Methods for Constructing Threat Models Based on Sensitive Information from Electricity Price Data

Abstract

This invention provides a method for constructing a threat model based on sensitive information reverse inference using electricity price data, belonging to the field of smart grid analysis technology. This invention constructs a homogeneous linear equation model between electricity price and admittance matrix based on a DC power flow model and a local marginal price theory model. It extracts node and edge features from power data, inputs them into a dynamic routing encoder, outputs encoded feature sequences of nodes and edges, performs time-series modeling on the encoded features, outputs the grid admittance parameter sequence at each time step, and corrects and optimizes the parameter sequence. A differential privacy mechanism is used to perturb the electricity price data. Combined with the optimized parameter sequence, the sensitive information reverse inference threat model is constructed. This invention utilizes dynamic feature encoding and time-series modeling techniques, combined with a differential privacy strategy, to achieve effective reverse inference of grid admittance parameters based on publicly available data, and also completes privacy protection and risk assessment of electricity price data using the differential privacy strategy.

Description

Technical Field

[0001] This invention relates to the field of smart grid analysis technology, specifically to a method for constructing a threat model based on sensitive information from electricity price data through reverse reasoning. Background Technology

[0002] With the reform of the power market and the development of smart grids, a large amount of local marginal and related electricity price data of nodes in power grid dispatch and market operation are publicly disclosed. Since there is an inherent mathematical relationship between electricity price data and power grid physical parameters, attackers or third parties may be able to reconstruct some sensitive parameters and structures of the power grid by reverse reasoning analysis, combined with publicly disclosed electricity prices, shadow prices and other data, in order to achieve in-depth mining of the power grid status, thereby posing a potential threat to the power grid environment.

[0003] In existing technologies, traditional power grid state estimation or parameter identification methods mostly rely on static models, which make it difficult to effectively capture the dynamic time-series relationship between electricity price data and power grid admittance parameters. Furthermore, they lack the means to systematically assess and protect against privacy leakage risks during the reverse reasoning process. Moreover, existing differential privacy protection mechanisms in power system data applications mainly focus on simple data perturbations, lacking methods for joint modeling and optimization that combine power grid physical laws and electricity price data characteristics. This makes it difficult to balance data practicality and privacy protection effects, and it is impossible to effectively quantify the threat level of reverse reasoning, thus limiting the scientific formulation and implementation of privacy protection strategies.

[0004] Therefore, it is necessary to provide a method for constructing a threat model based on sensitive information from electricity price data to solve the aforementioned problem.

[0005] The information disclosed in the background section is only intended to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0006] The purpose of this invention is to provide a method for constructing a threat model based on sensitive information from electricity price data through reverse reasoning, in order to solve the problems mentioned in the background art.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] A method for constructing a threat model based on sensitive information from electricity price data through reverse reasoning, comprising the following steps:

[0009] Step 1: Construct a DC power flow model and a local marginal price theoretical model. Based on the two constructed mathematical theoretical models, establish a homogeneous linear equation model between electricity price and grid admittance matrix.

[0010] Step 2: Extract node and edge features from the collected power data and vectorize them. Input the feature vectors into the dynamic routing encoder. Combine the constructed homogeneous linear equation model to dynamically select and weight the input feature vectors to output the encoded feature sequence of nodes and edges.

[0011] Step 3: Based on the selective state-space model, perform time-series modeling on the encoded feature sequence, establish the dynamic relationship between electricity price data and admittance matrix, and output the power grid admittance parameter sequence at each time point in the time series;

[0012] Step 4: Based on the output grid admittance parameter sequence, and combined with the physical laws of the power flow equations of the power system, the grid admittance parameter sequence is corrected, and the grid admittance parameter sequence is optimized through loss function constraints;

[0013] Step 5: Based on the optimized grid admittance parameter sequence, a differential privacy mechanism is introduced to apply noise perturbation to the publicly available electricity price data. By combining the differential privacy strategy, the reverse reasoning model based on electricity price data is constructed.

[0014] Furthermore, the methods used to construct the DC power flow model and the local marginal price theory model are as follows:

[0015] This method acquires local marginal prices for different time periods in the electricity market to reflect economic signals indicating the balance of power supply and demand and congestion at each node in the power grid. Correspondingly, it acquires shadow prices for line capacity constraints to reflect the marginal impact of line congestion on prices. Based on the acquired power grid topology information, it determines the number of nodes in the power grid. Total number of lines Their connections constitute the incident matrix. ;

[0016] Based on the DC power flow model, the node voltage phase angle vector of the power grid is: The node injected power vector is The nodal admittance matrix is Then there is Node admittance matrix From the incident matrix and the inverse vector of nodal admittance Composition, in which , Indicates the first in the power grid The reciprocal of the reactance of the line, The node is located at the first Line susceptance, Index the power grid line where the node is located. from arrive It covers every line in the power grid and constructs a DC power flow model based on the calculated admittance matrix. The formula used to construct the DC power flow model is as follows:

[0017]

[0018] in, This represents the transpose of the incident matrix. The nodal admittance vector. It is a vector A diagonal matrix consisting of diagonal elements. This is the vector of reciprocal reactances of the nodes, that is, the reciprocal of the reactance of each line to which the node is located. Taking the derivative of each element in the matrix one by one, we can obtain the following relationship: , Represented by vector A diagonal matrix consisting of diagonal elements;

[0019] Based on the relationship between congestion price and shadow price, the Lagrange multiplier corresponding to the line capacity constraint is the shadow price. A theoretical model of local marginal price is constructed by utilizing the mapping relationship between local marginal price and line congestion shadow price. The formula used is as follows:

[0020]

[0021] in, Indicates the node at time [time]. The congestion component of the local marginal price. This represents the base price when there is no congestion. A vector containing only 1s, used to convert scalars. Extend to all nodes, yes The transpose of the matrix is ​​used to map line congestion prices to node prices. Indicates that the node is Price shadow based on real-time network congestion. It is the power transmission distribution factor matrix, used to represent the influence factor of the line on the node.

[0022] Furthermore, a homogeneous linear equation model between electricity price and grid admittance matrix is ​​established, based on the following method:

[0023] Based on the established DC power flow model, the following derivation is performed using the admittance matrix and the incident matrix. The matrix is ​​based on the following formula:

[0024]

[0025] in, This represents the inverse of the node admittance matrix, characterizing the response of node power changes to changes in node voltage phase angle. This indicates that changes in node voltage phase angle are converted into changes in line power.

[0026] based on The relationship between the matrix, admittance matrix, and incident matrix, combined with the mapping relationship between local marginal price and line congestion shadow price, is used to establish the relationship between electricity price and grid admittance. The formula used is as follows:

[0027]

[0028] in, This represents the transpose of the inverse matrix of the nodal admittances;

[0029] The homogeneous linear equations are established by simultaneously solving the relationship between electricity price and grid admittance in a DC power flow model. The formula used is as follows:

[0030]

[0031] Among them, the homogeneous linear equation model It is used to calculate the price difference between two nodes at the end of a line, reflecting the difference in electricity prices at both ends of the line;

[0032] collect Electricity price and shadow price data at different times were used to write the corresponding homogeneous linear equations. These equations were then stacked to form a system of linear equations, which were used to deduce the unknown admittance reciprocal vector. This is to complete the construction of a homogeneous linear equation model between electricity price and grid admittance matrix.

[0033] Furthermore, node and edge features are extracted and vectorized. The input feature vectors are dynamically selected and weighted to output a sequence of node and edge encoded features. The method used is as follows:

[0034] For the first in the power grid Each node constructs a node feature vector, including but not limited to: the node's local marginal price, node type, and historical node price statistics, which are collectively denoted as... ,in Indicates the first The feature vector of each node The index of the node, and ; for the connection nodes in the power grid With nodes The Each line constructs an edge feature vector, including but not limited to: the congestion shadow price corresponding to the line, the reciprocal of the line reactance, and the line capacity constraint, which are collectively denoted as... ,in Indicates the connection node With nodes No. If the edge feature vectors of a line are given, then the feature vectors of all nodes form a matrix. The matrix is ​​composed of all edge eigenvectors. ;

[0035] Using the node feature matrix and edge feature matrix as input, and based on the graph structure message passing mechanism of the dynamic routing encoder, combined with power grid topology information, node and edge features are dynamically selected and weighted to update the hidden layer encoding features of nodes and edges. The formula describing this process is as follows:

[0036]

[0037] in, This indicates that in the graph neural network... The first in the layer The encoded feature vector of each node, It is an activation function used to enhance the expressive power of the model. Indicates the first The first in the layer The node is the first The dynamic weighting coefficients of the features of each neighboring node, and satisfying ,and Calculated by the attention mechanism, Indicates the first Layer node feature linear transformation matrix, This indicates that in the graph neural network... The first in the layer The encoded feature vectors of the neighboring nodes, hour, It is the first The original input feature vectors of the neighboring nodes, Indicates the first The set of neighboring nodes of a node. It is the index of adjacent nodes. Indicates the first In the layer to the first The dynamic weighting coefficients of the edge features, and satisfying ,and Calculated by the attention mechanism, Indicates the first Layer edge feature linear transformation matrix, Indicates the first Layer edge The encoded feature vector, For connecting nodes Its neighboring nodes The set of edges;

[0038] After multiple iterations of the dynamic routing encoder and weighted by physical constraints, the final output is... , ,in and This refers to the encoded feature sequence of nodes and edges.

[0039] Furthermore, time-series modeling is performed on the encoded feature sequence to establish a dynamic relationship between electricity price data and the admittance matrix, so as to output the power grid admittance parameter sequence at each time point within the time series. The method used is as follows:

[0040] Based on the node-encoded feature sequence and edge-encoded feature sequence output by the dynamic routing encoder, for continuous time intervals... The feature sequences constitute the temporal input set, where Let represent the total number of consecutive time points used for time series analysis. A selective state-space model is constructed, with node and edge encoded feature sequences as observations. The inverse vector of node admittance is taken as the hidden state of the system. The model dynamics are as follows:

[0041]

[0042]

[0043] in, Indicates in The reciprocal vector of the line reactance at time t. In order to be in The change information of the input node at any given time. For process noise, Indicates in The reciprocal vector of the line reactance at time t. For the model's observations, For selective observation mapping function, To observe the noise, Indicates in Encoded feature sequence of time nodes, Indicates in The encoded feature sequence of the edge at time step;

[0044] Based on the theory of DC power flow and local marginal price, the observation equation is specified as follows:

[0045]

[0046] in, , Is The transpose of the inverse of the nodal admittance matrix at time t. Is time in vector A diagonal matrix consisting of diagonal elements. Indicates in The predicted value of the local marginal price at any given time point. Indicates in Predicted value of shadow price for line congestion at any given time;

[0047] At each time step, the encoded feature sequences of the acquired nodes and edges are combined and substituted into the homogeneous linear equation system constraints, based on the following formula:

[0048]

[0049] Among them, for time series observation sets Stacked linear equations and Kalman filtering was used to... The state is updated, and the final output is the sequence of grid admittance parameters at each time point within the time series. .

[0050] Furthermore, by combining the physical laws of the power flow equations, the power grid admittance parameter sequence is corrected, and then optimized through loss function constraints. The method used is as follows:

[0051] The power grid admittance parameter sequence obtained by reverse reasoning As the initial parameter sequence, the corresponding node admittance matrix is ​​calculated according to the DC power flow model of the power system. The system state is reconstructed using the grid topology and line parameters. Combined with the actual collected local marginal price and line congestion shadow price data, a homogeneous linear equation model is used as physical constraints to evaluate the matching degree between the grid admittance parameters and the electricity price data. By constructing a loss function with physical constraint deviation and electricity price data fitting error as the core, an optimization algorithm is used to adjust the admittance parameter sequence and minimize the loss function. The formula used is as follows:

[0052]

[0053] in, This represents the loss function, used to measure the degree of matching between grid admittance parameters and electricity price data. It is the Euclidean norm of a vector, used to measure the magnitude of error. yes Local marginal price data of nodes as actually observed at any given time. yes Real-time observed shadow price data for line congestion. This is a regularization term used to constrain the variation of the inverse vector of the line reactance over time, preventing overfitting. This represents the reciprocal vector of line reactance in the predicted power grid admittance parameter sequence, which is the predicted value of admittance parameters based on the optimization algorithm iteration process. It is an approximate reconstruction of the reciprocal vector of the actual power grid line reactance.

[0054] The gradient descent method is used to iteratively update the power grid admittance parameter sequence to minimize the loss function. The iteration stops when the degree of matching between the power grid admittance parameters output by the loss function and the electricity price data meets a preset threshold, and the final corrected power grid admittance parameter sequence is output. .

[0055] Furthermore, a differential privacy mechanism is introduced to apply noise perturbation to the publicly available electricity price data. By combining the differential privacy strategy, a threat model for inverse reasoning about sensitive information in the electricity price data is constructed. The method used is as follows:

[0056] For the local marginal price data of the node actually observed at each moment Introducing the satisfaction - Differential privacy Laplace noise perturbation generates perturbed local marginal price data based on the following formula:

[0057]

[0058] in, Indicates in Local marginal disturbance price data at any given time. This represents an independent and identically distributed noise vector;

[0059] Based on local marginal disturbance price data, observed line congestion shadow price data, and the corrected and optimized power grid admittance parameter sequence, a homogeneous linear equation system is reconstructed. An optimization method is used to inversely infer the admittance parameters, and the optimization objective function is:

[0060]

[0061] in, It is used for reverse reasoning of the power grid admittance parameter sequence. The cost function, for Minimization is performed to obtain the inferred values ​​of the grid admittance parameters through reverse reasoning;

[0062] The inferred values ​​of the grid admittance parameters obtained through reverse reasoning are compared with the optimized and corrected grid admittance parameter values. The mean square error is used to evaluate the accuracy of the reverse reasoning, based on the following formula:

[0063]

[0064] in, This represents the mean square error, used to measure the accuracy of the reverse inference of the grid admittance parameters. Indicates the first The line is The inferred power grid admittance value obtained through reverse reasoning at every moment. Indicates the first The line is The power grid admittance parameters are optimized and corrected at all times; the mean square error is... Perform differential privacy strategy analysis. The smaller the value, the higher the accuracy of reverse reasoning, and the greater the risk of sensitive information leakage; conversely, the smaller the value, the higher the accuracy of reverse reasoning. The larger the value, the better the privacy protection.

[0065] Using electricity price data perturbed by differential privacy mechanism, line congestion shadow price data, and power grid topology information as inputs, an optimization model based on these data is constructed to inversely infer the inferred values ​​of the power grid admittance parameters. The error between the estimated and actual values ​​of the power grid admittance parameters is used as an assessment indicator of privacy leakage risk to complete the construction of the inverse reasoning threat model.

[0066] Compared with the prior art, the beneficial effects of the present invention are:

[0067] This invention achieves accurate identification and dynamic modeling of the complex temporal relationship between electricity price data and grid admittance parameters by constructing a homogeneous linear equation model based on a DC power flow model, a local marginal price theory model, and a dynamic routing encoder. Furthermore, this invention combines differential privacy mechanisms with grid physical constraints and electricity price data characteristics to design a data perturbation strategy, specifically quantifying the risks of reverse inference. This ensures both the practicality and accuracy of electricity price data while significantly reducing the risk of sensitive information leakage, achieving a balance between privacy protection and data application. Attached Figure Description

[0068] Figure 1 This is a schematic diagram of the overall method flow of the present invention. Detailed Implementation

[0069] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0070] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0071] Example:

[0072] Please see Figure 1 A method for constructing a threat model based on sensitive information from electricity price data through reverse reasoning, comprising the following steps:

[0073] Step 1: Construct a DC power flow model and a local marginal price theoretical model. Based on the two constructed mathematical theoretical models, establish a homogeneous linear equation model between electricity price and grid admittance matrix.

[0074] In a specific embodiment of this invention, we construct a basic model based on DC power flow model and local marginal price theory to systematically reflect the physical and economic impact mechanisms of grid node voltage phase angle, power injection, and line capacity constraints on electricity price formation. Furthermore, by deriving the PTDF matrix and establishing a homogeneous linear equation system, and by comprehensively utilizing multi-time electricity price and shadow price data, we achieve reverse reasoning of the grid admittance inverse vector. This method not only improves the accuracy of grid parameter identification and the ability to depict time-series dynamics, but also provides a solid mathematical foundation and model support for the reverse reasoning threat assessment of sensitive information.

[0075] It should be noted that the reason for choosing to construct a DC power flow model and a local marginal price theory model, and combining them to comprehensively construct a homogeneous linear equation model between electricity price and grid admittance matrix, is mainly because the DC power flow model can effectively simplify the calculation of optimal power flow in the grid and reveal the linear relationship between node voltage phase angle and power injection, while the local marginal price theory model closely links the economic signals of the electricity market with the physical constraints of the grid. The combination of the two models achieves an accurate characterization and analytical expression of the relationship between electricity price data and grid admittance parameters, enabling the systematic and efficient reasoning and identification of key physical parameters of the grid using electricity price and shadow price data at multiple times.

[0076] Furthermore, the methods used to construct the DC power flow model and the local marginal price theory model are as follows:

[0077] This method acquires local marginal prices for different time periods in the electricity market to reflect economic signals indicating the balance of power supply and demand and congestion at each node in the power grid. Correspondingly, it acquires shadow prices for line capacity constraints to reflect the marginal impact of line congestion on prices. Based on the acquired power grid topology information, it determines the number of nodes in the power grid. Total number of lines Their connections constitute the incident matrix. ;

[0078] Based on the DC power flow model, the node voltage phase angle vector of the power grid is: The node injected power vector is The nodal admittance matrix is Then there is Node admittance matrix From the incident matrix and the inverse vector of nodal admittance Composition, in which , Indicates the first in the power grid The reciprocal of the reactance of the line, The node is located at the first Line susceptance, Index the power grid line where the node is located. from arrive It covers every line in the power grid and constructs a DC power flow model based on the calculated admittance matrix. The formula used is:

[0079]

[0080] in, This represents the transpose of the incident matrix. The nodal admittance vector. It is a vector A diagonal matrix consisting of diagonal elements. This is the vector of reciprocal reactances of the nodes, that is, the reciprocal of the reactance of each line to which the node is located. Taking the derivative of each element in the matrix one by one, we can obtain the following relationship: , Represented by vector A diagonal matrix consisting of diagonal elements;

[0081] Based on the relationship between congestion price and shadow price, the Lagrange multiplier corresponding to the line capacity constraint is the shadow price. A theoretical model of local marginal price is constructed by utilizing the mapping relationship between local marginal price and line congestion shadow price. The formula used is as follows:

[0082]

[0083] in, Indicates the node at time [time]. The congestion component of the local marginal price. This represents the base price when there is no congestion. A vector containing only 1s, used to convert scalars. Extend to all nodes, yes The transpose of the matrix is ​​used to map line congestion prices to node prices. Indicates that the node is Price shadow based on real-time network congestion. It is the power transmission distribution factor matrix, used to represent the influence factor of the line on the node.

[0084] Furthermore, a homogeneous linear equation model between electricity price and grid admittance matrix is ​​established, based on the following method:

[0085] Based on the established DC power flow model, the following derivation is performed using the admittance matrix and the incident matrix. The matrix is ​​based on the following formula:

[0086]

[0087] in, This represents the inverse of the node admittance matrix, characterizing the response of node power changes to changes in node voltage phase angle. This indicates that changes in node voltage phase angle are converted into changes in line power.

[0088] based on The relationship between the matrix, admittance matrix, and incident matrix, combined with the mapping relationship between local marginal price and line congestion shadow price, is used to establish the relationship between electricity price and grid admittance. The formula used is as follows:

[0089]

[0090] in, This represents the transpose of the inverse matrix of the nodal admittances;

[0091] The homogeneous linear equations are established by simultaneously solving the relationship between electricity price and grid admittance in a DC power flow model. The formula used is as follows:

[0092]

[0093] Among them, the homogeneous linear equation model It is used to calculate the price difference between two nodes at the end of a line, reflecting the difference in electricity prices at both ends of the line;

[0094] collect Electricity price and shadow price data at different times were used to write the corresponding homogeneous linear equations. These equations were then stacked to form a system of linear equations, which were used to deduce the unknown admittance reciprocal vector. This is to complete the construction of a homogeneous linear equation model between electricity price and grid admittance matrix.

[0095] Step 2: Extract node and edge features from the collected power data and vectorize them. Input the feature vectors into the dynamic routing encoder. Combine the constructed homogeneous linear equation model to dynamically select and weight the input feature vectors to output the encoded feature sequence of nodes and edges.

[0096] In a specific embodiment of the present invention, by extracting multidimensional features of power grid nodes and lines, and using a dynamic routing encoder combined with a graph structure message passing mechanism for dynamic selection and weighting, efficient expression and deep modeling of complex topological relationships and time-varying features of the power grid are achieved. This not only improves the ability to represent the mapping relationship between electricity price data and power grid physical parameters, but also enhances the model's accuracy in capturing the interaction effects between nodes and changes in line status.

[0097] It should be noted that the reason we perform dynamic weighting and multi-layer encoding on the feature vectors is that the state of each node and line in the power grid is affected by the neighborhood structure and a variety of physical and economic factors. Single or static features are difficult to fully reflect their dynamic changes and interdependencies. By introducing an attention mechanism to achieve dynamic weight allocation, the model can adaptively focus on key information and important connections, avoid noise interference, and improve information transmission efficiency.

[0098] Furthermore, node and edge features are extracted and vectorized. The input feature vectors are dynamically selected and weighted to output a sequence of node and edge encoded features. The method used is as follows:

[0099] For the first in the power grid Each node constructs a node feature vector, including but not limited to: the node's local marginal price, node type, and historical node price statistics, which are collectively denoted as... ,in Indicates the first The feature vector of each node The index of the node, and ; for the connection nodes in the power grid With nodes The Each line constructs an edge feature vector, including but not limited to: the congestion shadow price corresponding to the line, the reciprocal of the line reactance, and the line capacity constraint, which are collectively denoted as... ,in Indicates the connection node With nodes No. If the edge feature vectors of a line are given, then the feature vectors of all nodes form a matrix. The matrix is ​​composed of all edge eigenvectors. ;

[0100] Using the node feature matrix and edge feature matrix as input, and based on the graph structure message passing mechanism of the dynamic routing encoder, combined with power grid topology information, node and edge features are dynamically selected and weighted to update the hidden layer encoding features of nodes and edges. The formula describing this process is as follows:

[0101]

[0102] in, This indicates that in the graph neural network... The first in the layer The encoded feature vector of each node, It is the sigmoid activation function, used to transform a linear relationship into a non-linear one. Indicates the first The first in the layer The node is the first The dynamic weighting coefficients of the features of each neighboring node, and satisfying ,and Calculated by the attention mechanism, Indicates the first Layer node feature linear transformation matrix, This indicates that in the graph neural network... The first in the layer The encoded feature vectors of the neighboring nodes, hour, It is the first The original input feature vectors of the neighboring nodes, Indicates the first The set of neighboring nodes of a node. It is the index of adjacent nodes. Indicates the first In the layer to the first The dynamic weighting coefficients of the edge features, and satisfying ,and Calculated by the attention mechanism, Indicates the first Layer edge feature linear transformation matrix, Indicates the first Layer edge The encoded feature vector, For connecting nodes Its neighboring nodes The set of edges;

[0103] After multiple iterations of the dynamic routing encoder and weighted by physical constraints, the final output is... , ,in and This refers to the encoded feature sequence of nodes and edges.

[0104] Step 3: Based on the selective state-space model, perform time-series modeling on the encoded feature sequence, establish the dynamic relationship between electricity price data and admittance matrix, and output the power grid admittance parameter sequence at each time point in the time series.

[0105] In a specific embodiment of this invention, the encoded feature sequences of nodes and edges output by the dynamic routing encoder are used as observations to construct a selected state-space model. The line susceptance vector is used as the hidden state variable of the system to describe its dynamic change over time. By introducing a continuous time-series input set, and using observation equations based on the DC power flow model and local marginal price theory, the dynamic mapping relationship between electricity price data and grid admittance parameters is concretized into mathematical expressions. Combined with the constraints of the homogeneous linear equation system, a complete time-series linear equation system is formed. The state-space model is then recursively estimated and updated using the Kalman filter algorithm to achieve efficient and accurate inference of the grid admittance parameter sequence at each time step within the time series. We systematically integrate the time-varying dynamic characteristics of grid topology features, market price information, and grid physical parameters. Through the time-series reasoning capabilities of the state-space model and Kalman filter, we accurately capture the changing patterns of grid admittance parameters over time, effectively improving the time-series analysis capability and prediction accuracy of sensitive information reverse reasoning.

[0106] Furthermore, time-series modeling is performed on the encoded feature sequence to establish a dynamic relationship between electricity price data and the admittance matrix, so as to output the power grid admittance parameter sequence at each time point within the time series. The method used is as follows:

[0107] Based on the node-encoded feature sequence and edge-encoded feature sequence output by the dynamic routing encoder, for continuous time intervals... The feature sequences constitute the temporal input set, where Let represent the total number of consecutive time points used for time series analysis. A selective state-space model is constructed, with node and edge encoded feature sequences as observations. The inverse vector of node admittance is taken as the hidden state of the system. The model dynamics are as follows:

[0108]

[0109]

[0110] in, Indicates in The reciprocal vector of the line reactance at time t. In order to be in The change information of the input node at any given time. For process noise, Indicates in The reciprocal vector of the line reactance at time t. For the model's observations, For selective observation mapping function, To observe the noise, Indicates in Encoded feature sequence of time nodes, Indicates in The encoded feature sequence of the edge at time step;

[0111] Based on the theory of DC power flow and local marginal price, the observation equation is specified as follows:

[0112]

[0113] in, , Is The transpose of the inverse of the nodal admittance matrix at time t. Is time in vector A diagonal matrix consisting of diagonal elements. Indicates in The predicted value of the local marginal price at any given time point. Indicates in Predicted value of shadow price for line congestion at any given time;

[0114] At each time step, the encoded feature sequences of the acquired nodes and edges are combined and substituted into the homogeneous linear equation system constraints, based on the following formula:

[0115]

[0116] Among them, for time series observation sets Stacked linear equations and Kalman filtering was used to... The system is updated, and the final output is a sequence of grid admittance parameters for each time step within the time series. .

[0117] Step 4: Based on the output grid admittance parameter sequence, and combined with the physical laws of the power flow equations of the power system, the grid admittance parameter sequence is corrected, and the grid admittance parameter sequence is optimized through loss function constraints.

[0118] In a specific embodiment of this invention, we correct and optimize the power grid admittance parameter sequence obtained through reverse reasoning by combining the physical laws of power system flow equations. The reason for this correction is that the admittance parameter sequence is the core physical parameter of the power grid model, directly related to the accuracy of power grid state estimation and safe operation. Due to potential issues such as data noise, simplified model assumptions, or incomplete input features during reverse reasoning, the initially estimated admittance parameter sequence often contains biases and errors. Without correction, this can lead to distortions in subsequent analysis and decision-making. Therefore, we employ a loss function based on physical constraints, closely integrating the power grid admittance parameters with actual observed electricity price data and shadow prices. By minimizing physical constraint bias and fitting errors, and introducing a regularization term to prevent overfitting, we iteratively optimize the admittance parameter sequence. This is a crucial means to ensure that the parameter estimation results are scientifically reasonable and meet the actual operating conditions of the power system. The core purpose of this approach is to improve the matching degree between the admittance parameter sequence and the actual power grid operating state, thereby enhancing the reliability and stability of the model.

[0119] Furthermore, by combining the physical laws of the power flow equations, the power grid admittance parameter sequence is corrected, and then optimized through loss function constraints. The method used is as follows:

[0120] The power grid admittance parameter sequence obtained by reverse reasoning As the initial parameter sequence, the corresponding node admittance matrix is ​​calculated according to the DC power flow model of the power system. The system state is reconstructed using the grid topology and line parameters. Combined with the actual collected local marginal price and line congestion shadow price data, a homogeneous linear equation model is used as physical constraints to evaluate the matching degree between the grid admittance parameters and the electricity price data. By constructing a loss function with physical constraint deviation and electricity price data fitting error as the core, an optimization algorithm is used to adjust the admittance parameter sequence and minimize the loss function. The formula used is as follows:

[0121]

[0122] in, This represents the loss function, used to measure the degree of matching between grid admittance parameters and electricity price data. It is the Euclidean norm of a vector, used to measure the magnitude of error. yes Local marginal price data of nodes as actually observed at any given time. yes Real-time observed shadow price data for line congestion. This is a regularization term used to constrain the variation of the inverse vector of the line reactance over time, preventing overfitting. This represents the reciprocal vector of line reactance in the predicted power grid admittance parameter sequence, which is the predicted value of admittance parameters based on the optimization algorithm iteration process. It is an approximate reconstruction of the reciprocal vector of the actual power grid line reactance.

[0123] The gradient descent method is used to iteratively update the power grid admittance parameter sequence to minimize the loss function. The iteration stops when the degree of matching between the power grid admittance parameters output by the loss function and the electricity price data meets a preset threshold, and the final corrected power grid admittance parameter sequence is output. .

[0124] Step 5: Based on the optimized grid admittance parameter sequence, a differential privacy mechanism is introduced to apply noise perturbation to the publicly available electricity price data. By combining the differential privacy strategy, the reverse reasoning model based on electricity price data is constructed.

[0125] In a specific embodiment of the present invention, by applying Laplace noise perturbation to publicly available local marginal price data, an effective threat model for inverse reasoning of sensitive information in electricity price data is constructed. The importance of this method lies in the fact that, while ensuring the privacy and security of electricity price data, it can still construct an optimized model based on the perturbed data combined with line congestion shadow prices and grid topology information to perform inverse reasoning of admittance parameters. This effectively balances data availability and privacy protection. By minimizing the loss function containing the perturbed price data, the inferred values ​​of grid admittance parameters obtained through inverse reasoning are obtained. The mean square error is used to assess the risk of privacy leakage, quantifying the accuracy of inverse reasoning and the effect of privacy protection. This enables a scientific assessment and control of the threat of sensitive information leakage, thereby improving the security and credibility of power system data sharing.

[0126] It should be noted that the core of the reverse inference threat model construction method lies in analyzing publicly available electricity price data and related market information, utilizing the physical laws and mathematical models of the power system to infer key sensitive parameters within the power grid. First, based on the time-series nodes and line characteristics extracted by the dynamic routing encoder, a state-space model is established, and recursive algorithms such as Kalman filtering are used to achieve a preliminary estimate of the admittance parameters. Second, combining the DC power flow model of the power system and actual electricity price data, the preliminary estimated admittance parameter sequence is optimized and corrected by constructing physical constraints and loss functions to improve the accuracy and physical consistency of parameter estimation. Finally, addressing the issue of potentially publicly available electricity price data in practical applications, a differential privacy mechanism is introduced to perturb the electricity price data, constructing a reverse inference optimization model with privacy protection, and comprehensively evaluating the accuracy of reverse inference and the risk of privacy leakage.

[0127] Furthermore, a differential privacy mechanism is introduced to apply noise perturbation to the publicly available electricity price data. By combining the differential privacy strategy, a threat model for inverse reasoning about sensitive information in the electricity price data is constructed. The method used is as follows:

[0128] For the local marginal price data of the node actually observed at each moment Introducing the satisfaction - Differential privacy Laplace noise perturbation generates perturbed local marginal price data based on the following formula:

[0129]

[0130] in, Indicates in Local marginal disturbance price data at any given time. This represents an independent and identically distributed noise vector;

[0131] Based on local marginal disturbance price data, observed line congestion shadow price data, and the corrected and optimized power grid admittance parameter sequence, a homogeneous linear equation system is reconstructed. An optimization method is used to inversely infer the admittance parameters, and the optimization objective function is:

[0132]

[0133] in, It is used for reverse reasoning of the power grid admittance parameter sequence. The cost function, for Minimization is performed to obtain the inferred values ​​of the grid admittance parameters through reverse reasoning;

[0134] The inferred values ​​of the grid admittance parameters obtained through reverse reasoning are compared with the optimized and corrected grid admittance parameter values. The mean square error is used to evaluate the accuracy of the reverse reasoning, based on the following formula:

[0135]

[0136] in, This represents the mean square error, used to measure the accuracy of the reverse inference of the grid admittance parameters. Indicates the first The line is The inferred power grid admittance value obtained through reverse reasoning at every moment. Indicates the first The line is The power grid admittance parameters are optimized and corrected at all times; the mean square error is... Perform differential privacy strategy analysis. The smaller the value, the higher the accuracy of reverse reasoning, and the greater the risk of sensitive information leakage; conversely, the smaller the value, the higher the accuracy of reverse reasoning. The larger the value, the better the privacy protection.

[0137] Using electricity price data perturbed by differential privacy mechanism, line congestion shadow price data, and power grid topology information as inputs, an optimization model based on these data is constructed to inversely infer the inferred values ​​of the power grid admittance parameters. The error between the estimated and actual values ​​of the power grid admittance parameters is used as an assessment indicator of privacy leakage risk to complete the construction of the inverse reasoning threat model.

[0138] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0139] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.

[0140] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.

[0141] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A method for constructing a threat model based on sensitive information from electricity price data through reverse reasoning, characterized in that, The specific steps include: Step 1: Construct a DC power flow model and a local marginal price theoretical model. Based on the two constructed mathematical theoretical models, establish a homogeneous linear equation model between electricity price and grid admittance matrix. Step 2: Extract node and edge features from the collected power data and vectorize them. Input the feature vectors into the dynamic routing encoder. Combine the constructed homogeneous linear equation model to dynamically select and weight the input feature vectors to output the encoded feature sequence of nodes and edges. Step 3: Based on the selective state-space model, perform time-series modeling on the encoded feature sequence, establish the dynamic relationship between electricity price data and admittance matrix, and output the power grid admittance parameter sequence at each time point in the time series; Step 4: Based on the output grid admittance parameter sequence, and combined with the physical laws of the power flow equations of the power system, the grid admittance parameter sequence is corrected, and the grid admittance parameter sequence is optimized through loss function constraints; Step 5: Based on the optimized grid admittance parameter sequence, a differential privacy mechanism is introduced to apply noise perturbation to the publicly available electricity price data. By combining the differential privacy strategy, the reverse reasoning model based on electricity price data is constructed. Time-series modeling of the encoded feature sequence is performed to establish a dynamic relationship between electricity price data and the admittance matrix, so as to output the power grid admittance parameter sequence at each time point within the time series. The method used is as follows: Based on the node-encoded feature sequence and edge-encoded feature sequence output by the dynamic routing encoder, for continuous time intervals... The feature sequences constitute the temporal input set, where Let represent the total number of consecutive time points used for time series analysis. A selective state-space model is constructed, with node and edge encoded feature sequences as observations. The inverse vector of node admittance is taken as the hidden state of the system. The model dynamics are as follows: in, Indicates in The reciprocal vector of the line reactance at time t. In order to be in The change information of the input node at any given time. For process noise, Indicates in The reciprocal vector of the line reactance at time t. For the model's observations, This is a selective observation mapping function used to establish the relationship between system observations and hidden states. To observe the noise, Indicates in Encoded feature sequence of time nodes, Indicates in The encoded feature sequence of the edge at time step; Based on the theory of DC power flow and local marginal price, the observation equation is specified as follows: in, , Is The transpose of the inverse of the nodal admittance matrix at time t. Is time in vector A diagonal matrix consisting of diagonal elements. Indicates in The predicted value of the local marginal price at any given time point. Indicates in Predicted value of shadow price for line congestion at any given time; At each time step, the encoded feature sequences of the acquired nodes and edges are combined and substituted into the homogeneous linear equation system constraints, based on the following formula: Among them, for time series observation sets Stacked linear equations and Kalman filtering was used to... The state is updated, and the final output is the sequence of grid admittance parameters at each time point within the time series. .

2. The method for constructing a threat model based on sensitive information from electricity price data according to claim 1, characterized in that, The methods used to construct the DC power flow model and the local marginal price theory model are as follows: This method acquires local marginal prices for different time periods in the electricity market to reflect economic signals indicating the balance of power supply and demand and congestion at each node in the power grid. Correspondingly, it acquires shadow prices for line capacity constraints to reflect the marginal impact of line congestion on prices. Based on the acquired power grid topology information, it determines the number of nodes in the power grid. Total number of lines Their connections constitute the incident matrix. ; Based on the DC power flow model, the node voltage phase angle vector of the power grid is: The node injected power vector is The nodal admittance matrix is Then there is Node admittance matrix From the incident matrix and the inverse vector of nodal admittance Composition, in which , Indicates the first in the power grid The reciprocal of the reactance of the line, The node is located at the first Line susceptance, Index the power grid line where the node is located. from arrive It covers every line in the power grid and constructs a DC power flow model based on the calculated admittance matrix. The formula used is: in, This represents the transpose of the incident matrix. The nodal admittance vector. It is a vector A diagonal matrix consisting of diagonal elements. This is the vector of reciprocal reactances of the nodes, that is, the reciprocal of the reactance of each line to which the node is located. Taking the derivative of each element in the matrix one by one, we can obtain the following relationship: , Represented by vector A diagonal matrix consisting of diagonal elements; Based on the relationship between congestion price and shadow price, the Lagrange multiplier corresponding to the line capacity constraint is the shadow price. A theoretical model of local marginal price is constructed by utilizing the mapping relationship between local marginal price and line congestion shadow price. The formula used is as follows: in, Indicates the node at time [time]. The congestion component of the local marginal price is used to reflect supply and demand balance and network congestion. This represents the base price when there is no congestion. A vector containing only 1s, used to convert scalars. Extend to all nodes, yes The transpose of the matrix is ​​used to map line congestion prices to node prices. Indicates that the node is Price shadow based on real-time network congestion. It is the power transmission distribution factor matrix, used to represent the influence factor of the line on the node.

3. The method for constructing a threat model based on sensitive information from electricity price data according to claim 2, characterized in that, The homogeneous linear equation model between electricity price and grid admittance matrix is ​​established using the following method: Based on the established DC power flow model, the following derivation is performed using the admittance matrix and the incident matrix. The matrix is ​​based on the following formula: in, This represents the inverse of the node admittance matrix, characterizing the response of node power changes to changes in node voltage phase angle. This indicates that changes in node voltage phase angle are converted into changes in line power. based on The relationship between the matrix, admittance matrix, and incident matrix, combined with the mapping relationship between local marginal price and line congestion shadow price, is used to establish the relationship between electricity price and grid admittance. The formula used is as follows: in, This represents the transpose of the inverse of the nodal admittance matrix; The homogeneous linear equations are established by simultaneously solving the relationship between electricity price and grid admittance in a DC power flow model. The formula used is as follows: Among them, the homogeneous linear equation model It is used to calculate the price difference between two nodes at the end of a line, reflecting the difference in electricity prices at both ends of the line; collect Electricity price and shadow price data at different times were used to write the corresponding homogeneous linear equations. These equations were then stacked to form a system of linear equations, which were used to deduce the unknown admittance reciprocal vector. This is to complete the construction of a homogeneous linear equation model between electricity price and grid admittance matrix.

4. The method for constructing a threat model based on sensitive information from electricity price data according to claim 3, characterized in that, The node and edge features are extracted and vectorized. The input feature vectors are dynamically selected and weighted to output a sequence of node and edge encoded features. The method used is as follows: For the first in the power grid Each node constructs a node feature vector, including but not limited to: the node's local marginal price, node type, and historical node price statistics, which are collectively denoted as... ,in Indicates the first The feature vector of each node The index of the node, and ; for the connection nodes in the power grid With nodes The Each line constructs an edge feature vector, including but not limited to: the congestion shadow price corresponding to the line, the reciprocal of the line reactance, and the line capacity constraint, which are collectively denoted as... ,in Indicates the connection node With nodes No. If the edge feature vectors of a line are given, then the feature vectors of all nodes form a matrix. The matrix is ​​composed of all edge eigenvectors. ; Using the node feature matrix and edge feature matrix as input, and based on the graph structure message passing mechanism of the dynamic routing encoder, combined with power grid topology information, node and edge features are dynamically selected and weighted to update the hidden layer encoding features of nodes and edges. The formula describing this process is as follows: in, This indicates that in the graph neural network... The first in the layer The encoded feature vector of each node, It is an activation function used to enhance the expressive power of the model. Indicates the first The first in the layer The node is the first The dynamic weighting coefficients of the features of each neighboring node, and satisfying ,and Calculated by the attention mechanism, Indicates the first Layer node feature linear transformation matrix, This indicates that in the graph neural network... The first in the layer The encoded feature vectors of the neighboring nodes, hour, It is the first The original input feature vectors of the neighboring nodes, Indicates the first The set of neighboring nodes of a node. It is the index of adjacent nodes. Indicates the first In the layer to the first The dynamic weighting coefficients of the edge features, and satisfying ,and Calculated by the attention mechanism, Indicates the first Layer edge feature linear transformation matrix, Indicates the first Layer edge The encoded feature vector, For connecting nodes Its neighboring nodes The set of edges; After multiple iterations of the dynamic routing encoder and weighted by physical constraints, the final output is... , ,in and This refers to the encoded feature sequence of nodes and edges.

5. The method for constructing a threat model based on sensitive information from electricity price data according to claim 1, characterized in that, Based on the physical laws of power flow equations, the power grid admittance parameter sequence is corrected, and then optimized through loss function constraints. The method used is as follows: The power grid admittance parameter sequence obtained by reverse reasoning As the initial parameter sequence, the corresponding node admittance matrix is ​​calculated according to the DC power flow model of the power system. The system state is reconstructed using the grid topology and line parameters. Combined with the actual collected local marginal price and line congestion shadow price data, a homogeneous linear equation model is used as physical constraints to evaluate the matching degree between the grid admittance parameters and the electricity price data. By constructing a loss function with physical constraint deviation and electricity price data fitting error as the core, an optimization algorithm is used to adjust the admittance parameter sequence and minimize the loss function. The formula used is as follows: in, This represents the loss function, used to measure the degree of matching between grid admittance parameters and electricity price data. It is the Euclidean norm of a vector, used to measure the magnitude of error. yes Local marginal price data of nodes as actually observed at any given time. yes Real-time observed shadow price data for line congestion. This is a regularization term used to constrain the variation of the inverse vector of the line reactance over time, preventing overfitting. This represents the reciprocal vector of line reactance in the predicted power grid admittance parameter sequence, which is the predicted value of admittance parameters based on the optimization algorithm iteration process. It is an approximate reconstruction of the reciprocal vector of the actual power grid line reactance. The gradient descent method is used to iteratively update the power grid admittance parameter sequence to minimize the loss function. The iteration stops when the degree of matching between the power grid admittance parameters output by the loss function and the electricity price data meets a preset threshold, and the final corrected power grid admittance parameter sequence is output. .

6. The method for constructing a threat model based on sensitive information from electricity price data according to claim 5, characterized in that, A differential privacy mechanism is introduced to apply noise perturbation to publicly available electricity price data. By combining this with a differential privacy strategy, a threat model for inverse reasoning about sensitive information in the electricity price data is constructed. The method used is as follows: For the local marginal price data of the node actually observed at each moment Introducing satisfaction - Differential privacy Laplace noise perturbation generates perturbed local marginal price data based on the following formula: in, Indicates in Local marginal disturbance price data at any given time. This represents an independent and identically distributed noise vector; Based on local marginal disturbance price data, observed line congestion shadow price data, and the corrected and optimized power grid admittance parameter sequence, a homogeneous linear equation system is reconstructed. An optimization method is used to inversely infer the admittance parameters, and the optimization objective function is: in, It is used for reverse reasoning of the power grid admittance parameter sequence. The cost function, for Minimization is performed to obtain the inferred values ​​of the grid admittance parameters through reverse reasoning; The inferred values ​​of the grid admittance parameters obtained through reverse reasoning are compared with the optimized and corrected values. The mean square error is used to evaluate the accuracy of the reverse reasoning, based on the following formula: in, This represents the mean square error, used to measure the accuracy of the reverse inference of the grid admittance parameters. Indicates the first The line is The inferred power grid admittance value obtained through reverse reasoning at every moment. Indicates the first The line is The power grid admittance parameters are optimized and corrected at all times; the mean square error is... Perform differential privacy strategy analysis. The smaller the value, the higher the accuracy of reverse reasoning, and the greater the risk of sensitive information leakage; conversely, the smaller the value, the higher the accuracy of reverse reasoning. The larger the value, the better the privacy protection. Using electricity price data perturbed by differential privacy mechanism, line congestion shadow price data, and power grid topology information as inputs, an optimization model based on these data is constructed to inversely infer the inferred values ​​of the power grid admittance parameters. The error between the estimated and actual values ​​of the power grid admittance parameters is used as an assessment indicator of privacy leakage risk to complete the construction of the inverse reasoning threat model.

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