model based on the interval fundamental wave measurement value at the initial time, and obtain the start-up value for interval dynamic harmonic state estimation. The filtering estimation module is used to recursively solve the interval dynamic harmonic state estimation model using an improved extended interval Kalman filter algorithm to obtain the corrected interval state variables. The robust constraint module is used for a robust filtering mechanism based on interval constraints. It performs a rationality check on each actual measurement interval and adaptively adjusts the weights in the filter update to obtain a shrinking measurement interval. The status output module is used to participate in the filter update using the contraction measurement interval and output the interval harmonic status quantity of each node.

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