A topology-aware power system dynamic modeling method, system, device and storage medium based on a physical information graph neural network

Abstract

The application discloses a kind of topological perception electric power system dynamic modeling method, system, equipment and storage medium based on physical information graph neural network, it is related to electric power system frequency dynamic characteristic modeling and safety evaluation technical field, including constructing electric power system heterogeneous graph, equivalent inertia and damping are adaptively inferred by heterogeneous graph neural network;Establish physical structured neural ordinary differential equation, and frequency dynamics is decomposed into swing equation physical component and characteristic linear modulation residual component;Design the differentiable frequency response mechanism containing energy storage state of charge hard constraint;End-to-end training is realized using multistage physical constraint and accompanying sensitivity method.The application can accurately predict the frequency trajectory, frequency rate of change and energy storage state under different topologies and working conditions, and provide support for low-inertia electric power system frequency safety evaluation.

Description

Technical Field

[0001] This invention relates to the field of power system frequency dynamic characteristic modeling and security assessment technology, and more specifically to a topology-sensing power system dynamic modeling method, system, device and storage medium based on physical information graph neural network. Background Technology

[0002] The accelerated global carbon neutrality transition is driving the large-scale replacement of synchronous generators with inverter-type resource-integrated generators (IBRs), leading to a continuous decrease in the system's equivalent rotating inertia and more severe frequency transient responses after disturbances. Accurate system-level frequency dynamics modeling has become a crucial prerequisite for frequency security assessment, reserve decision-making, and control parameter tuning. The core objects that need to be determined in system-level frequency dynamics modeling include the inertia center frequency deviation trajectory, the rate of change of frequency (RoCoF), and the state of charge evolution process of energy storage devices.

[0003] Existing system-level frequency dynamic characteristic modeling methods can be categorized into three types: model-driven methods, data-driven methods, and hybrid methods. Model-driven methods, represented by the System Frequency Response (SFR) model and its extensions, describe frequency dynamics through aggregated parameters such as equivalent inertia, equivalent damping, and droop coefficient. These methods offer strong physical interpretability and high computational efficiency, but their parameters typically rely on offline identification or capacity-weighted aggregation, making them unable to adaptively adjust to changes in grid topology and inverter resource penetration rates. Their generalization ability is insufficient under conditions of topology switching and resource status changes. Data-driven methods directly map frequency trajectories or indicators from operational data using deep learning, achieving high accuracy but lacking physical interpretability. Their generalization ability is limited under conditions outside the training distribution. Hybrid methods embed physical laws as soft constraints into the loss function, but penalty-based constraint satisfaction methods may fail in scenarios with insufficient penalty weights or extrapolation.

[0004] Therefore, the existing technology has at least the following shortcomings: (1) The equivalent parameters of the existing model-driven methods rely on fixed coefficients or scenario-by-scenario fitting, which cannot adaptively infer the equivalent inertia and equivalent damping of the system from the power grid topology and operating conditions. The generalization ability is insufficient under the conditions of network topology change and inverter resource penetration rate change. (2) In existing frequency modeling methods, primary frequency modulation (PFR) and fast frequency response (FFR) are usually simplified to exogenous inputs or pre-set response modules, lacking the ability to model closed loops that depend on real-time state variables such as frequency deviation and frequency change rate. In addition, the estimation of frequency change rate generally adopts discrete time difference method, which is easy to introduce high-frequency noise amplification and discretization artifacts, affecting the gradient propagation stability of continuous time model. (3) Existing methods mostly use soft penalty methods to constrain the state of charge of energy storage systems, which cannot structurally guarantee the consistency between power output and energy state during the reasoning stage. This may result in physically infeasible outputs where power injection depletes energy reserves and exceeds the operating boundary.

[0005] Therefore, how to achieve accurate frequency dynamic modeling is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0006] In view of this, the present invention provides a method, system, device and storage medium for dynamic modeling of topology-aware power systems based on physical information graph neural networks. It unifies heterogeneous graph neural network parameter inference, dynamic characteristic modeling of physical structured neural ordinary differential equations, differentiable frequency response closed-loop mechanism, energy storage state of charge hard constraint and multi-level physical constraint training into a differentiable architecture, realizing end-to-end modeling and prediction from grid topology and operating conditions to system-level frequency trajectory, frequency change rate and energy storage state.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: A dynamic modeling method for topology-sensing power systems based on physical information graph neural networks includes: S1, construct a heterogeneous graph representation of the power system, extract static features from various types of nodes, and extract temporal features from renewable energy nodes in the various types of nodes through a temporal convolutional network, and output the heterogeneous graph structure, static features, and temporal features; S2, based on the heterogeneous graph structure and static and temporal features, obtain the node spatial embeddings of various types of nodes through a heterogeneous graph neural network, perform graph-level aggregation on the node spatial embeddings and fuse global operating condition parameters to obtain a fusion vector, and infer the equivalent physical parameters of the system through a bounded scaling layer based on the fusion vector; S3, construct a joint state space of frequency and energy storage, unify the frequency deviation, continuous time observer state and energy storage state into a joint state vector, establish a physical structured dynamic characteristic model based on the joint state vector and the equivalent physical parameters of the system, decompose the time derivative of the frequency deviation, and obtain the physical components and the residual components modulated by the FiLM mechanism. S4. Establish a differentiable frequency response mechanism. Estimate the frequency change rate based on the real-time frequency deviation using a continuous-time frequency change rate observer. Construct a fast frequency response model and a primary frequency modulation model respectively. Calculate the aggregated frequency response power based on the fast frequency response model and the primary frequency modulation model and inject it into the physical structured dynamic characteristic model. At the same time, update the energy storage energy state. S5 constructs a multi-level physical constraint training objective that includes swing equation consistency loss, energy power consistency loss, initial frequency change rate matching loss, and trajectory fidelity loss. The physical constraint weights are dynamically adjusted using a course learning strategy to jointly train the model constructed from S1 to S4. After training, the data to be evaluated is evaluated, and the system frequency deviation trajectory, frequency change rate estimate, and energy storage state are output.

[0008] Preferably, the extraction of temporal features through a temporal convolutional network specifically includes: extracting multi-scale features from the historical power sequence of renewable energy nodes using K-layer dilated causal convolution, updating the hidden state of each layer through a gated convolution mechanism; performing global average temporal pooling on the hidden states of each layer, and aggregating multi-scale features through an attention mechanism to obtain the temporal embedding vector of the renewable energy nodes.

[0009] Preferably, the step of obtaining the spatial embedding of various types of nodes through a heterogeneous graph neural network specifically includes: projecting static features to a unified latent space using a corresponding type of multilayer perceptron for different types of nodes, wherein renewable energy nodes are additionally spliced ​​with temporal features to obtain an initial embedding vector; and using an L-layer heterogeneous graph neural network with residual connections to aggregate the features of neighboring nodes using a differentiated weight matrix for different topological relationships to obtain the node spatial embedding.

[0010] Preferably, the step of performing graph-level aggregation of node spatial embeddings and fusing global operating condition parameters specifically includes: performing global average pooling, global maximum pooling, and global attention pooling on the node spatial embeddings respectively, and concatenating them to obtain a spatial embedding vector; weighting and aggregating the temporal embeddings of renewable energy nodes according to their rated capacity to obtain a temporal embedding vector; and concatenating the spatial embedding vector, the temporal embedding vector, and the global operating condition parameter vector to obtain a fused vector.

[0011] Preferably, the step of inferring the equivalent physical parameters of the system based on the fusion vector through a bounded scaling layer specifically includes: inferring a multilayer perceptron from the input parameters of the fusion vector, mapping the output to a preset feasible range of physical parameters through a sigmoid activation function and linear scaling, and obtaining the equivalent inertia constant and the equivalent damping coefficient of the system.

[0012] Preferably, the decomposition of the time derivative of the frequency deviation specifically includes decomposing it into physical components and residual components through a neural dynamic characteristic function: ; The physical components directly realize the structure of the rocking equation: ; in, For physical components; The aggregated frequency response power is derived from the primary frequency modulation power. and fast frequency response power composition; The disturbance power; Equivalent damping; The predicted inertia center frequency deviation; The residual components employ a characteristic linear modulation (FiLM) mechanism: ; in, These are the topological condition residual components; It is a lightweight neural network; This is the scaling factor; Offset factor; This is the fusion vector.

[0013] Preferably, the estimation of the frequency change rate based on the real-time frequency deviation using a continuous-time frequency change rate observer specifically includes: ; in, The time derivative of the observer state; Let be the observer time constant, and the estimated rate of change of the observer frequency satisfies: ;in, For the estimated rate of change of frequency The observer is equivalent to a cutoff frequency of The band-limited differentiator provides a smooth estimate of the rate of change of frequency while maintaining differentiability.

[0014] A dynamic modeling system for topology-sensing power systems based on physical information graph neural networks, comprising: The heterogeneous graph construction and feature extraction module constructs a heterogeneous graph representation of the power system, extracts static features from various types of nodes, and extracts temporal features from renewable energy nodes in the various types of nodes through a temporal convolutional network, outputting the heterogeneous graph structure and static and temporal features; The graph-level parameter inference module obtains the node spatial embeddings of various types of nodes through a heterogeneous graph neural network based on the heterogeneous graph structure, static features, and temporal features. It then performs graph-level aggregation on the node spatial embeddings and fuses global operating condition parameters to obtain a fusion vector. Based on the fusion vector, it infers the equivalent physical parameters of the system through a bounded scaling layer. The physical structured dynamic characteristic modeling module constructs a joint state space of frequency and energy storage, unifies the frequency deviation, continuous-time observer state, and energy storage state into a joint state vector, establishes a physical structured dynamic characteristic model based on the joint state vector and the equivalent physical parameters of the system, decomposes the time derivative of the frequency deviation, and obtains the physical components and the residual components modulated by the FiLM mechanism. The differentiable frequency response calculation module establishes a differentiable frequency response mechanism. It estimates the frequency change rate based on the real-time frequency deviation using a continuous-time frequency change rate observer, and constructs a fast frequency response model and a primary frequency modulation model respectively. Based on the fast frequency response model and the primary frequency modulation model, it calculates the aggregated frequency response power and injects it into the physical structured dynamic characteristic model, while updating the energy storage state. The multi-level training and prediction output module constructs a multi-level physical constraint training objective that includes swing equation consistency loss, energy power consistency loss, initial frequency change rate matching loss, and trajectory fidelity loss. It adopts a course learning strategy to dynamically adjust the weights of physical constraints and jointly trains the models constructed by the above modules. After training, the data to be evaluated is evaluated, and the system frequency deviation trajectory, frequency change rate estimate, and energy storage state are output.

[0015] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements a dynamic modeling method for a topology-sensing power system based on a physical information graph neural network.

[0016] A computer-readable storage medium having a computer program stored thereon that, when executed by a processor, implements a dynamic modeling method for a topology-sensing power system based on a physical information graph neural network.

[0017] As can be seen from the above technical solutions, compared with the prior art, the present invention discloses a method, system, device and storage medium for dynamic modeling of topology-sensing power systems based on physical information graph neural networks, with the following beneficial effects: 1. This invention adaptively infers the equivalent inertia and equivalent damping parameters of the system from the power grid topology and operating conditions through a heterogeneous graph neural network supernetwork. Compared with fixed coefficient or scenario-by-scenario fitting methods, it can generalize to network topologies and inverter resource penetration levels that do not appear in the training set. 2. This invention directly embeds the swing equation structure into the neural ordinary differential equation framework and supplements it with characteristic linear modulation residual components. This captures unmodeled dynamics while ensuring physical interpretability, so that the predicted output has a clear physical meaning. 3. This invention replaces the discrete-time difference with a continuous-time frequency change rate observer, eliminating high-frequency noise amplification and discretization artifacts, and ensuring stable gradient propagation in the state-dependent frequency response feedback loop. 4. This invention implements structural hard constraints on the state of charge of energy storage through differentiable gated functions, and combines energy power consistency training loss to strictly ensure that the energy storage device operates within the physical boundary during the inference stage, avoiding infeasible predictions of energy depletion or overflow. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0019] Figure 1 A flowchart of the method steps provided by the present invention; Figure 2 This is a schematic diagram of the overall framework of the physical information graph and the ordinary differential equations provided by the present invention. Figure 3 This is a schematic diagram of the heterogeneous graph neural network supernetwork structure provided by the present invention; Figure 4 This is a schematic diagram of the physical structured dynamic characteristic module provided by the present invention. Detailed Implementation

[0020] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0021] This invention discloses a dynamic modeling method for topology-sensing power systems based on physical information graph neural networks, such as... Figure 1 As shown, it includes: S1, construct a heterogeneous graph representation of the power system, extract static features from various types of nodes, and extract temporal features from renewable energy nodes in various types of nodes through a temporal convolutional network, outputting the heterogeneous graph structure and static and temporal features; S2, based on the heterogeneous graph structure and static and temporal features, obtain the node spatial embedding of various types of nodes through the heterogeneous graph neural network, perform graph-level aggregation on the node spatial embedding and fuse global operating condition parameters to obtain the fusion vector, and infer the equivalent physical parameters of the system through the bounded scaling layer based on the fusion vector; S3. Construct a joint state space of frequency and energy storage, unify the frequency deviation, continuous-time observer state and energy storage state into a joint state vector, establish a physical structured dynamic characteristic model based on the joint state vector and the equivalent physical parameters of the system, decompose the time derivative of the frequency deviation, and obtain the physical components and the residual components modulated by the FiLM mechanism. S4. Establish a differentiable frequency response mechanism. Estimate the frequency change rate based on the real-time frequency deviation using a continuous-time frequency change rate observer. Construct a fast frequency response model and a primary frequency regulation model respectively. Calculate the aggregated frequency response power based on the fast frequency response model and the primary frequency regulation model and inject it into the physical structured dynamic characteristic model. At the same time, update the energy storage energy state. S5 constructs a multi-level physical constraint training objective that includes swing equation consistency loss, energy power consistency loss, initial frequency change rate matching loss, and trajectory fidelity loss. The physical constraint weights are dynamically adjusted using a course learning strategy to jointly train the model constructed from S1 to S4. After training, the data to be evaluated is evaluated, and the system frequency deviation trajectory, frequency change rate estimate, and energy storage state are output.

[0022] Among them, the differentiable frequency response mechanism includes a continuous-time frequency change rate observer, a fast frequency response model based on state feedback, and a single-frequency modulation model. The fast frequency response model includes a differentiable saturation function, a time-series platform gating function, and a hard-constraint gating function based on the state of charge. As a further limitation of the first aspect of the present invention, heterogeneous graph representation is defined as

[0023] In the formula: It is a heterogeneous graph; A set of nodes; Let it be the set of edges; It is a set of relation types. The node set satisfies...

[0024] In the formula: It is a set of power generation nodes, including synchronous machine nodes and inverter-type resource nodes; For the set of load nodes; It is the set of bus nodes.

[0025] For renewable energy nodes Its historical power characteristic matrix is ,in For the number of renewable energy nodes, This represents the length of the historical time window. For nodes... The original power sequence ,pass Temporal feature extraction is performed using a multi-layered temporal convolutional network (TCN). Layer update rules satisfied

[0026] In the formula: Initially hidden state; For the first Hidden layer state; For dilated causal convolution operations, the dilation rate is... Learnable convolutional kernels for gated branches; Learnable convolutional kernels for the output branch; To hide the channel dimension; For the first Layer filter size; Use the Sigmoid activation function; It is the hyperbolic tangent activation function; This is an element-wise product.

[0027] Global average time pooling is performed on the hidden states of each layer to obtain ,in To hide the channel dimension

[0028] In the formula: For the first Layer in time step The eigenvector at that location.

[0029] The pooling features from each layer are concatenated column-wise to form a multi-scale feature matrix. ,in To hide the channel dimension, The total number of layers in the temporal convolutional network is aggregated into the final temporal embedding through an attention mechanism.

[0030] In the formula: For nodes Temporal embedding vectors, To hide the channel dimension; For the first Attention weights of layers; For attention weight vectors, This represents the total number of layers in the temporal convolutional network. For attention query weight matrix; This is the attention score vector; This is the attention bias vector; Hiding dimensions for attention; The normalized exponential function maps each component of the vector to a non-negative probability weight that sums to 1. It is the hyperbolic tangent activation function.

[0031] As a further limitation of the first aspect of the present invention, the node embedding initialization in the heterogeneous graph neural network satisfies

[0032] In the formula: For nodes The initial embedding vector, The common hidden dimension of the graph neural network; For renewable energy nodes The static feature vector includes rated capacity, grid-connected voltage level, and control parameters, among which... For static feature dimensions of renewable energy nodes; For nodes Type-specific static feature vectors, including physical attributes such as generator rated capacity, load reference power, or bus rated voltage. For type The corresponding static feature dimension; These correspond to the generation node, load node, and bus node, respectively. For type The corresponding multilayer perceptron; For multilayer sensing machines corresponding to renewable energy nodes; For splicing operations; This is a subset of renewable energy nodes.

[0033] The message passing rules of heterogeneous graph neural networks are Cascading updates, the first generation Layer update satisfies

[0034] In the formula: For nodes In the Layer embedding vectors, Hidden dimensions for public use; For the first Layer self-loop weight matrix; For the first Hierarchical Relationship The corresponding message weight matrix; For nodes In relation The set of neighboring nodes; Let cardinality be the cardinality of the neighbor set. Set a Sigmoid S-type activation function; update the residual connection structure.

[0035] As a further limitation of the first aspect of the present invention, the graph-level aggregation and physical parameter inference process includes: Let the final layer node embedding set be Spatial embedding vectors satisfy

[0036] In the formula: This is a global average pooling operation; This is a global max pooling operation; This is a global attention pooling operation; For splicing operations; Embed the total dimension into the stitched space. This is a public hidden dimension.

[0037] Temporal embedding vectors satisfy

[0038] In the formula: For capacity-weighted timing embedding, To hide the channel dimension; For nodes Capacity weights; For renewable energy nodes Rated capacity.

[0039] The fusion vector satisfies

[0040] In the formula: This is a global operating condition parameter vector, which must include at least the disturbance amplitude and IBR permeability; For the total dimension of the fused vector, where For public hidden dimensions, To hide the channel dimension, This refers to the dimension of the global operating condition parameters.

[0041] Inferring equivalent physical parameters of the system through bounded scaling layers

[0042] In the formula: This is the inferred equivalent physical parameter vector; The inferred equivalent inertia of the system; The inferred equivalent damping of the system; and These are the lower and upper bounds of the physical parameters, respectively. It is an element-wise Sigmoid S-type activation function with an output range of (0,1). To infer the parameters of a multilayer perceptron; This is an element-wise product. The bounded scaling layer uses a sigmoid activation function to constrain the output to a physically feasible region. Inside.

[0043] As a further limitation of the first aspect of the present invention, the simultaneous state vector is defined as follows:

[0044] In the formula: For a moment The simultaneous state vectors; The predicted inertia center frequency deviation; The auxiliary state variables of the continuous-time observer have a dimension of for Energy state vector of a fast frequency response device; The total number of high-frequency response devices; Let be the total dimension of the simultaneous state vectors, where 2 corresponds to the frequency bias and the observer state.

[0045] The initial conditions of the simultaneous states satisfy the physical steady-state constraints.

[0046] In the formula: The moment the disturbance occurs; Let be the initial state-of-charge vector of each energy storage device. This represents the total number of devices with fast frequency response.

[0047] The core ordinary differential equation of the physical structured dynamic characteristic model satisfies

[0048] In the formula: This is a neural dynamic characteristic function, whose output corresponds to the predicted rate of change of frequency; This represents the power of the aggregated frequency response.

[0049] The neural dynamic characteristic function is decomposed into physical components and residual components.

[0050] Physical components directly realize the structure of the rocking equation

[0051] In the formula: For physical components; The aggregated frequency response power is derived from the primary frequency modulation power. and fast frequency response power composition; The disturbance power; This represents the predicted deviation of the center frequency of inertia.

[0052] The disturbance power is modeled using a differentiable step function.

[0053] In the formula: The power deficit at the moment the disturbance occurs; The Sigmoid activation function is used to smoothly approximate step transitions. is the step smoothing constant.

[0054] The residual components employ a characteristic linear modulation (FiLM) mechanism.

[0055] In the formula: These are the topological condition residual components; It is a lightweight neural network; This is the scaling factor; The offset factor; both are derived from the global fusion vector. Generated through the following mapping

[0056] In the formula To correct the activation function of the linear unit, the scaling factor and offset factor are generated to satisfy...

[0057] In the formula: The weight matrix of the residual hidden layer. To hide dimensions in the residual network, This represents the total dimension of the fused vector. It is the bias vector; and The output header parameter for the scaling factor; and The output header parameter for the offset factor; This is a softplus activation function used to ensure the scaling factor. .

[0058] As a further limitation of the first aspect of the present invention, the auxiliary state variable dynamic characteristics of the continuous-time frequency change rate observer satisfy...

[0059] In the formula: The time derivative of the observer state; Let be the observer's time constant. The observer's estimated rate of frequency change satisfies...

[0060] In the formula: For the estimated rate of change of frequency The observer is equivalent to a cutoff frequency of The band-limited differentiator provides a smooth estimate of the rate of change of frequency while maintaining differentiability.

[0061] Aggregate frequency response power satisfies

[0062] In the formula: This represents the total number of primary frequency regulation units; For the first Power injection from a primary frequency regulation unit; For the first Power injection for a fast frequency response device.

[0063] As a further limitation of the first aspect of the present invention, the fast frequency response model in the first... Power injection of the equipment meets

[0064] In the formula: For equipment droop response gain; For equipment The frequency change rate response gain; For equipment The platform response amplitude; For equipment Power capacity; It is a hard-constraint gate function for the charged state; This is a timing platform gating function.

[0065] Differentiable saturable function is defined as

[0066] In the formula: It is a saturation smoothing factor; The hyperbolic tangent activation function has an output range of . It is used to smoothly approximate hard saturation limiting.

[0067] Timing platform gating function satisfies

[0068] In the formula: For equipment The platform activation start time; For equipment The platform's termination deadline; This is the transition sharpness parameter; The hyperbolic tangent activation function is used, and the difference between two hyperbolic tangent functions forms a smooth switch within the time window.

[0069] The hard-constraint gate function for the charged state satisfies

[0070] In the formula: For equipment The lower limit of the energy state; For equipment The upper limit of energy states; This is the steepness parameter, used to control the sharpness of the transition of the gating function near the boundary; This is a Sigmoid-S-type activation function. When... near or hour, Approaching zero, effectively shutting off power output.

[0071] Energy state dynamic characteristics satisfy

[0072] In the formula: For equipment The time derivative of the energy state; For equipment The charging efficiency; For equipment The discharge efficiency; For the soft positive part function, use the Sigmoid activation function. For the modified linear unit ReLU function Perform a smooth approximation; For smoothing parameters.

[0073] As a further limitation of the first aspect of the present invention, in the primary frequency modulation model, the first... Power injection of the Taiwanese unit meets

[0074] In the formula: For the unit The adjustment coefficient; For the unit Activation delay; For the unit The governor time constant; For the unit The power capacity; the differentiable step function satisfies

[0075] As a further limitation of the first aspect of the present invention, in the multi-level physical constraint training objective, the consistency loss of the swing equation satisfies

[0076] In the formula: A set of indexes for discretized time intervals; This represents the total number of time intervals. This is the net power imbalance. The gradient truncation operator prevents gradient backpropagation to maintain parameter interpretability; the integral is approximated using the trapezoidal rule.

[0077] Exponential decay weights satisfy

[0078] In the formula: This represents the initial weight magnitude; The attenuation rate; This is the lower bound of the weight; For the first At each time step, the normalized weights satisfy...

[0079] This ensures that the gradient scale does not depend on the choice of weight hyperparameters.

[0080] Energy power consistency loss satisfies

[0081] In the formula: This is the set of time sampling points for energy assessment. This represents the total number of sampling points; The Sigmoid activation function is used to smoothly determine the power direction. For the barrier penalty item, satisfy

[0082] In the formula: It is a bounded soft penalty function; This represents the barrier distance parameter.

[0083] Initial frequency change rate matching loss satisfies

[0084] Trajectory fidelity loss satisfies

[0085] In the formula: This represents the total number of trajectory sampling points; For the first Reference frequency deviation at each sampling time; For time-dependent weighting functions; These are the initial transient weighting coefficients; This is the weight decay time constant.

[0086] Composite training objectives are met

[0087] In the formula: Weights are applied to the trajectory fidelity loss. Weights for energy consistency loss; For the initial Loss weights; The course learning weights for the consistency loss of the swing equation satisfy... ,in For the current training round, This refers to the number of preheating cycles.

[0088] The accompanying sensitivity method defines the accompanying state. Calculate the inverse dynamic characteristics and parameter gradients.

[0089] In the formula: This is the accompanying state vector; It is a combined dynamic characteristic function containing frequency deviation, observer state, and energy storage state; For all trainable parameters. The accompanying sensitivity method uses... Gradient calculation is performed with constant memory complexity, ensuring computational scalability during training.

[0090] Example 1: This embodiment uses a modified IEEE 118-node test system as an example to illustrate a topology-sensing frequency dynamic characteristic modeling method based on physical information graph constant differential equations. The system includes 54 generator sets (including synchronous and inverter resources), 91 load nodes, and 186 transmission lines. This is achieved by deploying [methods] at high-load buses. The BESS battery energy storage system has a total storage capacity of 1260MW and a single unit storage duration of 2 hours. Inverter-type resource penetration coverage... to The overall process of this embodiment is shown in [link to embodiment]. Figure 2 .

[0091] Step 1: Heterogeneous graph construction and feature extraction.

[0092] Constructing heterogeneous graphs Nodes are categorized into generation nodes (including synchronous generators and inverters), load nodes, and bus nodes. The static characteristics of each node include physical attributes such as rated capacity, reference power, and rated voltage. For renewable energy nodes, the historical power time window length is used. Construct a power sequence using sampling points. Its heterogeneous graph neural network supernetwork structure is shown in Figure 3 .

[0093] Temporal convolutional networks are set to Layers, number of channels Filter size The expansion rates are in the following order: Each layer employs a gated convolution mechanism for feature extraction, and then global average temporal pooling and attention aggregation are used to obtain the temporal embeddings of each renewable energy node. The attention dimension is set to .

[0094] The common hidden dimension of the heterogeneous graph neural network is set to The message passing layer is set to 3. Nodes of each type are projected onto the public hidden space through their corresponding multilayer perceptrons, with renewable energy nodes additionally stitched with temporal embeddings. After the layer message is passed, each node obtains the spatial embedding of the fused topology information.

[0095] Step 2: Graph-level aggregation and physical parameter inference.

[0096] The final layer node embeddings are subjected to graph-level pooling, and spatial embeddings are obtained by concatenating three pooling methods: global average, global max, and soft attention. The time-series embedding of renewable energy nodes is obtained by weighting the sum by rated capacity. .

[0097] Spatial embedding, temporal embedding, and global operating parameters (Including perturbation amplitude and IBR penetration) are concatenated into a fusion vector The equivalent inertia of the system is inferred through two layers of multilayer perceptron and a bounded sigmoid scaling layer. and equivalent damping In this embodiment, the upper and lower bounds of inertia are set as follows: These correspond to the physical feasible ranges of inertia and damping, respectively.

[0098] Step 3: Constructing the combined state and modeling the physical structured dynamic characteristics.

[0099] Constructing simultaneous state vectors The initial conditions are set to... and Its physical structured dynamic characteristic module can be found in Figure 4 .

[0100] The physical structured dynamic characteristic model decomposes the time derivative of the frequency deviation into physical components. and FiLM residual components The physical components are based on the rocking equation structure and are derived using step 2. and The disturbance power is modeled using a differentiable step function, with a smoothing constant. Residual components Set up two layers, with hidden dimensions. The output is fused into a topology vector via the FiLM mechanism. Conditional modulation.

[0101] An adaptive step-size Dormand-Prince (dopri5) numerical integrator was used to integrate the simultaneous states using ordinary differential equations. The simulation time domain covered 30 seconds after the perturbation, and the sampling frequency was 100Hz.

[0102] Step 4: Differentiable frequency response mechanism.

[0103] The time constant of the continuous-time RoCoF observer is set to .

[0104] Fast frequency response device parameters are configured for scenario randomization: droop gain RoCoF gain Platform activation time Platform termination time Saturation smoothing factor SoC gate steepness parameters Lower bound of energy constraint The charge / discharge efficiency meets the round-trip efficiency requirement. .

[0105] Primary frequency control units according to droop coefficient Activation delay and governor time constant The configuration achieves the closed-loop response through a differentiable step function and a saturation function.

[0106] Step 5: Multi-level physical constraint training.

[0107] The training dataset contains 15,000 frequency trajectories, categorized by... The dataset is divided into training, validation, and test sets. To ensure topology generalization, the dataset includes a basic topology (60%) and random topologies. Line disconnection ( ) and key Double fault ( ).in of and all The operating conditions are retained as an off-distribution test set.

[0108] The composite training objectives employ a course-based learning strategy, including warm-up rounds. This causes the consistency loss weights of the swing equation to increase linearly from 0 to 1. The exponentially decaying weights in the swing equation loss are set to... Prioritize ensuring power balance constraints during the inertial response phase. Barrier distance parameters in energy consistency loss. Each loss weight is set to... , .

[0109] Using the accompanying sensitivity method The parameter gradient is calculated with constant memory complexity. The optimizer uses Adam, with an initial learning rate of... The training run consisted of 200 rounds. The total number of parameters in the model was approximately 1.1M.

[0110] Step 6: Online reasoning.

[0111] After training, the heterogeneous grid diagram and operating parameters are input into the model for new topology configurations and operating conditions. The model first infers the equivalent inertia and damping under the current operating conditions through a GNN supernetwork, and then outputs the inertia center frequency deviation trajectory through physical structured neural ODE integration. RoCoF estimation and energy storage status The inference time for a single 30-second trajectory is approximately 18ms (GPU) or 142ms (CPU), demonstrating engineering feasibility for online frequency security assessment.

[0112] A dynamic modeling system for topology-sensing power systems based on physical information graph neural networks, comprising: The heterogeneous graph construction and feature extraction module constructs a heterogeneous graph representation of the power system, extracts static features from various types of nodes, and extracts temporal features from renewable energy nodes in various types of nodes through a temporal convolutional network, outputting the heterogeneous graph structure and static and temporal features; The graph-level parameter inference module obtains the node spatial embeddings of various types of nodes through a heterogeneous graph neural network based on the heterogeneous graph structure, static features, and temporal features. It then performs graph-level aggregation on the node spatial embeddings and fuses global operating condition parameters to obtain a fusion vector. Based on the fusion vector, it infers the equivalent physical parameters of the system through a bounded scaling layer. The physical structured dynamic characteristic modeling module constructs a joint state space of frequency and energy storage, unifies the frequency deviation, continuous-time observer state and energy storage state into a joint state vector, establishes a physical structured dynamic characteristic model based on the joint state vector and the equivalent physical parameters of the system, decomposes the time derivative of the frequency deviation, and obtains the physical components and the residual components modulated by the FiLM mechanism. The differentiable frequency response calculation module establishes a differentiable frequency response mechanism. It estimates the frequency change rate based on the real-time frequency deviation through a continuous-time frequency change rate observer, and constructs a fast frequency response model and a primary frequency modulation model respectively. Based on the fast frequency response model and the primary frequency modulation model, it calculates the aggregated frequency response power and injects it into the physical structured dynamic characteristic model, while updating the energy storage energy state. The multi-level training and prediction output module constructs a multi-level physical constraint training objective that includes swing equation consistency loss, energy power consistency loss, initial frequency change rate matching loss, and trajectory fidelity loss. It adopts a course learning strategy to dynamically adjust the weights of physical constraints and jointly trains the models constructed by the above modules. After training, the data to be evaluated is evaluated, and the system frequency deviation trajectory, frequency change rate estimate, and energy storage state are output.

[0113] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements a dynamic modeling method for a topology-sensing power system based on a physical information graph neural network.

[0114] A computer-readable storage medium having a computer program stored thereon that, when executed by a processor, implements a dynamic modeling method for a topology-sensing power system based on a physical information graph neural network.

[0115] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. The methods disclosed in the embodiments are described simply because they correspond to the methods disclosed in the embodiments; relevant parts can be found in the method section.

[0116] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A dynamic modeling method for topology-sensing power systems based on physical information graph neural networks, characterized in that, include: S1, construct a heterogeneous graph representation of the power system, extract static features from various types of nodes, and extract temporal features from renewable energy nodes in the various types of nodes through a temporal convolutional network, and output the heterogeneous graph structure, static features, and temporal features; S2, based on the heterogeneous graph structure and static and temporal features, obtain the node spatial embeddings of various types of nodes through a heterogeneous graph neural network, perform graph-level aggregation on the node spatial embeddings and fuse global operating condition parameters to obtain a fusion vector, and infer the equivalent physical parameters of the system through a bounded scaling layer based on the fusion vector; S3, construct a joint state space of frequency and energy storage, unify the frequency deviation, continuous time observer state and energy storage state into a joint state vector, establish a physical structured dynamic characteristic model based on the joint state vector and the equivalent physical parameters of the system, decompose the time derivative of the frequency deviation, and obtain the physical components and the residual components modulated by the FiLM mechanism. S4. Establish a differentiable frequency response mechanism. Estimate the frequency change rate based on the real-time frequency deviation using a continuous-time frequency change rate observer. Construct a fast frequency response model and a primary frequency modulation model respectively. Calculate the aggregated frequency response power based on the fast frequency response model and the primary frequency modulation model and inject it into the physical structured dynamic characteristic model. At the same time, update the energy storage energy state. S5 constructs a multi-level physical constraint training objective that includes swing equation consistency loss, energy power consistency loss, initial frequency change rate matching loss, and trajectory fidelity loss. The physical constraint weights are dynamically adjusted using a course learning strategy to jointly train the model constructed from S1 to S4. After training, the data to be evaluated is evaluated, and the system frequency deviation trajectory, frequency change rate estimate, and energy storage state are output.

2. The dynamic modeling method for topology-sensing power systems based on physical information graph neural networks according to claim 1, characterized in that, The extraction of temporal features through a temporal convolutional network specifically includes: extracting multi-scale features from the historical power sequence of renewable energy nodes using K-layer dilated causal convolution, updating the hidden state of each layer through a gated convolution mechanism; performing global average temporal pooling on the hidden states of each layer, and then aggregating the multi-scale features through an attention mechanism to obtain the temporal embedding vector of the renewable energy nodes.

3. The dynamic modeling method for topology-sensing power systems based on physical information graph neural networks according to claim 1, characterized in that, The process of obtaining spatial embeddings of various types of nodes through heterogeneous graph neural networks specifically includes: projecting static features onto a unified latent space using a corresponding type of multilayer perceptron for different types of nodes, wherein renewable energy nodes are additionally spliced ​​with temporal features to obtain an initial embedding vector; and using an L-layer heterogeneous graph neural network with residual connections to aggregate neighbor node features using a differentiated weight matrix for different topological relationships to obtain node spatial embeddings.

4. The dynamic modeling method for topology-sensing power systems based on physical information graph neural networks according to claim 1, characterized in that, The graph-level aggregation of node spatial embeddings and the fusion of global operating condition parameters specifically include: performing global average pooling, global maximum pooling, and global attention pooling on the node spatial embeddings respectively, and concatenating them to obtain a spatial embedding vector; weighting and aggregating the temporal embeddings of renewable energy nodes according to their rated capacity to obtain a temporal embedding vector; and concatenating the spatial embedding vector, the temporal embedding vector, and the global operating condition parameter vector to obtain a fused vector.

5. The dynamic modeling method for topology-sensing power systems based on physical information graph neural networks according to claim 1, characterized in that, The inference of equivalent physical parameters of the system based on the fusion vector through a bounded scaling layer specifically includes: inferring the input parameters of the fusion vector into a multilayer perceptron, mapping the output to a preset feasible range of physical parameters through a sigmoid activation function and linear scaling, and obtaining the equivalent inertia constant and the equivalent damping coefficient of the system.

6. The dynamic modeling method for topology-sensing power systems based on physical information graph neural networks according to claim 1, characterized in that, The decomposition of the time derivative of the frequency deviation specifically includes decomposing it into physical components and residual components through a neural dynamic characteristic function: ; The physical components directly realize the structure of the rocking equation: ； in, For physical components; The aggregated frequency response power is derived from the primary frequency modulation power. and fast frequency response power composition; The disturbance power; Equivalent damping; The predicted inertia center frequency deviation; The residual components employ a characteristic linear modulation (FiLM) mechanism: ； in, These are the topological conditional residual components; It is a lightweight neural network; This is the scaling factor; Offset factor; This is the fusion vector.

7. The dynamic modeling method for topology-sensing power systems based on physical information graph neural networks according to claim 6, characterized in that, The estimation of the frequency change rate based on the real-time frequency deviation using a continuous-time frequency change rate observer specifically includes: ； in, The time derivative of the observer state; Let be the observer time constant, and the estimated rate of change of the observer frequency satisfies: ;in, For the estimated rate of change of frequency The observer is equivalent to a cutoff frequency of The band-limited differentiator provides a smooth estimate of the rate of change of frequency while maintaining differentiability.

8. A dynamic modeling system for a topology-sensing power system based on a physical information graph neural network, employing the dynamic modeling method for a topology-sensing power system based on a physical information graph neural network as described in any one of claims 1-7, characterized in that, include: The heterogeneous graph construction and feature extraction module constructs a heterogeneous graph representation of the power system, extracts static features from various types of nodes, and extracts temporal features from renewable energy nodes in the various types of nodes through a temporal convolutional network, outputting the heterogeneous graph structure and static and temporal features; The graph-level parameter inference module obtains the node spatial embeddings of various types of nodes through a heterogeneous graph neural network based on the heterogeneous graph structure, static features, and temporal features. It then performs graph-level aggregation on the node spatial embeddings and fuses global operating condition parameters to obtain a fusion vector. Based on the fusion vector, it infers the equivalent physical parameters of the system through a bounded scaling layer. The physical structured dynamic characteristic modeling module constructs a joint state space of frequency and energy storage, unifies the frequency deviation, continuous-time observer state, and energy storage state into a joint state vector, establishes a physical structured dynamic characteristic model based on the joint state vector and the equivalent physical parameters of the system, decomposes the time derivative of the frequency deviation, and obtains the physical components and the residual components modulated by the FiLM mechanism. The differentiable frequency response calculation module establishes a differentiable frequency response mechanism. It estimates the frequency change rate based on the real-time frequency deviation using a continuous-time frequency change rate observer, and constructs a fast frequency response model and a primary frequency modulation model respectively. Based on the fast frequency response model and the primary frequency modulation model, it calculates the aggregated frequency response power and injects it into the physical structured dynamic characteristic model, while updating the energy storage state. The multi-level training and prediction output module constructs a multi-level physical constraint training objective that includes swing equation consistency loss, energy power consistency loss, initial frequency change rate matching loss, and trajectory fidelity loss. It adopts a course learning strategy to dynamically adjust the weights of physical constraints and jointly trains the models constructed by the above modules. After training, the data to be evaluated is evaluated, and the system frequency deviation trajectory, frequency change rate estimate, and energy storage state are output.

9. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements a dynamic modeling method for topology-aware power systems based on a physical information graph neural network as described in any one of claims 1-7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by the processor, the program implements a dynamic modeling method for topology-aware power systems based on a physical information graph neural network as described in any one of claims 1-7.

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