A joint probability prediction method for nodal electricity prices

Abstract

This invention relates to the field of power system electricity price forecasting technology, and discloses a joint probabilistic forecasting method for nodal electricity prices, comprising: constructing a dual-state monitoring system to simultaneously track the physical state of the power grid and market liquidity indicators, generating physical constraint state vectors and market liquidity state vectors; designing critical early warning indicators by nonlinearly combining the degree of physical constraint and liquidity level; introducing a state-space mapping algorithm to divide the physical liquidity state space into stable, metastable, and critical regions, constructing a refined representation of the system state; based on a directed causal graph propagation mechanism model, tracking how changes in physical constraints affect market participant behavior and thus market liquidity; applying conditional extreme value theory to model extreme price distributions for identified critical states; and by establishing a coupled model of physical constraints and market liquidity, this invention effectively solves the technical problem that existing methods cannot capture the complex interaction between the two.

Description

Technical Field

[0001] This invention relates to the field of power system electricity price prediction technology, and more specifically, to a joint probability prediction method for nodal electricity prices. Background Technology

[0002] In existing technologies, commonly used electricity price forecasting methods mainly include statistical regression methods, artificial intelligence methods, and hybrid forecasting methods. Statistical regression methods mainly rely on historical data to build mathematical models for forecasting, such as time series analysis and state-space models; artificial intelligence methods mainly utilize machine learning algorithms for forecasting, such as neural networks and support vector machines; hybrid forecasting methods combine multiple forecasting methods to improve forecast accuracy.

[0003] However, existing electricity price forecasting technologies still have the following shortcomings:

[0004] Existing forecasting methods typically treat power system physical constraints and market behavior as independent factors, neglecting their coupling relationship. This is particularly true in emergency situations such as extreme weather and equipment failures, where the interaction between physical constraints and market liquidity intensifies, leading to decreased forecast accuracy. Current extreme electricity price forecasting methods often employ simple statistical extrapolation or threshold triggering mechanisms, failing to accurately identify the system's critical state. This results in high false alarm and false negative rates, hindering the provision of reliable early warning information to market participants. Traditional forecasting methods lack in-depth analysis of the extreme electricity price formation mechanism, failing to effectively quantify the contribution of different factors and their propagation paths. In complex power systems, changes in physical constraints can indirectly trigger price fluctuations by influencing market participant behavior; such complex causal relationships are difficult to accurately characterize by existing models. Furthermore, existing forecasting methods generally suffer from high computational complexity and insufficient real-time performance. In emergency situations with rapidly changing system states, they struggle to perform large-scale probability calculations and risk assessments in a timely manner, failing to meet the electricity market's requirements for forecast timeliness.

[0005] Therefore, there is an urgent need to develop an electricity price forecasting method that can effectively capture the coupling relationship between physical constraints and market liquidity, accurately identify the critical state of the system, deeply analyze the extreme electricity price formation mechanism, and has strong real-time computing capabilities. Summary of the Invention

[0006] This invention provides a joint probability prediction method for nodal electricity prices, which solves the technical problems of traditional electricity price prediction methods, such as the inability to capture the complex coupling relationship between physical system constraints and market liquidity, the lack of accurate identification of critical state of the system, the inability to effectively quantify the contribution of different factors to the formation of extreme electricity prices, and the high computational complexity and insufficient real-time performance.

[0007] This invention provides a joint probability prediction method for nodal electricity prices, comprising:

[0008] A dual-state monitoring system is constructed to simultaneously track the physical state of the power grid and market liquidity indicators, generating physical constraint state vectors and market liquidity state vectors, and subsequent analysis is carried out based on the generated state vectors;

[0009] Based on the physical constraint state vector and the market liquidity state vector, a critical early warning indicator is designed by combining the degree of physical constraint and the liquidity level nonlinearly, thereby identifying potential extreme price events;

[0010] Based on the critical early warning index designed, a state space mapping algorithm is introduced to divide the physical flow state space into a stable region, a metastable region, and a critical region, thereby constructing a refined representation of the system state.

[0011] Based on the state space partitioning results, a propagation mechanism model based on directed causal graphs is developed to track the propagation path of changes in physical constraints affecting market participants' behavior and thus market liquidity, ultimately leading to price fluctuations.

[0012] Based on the analysis results of the propagation mechanism model, the extreme price distribution is modeled using conditional extreme value theory. For the identified critical states, the probability prediction and risk quantification results of extreme electricity price events are provided.

[0013] Furthermore, the steps for constructing the dual-state monitoring system include:

[0014] The power system state estimation algorithm is used to analyze real-time physical data of the power grid and generate physical constraint state vectors. The physical constraint state vectors include line power flow ratio, node voltage margin, generator output margin and key indicators of network topology.

[0015] Analyze real-time electricity market trading data to generate a market liquidity state vector, which includes key indicators such as order depth, bid-ask spread, trading volume change rate, and price volatility.

[0016] Construct a database linking physical liquidity status to store historical status data and corresponding price results.

[0017] Furthermore, the steps for designing critical early warning indicators include:

[0018] The two-way sensitivity analysis method is used to quantify the sensitivity of each indicator in the physical constraint state vector and liquidity state vector to the impact of extreme price events;

[0019] Based on the results of sensitivity analysis, key indicators that have an impact on extreme price events were selected, and the weight coefficients of each indicator were determined.

[0020] A critical early warning index is constructed, which forms a comprehensive measure of the critical state of the system by nonlinearly combining key physical constraint indexes and liquidity indexes.

[0021] Furthermore, the nonlinear combination function of the physical constraint index is implemented using a radial basis function network, the nonlinear combination function of the liquidity index is implemented using a deep neural network based on an attention mechanism, and the nonlinear combination function of the interaction between physical constraints and liquidity is implemented using a tensor network.

[0022] Furthermore, the step of introducing the state-space mapping algorithm includes:

[0023] Construct a high-dimensional physical liquidity state space, which is jointly defined by the physical constraint state vector and the liquidity state vector;

[0024] Dimensionality reduction techniques are used to project high-dimensional space onto two-dimensional and three-dimensional representations;

[0025] Based on the occurrence of extreme price events in historical data, the state space is divided into a stable region, a metastable region, and a critical region.

[0026] Analyze the dynamic evolution trajectory of the system state in the state space to identify dangerous path patterns that lead the system into the critical region.

[0027] Furthermore, the state space region division adopts a hybrid method that integrates statistical physics theory and machine learning. A density-based clustering algorithm is applied to identify density-uniform regions in the state space, and a support vector data description algorithm is used to learn the boundaries of each region.

[0028] Furthermore, the steps for developing a propagation mechanism model based on a directed causal graph include:

[0029] Based on domain knowledge and data analysis, a directed graph model is constructed to represent the causal relationship between physical constraints, market behavior, and price changes.

[0030] The causal discovery algorithm is used to analyze historical data and learn the strength parameters of each connection in the causal graph.

[0031] Based on the learned causal graph, we analyze the main paths through which changes in physical constraints are transmitted to changes in liquidity via market behavior, including path importance assessment, key node identification, and path time lag analysis.

[0032] Furthermore, the steps for modeling extreme price distributions using conditional extreme value theory include:

[0033] For historical price data, determine an appropriate threshold level and extract extreme price samples that exceed the threshold;

[0034] For the system state in the critical region, a distribution model of extreme electricity prices is established by applying conditional extremum theory, and the generalized Pareto distribution is used to fit the data exceeding the threshold.

[0035] Based on the fitted conditional extreme value distribution, risk indicators are calculated, including conditional exceedance probability, conditional value at risk, conditional expected excess loss, and extreme event duration estimate.

[0036] Furthermore, the shape and scale parameters of the generalized Pareto distribution are mapped to the system state through a conditional parameterization model, thereby enabling the extreme distribution to adaptively adjust the system state.

[0037] The present invention provides a computer storage medium, including a memory and one or more processors, wherein the memory stores executable code, and when the one or more processors execute the executable code, it is used to implement the above-described joint probability prediction method for nodal electricity prices.

[0038] The beneficial effects of this invention are as follows: by establishing a coupled model of physical constraints and market liquidity, the technical problem that existing methods cannot capture the complex interaction between the two is effectively solved. The early warning system can accurately identify the critical state caused by the synergistic effect of physical constraints and liquidity, improve the accuracy of extreme price prediction, and reduce the false alarm rate and the missed alarm rate.

[0039] By introducing a state-space mapping algorithm, a refined representation and regional division of the system state are achieved. Compared with the traditional simple threshold triggering mechanism, it provides a more accurate critical state identification capability. Through state trajectory analysis, the system can identify dangerous system trajectories that may lead to extreme prices in advance, providing sufficient response time for market participants.

[0040] The directed causal graph propagation mechanism model developed in this invention reveals the intrinsic mechanism by which changes in physical constraints affect market liquidity and thus lead to price fluctuations, making the prediction results interpretable. Compared with traditional "black box" models, this solution can provide analysis of the causes of extreme price formation and identification of key factors, supporting the formulation of targeted risk management strategies.

[0041] By applying conditional extreme value theory to model extreme prices and focusing the computation on specific regions of the physical liquidity state space, computational complexity is reduced, computational efficiency is improved, and the need for real-time early warning is met. At the same time, the accuracy of risk quantification is also improved, reducing the estimation error of conditional risk value and providing a more reliable basis for risk hedging and trading decisions. Attached Figure Description

[0042] Figure 1 This is a flowchart of a joint probability prediction method for nodal electricity prices in this invention;

[0043] Figure 2 It is a bar chart comparing the sensitivity of different physical constraints and market liquidity factors to extreme prices. Detailed Implementation

[0044] The subject matter described herein will now be discussed with reference to exemplary embodiments. It should be understood that these embodiments are discussed only to enable those skilled in the art to better understand and implement the subject matter described herein, and changes may be made to the function and arrangement of the elements discussed without departing from the scope of this specification. Various processes or components may be omitted, substituted, or added as needed in the examples. Furthermore, some features described in the examples may be combined in other examples.

[0045] At least one embodiment of the present invention discloses a joint probability prediction method for nodal electricity prices, such as Figure 1 As shown, it includes:

[0046] Step 1: Construct a dual-state monitoring system to simultaneously track the physical state of the power grid and market liquidity indicators, generate physical constraint state vectors and market liquidity state vectors, and conduct subsequent analysis based on the generated state vectors;

[0047] This step utilizes a dual-channel monitoring framework for the physical market to simultaneously track the physical state of the power grid and market liquidity indicators, providing foundational data for subsequent critical state identification. This step includes the following sub-steps:

[0048] Step 1.1, Construction of the power grid physical condition monitoring module;

[0049] Power system state estimation algorithms are used to analyze real-time physical data of the power grid and generate physical constraint state vectors. This vector contains the following key metrics:

[0050] Line power flow ratio: The ratio of the actual power flow of each critical line to its rated capacity;

[0051] Node voltage margin: The margin between the voltage of each critical node and its upper and lower limits;

[0052] Generator output margin: The difference between the actual output of each generator set and its maximum / minimum output limit;

[0053] Network topology: the operational status of critical paths and devices.

[0054] The data preprocessing of the physical constraint state vector includes the following steps: First, the power flow ratio of the lines is normalized by dividing the percentage value by 100 to convert it into a range of zero to one; second, the node voltage margin is standardized by using the minimum-maximum standardization method to uniformly map the margin values ​​of different voltage levels to the zero-to-one range; then, the generator output margin is normalized by dividing the power value by the rated capacity of the corresponding unit to obtain the standardized output ratio; finally, the network topology state is encoded by using one-hot encoding to convert the operating status of lines and equipment (such as commissioning, shutdown, and maintenance) into numerical vectors to ensure that all physical constraint indicators have the same numerical range and comparability.

[0055] The power system state estimation algorithm in this sub-step is implemented using weighted least squares combined with a power flow model. The algorithm first collects measurement data from the power grid (such as line power and node voltage), and then obtains the optimal estimate by solving an optimization problem.

[0056] The core of power system state estimation algorithms is an optimization problem aimed at minimizing the weighted squared error. First, measurement data, such as power and voltage, are collected from various nodes and lines in the power grid. Then, each measurement is assigned a different weight, reflecting its reliability; more reliable data receives a higher weight. Next, the difference between each measurement and its theoretical value is calculated, and these differences are squared and multiplied by their respective weights. Finally, all weighted squared errors are summed, and an optimization algorithm is used to find the system state variable value that minimizes the total error. In this way, the optimal estimate of the power grid's physical state can be obtained, and various key physical constraints can be calculated based on this estimate.

[0057] Nonlinear function connecting state variables and measurement values The specific form of expression depends on the measurement type. For power measurements, the function is based on AC power flow equations; for voltage amplitude measurements, the function directly selects the corresponding state variables. Measurement weights The weight is usually set as the reciprocal of the measurement variance, reflecting the reliability of the measurement; a larger weight indicates a more reliable measurement. The optimization problem is solved using the Newton-Raphson method or the Gauss-Newton method, iteratively approaching the optimal solution until the residual is less than a preset threshold or the maximum number of iterations is reached.

[0058] nonlinear functions The specific implementation is as follows: For power measurement types, the function is based on AC power flow equations. First, it calculates the power transmission between nodes based on the node voltage amplitude and phase angle. The calculation process includes steps such as voltage difference calculation, impedance parameter application, and trigonometric function calculation, and finally obtains the theoretical power value. For voltage amplitude measurement types, the function directly selects the corresponding voltage amplitude component from the state variables. For other types of measurements, the function establishes a mathematical mapping relationship between state variables and measured values ​​based on the physical laws of the power system, ensuring that the measurement equations can accurately reflect the physical operating state of the power grid.

[0059] Measurement weight Data preprocessing needs to address the issue of differences in the magnitude of variance among different types of measurements: First, the historical variance of each type of measurement is calculated, including the variance of power measurement, voltage measurement, and other types of measurements; then, a logarithmic transformation is performed on the reciprocal of the variance to compress the differences in numerical range; next, a grouping standardization method is used to internally standardize the weights of measurements of the same type to ensure that the relative weight relationship between similar measurements is maintained; finally, all weights are globally normalized to make the sum of the weights equal to one, avoiding the impact of excessively large or small weight values ​​on the convergence of the optimization algorithm.

[0060] Step 1.2, Construction of the market liquidity status monitoring module;

[0061] Analyze real-time electricity market transaction data to generate a market liquidity state vector. This vector contains the following key metrics:

[0062] Order depth: The cumulative order volume at all price levels in the market;

[0063] Bid-ask spread: The difference between the highest bid price and the lowest ask price in the market;

[0064] Volume change rate: The rate at which the volume of transactions changes per unit of time;

[0065] Price volatility: the standard deviation of price changes in the short term.

[0066] Liquidity indicators are also normalized to form a unified representation of market liquidity status. The data preprocessing for the market liquidity status vector employs a multi-level standardization strategy: first, order depth is logarithmically transformed and then normalized to minimize fluctuations and skewed distributions in order volume; second, bid-ask spreads are standardized using a sliding window method, based on the historical mean and standard deviation, to adapt to dynamic changes in market conditions; then, the rate of change in trading volume is truncated and standardized, first limiting extreme outliers to a reasonable range, and then performing zero-mean unit variance standardization; finally, price volatility is standardized using quantiles, mapping volatility indicators to the zero-to-one range to ensure that each liquidity indicator has equal weight and influence in numerical calculations.

[0067] The market liquidity monitoring module comprises a multi-layered data processing pipeline, consisting of a data acquisition layer, a preprocessing layer, an indicator calculation layer, and a feature fusion layer. The data acquisition layer is responsible for acquiring raw transaction data in real time from the electricity market trading system, including order information, transaction records, and price sequences. The preprocessing layer cleans, denoises, and standardizes the raw data. The indicator calculation layer calculates various liquidity indicators based on the processed data. The feature fusion layer integrates these indicators into a unified liquidity status vector. This module is adaptable to different electricity market trading mechanisms and supports liquidity monitoring under various trading methods, including continuous bidding and call auction.

[0068] Step 1.3, construct the state association database;

[0069] A physical liquidity status-related database is constructed to store historical status data and corresponding price results, providing data support for subsequent model training. The database includes:

[0070] Physical constraint state vector Historical records;

[0071] Market Liquidity State Vector Historical records;

[0072] The corresponding nodal electricity price data at that time;

[0073] Information indicating extreme price events.

[0074] The data preprocessing for extreme price event markers employs a hierarchical coding strategy: First, one-hot coding is used for event types (price increase, price decrease, normal fluctuation) to convert classification labels into binary vector representations; second, ordinal coding is used for event severity levels to map mild, moderate, and severe levels to continuous numerical values; then, logarithmic transformation and standardization are performed on event durations to address their skewed distribution characteristics; finally, a correspondence between event markers and timestamps is established to ensure that the marker information can be accurately linked to the corresponding system status data.

[0075] The state-related database adopts a time-series database architecture, optimized for high-frequency time-series data. It employs a tiered storage strategy, storing recent hot data in high-speed storage media and migrating historical cold data to high-capacity storage devices, while maintaining a unified access interface. The database also implements efficient time-range queries and multi-dimensional conditional filtering, supporting rapid retrieval of data for specific time periods and system states. To ensure real-time performance, the database uses a stream processing framework for incremental updates; new state data is written and indexed as soon as it is generated, and can be immediately used for subsequent analysis.

[0076] Step 2: Based on the physical constraint state vector and the market liquidity state vector, a critical early warning indicator is designed by combining the degree of physical constraint and the liquidity level nonlinearly to identify potential extreme price events;

[0077] This step constructs a critical early warning indicator by combining nonlinear physical constraints and liquidity levels, enabling the early identification of potential extreme price events. This step includes the following sub-steps:

[0078] Step 2.1, Two-way sensitivity analysis;

[0079] Applying a two-way sensitivity analysis method, the physical constraint state vector is quantified. and market liquidity state vector The sensitivity of various indicators to the impact of extreme price events. The specific calculations are as follows:

[0080] In the two-way sensitivity analysis, the probability pairs of extreme price events are first calculated. Sensitivity of each physical constraint index That is, calculating the specific physical constraint index. The rate of change of the probability of extreme price events when small changes occur. Next, the probability of extreme price events is calculated relative to the probability of the first... Sensitivity of individual liquidity indicators That is, calculating when a specific liquidity indicator The rate of change of the probability of extreme price events when small changes occur. These two types of sensitivity indicators can quantify the impact of different physical constraints and market liquidity factors on the formation of extreme price events, thereby identifying key driving factors.

[0081] like Figure 2 As shown in Table 4, the sensitivity analysis results of different physical constraints and market liquidity factors on extreme prices are presented, quantifying the contribution of each factor to the formation of extreme prices and providing a basis for the selection of key indicators. As shown in Table 4, the line flow ratio and bid-ask spread have the highest sensitivity to extreme price events, reaching 0.85 and 0.78 respectively, indicating that these two indicators are key factors influencing the formation of extreme prices.

[0082] The two-way sensitivity analysis method is implemented by combining Monte Carlo simulation and perturbation analysis. First, each indicator in the historical data is subjected to a small perturbation. Then, the changes in the output probability are observed using a trained extreme event prediction model. To improve computational efficiency, this system employs an adaptive sampling strategy, performing denser sampling in potentially high-sensitivity areas. Furthermore, the system considers the mutual influence between indicators, introducing interactive sensitivity analysis to identify the impact of indicator combinations on extreme events. The sensitivity calculation results not only serve as the basis for subsequent weight determination but also provide market regulators with a reference for key monitoring indicators.

[0083] Data preprocessing for sensitivity indicators ensures the reliability of the analysis results: First, outlier detection and processing are performed on the calculated sensitivity values, using the interquartile range method to identify and handle extreme sensitivity values; second, sensitivity is standardized to map the sensitivity values ​​of different indicators to the same numerical range, facilitating subsequent comparison and weight allocation; then, the sensitivity time series is smoothed using moving average or exponential smoothing methods to reduce the impact of short-term fluctuations; finally, confidence intervals for sensitivity are established, and statistical tests are used to ensure the statistical significance of the sensitivity analysis results.

[0084] Step 2.2, Key Indicator Screening and Weighting;

[0085] Based on the sensitivity analysis results, key indicators with a significant impact on extreme price events were identified, and the weight coefficients of each indicator were determined. The weight allocation followed these principles:

[0086] The more sensitive the indicator, the greater its weight;

[0087] Consider the interrelationships between indicators to avoid information duplication;

[0088] The rationality of adjusting the weights was verified through historical data.

[0089] Key indicator selection and weighting employ a multi-stage automated process. First, a pre-screening based on sensitivity thresholds eliminates indicators with below-average sensitivity. Then, Principal Component Analysis (PCA) is used to identify highly correlated indicator groups, selecting the most sensitive indicator from each group as a representative. Next, LASSO (Least Absolute Shrinkage and Selection Operator) regularized regression is used to further screen indicators with independent predictive power. Finally, Bayesian optimization determines the optimal weight combination, which maximizes predictive performance on the validation set (e.g., F1 score or area under the precision-recall curve). The weight optimization process also incorporates a time-sliding window cross-validation mechanism to ensure robustness of weight allocation under different market conditions.

[0090] Step 2.3, Construction of critical early warning indicators;

[0091] A Critical Index (CI) is constructed, which forms a comprehensive measure of the system's critical state by nonlinearly combining key physical constraint indicators and liquidity indicators. The calculation formula is as follows:

[0092] In constructing the critical warning indicator, the following steps are taken: First, the nonlinear combination value of the physical constraint indicator is calculated, representing the contribution of the physical system state to the critical state. Second, the nonlinear combination value of the liquidity indicator is calculated, representing the contribution of market liquidity to the critical state. Then, the nonlinear combination value of the interaction between physical constraints and liquidity is calculated, representing the contribution of the combined effect of these two factors to the critical state. Finally, based on the relative importance of the three combination values, different weighting coefficients are assigned, and the final critical warning indicator value is obtained through weighted summation. This indicator comprehensively reflects the degree of proximity of the current system state to the critical state; a higher indicator value indicates that the system is closer to the critical state that could trigger extreme price events.

[0093] The critical early warning index is constructed using a multi-level nonlinear combination method, overcoming the limitation of traditional linear combination methods in capturing complex relationships. The nonlinear combination function of the physical constraint index... A radial basis function network is used, which can effectively capture the synergistic effect of different combinations of physical constraint states through adaptive basis functions; a nonlinear combination function of liquidity indicators. This employs a deep neural network based on an attention mechanism, which dynamically adjusts the importance of different liquidity indicators according to the current market state; a nonlinear combination function of the interaction between physical constraints and liquidity terms. A tensor network is employed, specifically designed to model high-order interactions between the two classes of indicators. The outputs of three nonlinear combination functions are passed through weight parameters. , and These will be integrated into the final critical early warning indicators. , and These represent the contribution weights of the physical constraint combination, liquidity combination, and cross-term combination to the final indicator, respectively. The weight parameters are optimized using reinforcement learning methods, and the reward function is designed as a weighted sum of the lead time for successfully predicting extreme events and the accuracy, encouraging the system to issue warnings as early as possible while maintaining accuracy.

[0094] Nonlinear combination function of physical constraint index The specific implementation is as follows: First, the various indices in the physical constraint state vector are normalized. Then, a nonlinear transformation is performed through a radial basis function network. This network contains multiple radial basis function nodes. Each node calculates the Euclidean distance between the input vector and the center vector and then activates it through a Gaussian kernel function. Finally, the outputs of all nodes are weighted and summed. The weights are obtained through adaptive learning of the training data. The output value reflects the degree of contribution of the physical system state to the critical state.

[0095] Nonlinear combination function of liquidity indicators The specific implementation is as follows: First, the liquidity state vector is input into a multi-layer neural network. An attention mechanism module is embedded in the network. This module can dynamically calculate the importance weights of each liquidity indicator. The weight calculation is based on the similarity between the current market state and historical key states. Then, the weighted features are transformed through a non-linear activation function, and finally, a value reflecting the contribution of the market liquidity state to the critical state is output.

[0096] Nonlinear combination function of physical constraints and liquidity terms The specific implementation is as follows: First, the physical constraint vector and the mobility vector are subjected to tensor outer product operation to form a high-order interaction tensor. Then, the key interaction patterns are extracted through tensor decomposition technology. Next, the extracted interaction features are subjected to nonlinear transformation. Finally, the contribution value of the synergistic effect of physical constraints and mobility to the critical state is output through a fully connected layer. This function pays special attention to the nonlinear coupling effect between the two types of factors.

[0097] Step 3: Based on the designed critical early warning indicators, a state space mapping algorithm is introduced to divide the physical flow state space into stable, metastable and critical regions, and to construct a refined representation of the system state.

[0098] This step divides the physical fluidity state space into stable, metastable, and critical regions, constructing a refined representation of the system state. This step includes the following sub-steps:

[0099] Step 3.1, Construction of the physical fluidity state space;

[0100] Construct a high-dimensional physical fluidity state space, which consists of physical constraint state vectors. and market liquidity state vector Common definition. To facilitate visualization and computation, dimensionality reduction techniques are used to project high-dimensional space onto a two- or three-dimensional representation:

[0101] To facilitate visualization and computation, the high-dimensional physical constraint state vector and the flow state vector need to be integrated and transformed into a low-dimensional representation. First, the physical constraint state vector and the flow state vector are merged to form a composite state vector. Then, a dimensionality reduction algorithm (such as principal component analysis, t-SNE, or autoencoder) is applied to process this composite state vector, mapping it to a two-dimensional or three-dimensional space to obtain a low-dimensional representation of the system state. This dimensionality reduction process preserves the key structural information of the original high-dimensional data while reducing the computational complexity of subsequent analysis.

[0102] The data preprocessing for state-space dimensionality reduction includes several key steps: First, missing values ​​are processed in the merged integrated state vector, and time series interpolation is used to fill in the missing data; second, feature scaling is performed to ensure that physical constraint indicators and mobility indicators have equal influence weights during the dimensionality reduction process; then, correlation analysis is performed to identify and process highly correlated redundant features to avoid the impact of information duplication on the dimensionality reduction results; next, the hyperparameters of the dimensionality reduction algorithm are optimized, and the optimal combination of dimensionality reduction parameters is determined through cross-validation; finally, the quality of the dimensionality reduction results is evaluated to ensure that the low-dimensional representation can effectively preserve the key information and structural features of the original data.

[0103] In constructing the physical fluidity state space, this system employs an innovative multi-representation learning framework. This framework first applies nonlinear dimensionality reduction to the original high-dimensional feature space. However, unlike traditional dimensionality reduction methods that only preserve the global structure, this system specifically emphasizes preserving the local structure relevant to extreme events. Specifically, the system uses a combination of variational autoencoders and adversarial training. The variational autoencoder learns a compact latent space representation, while the adversarial training ensures that the dimensionality reduction process retains key information relevant to extreme events. The loss function for the dimensionality reduction process is designed as a weighted combination of reconstruction error, KL (Kullback-Leibler) divergence, and adversarial loss. The adversarial loss specifically assigns higher weights to extreme event samples, ensuring that these key samples remain distinguishable in the dimensionality-reduced space. Furthermore, the system implements multi-scale representations, simultaneously preserving both macroscopic structure (overall market state distribution) and microscopic structure (local state evolution patterns before extreme events), facilitating subsequent analysis of system dynamics at different scales.

[0104] Step 3.2, State space region partitioning;

[0105] Based on the occurrence of extreme price events in historical data, the state space is divided into three regions:

[0106] Stable Zone: When the system is in this zone, the probability of extreme price events is extremely low.

[0107] Metastable Zone: When the system is in this zone, there is a certain risk, but it has not yet reached a critical state.

[0108] Critical Zone: When the system is in this zone, the probability of extreme price events increases significantly.

[0109] The regional boundary is determined by combining clustering algorithms and expert knowledge, forming a nonlinear decision boundary.

[0110] The state space region partitioning employs a hybrid approach integrating statistical physics theory and machine learning. This method first uses a density-based spatial clustering algorithm (DBSCAN) to identify density-uniform regions in the state space. Then, drawing on the concept of critical points from phase transition theory, the region with the largest state density gradient is used as the potential region boundary. To accurately characterize these nonlinear boundaries, the system uses a Support Vector Data Description (SVDD) algorithm to learn the boundaries of each region. This algorithm generates compact, closed boundaries that accurately describe the shape of different state regions. During boundary determination, the system also incorporates domain expert knowledge. Through a semi-supervised learning framework, experts can adjust and label the initial partitioning results, and the system continuously optimizes the region boundaries based on this feedback. Furthermore, the system implements time-varying boundary mapping, automatically updating boundary parameters periodically based on new data to adapt to dynamic changes in market conditions.

[0111] Regarding the specific implementation of the critical point concept borrowed from phase transition theory: In phase transition theory, a critical point refers to a special state point where a system transitions from one equilibrium state to another, and the macroscopic properties of the system near this point are extremely sensitive to small disturbances. This application borrows this physical concept to identify critical states in the electricity price system in the following way: First, the local density function of each point in the state space is calculated using the kernel density estimation method to establish a state density distribution map; second, the gradient change of this density function in space is calculated to identify regions with significantly increased gradient values, which usually represent boundaries where the system state may change abruptly; then, the watershed algorithm is applied to segment the gradient field, and the ridge with the largest gradient is taken as the region boundary; finally, the physical meaning of these boundaries is verified by calculating the differences in statistical characteristics of state points on both sides of the boundary (such as the frequency of extreme price events). This method directly borrows the technique for identifying phase boundaries in phase transition theory, which can accurately capture the nonlinear transition regions in the state space and achieve precise division of the stable region, metastable region, and critical region.

[0112] Furthermore, this application draws upon the order parameter analysis method from phase transition theory. This application defines an order parameter that characterizes the properties of a state-space region, and this order parameter has significantly different values ​​in different state regions. By analyzing the spatial distribution and abrupt change characteristics of the order parameter, the system can more accurately locate the boundary positions of the regions. In practical applications, the system selects the conditional probability of extreme price events or the system's response magnitude to perturbations as the order parameter; these indicators can effectively reflect the critical characteristics of the system.

[0113] This application also draws upon the phenomenon of critical slowing down in phase transition theory. When a physical system approaches its critical point, the rate at which it returns to equilibrium slows significantly, manifesting as increased autocorrelation and volatility. This application identifies system states that may exhibit critical slowing down by analyzing the statistical characteristics of electricity price time series, such as the autocorrelation function and the rate of change of variance, serving as supplementary evidence for identifying critical regions. This multi-dimensional approach allows the system to verify the accuracy of critical regions from different perspectives, significantly improving the reliability of critical state early warnings.

[0114] Step 3.3, State Trajectory Analysis;

[0115] Analyze the dynamic evolution trajectory of the system state in the state space to identify dangerous path modes that may lead the system into the critical section. Specific methods include:

[0116] Trajectory clustering: Clustering historical state trajectories to discover typical evolutionary patterns;

[0117] Transition probability estimation: Calculating the conditional probability of a system transitioning from one state region to another;

[0118] Key turning point identification: Identify the key points in the trajectory that may lead to a qualitative change in the system state.

[0119] The state trajectory analysis module employs a combination of dynamic systems theory and time-series pattern mining. First, the system uses the Dynamic Time Warping (DTW) algorithm to calculate the similarity between different state trajectories and then performs trajectory clustering to identify recurring typical state evolution patterns in the market. For each typical pattern, the system further constructs a conditional Markov model to capture the state transition patterns of the system under different external conditions. Specifically, the system develops a key inflection point identification algorithm based on information theory. This algorithm identifies critical moments when the dynamic properties of the system undergo significant changes by calculating the information gain of each point in the trajectory. Key inflection points typically correspond to important moments of change in market participant behavior patterns or changes in the physical system state, and are of significant value in predicting extreme price events. Furthermore, the system also implements trajectory prediction functionality, capable of predicting the evolution path of the system state in the short term based on the current state and historical trajectory patterns, providing forward-looking information for the early warning system.

[0120] Step 4: Based on the state space partitioning results, develop a propagation mechanism model based on a directed causal graph to track the propagation path of changes in physical constraints affecting market participants' behavior and thus market liquidity, ultimately leading to price fluctuations.

[0121] This step involves constructing a causal model between physical constraints and market liquidity to track how changes in physical constraints affect market participant behavior, thereby influencing market liquidity and ultimately leading to price fluctuations. This step includes the following sub-steps:

[0122] Step 4.1, Construction of the causal relationship graph;

[0123] Based on domain knowledge and data analysis, a directed graph model is constructed to represent the causal relationships between physical constraints, market behavior, and price changes. The model includes the following main node types:

[0124] Physical constraint nodes: key indicators representing the physical state of the power grid;

[0125] Market behavior nodes: These represent the behavioral decisions of market participants;

[0126] Liquidity node: A key indicator representing market liquidity;

[0127] Price nodes: represent the level of electricity prices and their changes.

[0128] The connections between nodes represent potential causal paths, and the initial connection structure is determined based on electricity market theory and expert knowledge.

[0129] It should be noted that the causal relationship graph can be constructed in various ways. In some embodiments, a knowledge graph-based approach can be used to integrate domain expert experience to construct an initial causal structure. In other embodiments, a data-driven approach based on Bayesian networks can be applied to learn potential causal relationships from historical data. Furthermore, the system can integrate these two methods, first using expert knowledge to construct an initial causal structure, and then using data analysis to verify and refine the structure.

[0130] The causal relationship diagram provided in this application has a hierarchical structure, dividing the system into three levels: the physical layer, the behavioral layer, and the market layer. It clearly describes how physical constraints influence the behavior of market participants, thereby changing market liquidity and ultimately leading to price fluctuations—the complete propagation path. It should be understood that this hierarchical structure has significant advantages in causal analysis of complex systems, effectively distinguishing between direct and indirect effects.

[0131] Step 4.2, learning the strength of causal relationships;

[0132] The causal discovery algorithm is applied to analyze historical data and learn the strength parameters of each connection in the causal graph. The main steps include:

[0133] Data preprocessing: stationarity processing and standardization are performed on time series data;

[0134] Conditional independence test: Verifies the conditional independence relationship between variables;

[0135] Parameter learning: estimating the strength parameters of causal connections.

[0136] The final result is a weighted causal graph that represents the strength and direction of the influence between the factors.

[0137] Optionally, the strength of causal relationships can be learned using Granger causality tests based on time-series data, determining potential causal directions by analyzing temporal relationships. Alternatively, the system can apply structured equation modeling (SEM) to estimate the strength of causal relationships between different variables through parameter fitting. In scenarios with high market volatility, the system can employ time-varying parameter models to capture the dynamic characteristics of causal relationship strength as market conditions change.

[0138] Furthermore, this application also provides a method for identifying nonlinear causal relationships. By introducing the transfer entropy metric based on information theory, this method can effectively capture the nonlinear dependencies between variables and overcome the limitations of traditional linear causal methods.

[0139] Step 4.3, Propagation Path Analysis;

[0140] Based on the learned causal graph, the main paths through which changes in physical constraints are transmitted to changes in liquidity via market behavior are analyzed. These mainly include:

[0141] Path importance assessment: Calculate the contribution of each propagation path to the final price impact;

[0142] Key node identification: Identifying key intermediary nodes in the propagation network;

[0143] Path delay analysis: estimating the time delay required for the propagation of causal effects.

[0144] By analyzing the propagation path, we can predict the market liquidity response pattern and time window after changes in the physical system, providing key time parameters for the early warning system.

[0145] According to one embodiment of this application, the system can calculate the cumulative effect of each propagation path and obtain the total path strength by multiplying the strength parameters of the causal connections. In another embodiment, the system can consider nonlinear amplification or suppression effects in the path and use a more complex combination function to calculate the total path impact. Furthermore, the system can generate a large number of possible system state evolution scenarios using Monte Carlo simulation methods to assess the relative importance of different propagation paths under various market conditions.

[0146] It should be noted that the propagation path analysis in this system not only focuses on the static importance of the path, but also pays special attention to the temporal dynamic characteristics of the path. The system estimates the propagation delay of causal effects between different nodes through time-delay correlation analysis, providing the early warning system with key time window parameters, enabling the early warning system to provide sufficient reaction time before extreme price events occur.

[0147] Step 5: Based on the analysis results of the propagation mechanism model, apply the conditional extreme value theory to model the extreme price distribution, and provide probability prediction and risk quantification results for the identified critical states of extreme electricity price events;

[0148] This step, targeting the identified critical states, employs conditional extrema theory to accurately model the probability distribution of extreme prices, providing risk quantification results. This step includes the following sub-steps:

[0149] Step 5.1, Threshold selection and extraction of data exceeding the threshold;

[0150] For historical price data, an appropriate threshold level is determined, and extreme price samples exceeding this threshold are extracted. The threshold is determined using the following method:

[0151] Mean remaining lifetime plot analysis: Observe the relationship between the threshold and the mean value of exceeding the threshold;

[0152] Parameter stability test: Verify the stability of model parameters under different thresholds;

[0153] Extreme quantile analysis: Determine reasonable extreme quantiles based on risk management needs.

[0154] According to the technical solution of this application, the selection of a threshold is crucial for the accurate modeling of extreme price distributions. A threshold that is too low may result in the model including non-extreme data, while a threshold that is too high may lead to insufficient samples, affecting statistical reliability. To address this issue, this system employs an adaptive threshold selection method, dynamically adjusting the threshold level based on different market conditions and node characteristics.

[0155] In some embodiments, the system can automatically determine reasonable threshold levels based on statistics such as kurtosis and skewness. In other embodiments, the system can employ a multi-threshold approach to integrate modeling results at different threshold levels, improving the robustness of predictions. Furthermore, the system can match thresholds with risk tolerance according to the specific needs of market risk management, ensuring that extreme events that are truly important to decision-making are captured.

[0156] Step 5.2, Fitting the Conditional Extreme Value Distribution;

[0157] For the system state in the critical region, a distribution model of extreme electricity prices is established using conditional extremum theory. Specifically, a generalized Pareto distribution is used to fit the data exceeding the threshold.

[0158] In the process of fitting the conditional extreme value distribution, the shape parameters of the distribution under specific physical constraints and market liquidity conditions are first determined. and scale parameters These two parameter values ​​will be dynamically adjusted according to changes in the system state. Then, for values ​​exceeding the preset threshold... Price section Calculate its conditional distribution function value under the current system state. .

[0159] in, This is the physical constraint state vector. This represents the market liquidity state vector. It is the conditional distribution function; This is the symbol for conditional probability, representing the probability under given conditions.

[0160] Conditional distribution function The specific implementation is as follows: First, based on the current physical constraint state vector and liquidity state vector, the shape parameter and scale parameter of the generalized Pareto distribution are calculated through a conditional parameterization model. The parameterization model uses a neural network or Gaussian process regression to map the state vector to the distribution parameters. Then, the excess price data is substituted into the cumulative distribution function formula of the generalized Pareto distribution for calculation. Specifically, the excess price is first standardized by dividing by the scale parameter, then combined with the shape parameter through a power function operation, and finally the cumulative probability value is obtained through subtraction. This function can dynamically adjust the distribution characteristics of extreme prices according to the system state.

[0161] Specifically, when the portion of the price exceeding the threshold is a certain value, this value is first divided by the scale parameter to obtain a normalized value, then combined with the shape parameter to calculate a provisional value. Finally, the cumulative distribution function value corresponding to this price level, i.e., the probability of not exceeding this price level, is obtained through exponentiation and subtraction operations. This modeling method based on the generalized Pareto distribution can accurately capture the tail distribution characteristics of extreme prices, providing theoretical support for risk quantification.

[0162] Shape and scale parameters are mapped to the system state through a conditional parameterization model, enabling adaptive adjustment of the system state to extreme distributions.

[0163] It should be understood that the technical solution of this application is not limited to using the generalized Pareto distribution. In some embodiments, the system can select a more suitable family of extreme value distributions, such as the generalized extreme value distribution (GEV), the Fréchet distribution, or the Gumbel distribution, based on the characteristics of the electricity price data. Furthermore, the system can employ nonparametric kernel density estimation methods to reduce biases caused by parameter assumptions in regions with sufficient samples.

[0164] It is worth noting that the innovation of this system lies in the introduction of conditional parameterization, which allows the parameters of the extreme value distribution to change dynamically with the system state. In one embodiment, the system uses a neural network model to establish a mapping function from the physical constraint state and liquidity state to the distribution parameters. In another embodiment, the system uses Gaussian process regression to achieve accurate parameter prediction while maintaining smoothness. This conditional parameterization method enables the distribution model of extreme prices to adapt to changes in the system state, achieving higher accuracy compared to traditional static extreme value distribution models.

[0165] Step 5.3, Calculation of extreme risk indicators;

[0166] Based on the fitted conditional extreme value distribution, key risk indicators are calculated for risk assessment and decision support:

[0167] Conditional exceedance probability: The probability that the electricity price exceeds a specific threshold under a given system state;

[0168] Conditional Value at Risk (CVaR): The expected extreme loss at a given confidence level;

[0169] Conditional Expected Shortfall: On average, how much the price will exceed a threshold once it surpasses it.

[0170] Extreme event duration estimation: The length of time that an extreme price event may last.

[0171] Optionally, the risk indicators calculated by this system can be adjusted and expanded according to specific application needs. For example, in electricity market trading decision support, the system can calculate the risk exposure of a specific trading portfolio to extreme prices; in system operation risk management, the system can calculate the risks of increased system costs and decreased reliability caused by extreme prices. In addition, the system can also calculate multi-node joint extreme risk indicators to assess the systemic impact of regional price risks.

[0172] It is important to emphasize that this system not only focuses on static risk indicators but also pays special attention to the dynamic evolution of risk. Through state trajectory analysis and causal propagation models, the system can predict the temporal evolution trend of risk indicators, providing market participants with estimates of risk lead times and enhancing the foresight of their decisions.

[0173] A computer storage medium includes a memory and one or more processors, wherein the memory stores executable code, and when the one or more processors execute the executable code, it is used to implement the above-described joint probability prediction method for nodal electricity prices.

[0174] The embodiments of the present invention have been described above. However, the embodiments are not limited to the specific implementation methods described above. The specific implementation methods described above are merely illustrative and not restrictive. Those skilled in the art can make more equivalent embodiments under the guidance of the present embodiments, and all of them are within the protection scope of the present embodiments.

Claims

1. A joint probability prediction method for nodal electricity prices, characterized in that, include: A dual-state monitoring system is constructed to simultaneously track the physical state of the power grid and market liquidity indicators, generating physical constraint state vectors and market liquidity state vectors, and subsequent analysis is performed based on the generated state vectors. The steps for constructing the dual-state monitoring system include: The power system state estimation algorithm is used to analyze real-time physical data of the power grid and generate physical constraint state vectors. The physical constraint state vectors include line power flow ratio, node voltage margin, generator output margin and key indicators of network topology. Analyze real-time electricity market trading data to generate a market liquidity state vector, which includes key indicators such as order depth, bid-ask spread, trading volume change rate, and price volatility. Construct a physical liquidity status-related database to store historical status data and corresponding price results; Based on the physical constraint state vector and the market liquidity state vector, a critical early warning indicator is designed by combining the degree of physical constraint and the liquidity level nonlinearly, thereby identifying potential extreme price events; Based on the critical early warning index designed, a state space mapping algorithm is introduced to divide the physical flow state space into a stable region, a metastable region, and a critical region, thereby constructing a refined representation of the system state. Based on the state-space partitioning results, a propagation mechanism model based on a directed causal graph is developed to track the propagation path of changes in physical constraints affecting market participant behavior, thereby influencing market liquidity and ultimately leading to price fluctuations. The steps for developing the propagation mechanism model based on a directed causal graph include: Based on domain knowledge and data analysis, a directed graph model is constructed to represent the causal relationship between physical constraints, market behavior, and price changes. The causal discovery algorithm is used to analyze historical data and learn the strength parameters of each connection in the causal graph. Based on the learned causal graph, we analyze the main paths through which changes in physical constraints are transmitted to changes in liquidity via market behavior, including path importance assessment, key node identification, and path time lag analysis. Based on the analysis results of the propagation mechanism model, the extreme price distribution is modeled using conditional extreme value theory. For the identified critical states, the probability prediction and risk quantification results of extreme electricity price events are provided.

2. The joint probability prediction method for nodal electricity prices according to claim 1, characterized in that, The steps for designing critical early warning indicators include: The two-way sensitivity analysis method is used to quantify the sensitivity of each indicator in the physical constraint state vector and liquidity state vector to the impact of extreme price events; Based on the results of sensitivity analysis, key indicators that have an impact on extreme price events were selected, and the weight coefficient of each indicator was determined. A critical early warning index is constructed, which forms a comprehensive measure of the critical state of the system by nonlinearly combining key physical constraint indexes and liquidity indexes.

3. The joint probability prediction method for nodal electricity prices according to claim 2, characterized in that, The nonlinear combination function of the physical constraint index is implemented using a radial basis function network, the nonlinear combination function of the liquidity index is implemented using a deep neural network based on an attention mechanism, and the nonlinear combination function of the interaction between physical constraints and liquidity is implemented using a tensor network.

4. The joint probability prediction method for nodal electricity prices according to claim 1, characterized in that, The steps of introducing the state-space mapping algorithm include: Construct a high-dimensional physical liquidity state space, which is jointly defined by the physical constraint state vector and the liquidity state vector; Dimensionality reduction techniques are used to project high-dimensional space onto two-dimensional and three-dimensional representations; Based on the occurrence of extreme price events in historical data, the state space is divided into a stable region, a metastable region, and a critical region. Analyze the dynamic evolution trajectory of the system state in the state space to identify dangerous path patterns that lead the system into the critical region.

5. The joint probability prediction method for nodal electricity prices according to claim 4, characterized in that, The state space region partitioning adopts a hybrid approach that integrates statistical physics theory and machine learning. A density-based clustering algorithm is applied to identify density-uniform regions in the state space, and a support vector data description algorithm is used to learn the boundaries of each region.

6. The joint probability prediction method for nodal electricity prices according to claim 1, characterized in that, The steps for modeling extreme price distributions using the applied conditional extreme value theory include: For historical price data, determine an appropriate threshold level and extract extreme price samples that exceed the threshold; For the system state in the critical region, a distribution model of extreme electricity prices is established by applying conditional extremum theory, and the generalized Pareto distribution is used to fit the data exceeding the threshold. Based on the fitted conditional extreme value distribution, risk indicators are calculated, including conditional exceedance probability, conditional value at risk, conditional expected excess loss, and extreme event duration estimate.

7. The joint probability prediction method for nodal electricity prices according to claim 6, characterized in that, The shape and scale parameters of the generalized Pareto distribution are mapped to the system state through a conditional parameterization model, enabling the extreme distribution to adaptively adjust the system state.

8. A computer storage medium, characterized in that, The device includes a memory and one or more processors, wherein the memory stores executable code, and the one or more processors execute the executable code to implement a nodal price joint probability prediction method according to any one of claims 1-7.

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