A complex power grid hybrid power quality robust state estimation method and system

Abstract

This invention relates to the field of power system technology, and in particular to a robust state estimation method and system for hybrid power quality in complex power grids. The method includes: unifying the amplitude data variation of voltage signals into power quality state quantities characterizing the system, and constructing hybrid power quality measurement equations based on harmonic admittance matrices and fundamental admittance matrices; constructing edges and weights of a graph structure based on the power grid topology, and generating an augmented dataset containing pseudo-measurement data through a graph convolutional neural network; establishing a robust state estimation model based on the augmented dataset with the objectives of minimizing structural risk and empirical risk; and using the alternating direction multiplier method to solve the robust state estimation model in a distributed manner to obtain the variation values ​​of power quality state quantities at each node of the entire power grid and estimate the power quality state of the entire power grid.

Description

Technical Field

[0001] This invention relates to the field of power system technology, and in particular to a robust state estimation method and system for hybrid power quality in complex power grids. Background Technology

[0002] With the large-scale grid connection of new energy power generation and the widespread application of power electronic equipment, the power grid faces increasingly complex power quality problems. Disturbances such as voltage sags, voltage rises, and harmonics occur frequently, posing a serious threat to the safe operation of sensitive loads. State estimation is a core technical means for power system operation monitoring. By processing limited measurement data, it obtains network-wide state information, providing a basis for decision-making in power quality assessment and management.

[0003] Under weak measurement conditions, traditional state estimation methods face severe challenges. On the one hand, the limited number of phasor measurement units leads to insufficient measurement redundancy, resulting in some nodes being unobservable or lacking observability, thus reducing the accuracy of traditional weighted least squares-based estimation methods. On the other hand, uncertainties such as bad data injection, sensor measurement bias, and communication delays severely affect the reliability of the estimation results. Furthermore, existing methods typically model only a single type of disturbance, making it difficult to uniformly characterize multiple types of complex disturbances such as voltage sags, swells, fluctuations, and harmonics.

[0004] To address the state estimation problem under weak measurement conditions, scholars have proposed various improvement schemes. Pseudo-measurement modeling methods utilize historical data or load forecasting techniques to generate virtual measurements to compensate for the deficiencies of actual measurements, but they are highly dependent on data quality and the prediction model. Robust estimation methods reduce the impact of outliers by introducing robust loss functions, but existing schemes do not fully utilize model parameter uncertainties and graph structure information. While distributed computing methods can reduce computational complexity, their integration with robust estimation models still requires optimization.

[0005] 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

[0006] The technical problem this invention aims to solve is to provide a robust state estimation method and system for mixed power quality in complex power grids, achieving unified characterization and high-precision robust estimation of mixed power quality under weak measurement conditions, while also considering computational efficiency and distributed deployment requirements.

[0007] To achieve the above objectives, the technical solution adopted by this invention is: a robust state estimation method for hybrid power quality in complex power grids, comprising the following steps: The amplitude data variation of the voltage signal is unified into a quantity characterizing the power quality state of the system, and a hybrid power quality measurement equation is constructed based on the harmonic admittance matrix and the fundamental admittance matrix. Based on the power grid topology, edges and weights of a graph structure are constructed, and an augmented dataset containing pseudo-measurement data is generated through a graph convolutional neural network. Based on the augmented dataset, a robust state estimation model is established with the objectives of minimizing structural risk and minimizing empirical risk. The robust state estimation model is solved in a distributed manner using the alternating direction multiplier method to obtain the variation values ​​of the power quality state quantities at each node of the entire power grid and to estimate the power quality state of the entire power grid.

[0008] Furthermore, the amplitude data of the voltage signal includes the amplitude of the fundamental wave, the amplitude of the harmonics, and the bidirectional amplitudes of voltage sags, swells, and fluctuations.

[0009] Furthermore, unifying the amplitude data variation of the voltage signal into a quantity characterizing the power quality state of the system includes the following steps: Amplitude parameters are used to characterize the fundamental wave, characteristic harmonics, and interharmonics. Let the first... The amplitude of the second harmonic component is ; The voltage signal at time t containing fundamental, multiple harmonics, and interharmonic components is represented using Fourier series. ; A unified model is used to represent the bidirectional amplitude abrupt changes of voltage sags, swells, and fluctuations, including voltage amplitude changes during... During the period by Mutation And the recovery process.

[0010] Furthermore, the construction of the hybrid power quality measurement equation based on the harmonic admittance matrix and the fundamental admittance matrix includes the following steps: A comprehensive state vector is defined based on the abrupt change depth of the power quality state parameters. Construct measurement equations in a block-diagonal form; Construct a block-diagonal measurement matrix, and use a block-diagonal structure to integrate matrices and vectors in a unified and independent mapping; A hybrid power quality measurement equation was formed by integrating and constructing the equation.

[0011] Furthermore, based on the power grid topology, a graph structure with edges and weights is constructed, and an augmented dataset containing pseudo-measurement data is generated using a graph convolutional neural network; this includes the following steps: The physical connection characteristics of the power grid topology and the electrical characteristic parameters of the lines are used as the edges and weights of the graph structure, and sparse, noisy power quality measurement data are used as node features to model the power grid topology weighted graph and construct a multi-dimensional feature matrix for standardization. By leveraging the spatial message passing characteristics of graph convolutional neural networks, state-space inference and filtering of bad data from non-power quality monitoring points are achieved, generating a power quality enhancement dataset that includes pseudo-measurement data.

[0012] Furthermore, the modeling of the power grid topology weighted graph and the standardization of the construction of the multidimensional feature matrix include the following steps: The distribution network is abstracted as a weighted undirected graph, and a weighted undirected graph structure is set. As a fixed input to the GCN, it encodes the spatial constraints of the power grid; Extract specific data from the amplitude data and map them to the input feature vectors of the nodes; construct... Initial feature matrix of the entire network in dimensionality ; ; Matrix elements According to the node Measurement intensity and characteristic column Assign values ​​to the physical properties.

[0013] Furthermore, generating the power quality enhancement dataset containing pseudo-measurement data includes the following steps: Message passing is achieved through multi-layer network iteration using the spatial convolution operator of GCN; Extracting the feature matrix of the GCN output layer The feature matrix of the output layer For graph convolutional neural networks The final mapping result after subspace message passing; Extract the calculated values ​​of the corresponding weak measurement nodes in the output matrix to generate pseudo measurement data with physical consistency; The actual measurements are integrated with the pseudo-measurement data to form the power quality enhancement dataset.

[0014] Furthermore, by utilizing the spatial convolution operator of GCN, message passing is achieved through multi-layer network iteration, as expressed by the formula: ; in, This is a hierarchical index, representing the order in which the message is transmitted within the power grid topology; The adjacency matrix after adding self-connections is defined as follows: , This is the adjacency matrix corresponding to the power grid topology. It is the identity matrix; it is the adjacency matrix with self-joins. Depend on Derivation, Representation matrix The degree matrix is ​​a diagonal matrix, and its diagonal elements are determined by the following formula. ; It is the first The node feature matrix of the layer has a dimension of Where N represents the number of nodes in the power grid, F l The dimension representing the feature of the l-th layer; Indicates the first The trainable weight matrix of the layer has dimensions of ; It is a nonlinear activation function used to perform nonlinear mapping on the results of linear transformations.

[0015] Furthermore, the establishment of a robust state estimation model with the objectives of minimizing structural risk and empirical risk includes the following steps: Define the empirical risk objective function Furthermore, the Huber loss function is employed to suppress the influence of outliers in the measurement data on the estimation results; Introducing graph regularization terms as structural risk constraints ; Integrating empirical risk and structural risk, the objective function of a robust power quality state estimation model is constructed as follows: .

[0016] Furthermore, the distributed solution of the robust state estimation model using the alternating direction multiplier method includes model decomposition and function construction, and distributed iteration and consistent solution. The model decomposition and function construction include the following steps: Network topology map Division Overlapping sub-regions Define the local state vector of each sub-region as The state of the common boundary nodes between adjacent sub-regions is defined as a consistency constraint variable. Construct an augmented Lagrange function that includes Lagrange multipliers and a quadratic penalty term; The distributed iterative and consensus-based solution includes the following steps: The ADMM algorithm is used to transform the global optimization problem into a three-step alternating iterative process, in which each sub-region is solved through independent parallel computation and information exchange between adjacent nodes. By monitoring the convergence status of the global original residual and the dual residual, the iteration stops and the final global synthesis state vector is output when the residual meets the preset convergence threshold. .

[0017] This invention also provides a robust state estimation system for hybrid power quality in complex power grids, comprising: The state characterization module is used to unify the amplitude data variation of the voltage signal into a power quality state quantity characterizing the system, and to construct a hybrid power quality measurement equation based on the harmonic admittance matrix and the fundamental admittance matrix. The graph enhancement module is used to construct the edges and weights of a graph structure based on the power grid topology, and generate an enhanced dataset containing pseudo-measurement data through a graph convolutional neural network. The model building module is used to build a robust state estimation model based on the augmented dataset, with the objectives of minimizing structural risk and empirical risk. The distributed solution module is used to solve the robust state estimation model in a distributed manner using the alternating direction multiplier method, to obtain the variation values ​​of the power quality state quantity in each node of the entire power grid and to estimate the power quality state of the entire power grid.

[0018] The beneficial effects of this invention are as follows: This invention achieves collaborative modeling of fundamental, harmonic, and transient disturbances through unified representation of state variables, overcoming the limitation of traditional methods that can only handle a single type of disturbance; through pseudo-measurement generation and graph structure feature learning using graph convolutional neural networks, it effectively improves the observability and accuracy of state estimation under weak measurement conditions; through the fusion design of the Huber loss function and graph regularization term, it maintains the physical consistency of the estimation results while suppressing the influence of bad data; through the distributed solution architecture of the alternating direction multiplier method, it achieves the dispersion of computational load and the protection of regional data privacy; this invention can achieve high-precision and robust estimation of power quality state under complex operating conditions of weak measurement, combined disturbances, and bad data interference. Attached Figure Description

[0019] 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.

[0020] Figure 1 This is a flowchart illustrating the robust state estimation method for hybrid power quality in complex power grids according to an embodiment of the present invention. Figure 2 This is a schematic diagram of the structure of the robust state estimation system for hybrid power quality of complex power grids in an embodiment of the present invention; Figure 3 This is a schematic diagram of the structure of a computer electronic device in an embodiment of the present invention. Detailed Implementation

[0021] 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.

[0022] 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.

[0023] 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.

[0024] like Figure 1 The robust state estimation method for hybrid power quality in complex power grids, as shown, includes the following steps: The amplitude data variation of the voltage signal is unified into a quantity characterizing the power quality state of the system, and a hybrid power quality measurement equation is constructed based on the harmonic admittance matrix and the fundamental admittance matrix. Based on the power grid topology, edges and weights of a graph structure are constructed, and an augmented dataset containing pseudo-measurement data is generated through a graph convolutional neural network. Based on the augmented dataset, a robust state estimation model is established with the objectives of minimizing structural risk and empirical risk. The robust state estimation model is solved in a distributed manner using the alternating direction multiplier method to obtain the variation values ​​of power quality state quantities at each node of the entire power grid and estimate the power quality state of the entire power grid.

[0025] This invention achieves collaborative modeling of fundamental, harmonic, and transient disturbances through a unified representation of state variables, overcoming the limitation of traditional methods that can only handle a single type of disturbance. By using graph convolutional neural networks for pseudo-measurement generation and graph structure feature learning, it effectively improves the observability and accuracy of state estimation under weak measurement conditions. Through the fusion design of the Huber loss function and graph regularization term, it maintains the physical consistency of the estimation results while suppressing the influence of bad data. The distributed solution architecture using the alternating direction multiplier method achieves distributed computational load and privacy protection for regional data. This invention can achieve high-precision and robust estimation of power quality state under complex operating conditions involving weak measurements, combined disturbances, and bad data interference.

[0026] Based on the above embodiments, the amplitude data of the voltage signal includes the amplitude of the fundamental wave, the amplitude of the harmonic wave, and the bidirectional amplitudes of voltage sags, swells, and fluctuations.

[0027] By unifying the fundamental amplitude, harmonic amplitude, voltage sag, voltage rise, and bidirectional amplitude of fluctuations into the power quality state quantity system for normalized characterization, the technical barrier of independent modeling for single power quality problems in existing technologies can be broken, improving the feasibility of simultaneous estimation of steady-state and transient multi-form power quality disturbances within the same framework. Furthermore, by constructing independent measurement sub-equations for various amplitude characteristics based on the fundamental admittance matrix and the corresponding harmonic admittance matrices at different frequencies, and integrating them into a block-diagonal structure of non-cross-coupled hybrid measurement equations, the measurement mapping relationship can be guaranteed to fully conform to the inherent electrical characteristics of the power grid at different frequencies, improving the physical consistency of the measurement model. It enhances the system's regularity and resistance to cascading error diffusion. By clarifying the amplitude dimension composition of power quality state quantities and the linear mapping rules between measurement data and the state quantities of physical nodes across the entire network, it can provide standardized feature definitions and spatial mapping logic for subsequent inference of pseudo-measurement data from non-monitoring points and filtering of bad data, thereby improving the adaptability of the system's observation improvement scheme in weak measurement scenarios. By adopting an amplitude feature system that fully matches the core power quality evaluation indicators of the national standard, it can directly connect to the conventional data collected by existing power grid power quality monitoring devices without the need for additional special hardware acquisition equipment, thus improving the engineering implementation adaptability of the solution and its compatibility with complex power grid scenarios.

[0028] Based on the above embodiments, the amplitude data variation of the voltage signal is unified into a quantity characterizing the power quality state of the system, including the following steps: Amplitude parameters are used to characterize the fundamental wave, characteristic harmonics, and interharmonics. Let the first... The amplitude of the second harmonic component is ; The voltage signal at time t containing fundamental, multiple harmonics, and interharmonic components is represented using Fourier series. ; A unified model is used to represent the bidirectional amplitude abrupt changes of voltage sags, swells, and fluctuations, including voltage amplitude changes during... During the period by Mutation And the recovery process.

[0029] This step uses amplitude parameters to uniformly characterize the fundamental wave, characteristic harmonics, and interharmonics, and clarifies the first... Amplitude of subharmonic components Quantization rules enable the incorporation of steady-state power quality characteristics at different frequencies into a standardized quantization system, improving the ability to perform simultaneous analysis and estimation of multi-dimensional steady-state power quality states within the same framework. This is achieved by employing Fourier series to analyze time-domain voltage signals containing fundamental, multiple harmonic, and interharmonic components. Normalized decomposition representation can accurately separate and quantify the intensity characteristics of each frequency component in the voltage signal, improving the accuracy of power quality steady-state feature extraction in weak measurement scenarios. By adopting a unified model to fully characterize the entire cycle of bidirectional amplitude mutations in voltage sags, sags, and fluctuations, covering the complete dynamic process of voltage amplitude mutations and recovery, transient power quality disturbances and steady-state frequency components can be incorporated into the same power quality state quantity system, improving the completeness of the unified characterization of steady-state and transient multi-form power quality characteristics. By constructing a unified power quality state quantity characterization system covering all steady-state frequency components and all transient cycle disturbances, a consistent state variable basis can be provided for subsequent hybrid measurement equation construction, weak measurement data enhancement, and robust state estimation, improving the logical closed-loop performance of the entire power quality state estimation scheme.

[0030] Based on the above embodiments, voltage signal The Fourier series representation is as follows: ; in, The DC component, For the first The amplitude of the second harmonic. , for the first The frequency of the subharmonic, the fundamental frequency For setting value, This corresponds to the phase.

[0031] In this step, by employing a component including DC, the first The normalized Fourier series form of the subharmonic amplitude, frequency, and phase parameters characterizes the time-domain voltage signal. It can perform accurate frequency domain orthogonal decomposition of voltage signals, completely separating the independent component characteristics of the fundamental wave, characteristic harmonics, and interharmonics, thus improving the accuracy of multi-frequency dimension power quality amplitude parameter extraction; by fixing the fundamental frequency in the Fourier series... The standardized design of the setpoints can unify the frequency domain decomposition benchmark of voltage signals under different monitoring points and sampling conditions across the entire network, eliminate component extraction errors caused by fundamental frequency fluctuations, and improve cross-node compatibility of sparse measurement data in weak measurement scenarios; the amplitude of the h-th harmonic is clearly defined in the Fourier series. The independent quantification dimension can directly anchor the core characterization parameters of the unified state quantity of power quality, providing direct frequency domain data support for the subsequent construction of hybrid measurement equations and state space inference, and improving the parameter matching degree and logical closed loop of the entire process of power quality state estimation.

[0032] Based on the above embodiments, the unified model representation of the bidirectional amplitude changes of voltage sags, swells, and fluctuations is as follows: ; in, yes Voltage amplitude at any given moment; This is the rated voltage amplitude; It is the moment the event begins; Duration of the event; It is the relative change in amplitude: The corresponding voltage sag. Corresponding voltage swell; When it is a time-varying function, it is used to describe voltage fluctuations; It is a unit step function.

[0033] In this step, a unified mathematical model is used to characterize the bidirectional amplitude mutations of voltage sags, swells, and fluctuations by incorporating rated voltage amplitude, event start and end times, duration, relative amplitude change, and a unit step function. This allows a standardized formula to fully cover the entire dynamic process of the three core transient power quality disturbances, improving the uniformity of transient power quality characteristic representation. By distinguishing voltage sags and swells in the unified model using the positive or negative values ​​of the relative amplitude change, and adapting the time-varying relative amplitude change to voltage fluctuation scenarios, integrated and accurate classification and quantitative characterization of different types of transient disturbances can be achieved. This avoids computational errors and logical redundancy caused by switching between multiple models, improving the identification and amplitude of transient power quality disturbances in weak measurement scenarios. The accuracy of value variation quantification; by anchoring the rated voltage amplitude benchmark and the core characterization parameters of the relative amplitude change in the unified model, the amplitude variation characteristics of transient voltage disturbances and the steady-state amplitude characteristics of fundamental and harmonic waves can be incorporated into the same power quality state quantity system, realizing the same-dimensional standardized quantification of steady-state and transient characteristics, and improving the adaptability of subsequent hybrid power quality measurement equation construction; by introducing event start time, duration parameters and unit step function into the unified model, the complete physical process of voltage amplitude mutation, continuity and recovery can be accurately reproduced, matching the actual occurrence law of power grid transient disturbances. The core parameters of the model can be directly connected to the conventional data collected by existing power quality monitoring devices, improving the adaptability of the solution for engineering implementation.

[0034] Based on the above embodiments, a hybrid power quality measurement equation is constructed based on the harmonic admittance matrix and the fundamental admittance matrix, including the following steps: The comprehensive state vector is defined based on the abrupt change depth of the power quality state parameters. Construct measurement equations in a block-diagonal form; Construct a block-diagonal measurement matrix, and use a block-diagonal structure to integrate matrices and vectors in a unified and independent mapping; A hybrid power quality measurement equation was formed by integrating and constructing the equation.

[0035] In this step, a unified integrated state vector for the entire network is defined based on the magnitude mutation of the power quality state quantity. Furthermore, it constructs block-diagonal measurement equations for each characteristic component of fundamental, harmonic, and transient disturbances, enabling the incorporation of multi-form and multi-dimensional power quality characteristics into a single linear measurement framework. This improves the mapping and matching degree between different types of power quality state quantities and their corresponding measurement data. By constructing block-diagonal measurement matrices and integrating the matrices and vectors of each component using a block-diagonal structure, it achieves independent mapping of each power quality characteristic component, avoiding the cascading propagation of measurement errors from a single component to other components and improving the anti-interference capability of the measurement model. By deriving the measurement matrices of each component based on the fundamental admittance matrix and the corresponding frequency harmonic admittance matrix, and integrating them into a unified hybrid power quality measurement equation, it ensures that the measurement model fully conforms to the inherent electrical characteristics of the power grid at different frequencies, improving the reliability of power quality state estimation results in complex power grid scenarios with weak measurement capabilities.

[0036] Based on the above embodiments, constructing a measurement equation in the form of a block diagonal includes the following steps: The fundamental wave component quantum equation is constructed based on the following equation: ; In the formula, the state variables Indicates the fundamental voltage amplitude at each node; measurement matrix From the fundamental waveguide admittance matrix Derivation; This represents the fundamental wave measurement error vector; Construct the first based on the following formula The quantum equations of the second harmonic component. : ; In the formula, the state variables Indicates the number of nodes Subharmonic voltage amplitude; measurement matrix Harmonic admittance matrix Derivation; Indicates the first Error terms in the equation for subharmonic measurement; Construct characteristic equations for voltage sag, swell, and fluctuation: ; In the formula, the state variables Indicates the depth of voltage amplitude abrupt change at each node; measurement matrix Obtained by linearizing the fundamental waveguide admittance matrix; This represents the error term in the equations for measuring voltage sags, swells, and fluctuations. In this step, by providing the fundamental component, the first... Independent measurement sub-equations are constructed for subharmonic components, voltage sags, voltage rises, and fluctuation characteristics. The measurement matrices of each sub-equation are derived from the fundamental and harmonic admittance matrices of the corresponding frequencies. This ensures that the measurement mapping relationship of each type of power quality characteristic perfectly matches the inherent electrical characteristics of the power grid under the corresponding operating conditions, improving the physical compliance and modeling accuracy of the measurement equations for each component. By defining dedicated state quantities, measurement matrices matching electrical characteristics, and independent error terms for the three types of characteristics—fundamental, harmonic, and transient disturbances—complete decoupled modeling of power quality characteristic components of different types and frequencies can be achieved, avoiding modeling interference and error propagation between different components and improving the stability of synchronous calculation of multi-dimensional power quality characteristics. For transient characteristics such as voltage sags, voltage rises, and fluctuations, dedicated measurement matrices are derived by linearizing the fundamental admittance matrix to construct sub-equations. This deeply binds the power grid propagation characteristics of transient voltage disturbances with the fundamental electrical physical model, improving the estimation accuracy of transient power quality state quantities in weak measurement scenarios.

[0037] Based on the above embodiments, constructing a block diagonal measurement matrix includes the following steps: By using a vertical stacking method, the measurement vectors of each feature component are sequentially integrated into the total system measurement vector. The state vectors are integrated sequentially into a system composite state vector. : ; The measurement matrix is ​​in the following block diagonal matrix form: ; in, Represents the zero matrix of the corresponding dimension.

[0038] In this step, by adopting a vertical stacking method, the measurement vectors and state vectors of each characteristic component are sequentially integrated into the system's total measurement vector and comprehensive state vector. This allows multi-dimensional power quality characteristics such as fundamental, harmonic, and transient disturbances to be incorporated into a unified global vector space, improving the efficiency of standardized integration of multi-form power quality state quantities and measurement data. By constructing a block-diagonal measurement matrix and setting zero matrices for corresponding dimensions in the off-diagonal blocks, independent mapping of each power quality characteristic component can be achieved, avoiding the cascading propagation of measurement errors from a single component to other components and improving the anti-interference capability of the multi-dimensional measurement model. Through the block-diagonal matrix structure design, the unified integration of the global measurement equations can be completed while preserving the independent electrical and physical characteristics of each component's sub-equations. This balances the physical compliance of modeling each component with the overall integrity of global state estimation, improving the accuracy of multi-dimensional power quality synchronous estimation in complex power grid scenarios with weak measurement capabilities.

[0039] Based on the above embodiments, the integrated construction of the hybrid power quality measurement equation includes the following steps: Integrated total measurement vector Comprehensive state vector Block diagonal measurement matrix and unified error vector The equation for measuring the mass of electrical energy in the pre-mixed state is obtained as follows: ; Among them, the unified error vector It is formed by vertically stacking the error vectors of each component.

[0040] In this step, by integrating the total measurement vector, the comprehensive state vector, the block diagonal measurement matrix, and the unified error vector, a globally unified linear hybrid power quality measurement equation is constructed. This equation can incorporate the measurement mapping of multi-dimensional power quality characteristics such as fundamental frequency, harmonics, voltage sag, voltage rise, and fluctuations into the same linear mathematical framework, improving the overall consistency of synchronous estimation of multi-form power quality status. By vertically stacking the error vectors of each characteristic component to form a unified system error vector, the independent error characteristics of each component can be fully preserved, while achieving unified quantitative management of global errors. This avoids cross-interference between error terms of different components and improves the adaptability of the measurement equation to noisy data in weak measurement scenarios and the accuracy of error analysis. By constructing a unified hybrid measurement equation based on the block diagonal measurement matrix, a linear mapping relationship between global measurement data and the state variables of all network nodes can be established while maintaining the independence and non-cross-coupling of each power quality characteristic component. This balances the physical independence of modeling each component and the completeness of global state estimation, improving the physical compliance of power quality state estimation in complex power grid scenarios with weak measurement.

[0041] Based on the above embodiments, an enhanced dataset containing pseudo-measurement data is generated by constructing edges and weights of a graph structure based on the power grid topology and using a graph convolutional neural network; the steps include: The physical connection characteristics of the power grid topology and the electrical characteristic parameters of the lines are used as the edges and weights of the graph structure, and sparse, noisy power quality measurement data are used as node features to model the power grid topology weighted graph and construct a multi-dimensional feature matrix for standardization. By leveraging the spatial message passing characteristics of graph convolutional neural networks, state-space inference and filtering of bad data from non-power quality monitoring points are achieved, generating a power quality enhancement dataset that includes pseudo-measurement data.

[0042] In this step, by using the physical connection characteristics and line electrical characteristic parameters of the power grid topology as edges and weights of the graph structure, and sparse, noisy power quality measurement data as node features, the power grid topology weighted graph modeling and multi-dimensional feature matrix standardization are completed. This allows for deep embedding of the power grid electrical physical constraints into the input framework of the graph neural network, achieving precise adaptation between the power grid topology space and the graph convolutional computation space, and improving the physical compliance and feature mapping accuracy of the graph model. By utilizing the spatial message passing characteristics of the graph convolutional neural network, state space inference for non-power quality monitoring points is achieved. Without adding new hardware monitoring equipment, pseudo-measurement data of non-monitoring points across the entire network can be supplemented based on topological electrical correlations, improving the network-wide coverage and completeness of the power quality measurement dataset. Through the multi-layer feature propagation and filtering mechanism of the graph convolutional neural network, noise suppression and outlier filtering of bad data in the original measurement data are achieved. This removes Gaussian noise and gross errors in the measurement data, avoids interference from bad data in subsequent state estimation, and improves the quality and anti-interference capability of the input measurement data.

[0043] Based on the above embodiments, modeling the power grid topology weighted graph and constructing a multi-dimensional feature matrix for standardization includes the following steps: The distribution network is abstracted as a weighted undirected graph, and a weighted undirected graph structure is set. As a fixed input to the GCN, it encodes the spatial constraints of the power grid; Extract special data from the amplitude data and map it to the input feature vector of the node; construct... Initial feature matrix of the entire network in dimensionality ; ; Matrix elements According to the node Measurement intensity and characteristic column Assign values ​​to the physical properties.

[0044] By abstracting the distribution network as a weighted undirected graph and using this graph structure as a fixed input to encode the spatial constraints of the power grid in a graph convolutional neural network (GCN), the physical connection characteristics of the power grid topology, the electrical characteristics of the lines, and the computational framework of the GCN can be deeply integrated. This embeds the inherent physical constraints of power grid operation into the underlying model, improving the physical compliance of the GCN feature learning process and enhancing the accuracy of spatial mapping. Furthermore, by extracting power quality amplitude feature data and mapping it to the input feature vectors of the graph nodes, a unified initial feature matrix for the entire network is constructed. It can standardize and integrate scattered and sparse multi-dimensional power quality measurement data into a matrix format that GCN can directly process, realize unified initialization of features of strong measurement nodes and weak measurement nodes without monitoring, and improve the standardization of GCN input data in weak measurement scenarios.

[0045] Based on the above embodiments, a weighted undirected graph can be represented as: ; Among them, node set Corresponding to each bus in the power grid; edge set For the corresponding transmission lines, transformers, and other branches connected to the busbar, an adjacency matrix is ​​established based on the power grid topology. Weight matrix It quantifies the electrical connection strength between nodes, and the weights Can be defined as a node and The absolute value of the line admittance between Or its related functions, the larger the admittance value, the tighter the electrical connection, and the higher its weight in information transmission.

[0046] In this step, by abstracting the distribution network into a weighted undirected graph containing a set of nodes, a set of edges, and a weight matrix, and constructing an adjacency matrix with nodes corresponding to buses and edges corresponding to branches, the physical topology of the power grid can be accurately mapped, improving the matching degree between GCN spatial message transmission and the power grid structure. By defining graph weights with the absolute value of line admittance and quantifying the electrical connection strength of nodes, the electrical coupling characteristics of the power grid can be integrated into the graph structure, improving the accuracy and physical rationality of GCN non-monitoring point state inference. By using this graph as a fixed input to encode power grid spatial constraints in GCN, the physical prior rules of the power grid can be embedded, avoiding the generalization bias of pure data-driven algorithms and improving the credibility of pseudo-measurement data in weak measurement scenarios.

[0047] Based on the above embodiments, matrix elements According to the node Measurement intensity and characteristic column The rules for assigning values ​​to physical properties are as follows: Fundamental component sequence ( ): ; Harmonic component clusters ( ): ; Amplitude mutation depth column ( ): ; in: Represents a node Measured voltage amplitude at the fundamental frequency Represents a node In the Measured voltage amplitude at each harmonic frequency point Represents a node The measured depth of bidirectional amplitude mutations that occur during voltage dips, rises, or fluctuations. 1.0 and 0 represent the per-unit rated operating prior value of the weak measurement node under the fundamental frequency and the steady-state initial prior value under harmonic and disturbance characteristics, respectively.

[0048] By classifying the physical attributes of fundamental components, harmonic components, and amplitude mutation depths, and combining this with the differentiated initial feature matrix based on node measurement intensity, it is possible to accurately distinguish between measured data from strong measurement nodes and prior values ​​from weak measurement nodes, thereby improving the matching degree between the initial feature matrix and the actual measurement configuration of the power grid. By setting standardized rated operating prior values ​​and steady-state initial prior values ​​for weak measurement nodes, it is possible to provide initial characteristics that conform to the power grid operation rules for nodes without monitoring, thereby improving the rationality and convergence speed of GCN state inference. Through the standardized assignment rules, it is possible to achieve standardized initialization of multi-dimensional power quality characteristics, thereby improving the consistency of GCN input data and the accuracy of pseudo-measurement data generation.

[0049] Based on the above embodiments, a power quality enhancement dataset containing pseudo-measurement data is generated, including the following steps: Message passing is achieved through multi-layer network iteration using the spatial convolution operator of GCN; Extracting the feature matrix of the GCN output layer The feature matrix of the output layer For graph convolutional neural networks The final mapping result after subspace message passing; Extract the calculated values ​​of the corresponding weak measurement nodes in the output matrix to generate pseudo measurement data with physical consistency; By integrating actual and pseudo-measurement data, a power quality enhancement dataset is formed.

[0050] By implementing message passing through a multi-layer network using the GCN spatial convolution operator, effective measurement information can be transmitted along the power grid topology, improving the physical consistency of state inference for non-monitoring points. By extracting the output feature matrix of the GCN after L spatial message passing, random noise and bad data in the original measurements can be filtered out, improving the quality of the measurement data. By extracting the calculated values ​​of weak measurement nodes to generate pseudo measurement data and integrating actual measurements to form an enhanced dataset, the measurement coverage of the entire network can be completed, solving the bottleneck of unobservable systems in weak measurement scenarios and improving the accuracy of subsequent power quality state estimation.

[0051] Based on the above embodiments, the hierarchical propagation model is expressed as follows: ; in, This is a hierarchical index, representing the order in which the message is transmitted within the power grid topology; The adjacency matrix after adding self-connections is defined as follows: , This is the adjacency matrix corresponding to the power grid topology. It is the identity matrix; it is the adjacency matrix with self-joins. Depend on Derivation, Representation matrix The degree matrix is ​​a diagonal matrix, and its diagonal elements are determined by the following formula. ; It is the first The node feature matrix of the layer has a dimension of Where N represents the number of nodes in the power grid, F l The dimension representing the feature of the l-th layer; Indicates the first The trainable weight matrix of the layer has dimensions of ; It is a nonlinear activation function used to perform nonlinear mapping on the results of linear transformations.

[0052] By defining a standardized hierarchical propagation model that includes self-connected adjacency matrices and normalized degree matrices, the message passing rules of the power grid topology can be accurately matched, conforming to the electrical coupling characteristics between nodes and improving the physical compliance of GCN feature propagation. Through a multi-level iterative feature propagation mechanism, effective measurement information can be transmitted along the power grid topology, enabling feature inference of non-monitored nodes and improving the rationality of weakly measured node state calculations. By introducing trainable weight matrices and nonlinear activation functions, measurement noise can be effectively filtered and core features extracted, improving the accuracy of pseudo-measurement data generation.

[0053] Based on the above embodiments, a robust state estimation model is established with the objectives of minimizing structural risk and empirical risk, including the following steps: Define the empirical risk objective function Furthermore, the Huber loss function is employed to suppress the influence of outliers in the measurement data on the estimation results; Introducing graph regularization terms as structural risk constraints ; Integrating empirical risk and structural risk, the objective function of a robust power quality state estimation model is constructed as follows: .

[0054] By defining an empirical risk objective function and adopting the Huber loss function, the interference of measurement outliers on the estimation results can be suppressed, and the robustness of the model to noisy and outlier data in weak measurement scenarios can be improved. By introducing a graph regularization term as a structural risk constraint, the physical constraints of the power grid topology can be embedded, improving the physical consistency of the state estimation results. By constructing a unified objective function by integrating empirical risk and structural risk, the estimation accuracy and physical compliance can be balanced, improving the accuracy of power quality state estimation for complex power grids.

[0055] Based on the above embodiments, the empirical risk objective function for: ; in, For measurements from augmented datasets, Let be the power quality state vector to be solved. For the corresponding measurement matrix row vectors; Huber function Defined as: ; in, For threshold function; Structural risk constraints : ; in, For regularization parameters; This represents the power quality state vector of all nodes in the network. Represents the state vector Transpose of; The graph Laplace matrix of the power grid is defined as follows: , This is an adjacency matrix based on physical admittance weights. It is a degree matrix, and its diagonal elements are the sum of the connection weights of each node; Represents the set of power grid nodes. For node indexing; Represents a node and nodes The connection weights between nodes are used to characterize the electrical coupling strength between nodes, and are preferably the absolute value of the corresponding line admittance or a function thereof; Represents a node In the graph convolutional neural network, the first Layer feature representation, Represents a node In the graph convolutional neural network, the first Layer feature representation.

[0056] By employing an empirical risk objective function with a Huber loss function, the model can adaptively suppress interference from outliers and abnormal data, improving its robustness to noisy data with weak measurements. By introducing structural risk constraints based on the Laplacian matrix of the physical admittance weight map, the electrical coupling characteristics between power grid nodes can be embedded, improving the physical consistency of the state estimation results. By constructing a unified objective function that integrates empirical risk and structural risk, the model can balance measurement fitting accuracy with power grid physical constraints, improving the accuracy of power quality state estimation for complex power grids.

[0057] Based on the above embodiments, the robust state estimation model is solved in a distributed manner using the alternating direction multiplier method, including model decomposition and function construction, and distributed iteration and consistent solution.

[0058] Model decomposition and function construction include the following steps: Network topology map Division Overlapping sub-regions Define the local state vector of each sub-region as The state of the common boundary nodes between adjacent sub-regions is defined as a consistency constraint variable. Construct an augmented Lagrange function that includes Lagrange multipliers and a quadratic penalty term; Distributed iterative and consensus-based solutions include the following steps: The ADMM algorithm is used to transform the global optimization problem into a three-step alternating iterative process, in which each sub-region is solved through independent parallel computation and information exchange between adjacent nodes. By monitoring the convergence status of the global original residual and the dual residual, the iteration stops and the final global synthesis state vector is output when the residual meets the preset convergence threshold. .

[0059] By dividing the entire network topology into overlapping sub-regions and defining boundary common node consistency constraint variables, the global optimization problem can be decomposed into local sub-problems, improving the computational adaptability of solving large-scale complex power grids. By constructing an augmented Lagrangian function containing Lagrange multipliers and a quadratic penalty term, boundary consistency constraints can be effectively handled, improving the convergence stability of the algorithm. Through ADMM distributed alternating iteration, each sub-region performs parallel computations and only exchanges adjacent information, which can reduce global communication overhead and improve solution efficiency. By monitoring the global residual convergence state to control iteration, solution accuracy and computational efficiency can be balanced, improving the consistency of global state estimation results.

[0060] Based on the above embodiments, the augmented Lagrange function containing Lagrange multipliers and a quadratic penalty term is expressed as: ; in, The objective function of the robust state estimation model In local subregions The specific mapping on, Indicates the first The Lagrange multipliers of the consistency constraints corresponding to each sub-region, It is its transpose; Indicates the first Local state vectors of each sub-region; It is a globally consistent variable used to coordinate the state of common nodes among sub-regions; The selection matrix is ​​used to select from globally consistent variables. Extracting from the first Components related to each sub-region; This is a penalty parameter used to adjust the convergence speed of the consistency constraint.

[0061] By constructing an augmented Lagrangian function that includes local objective function mapping, Lagrange multipliers, and a quadratic penalty term, the global constraint optimization problem can be decomposed into local problems that can be solved independently in sub-regions, improving the feasibility of distributed solutions for large-scale complex power grids. By introducing global consistency variables and selection matrices, the state constraints of common nodes in adjacent sub-regions can be accurately coordinated, improving the global consistency of the solution results in each sub-region. By setting adjustable penalty parameters, the convergence speed of consistency constraints can be flexibly controlled, improving the convergence stability of the algorithm.

[0062] Based on the above embodiments, the three-step alternating iterative process includes the following steps: Each sub-region in the first In the next iteration, the minimization subproblem is solved using the local augmented dataset, and its internal and boundary state variables are updated: ; in, Indicates the first The sub-regions in the first The local state vector is updated in the next iteration; Indicates the robust objective function at the th... Local forms on individual sub-regions; Indicates the first The sub-regions in the first Lagrange multipliers in the next iteration Indicates its transpose; Indicates the first Global consistency variables during the next iteration; This represents the selection matrix, used to select from globally consistent variables. Extracting from the first Components related to each sub-region; This is a penalty parameter used to adjust the convergence speed of the consistency constraint; This represents the value of the variable that minimizes the objective function; The state information of the boundary nodes of each sub-region is summarized, and the global consistency variable is updated by averaging the values. : ; in, Indicates the first The globally consistent variable is updated in the next iteration; The number of sub-regions; Indicates the first The sub-regions in the first The local state vector is updated in the next iteration; Indicates the first The sub-regions in the first Lagrange multipliers in the next iteration; This represents the selection matrix, used to map local variables to global variables. This indicates the transpose of the selection matrix, used to map local variables to the global variable space; Update the dual variable based on the deviation between the local estimate and the global consensus. : ; in, and They represent the first The sub-regions in the first Second and third Lagrange multipliers in the next iteration; Indicates the first The sub-regions in the first The local state vector is updated in the next iteration; Indicates the first The globally consistent variable is updated in the next iteration; Set the original residual and dual residuals Convergence threshold When the following conditions are met: The iteration terminates when the time is reached.

[0063] In this step, by independently solving the minimization subproblem and updating the local state variables based on the local augmented dataset in each sub-region, parallel computing across multiple regions can be achieved, reducing the computational pressure of global solution and improving the solution efficiency of large-scale complex power grid state estimation. By iteratively updating the global consistency variable and the dual variable, the state of common nodes in each sub-region can be accurately coordinated, ensuring the global consistency of local solution results and improving the overall accuracy of power quality state estimation. By setting convergence thresholds for the original residual and the dual residual to control the iteration termination, the solution accuracy and computational cost can be flexibly balanced, improving the convergence stability and engineering adaptability of the algorithm.

[0064] like Figure 2 As shown, the present invention also provides a robust state estimation system for hybrid power quality in complex power grids, comprising: The state characterization module is used to unify the amplitude data variation of the voltage signal into a power quality state quantity characterizing the system, and to construct a hybrid power quality measurement equation based on the harmonic admittance matrix and the fundamental admittance matrix. The graph enhancement module is used to construct the edges and weights of a graph structure based on the power grid topology, and generate an enhanced dataset containing pseudo-measurement data through a graph convolutional neural network. The model building module is used to build a robust state estimation model based on augmented datasets, with the objectives of minimizing structural risk and empirical risk. The distributed solution module is used to solve the robust state estimation model in a distributed manner using the alternating direction multiplier method, to obtain the variation values ​​of power quality state quantities in each node of the entire power grid and to estimate the power quality state of the entire power grid.

[0065] This system constructs unified power quality state variables and hybrid measurement equations through a state characterization module, breaking down the barriers between independent modeling of steady-state and transient power quality and improving the standardization of multi-morphological disturbance characterization within the same framework. Through a graph enhancement module, it constructs a weighted graph based on the power grid topology and generates an enhanced dataset containing pseudo-measurements via GCN, which can supplement data from weak measurement nodes and improve the system's global observability. Through a model building module, it establishes a robust state estimation model that considers both experience and structural risks, suppressing measurement outlier interference and improving the anti-interference capability of the state estimation results. Through a distributed solution module, it employs the ADMM algorithm for distributed model solving, enabling parallel computation on a large scale of the power grid and improving the solution efficiency and engineering adaptability of power quality state estimation for complex power grids.

[0066] like Figure 3As shown, the present invention also provides a computer device 400, including a processor 410, a memory 420, and a computer program stored in the memory 420 and executable on the processor 410. When the processor 410 executes the program, it implements the steps of the above-mentioned robust state estimation method for hybrid power quality of complex power grids, including: unifying the amplitude data variation of voltage signals into power quality state quantities characterizing the system, and constructing hybrid power quality measurement equations based on harmonic admittance matrices and fundamental admittance matrices; constructing edges and weights of a graph structure based on the power grid topology, and generating an enhanced dataset containing pseudo-measurement data through a graph convolutional neural network; establishing a robust state estimation model with the objectives of minimizing structural risk and empirical risk based on the enhanced dataset; and using the alternating direction multiplier method to solve the robust state estimation model in a distributed manner to obtain the variation values ​​of power quality state quantities in each node of the entire power grid and estimate the power quality state of the entire power grid.

[0067] This invention also provides a computer-readable storage medium 430, on which a computer program is stored. When the computer program is executed by a processor, it implements the steps of the above-described robust state estimation method for hybrid power quality in complex power grids, including: unifying the amplitude data variation of voltage signals into power quality state quantities characterizing the system, and constructing hybrid power quality measurement equations based on harmonic admittance matrices and fundamental admittance matrices; constructing edges and weights of a graph structure based on the power grid topology, and generating an augmented dataset containing pseudo-measurement data through a graph convolutional neural network; establishing a robust state estimation model with the objectives of minimizing structural risk and empirical risk based on the augmented dataset; and using the alternating direction multiplier method to solve the robust state estimation model in a distributed manner, obtaining the variation values ​​of power quality state quantities in each node of the entire power grid and estimating the power quality state of the entire power grid.

[0068] In the description of this invention, the terms "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 indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. "A plurality of" means two or more, unless otherwise explicitly specified.

[0069] In this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0070] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Furthermore, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0071] Any process or method description in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or more executable instructions for implementing a particular logical function or process, and the scope of the preferred embodiments of the invention includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as will be understood by those skilled in the art to which embodiments of the invention pertain.

[0072] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a ordered list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable media include: an electrical connection having one or more wires (electronic device), a portable computer disk drive (magnetic device), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Alternatively, the computer-readable medium may be paper or other suitable media on which the program can be printed, since the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in a computer memory.

[0073] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0074] Those skilled in the art will understand that all or part of the steps of the methods in the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, the program includes one or a combination of the steps of the method embodiments.

[0075] The storage medium mentioned above can be a read-only memory, a disk, or an optical disk, etc. Although embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present invention.

[0076] 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 complex power grid hybrid power quality robust state estimation method, characterized by, Includes the following steps: The amplitude data variation of the voltage signal is unified into a quantity characterizing the power quality state of the system, and a hybrid power quality measurement equation is constructed based on the harmonic admittance matrix and the fundamental admittance matrix. Based on the power grid topology, edges and weights of a graph structure are constructed, and an augmented dataset containing pseudo-measurement data is generated through a graph convolutional neural network. Based on the augmented dataset, a robust state estimation model is established with the objectives of minimizing structural risk and minimizing empirical risk. The robust state estimation model is solved in a distributed manner using the alternating direction multiplier method to obtain the variation values ​​of the power quality state quantities at each node of the entire power grid and to estimate the power quality state of the entire power grid.

2. The complex power grid hybrid power quality robust state estimation method of claim 1, wherein, The amplitude data of the voltage signal includes the amplitude of the fundamental wave, the amplitude of the harmonics, and the bidirectional amplitudes of voltage sags, swells, and fluctuations.

3. The complex power grid hybrid power quality robust state estimation method of claim 2, wherein, The process of unifying the amplitude data variation of the voltage signal into a quantity characterizing the power quality state of the system includes the following steps: The amplitude parameter is used to represent the fundamental wave, characteristic harmonic and inter-harmonic, and the amplitude of the first harmonic component is set as . ​ The voltage signal at time t is expressed by Fourier series including fundamental, multiple harmonic and interharmonic components ; A unified model is adopted to represent the bidirectional amplitude jumps of voltage sag, swell and fluctuation, including the process of voltage amplitude jumping from to and recovering to .

4. The robust state estimation method for hybrid power quality in complex power grids according to claim 1, characterized in that, The construction of the hybrid power quality measurement equation based on the harmonic admittance matrix and the fundamental admittance matrix includes the following steps: A comprehensive state vector is defined based on the abrupt change depth of the power quality state parameters. Construct measurement equations in a block-diagonal form; Construct a block-diagonal measurement matrix, and use a block-diagonal structure to integrate matrices and vectors in a unified and independent mapping; A hybrid power quality measurement equation was formed by integrating and constructing the equation.

5. The robust state estimation method for hybrid power quality in complex power grids according to claim 1, characterized in that, Based on the power grid topology, edges and weights of a graph structure are constructed, and an augmented dataset containing pseudo-measurement data is generated through a graph convolutional neural network. Includes the following steps: The physical connection characteristics of the power grid topology and the electrical characteristic parameters of the lines are used as the edges and weights of the graph structure, and sparse, noisy power quality measurement data are used as node features to model the power grid topology weighted graph and construct a multi-dimensional feature matrix for standardization. By leveraging the spatial message passing characteristics of graph convolutional neural networks, state-space inference and filtering of bad data from non-power quality monitoring points are achieved, generating a power quality enhancement dataset that includes pseudo-measurement data.

6. The robust state estimation method for hybrid power quality in complex power grids according to claim 5, characterized in that, The modeling of the power grid topology weighted graph and the standardization of the construction of the multidimensional feature matrix include the following steps: The distribution network is abstracted as a weighted undirected graph, and a weighted undirected graph structure is set. As a fixed input to the GCN, it encodes the spatial constraints of the power grid; Extract specific data from the amplitude data and map them to the input feature vectors of the nodes; construct... Initial feature matrix of the entire network in dimensionality ; ； Matrix elements According to the node Measurement intensity and characteristic column Assign values ​​to the physical properties.

7. The robust state estimation method for hybrid power quality in complex power grids according to claim 5, characterized in that, The process of generating a power quality enhancement dataset containing pseudo-measurement data includes the following steps: Message passing is achieved through multi-layer network iteration using the spatial convolution operator of GCN; Extracting the feature matrix of the GCN output layer The feature matrix of the output layer For graph convolutional neural networks The final mapping result after subspace message passing; Extract the calculated values ​​of the corresponding weak measurement nodes in the output matrix to generate pseudo measurement data with physical consistency; The actual measurements are integrated with the pseudo-measurement data to form the power quality enhancement dataset.

8. The robust state estimation method for hybrid power quality in complex power grids according to claim 7, characterized in that, Using the spatial convolution operator of GCN, message passing is achieved through multi-layer network iteration, as expressed by the formula: ； in, This is a hierarchical index, representing the order in which the message is transmitted within the power grid topology; The adjacency matrix after adding self-connections is defined as follows: , This is the adjacency matrix corresponding to the power grid topology. It is the identity matrix; it is the adjacency matrix with self-joins. Depend on Derivation, Representation matrix The degree matrix is ​​a diagonal matrix, and its diagonal elements are determined by the following formula. ; It is the first The node feature matrix of the layer has a dimension of Where N represents the number of nodes in the power grid, F l The dimension representing the feature of the l-th layer; Indicates the first The trainable weight matrix of the layer has dimensions of ; It is a nonlinear activation function used to perform nonlinear mapping on the results of linear transformations.

9. The robust state estimation method for hybrid power quality in complex power grids according to claim 1, characterized in that, The establishment of a robust state estimation model with the objectives of minimizing structural risk and empirical risk includes the following steps: Define the empirical risk objective function Furthermore, the Huber loss function is employed to suppress the influence of outliers in the measurement data on the estimation results; Introducing graph regularization terms as structural risk constraints ; Integrating empirical risk and structural risk, the objective function of a robust power quality state estimation model is constructed as follows: 。 10. The robust state estimation method for hybrid power quality in complex power grids according to claim 1, characterized in that, The distributed solution of the robust state estimation model using the alternating direction multiplier method includes model decomposition and function construction, and distributed iteration and consistent solution. The model decomposition and function construction include the following steps: Network topology map Division Overlapping sub-regions Define the local state vector of each sub-region as The state of the common boundary nodes between adjacent sub-regions is defined as a consistency constraint variable. Construct an augmented Lagrange function that includes Lagrange multipliers and a quadratic penalty term; The distributed iterative and consensus-based solution includes the following steps: The ADMM algorithm is used to transform the global optimization problem into a three-step alternating iterative process, in which each sub-region is solved through independent parallel computation and information exchange between adjacent nodes. By monitoring the convergence status of the global original residual and the dual residual, the iteration stops and the final global synthesis state vector is output when the residual meets the preset convergence threshold. .

11. A robust state estimation system for hybrid power quality in complex power grids, characterized in that, include: The state characterization module is used to unify the amplitude data variation of the voltage signal into a power quality state quantity characterizing the system, and to construct a hybrid power quality measurement equation based on the harmonic admittance matrix and the fundamental admittance matrix. The graph enhancement module is used to construct the edges and weights of a graph structure based on the power grid topology, and generate an enhanced dataset containing pseudo-measurement data through a graph convolutional neural network. The model building module is used to build a robust state estimation model based on the augmented dataset, with the objectives of minimizing structural risk and empirical risk. The distributed solution module is used to solve the robust state estimation model in a distributed manner using the alternating direction multiplier method, to obtain the variation values ​​of the power quality state quantity in each node of the entire power grid and to estimate the power quality state of the entire power grid.

Images