A parameter-incomplete time-varying power distribution network synchronous feasible region evaluation method and system

Abstract

The application provides a parameter-incomplete time-varying power distribution network synchronous feasible region evaluation method and system, which comprises the following steps: obtaining power distribution network partial node measurement and constructing incomplete observation data; dimensionality of the observation data is increased, dynamic modal characteristics are extracted, node electrical distance is estimated according to historical voltage sensitivity, prior graph constraints are constructed, and low-dimensional embedding is obtained through uniform manifold approximation projection; topology mode is identified based on the low-dimensional embedding, different topology modes are used as meta-learning tasks to train the feasible region evaluation meta-model, and the model is updated by using new samples after topology change through Gaussian process power flow mechanism residual constraint training; a joint state space model of topology mode and synchronous feasible region boundary parameters is constructed by adopting Bayesian joint inference, combined with Koopman linearization model and real-time measurement, and the joint state posterior probability distribution is obtained through particle filtering; the probability that the control parameter belongs to the synchronous feasible region is calculated according to the joint state posterior probability distribution, and the synchronous feasible region under the preset confidence level is output.

Description

Technical Field

[0001] This invention relates to the field of power system security assessment technology, and in particular to a method and system for assessing the synchronization feasibility domain of a time-varying distribution network with incomplete parameters. Background Technology

[0002] With the continuous integration of distributed resources such as photovoltaic, wind power, energy storage, and small hydropower into the distribution network, the types of resources and control methods in the distribution network are gradually increasing, and different resources also exhibit significant differences in dynamic response characteristics. Under load fluctuations, power changes, or other disturbances, the control parameters of various distributed resources directly affect the synchronous stability of the cluster. Therefore, when determining and adjusting control parameters, it is necessary to evaluate the parameter range that can meet the synchronous stability requirements.

[0003] Existing methods for assessing the synchronous feasible region mainly include physical model-based assessment methods and data-driven assessment methods based on operational data or simulation samples. The former typically establishes a dynamic model based on device parameters, network parameters, and network topology, and determines the steady state and feasible region boundary through time-domain simulation or solving relevant equations; the latter utilizes existing operational data or simulation samples to establish the correspondence between control parameters and steady state in order to determine the synchronous stable state.

[0004] However, in actual distribution networks, the internal and control parameters of some distributed resources cannot be fully obtained, and measuring devices are often only deployed at some nodes, resulting in limited operational information such as node voltage, power, and frequency. Furthermore, the operation of sectionalizing switches and tie switches, as well as the commissioning or decommissioning of distributed resources, alters network connectivity, causing changes in the distribution network topology and its dynamic characteristics during operation.

[0005] For physical model-based evaluation methods, missing parameters or state information can affect model building and calculation results. For data-driven models trained on existing samples, changes in network topology or operating state can lead to discrepancies between the original samples and the current system state, thus affecting the applicability of the evaluation results. While existing physical and data fusion methods can improve these issues to some extent, they typically still require relatively complete network parameters or are based on a relatively fixed network topology, making them difficult to directly apply to distribution network operation scenarios where parameter information is missing and network structure is constantly changing.

[0006] Therefore, in situations where complete device and network parameters cannot be obtained, only partial node measurements can be acquired, and the network topology may change, how to utilize existing measurement information to promptly identify system operating characteristics and topology changes, and update the synchronous feasible domain accordingly, while providing feasible domain results that reflect the uncertainty of the assessment, is a problem that existing synchronous feasible domain assessment methods still need to solve. Summary of the Invention

[0007] To address the aforementioned deficiencies in the prior art, the present invention aims to provide a method and system for evaluating the synchronization feasible region of a distribution network with incomplete parameters, thereby solving the technical problem of difficulty in accurately evaluating the synchronization feasible region of a distribution network online under conditions of missing parameter information and dynamic topology changes.

[0008] To achieve the above objectives, in a first aspect, the present invention provides a method for evaluating the synchronization feasible region of a time-varying distribution network with incomplete parameters, comprising the following steps: Obtain measurement sequences of some nodes in the distribution network to construct incomplete observation data; The incomplete observation data is subjected to Koopman dimensionality upscaling and dynamic modal features are extracted. The electrical distance between nodes is estimated based on historical voltage sensitivity. The electrical distance is used to construct a priori graph structure constraint. The upscaling data is subjected to uniform manifold approximate projection dimensionality reduction to obtain a low-dimensional embedding vector that simultaneously represents the dynamic mode of the cluster and the topological connection relationship of the distribution network. Topological modes are identified based on low-dimensional embedding vectors. A feasible region evaluation meta-model is trained using different topological modes as meta-learning tasks. The feasible region evaluation meta-model takes control parameter vectors as input and outputs synchronization stability probability. The training loss function includes a boundary classification loss term and a power flow mechanism residual constraint term determined by probabilistically modeling the power flow equation residuals under incomplete observations through a Gaussian process. When the topological mode changes, the feasible region evaluation meta-model is updated using samples containing control parameters and their corresponding stability labels under the changed topological mode. Bayesian joint inference is employed to construct a state-space model with topological modes and synchronous feasible region boundary parameters as the joint state. The updated feasible region evaluation meta-model is used as the dynamic core of the state transition model, and the changing trend of the synchronous feasible region boundary parameters is predicted according to the control input. Based on the joint state, the predicted state is obtained through a Koopman linearization model, and the predicted measurement value is determined according to the predicted state and the observation matrix. Particle filtering is used to update the particle weights according to the difference between the predicted measurement value and the real-time partial node measurement, and the posterior probability distribution of the joint state is obtained recursively. The probability that the control parameter vector belongs to the synchronization feasible region is determined based on the posterior probability distribution, and the synchronization feasible region under the preset confidence level is output.

[0009] As a further improvement to the above technical solution, the measurement sequence includes at least one of node voltage amplitude, node injected active power, node injected reactive power, and frequency; for measurements for which no measurement value was obtained, a missing marker is set in the incomplete observation data.

[0010] As a further improvement to the above technical solution, the Koopman dimensionality increase includes: mapping the incomplete observation data to a high-dimensional feature space through a dimensionality increase function, identifying the finite-dimensional transition matrix of the Koopman operator based on the time series data, and extracting the dynamic modal features based on the spectral decomposition results of the finite-dimensional transition matrix.

[0011] As a further improvement to the above technical solution, the dimensionality reduction of the uniform manifold approximate projection includes: estimating the electrical distance between nodes based on the historical voltage sensitivity matrix, constructing a prior graph structure based on the electrical distance, adding a graph matching regularization term to the cross-entropy loss of the uniform manifold approximate projection to maintain the prior graph structure, and obtaining the low-dimensional embedding vector based on the objective function after adding the graph matching regularization term.

[0012] As a further improvement to the above technical solution, the determination of the power flow mechanism residual constraint term includes: Taking the estimated operating state corresponding to the current control parameter vector as the center, the power flow equation residuals in the neighborhood of the corresponding operating point are obtained based on the incomplete observation data. The probability distribution of the power flow equation residuals is obtained by probabilistically modeling the residuals using a Gaussian process. The expected value of the residual norm of the power flow equation is determined based on the probability distribution, and the expected value is used to construct the residual constraint term of the power flow mechanism.

[0013] As a further improvement to the above technical solution, the current topological mode is identified by a classifier based on the low-dimensional embedding vector sequence within the sliding time window; a model-independent meta-learning approach is adopted, with different topological modes as meta-learning tasks, and a training loss function composed of the boundary classification loss term and the power flow mechanism residual constraint term is used in the process of intra-task parameter update and inter-task parameter optimization to obtain the feasible domain evaluation meta-model.

[0014] As a further improvement to the above technical solution, after detecting a change in topological mode, the initial model parameters for online updating of the feasible domain evaluation meta-model are determined based on the changed topological mode, and samples generated by active or naturally occurring disturbances under the changed topological mode are obtained, the samples including control parameters and their corresponding stability labels. Starting with the initial model parameters, gradient updates are performed under the constraints of the training loss function to obtain a feasible domain evaluation meta-model suitable for the changed topological modes.

[0015] As a further improvement to the above technical solution, the step of determining the posterior probability distribution of the joint state using particle filtering includes: Multiple weighted particles containing topological modes and synchronous feasible region boundary parameters are set up, and the synchronous feasible region boundary parameters of each particle are predicted based on the feasible region evaluation meta-model and control input. Based on the topological modes and synchronous feasible domain boundary parameters corresponding to each particle, the predicted state is obtained through the Koopman linearization model, and the predicted measurement value is determined according to the predicted state and the observation matrix. The observation likelihood of each particle is determined based on the difference between the predicted measurement value and the real-time partial node measurement, and the particle weights are updated based on the observation likelihood. The posterior probability distribution of the joint state is recursively determined based on the updated particles and their weights.

[0016] As a further improvement to the above technical solution, for the control parameter vector to be evaluated, the probability that the control parameter vector to be evaluated belongs to the synchronous feasible region is determined according to the synchronous feasible region boundary parameters and particle weights corresponding to each particle in the posterior probability distribution, and the synchronous feasible region boundary is determined according to the preset confidence level.

[0017] As a further improvement to the above technical solution, it also includes a synchronous feasible region rolling forecast step: using historical forecast errors to train a Gaussian process error model related to the current running point and forecast time scale, combining the Gaussian process error model with the posterior probability distribution of the current synchronous feasible region boundary parameters, determining the synchronous feasible region probability distribution at future forecast times, and outputting synchronous feasible region forecast results with confidence intervals at different forecast time scales.

[0018] Secondly, the present invention also provides a time-varying distribution network synchronization feasible domain evaluation system with incomplete parameters, including a data acquisition module, a topology-dynamic joint embedding module, a physical fusion meta-learning module and a Bayesian joint inference module;

[0019] The data acquisition module is used to acquire measurement sequences of some nodes in the distribution network and construct incomplete observation data; The topology-dynamic joint embedding module is used to perform Koopman dimensionality upscaling on the incomplete observation data and extract dynamic mode features, estimate the electrical distance between nodes based on historical voltage sensitivity, construct a prior graph structure constraint with the electrical distance, and perform uniform manifold approximate projection dimensionality reduction on the upscaled data to obtain a low-dimensional embedding vector that simultaneously represents the dynamic mode of the cluster and the topological connection relationship of the distribution network. The physical fusion meta-learning module is used to identify topological modes based on the low-dimensional embedding vector, train the feasible region evaluation meta-model with different topological modes as meta-learning tasks, construct the training loss function with the boundary classification loss term and the power flow mechanism residual constraint term determined by the Gaussian process, and update the feasible region evaluation meta-model with samples containing control parameters and their corresponding stability labels under the changed topological modes when the topological modes change. The Bayesian joint inference module is used to construct a state-space model with topological modes and synchronous feasible region boundary parameters as the joint state. The updated feasible region evaluation meta-model is used as the dynamic core of the state transition model. The module predicts the changing trend of the synchronous feasible region boundary parameters according to the control input. Based on the joint state, the predicted state is obtained through the Koopman linearization model, and the predicted measurement value is determined according to the predicted state and the observation matrix. The particle weights are updated according to the difference between the predicted measurement value and the real-time partial node measurement. The posterior probability distribution of the joint state is obtained through particle filtering recursion, and the synchronous feasible region under the preset confidence level is output accordingly.

[0020] As a further improvement to the above technical solution, the topology-dynamic joint embedding module is used to identify the finite-dimensional transition matrix of the Koopman operator based on time series data, extract dynamic mode features based on the spectral decomposition results of the finite-dimensional transition matrix, estimate the electrical distance between nodes based on the historical voltage sensitivity matrix, and add a graph matching regularization term to the cross-entropy loss of the uniform manifold approximate projection to maintain the prior graph structure.

[0021] As a further improvement to the above technical solution, the physical fusion meta-learning module is used to perform probabilistic modeling on the power flow equation residuals obtained based on incomplete observation data through a Gaussian process, with the estimated operating state corresponding to the current control parameter vector as the center, form power flow mechanism residual constraint terms according to the expectation of the power flow equation residual norm, and update the feasible domain evaluation meta-model using samples containing control parameters and their corresponding stability labels under the changed topological mode when the topological mode changes. As a further improvement to the above technical solution, the Bayesian joint inference module is used to set weighted particles containing topological modes and synchronous feasible region boundary parameters, predict the synchronous feasible region boundary parameters of each particle based on the updated feasible region evaluation meta-model and control input; obtain the predicted state through the Koopman linearization model, and determine the predicted measurement value based on the predicted state and the observation matrix; determine the observation likelihood of each particle based on the difference between the predicted measurement value and the real-time partial node measurement, update the particle weights based on the observation likelihood, and determine the posterior probability distribution of the joint state based on the updated particles and their weights.

[0022] Thirdly, the present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the method for evaluating the synchronous feasible domain of a distribution network with incomplete parameters as described in the first aspect.

[0023] Because the present invention adopts the above technical solutions, the beneficial effects of the present invention are as follows: This invention provides a method for evaluating the synchronous feasible region of a time-varying distribution network with incomplete parameters. This invention utilizes measurements from some nodes to extract the dynamic and topological characteristics of the distribution network, and combines these with power flow mechanism constraints to train and update the meta-model for feasible region evaluation. When the topology changes, the method can adjust the synchronous feasible region evaluation results based on new operational information. Simultaneously, by performing joint probabilistic inference on the topological modes and the boundary parameters of the synchronous feasible region, the obtained synchronous feasible region can reflect the uncertainty of the current operating state and evaluation results. Therefore, it is applicable to distribution network operating environments with incomplete parameter information, a limited number of measurement nodes, and changing network topology. Specifically:

[0024] 1. Koopman dimensionality enhancement is performed on incomplete observation data to extract dynamic modal features. Simultaneously, the electrical distance between nodes is determined based on historical voltage sensitivity. This electrical distance is used as a priori graph structure to constrain the dimensionality reduction process, ensuring that the resulting low-dimensional embedding vector simultaneously contains information on cluster dynamics and distribution network topology connections. Therefore, even when complete equipment and network parameters are unavailable, existing node measurements can be used to characterize the system's dynamic characteristics and topology, reducing the reliance on complete physical models and parameter information for synchronous feasible region assessment.

[0025] 2. Different topological modes are used as meta-learning tasks to train the feasible region assessment meta-model. A Gaussian process is used to probabilistically model the power flow equation residuals under incomplete observation conditions. The resulting power flow mechanism residuals constrain the model training, ensuring that the feasible region assessment meta-model establishes the relationship between control parameters and synchronous stable states while also considering the power flow mechanism. After a change in topological mode, the feasible region assessment meta-model is updated using samples containing control parameters and their corresponding stability labels under the changed topological mode. This allows the model to adjust according to topological changes without needing to rebuild a complete distribution network physical model for the changed topology.

[0026] 3. The topological modes and synchronous feasible region boundary parameters are treated as a joint state, and the updated feasible region assessment meta-model is used to predict the changing trend of the synchronous feasible region boundary parameters. The predicted measurement values ​​are determined by the Koopman linearization model and the observation matrix, and the particle weights are updated according to the difference between the predicted measurement values ​​and the real-time partial node measurements, so that the real-time measurements can participate in the recursive correction of the topological modes and synchronous feasible region boundary parameters, thereby enabling the synchronous feasible region assessment results to be updated with the changes in the operating state of the distribution network.

[0027] 4. By recursively obtaining the posterior probability distribution of the topological modes and the boundary parameters of the synchronous feasible region through particle filtering, the probability of the control parameter vector belonging to the synchronous feasible region can be determined. This avoids representing the synchronous feasible region with only a single defined boundary. In cases where parameter information is incomplete, measurement information is limited, or network topology changes, the synchronous feasible region can be given according to a preset information level, providing a basis that reflects the uncertainty of the assessment for the selection and adjustment of distribution network control parameters. Attached Figure Description

[0028] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0029] Figure 1 This is a schematic diagram of the process for evaluating the synchronization feasible domain of a time-varying distribution network with incomplete parameters, as disclosed in this invention. Figure 2 This is a schematic diagram illustrating the distribution of stable and unstable samples in the low-dimensional embedding space after approximate projection of a topology-guided uniform manifold disclosed in this invention, wherein: Figure 2 (a) is a schematic diagram of the distribution of stable samples, unstable samples and stability centers in the three-dimensional low-dimensional embedding space. Figure 2 (b) is a schematic diagram of the projection and boundary relationship between stable and unstable samples in the two-dimensional low-dimensional embedding space; Figure 3 This is a comparison chart of the few-shot learning performance of the physical fusion meta-learner disclosed in this invention under a new topology task. Figure 4 This is a schematic diagram illustrating the evolution of the probability density of the synchronous feasible region boundary over time and the output of the 95% confidence interval obtained by particle filtering joint inference disclosed in this invention, wherein: Figure 4 (a) is a schematic diagram of the evolution of the probability density of the boundary parameters of the synchronous feasible region over time; Figure 4 (b) is a schematic diagram of the boundary of the synchronous feasible region and the 95% confidence interval in the control parameter space.

[0030] The realization of the objective, functional characteristics and advantages of the present invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0031] 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 a part of the embodiments of the present invention, and not all of them. 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.

[0032] It should be noted that the technical solutions of the various embodiments of the present invention can be combined with each other, but only if they are based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0033] Example 1

[0034] This invention provides a method for evaluating the synchronous feasible region of a time-varying distribution network with incomplete parameters. This embodiment takes a distribution network containing various distributed resources as the evaluation object. A distribution network model is constructed in the PSCAD / EMTDC simulation platform. The distribution network includes 3 photovoltaic power plants, 1 wind farm, 2 small hydropower units, 4 energy storage devices, and several loads, with a total installed capacity of 200MW and a peak load of 150MW. 40% of the node configuration measurements are selected, and 30% of the converter control parameters are set to unknown to form operating conditions with incomplete node measurements and equipment parameters. Five typical operating topologies are set for model training, and one combined topology not used in the training is set for evaluation under topology change conditions.

[0035] Under each topology, operational data was obtained by randomly changing illumination, wind speed, and load and applying perturbations. This generated 2000 sets of scene data for offline training and 400 sets for online validation. See also... Figure 1 The specific implementation steps are as follows:

[0036] S1. Obtain partial node measurements and extract topology-dynamic joint features: The power distribution network includes Several heterogeneous resource nodes, within the time window Within this range, measurements are obtained from only a subset of the nodes; the number of nodes from which measurements can be obtained is [number missing]. ,satisfy: In the formula, This represents the total number of heterogeneous resource nodes in the distribution network. This indicates the number of nodes that can be measured. This formula indicates that in this embodiment, node measurement is in a partial node measurement state.

[0037] The measurement sequence includes node voltage amplitude. Node-injected active power Node-injected reactive power and frequency At least one of them. Among them, Indicates the node number. This indicates the measurement time. In actual implementation, one or more of the above-mentioned measurements are obtained based on the existing measurement device configuration at each node, and a time series is formed according to the measurement time. Therefore, the existing measurement information of the distribution network can be directly used for subsequent processing, without requiring all nodes to be equipped with measurement devices.

[0038] Construct an incomplete observation vector based on the obtained measurement data: ; In the formula, Indicates time Incomplete observation vectors, The dimension of the observation vector is represented; for unobtained measurements, the corresponding position is denoted as NaN. This formula is used to characterize the node operation information that is actually available at the current moment, and to preserve the missing measurement state so that dynamic and structural features can be directly extracted from the existing measurement sequence later.

[0039] The nonlinear dynamic relationship between the observed states of the distribution network and time is expressed as follows: ; In the formula, This represents a nonlinear mapping of partial observation states as the system operates. This equation describes the dynamic evolution relationship between the current observation states of some nodes and their observation states at the next time step.

[0040] To extract dynamic modal features from incomplete observation data, the Koopman operator is introduced, and an upgraded function vector is constructed. Mapping the above nonlinear dynamic process to a high-dimensional space makes it approximately satisfy: ; in: This represents the Koopman dimension-upgrading function. This represents the feature dimension after dimensionality increase. This represents the finite-dimensional approximation matrix of the Koopman operator. Identification can be achieved by solving the least squares problem on time series data, and by analyzing the matrix. Perform spectral decomposition to obtain the eigenvalues ​​of the dominant modes of the system. It is used to extract dynamic modal features related to oscillations or unstable states.

[0041] By introducing the Koopman operator, the nonlinear dynamic process reflected by some node measurements is mapped to a high-dimensional feature space, and its time evolution is described by an approximately linear state transition relationship. Thus, even when the device and network parameters cannot be fully obtained, the main dynamic characteristics of the system can still be identified by existing measurements.

[0042] Furthermore, the electrical distance between nodes is estimated based on the mean of the historical voltage sensitivity matrix, and a priori graph structure is constructed using the electrical distance. The electrical distance is used to reflect the degree of electrical association between nodes and serves as a topological constraint in the approximate projection dimensionality reduction process of a uniform manifold.

[0043] The high-dimensional features obtained from Koopman dimensionality reduction are input into the uniform manifold approximate projection model. A graph matching regularization term is added to the standard cross-entropy loss of the uniform manifold approximate projection model. This ensures that the dimensionality reduction result preserves the local neighborhood relationships of the high-dimensional features while also considering the topological connectivity reflected by the electrical distance between nodes. The objective function after adding the graph matching regularization term is expressed as: ; In the formula, This represents the overall objective function after adding topological constraints; The standard cross-entropy loss represents the approximate projection of a uniform manifold. The weight coefficients of the graph matching regularization term are represented. This represents a graph matching regularization term used to preserve the structure of the prior graph. This represents a mapping function from a high-dimensional feature space to a low-dimensional embedding space; This represents the Koopman dimension-upgrading function; This indicates incomplete observation data input. This represents the high-dimensional features obtained after dimensionality upscaling incomplete observation data using the Koopman algorithm. This represents the prior graph structure constructed based on the electrical distances between nodes. This formula, while preserving the proximity relationships of high-dimensional dynamic features, uses the electrical distances between nodes to constrain the low-dimensional mapping results, ensuring that the resulting low-dimensional features simultaneously retain cluster dynamic information and distribution network topology connection information. In this embodiment, the graph matching regularization term coefficient... .

[0044] The low-dimensional embedding vector is obtained after dimensionality reduction by approximate projection onto a uniform manifold: ; In the formula, Indicates time The low-dimensional embedding vector, This represents the dimension of the low-dimensional embedding space. In this embodiment... Since this low-dimensional embedding is constrained by both Koopman dynamic features and prior electrical distances between nodes, it can be used to characterize the current cluster dynamic modes and distribution network topology connections, and serve as input for subsequent topology mode identification.

[0045] like Figure 2 As shown, after Koopman dimensionality enhancement and the introduction of prior constraints on node electrical distance for uniform manifold approximation projection, stable and unstable samples exhibit certain clustering and separation characteristics in the low-dimensional embedding space. Figure 2 (a) shows the distribution of stable samples, unstable samples and stability centers in the three-dimensional low-dimensional embedding space; Figure 2 Side (b) shows the projection of the low-dimensional embedding vector into two-dimensional space, where the dashed line indicates the boundary between stable and unstable samples. Figure 2 As can be seen, after the uniform manifold approximation projection with topological constraints, samples of different stable states form different distribution structures in the low-dimensional space. The resulting low-dimensional embedding vectors can be used for subsequent topological mode identification and feasible region evaluation.

[0046] S2. Identify topological modes and update the feasible region evaluation meta-model: Define the topology labels corresponding to different distribution network topologies as follows: Based on the low-dimensional embedding vector sequence within the sliding window, a lightweight classifier is used. Identify the current topological mode. Since low-dimensional embedding vectors contain both dynamic and topological connectivity information, changes in network topology can be identified by utilizing feature changes reflected in measurement sequences, without relying on complete network parameters as a prerequisite for topology identification.

[0047] Using different topological modes as meta-learning tasks Construct a meta-model for feasible domain evaluation The feasible region evaluation meta-model uses the control parameter vectors of each distributed resource. As input, output the probability that the control parameter satisfies synchronous stability under the current system state. .

[0048] The feasible region evaluation meta-model employs a composite loss function that includes boundary classification loss and power flow mechanism residual constraints: ; In the formula, Representing topological modes The corresponding meta-learning task loss, Represents the boundary classification loss term. This represents the synchronization stability probability output by the feasible region evaluation metamodel. This indicates the stability label of the corresponding sample. This represents the residual constraint term of the power flow mechanism. This indicates the weight of the constraint term.

[0049] for With current control parameters Centered on the corresponding estimated state, a Gaussian process is used to probabilistically model the power flow equation residuals near the operating point, based on incomplete observation data. The expected norm of this residual probability distribution is used as the constraint for the power flow mechanism residuals. Thus, the feasible region evaluation meta-model learns the synchronous stable boundary based on stability labels, and uses the power flow mechanism information contained in existing measurements to constrain the model update direction, enabling the model to limit boundary offsets using existing physical information even when parameter information is incomplete.

[0050] When the topology is detected online by Change to At that time, model parameters that are similar to the changed topology are selected from the meta-learner parameter library as initial parameters. And obtain a small number of samples containing control parameters and their corresponding stability labels under the changed topology. Starting from the topology, a few steps of gradient descent are performed under the constraint of the composite loss function to obtain the feasible region evaluation meta-model corresponding to the changed topology. .

[0051] S3. Construct the joint state and perform particle filter recursive estimation: To address the uncertainties in topological modes and synchronous feasible region boundary parameters under conditions of incomplete parameters and partial node measurements, the synchronous feasible region evaluation process is constructed as a Bayesian joint inference process. Using the topological modes and synchronous feasible region boundary parameters as the joint state, a priori prediction of the current joint state is formed based on the previous joint state and control input. This prior prediction is then updated using real-time partial node measurements to obtain the posterior probability distribution of the current joint state. The Bayesian joint inference is implemented using particle filtering, with multiple weighted particles approximating the probability distribution of the joint state.

[0052] Specifically, to simultaneously estimate the current topological mode and the boundary of the synchronous feasible region under partial node measurement conditions, the two are combined into an augmented joint state: ; In the formula, Indicates time The state of union, Indicates the current topological mode. This represents the parameters describing the boundary of the synchronous feasible region. This formula places the topological state and the feasible region boundary state in the same recursive estimation process, enabling real-time partial node measurements to simultaneously correct both.

[0053] In this embodiment, the augmented state It is set to 7 dimensions, including a 1-dimensional topological indicator variable and 6-dimensional boundary parameters.

[0054] Based on the joint state, a state-space model is constructed, and its state transition model is expressed as follows: ; In the formula, This indicates the joint state at the previous moment. Indicates the current control input. This represents the conditional probability distribution of the current joint state, given the previous joint state and the current control input. This formula describes the relationship between the topological modes and the boundary parameters of the synchronous feasible region as a function of the previous state and the current control input. During state transitions, the feasible region evaluation meta-model is updated after the topological change. As the core of the state transition model's dynamics, based on the control input... Predict the changing trends of the boundary parameters of the synchronous feasible domain so that the boundary state prediction corresponds to the current topology and control input.

[0055] Based on the topological modes in the current joint state and synchronous feasible region boundary parameters Using the corresponding Koopman linearization model Obtain the predicted state and use the observation matrix The predicted state is mapped to the actual observable nodes. Considering measurement noise, the observation equation is expressed as: ; In the formula, Indicates time Partial node measurement Indicates a joint state The predicted state obtained by the Koopman linearization model under the given conditions Represents the observation matrix. This represents measurement noise. The physical meaning of this formula is to map the predicted state corresponding to the candidate joint state to the actual measurement space, so as to form a predicted measurement relationship that can be compared with the real-time partial node measurements.

[0056] The corresponding observation model is expressed as follows: ; In the formula, Represents a given joint state The conditional probability of the current partial node measurements is obtained in real time. This formula is used to reflect the degree of matching between the predicted measurements corresponding to the candidate joint state and the real-time partial node measurements, and serves as the basis for particle weight updates.

[0057] Particle filtering is used to recursively estimate the joint state, with a set of weighted particles representing the current joint state: ; In the formula, Indicates the first A group of particles in a combined state. Indicates the first The weight of each particle, This represents the number of particles. The physical meaning of this formula is that it approximates the probability distribution of the current joint state using multiple particles with different topological modes, boundary parameters, and corresponding weights.

[0058] After predicting the state of each particle, the predicted measurements of each particle are compared with the real-time measurements of some nodes. The difference determines the observation likelihood, and the particle weights are updated accordingly; after weight normalization and resampling, the posterior probability distribution of the joint state is recursively obtained: ; In the formula, Represents the time from the initial moment to the current moment. The obtained partial node measurement sequence, This represents the joint probability estimate of the current topological mode and the boundary parameters of the synchronous feasible region after integrating historical and current measurements. By continuously refining the joint state through real-time measurements from some nodes, the corresponding posterior probabilities are preserved for different topological modes and different boundary states of the synchronous feasible region. This avoids representing the current system state with only a single topological result and a single boundary value when measurements are incomplete. In this embodiment, the number of particles... .

[0059] S4. Determine the feasible probability of the control parameters and output the synchronization feasible region: After obtaining the joint state posterior probability distribution, the posterior distribution of the synchronous feasible region boundary parameters is obtained from the joint posterior distribution. The uncertainty of the topological mode has been incorporated into the posterior recursion through the joint state particles and their weights. Therefore, the posterior distribution of the boundary parameters reflects the combined influence of different topological states and boundary states under the current partial measurement conditions.

[0060] For any control parameter vector The probability that it belongs to the synchronous feasible region is expressed as: ; In the formula, Represents the control parameter vector The probability that it belongs to the synchronous feasible region. Indicated by boundary parameters A defined synchronization feasible domain, The characteristic function is represented when the control parameter vector... Set to 1 if it is within the corresponding synchronization feasible region, otherwise set to 0. This represents the posterior distribution of the synchronous feasible region boundary parameters obtained by joint posterior analysis using particle filtering. By synthesizing different possible synchronous feasible region boundaries and their posterior probabilities, the probability that a given control parameter belongs to the synchronous feasible region is obtained. Therefore, when uncertainties exist in topology identification and boundary estimation, the evaluation result is not represented by a single definite boundary, but rather by the feasible probability of the control parameter reflecting the corresponding uncertainty.

[0061] At the preset credit level Next, output the synchronization feasible region: ; In the formula, Indicates confidence level The following synchronization feasible domain, Indicates the preset credit level. Represents the control parameter vector The probability of belonging to the synchronization feasible region. The control parameter vector with a feasible probability not lower than a preset confidence level is defined as the synchronization feasible region, thus representing the synchronization stability evaluation result as a probability region with a confidence level. In this embodiment, Take 95%, and output the synchronization feasible region at a 95% confidence level.

[0062] like Figure 4 As shown, Figure 4 This is used to represent the update of the posterior probability distribution of the synchronous feasible region boundary parameters and the probability boundary over time during Bayesian joint inference using particle filtering. Figure 4 (a) Taking the synchronous feasible region boundary parameter θ1 as an example, the probability density distributions at t=0 s, t=5 s, t=10 s, and t=15 s are given. As real-time partial node measurements are continuously input and particle weights are constantly updated, the posterior probability density of θ1 is adjusted accordingly, and the distribution range gradually converges, indicating that the estimation of the current feasible region boundary parameter gradually becomes more concentrated. Figure 4 Figure (b) shows the boundary of the synchronous feasible region in the parameter space formed by control parameters u1 and u2, where one side of the boundary corresponds to the stable region and the other side corresponds to the unstable region; the shaded area represents the range where the boundary may occur between t=5 s and t=10 s, and the solid line represents the probability boundary determined at a 95% confidence level at t=15 s. Figure 4As can be seen, particle filtering uses real-time measurements to recursively update the joint state of the topological mode and the boundary parameters of the synchronous feasible region. It can not only obtain the position of the boundary of the synchronous feasible region, but also characterize the uncertainty of the boundary estimation through the posterior probability distribution and confidence interval. This corresponds to the processing of the synchronous feasible region based on Bayesian joint inference outputting a pre-set confidence level in this invention.

[0063] Through the above process, when complete equipment and network parameters are not available, only partial node measurements are obtained, and the network topology changes, the system dynamic modes are extracted using the time-series features of the partial measurements. These are then combined with electrical distance constraints formed by historical voltage sensitivity to identify topology-related features. After detecting a topology change, the feasible region evaluation meta-model is updated using a small number of control parameters and stability label samples under the changed topology. Furthermore, the topology modes and synchronous feasible region boundary parameters are treated as a joint state. This joint state is recursively corrected using particle filtering through Koopman prediction and real-time partial node measurements. Finally, the feasible probability of the control parameters is determined according to the joint posterior, and the synchronous feasible region under a preset confidence level is output. Thus, the synchronous feasible region can be updated according to changes in system operating characteristics and topology state, while retaining some evaluation uncertainties introduced by observation and topology identification in the output results.

[0064] In a preferred embodiment, the dimension of the finite-dimensional transition matrix A is expressed as: In the formula, A represents the finite-dimensional transition matrix of the Koopman operator; K represents the dimensionality of the upgraded feature space; R represents the real number field; and K×K indicates that matrix A has K rows and K columns. This formula is used to define the dimensional correspondence between the finite-dimensional transition matrix and the high-dimensional feature space.

[0065] The finite-dimensional transition matrix A is identified based on the time series of incomplete observation data. Specifically, high-dimensional features corresponding to adjacent measurement times are used as data pairs, and A is determined by solving a least-squares problem, so that the high-dimensional features obtained from the transition of A at the next time step match the actual dimensionality increase result. This identification process directly utilizes the temporal relationships of existing measurements and does not require prior complete acquisition of the internal parameters of each distributed resource and all network parameters.

[0066] After identifying the finite-dimensional transition matrix A, spectral decomposition is performed on A to extract the eigenvalues ​​corresponding to the dominant dynamic modes of the system. Where λ represents the eigenvalues ​​of the Koopman finite-dimensional transition matrix; This represents the eigenvalue corresponding to the j-th dynamic mode; j represents the sequence number of the dynamic mode. The eigenvalue is used to characterize the evolutionary properties of the corresponding dynamic mode and to identify oscillatory or unstable modes.

[0067] In one specific embodiment, the dimension-upgraded function vector may include radial basis functions and a polynomial kernel, and the feature dimension K after dimension upgrade is 512. Through dimension upgrade, transition matrix identification, and spectral decomposition, dynamic modal features can be extracted from existing time-series measurements even when the node measurements, equipment, and network parameters in the measurement information are incomplete. This provides a dynamic feature foundation for subsequent construction of topological constraints based on node electrical distances and low-dimensional embedding.

[0068] In a preferred embodiment, after obtaining the low-dimensional embedding vector, the topological mode of the current distribution network is identified based on the sequence of low-dimensional embedding vectors within the sliding time window, and meta-learning tasks are constructed for different topological modes.

[0069] Define the topology label as: In the formula, This indicates the topology mode label of the distribution network; 'i' represents the topology mode number. This represents the i-th topology mode. Different topology modes correspond to different network connection states.

[0070] Since the aforementioned low-dimensional embedding vectors simultaneously contain cluster dynamic mode information and distribution network topology connection information, topology mode identification can be performed using low-dimensional embedding vectors from consecutive time points. The sequence of low-dimensional embedding vectors within the sliding time window is input into the classifier, and its input form is expressed as: ; In the formula, This represents a classifier used for topological mode identification; This represents the low-dimensional embedding vector obtained after dimensionality reduction by approximate projection of a uniform manifold with Koopman dimensionality increase and topological constraints. Indicates the current measurement time; Indicates the start time of the current sliding time window; Indicates from time At that time A low-dimensional embedding vector sequence; w represents the sliding time window.

[0071] The classifier determines the current topological mode based on the changes in the low-dimensional embedding vector within the sliding time window. Since the low-dimensional embedding vector already contains topological information introduced by electrical distance constraints, topological mode identification can still be performed using changes in connectivity reflected by existing measurements even when some network parameters cannot be fully obtained.

[0072] Furthermore, a meta-model for feasible region evaluation is constructed: In the formula, M represents the feasible region evaluation meta-model; φ represents the model parameters of the feasible region evaluation meta-model. This represents the meta-model for evaluating the feasible region, determined by the parameter φ.

[0073] The feasible region evaluation metamodel takes the control parameter vector u of each distributed resource as input and outputs the probability that the corresponding control parameter point satisfies the synchronization and stability requirements under the current system state. Where u represents a vector of control parameters involved in the synchronous stability assessment.

[0074] To enable the feasible region evaluation meta-model to adapt to different topological modes, a model-independent meta-learning approach is adopted, treating different topological modes as independent meta-learning tasks: In the formula, T represents the meta-learning task; k represents the task number. This represents the meta-learning task corresponding to the k-th topological mode.

[0075] During the meta-learning process, intra-task parameters are updated for each topological mode, and inter-task parameter optimization is performed based on the update results corresponding to multiple topological modes. Both intra-task parameter updates and inter-task parameter optimization employ a training loss function composed of a boundary classification loss term and a power flow mechanism residual constraint term. ; The training loss described above considers both the stability classification results of the samples and the power flow mechanism information obtainable under incomplete observation conditions. Specifically, the boundary classification loss term adjusts the classification boundary between the control parameters and the synchronous stable state, while the power flow mechanism residual constraint term restricts the update direction of the model parameters. When equipment and network parameters are incomplete, the power flow residual information formed by existing measurements can be used to constrain the model training.

[0076] In one specific embodiment, the feasible region evaluation meta-model employs a 4-layer fully connected network. During the meta-training phase, five topological modes are selected as independent tasks. For each task, 50 samples are used for intra-task parameter updates, and another 50 samples are used for inter-task parameter optimization. The residual probability modeling of the power flow mechanism adopts a Matérn 5 / 2 kernel Gaussian process.

[0077] When a change in the current topological mode is detected based on the output of the topology classifier, the change is represented as: ; In the formula, Represents the topological mode before the change; This represents the changed topology mode. This formula indicates that the distribution network has changed from its original topology connection state to a new topology connection state.

[0078] After detecting a topological mode change, the parameters are retrieved from the meta-learner parameter library. The model parameters corresponding to the closest existing topology are used as the initial model parameters for online updates: ; This represents the initial model parameters applicable to online updates of the topological modes after changes.

[0079] Subsequently, samples are collected under the changed topology modes by actively applying a small amount of disturbance or by utilizing disturbances that naturally occur during the operation of the distribution network. The samples include the control parameter vector u and its corresponding stability label y, which are used to reflect the synchronous stable state corresponding to different control parameters under the changed topology conditions.

[0080] In one specific embodiment, control parameter-stability label samples under the new topology can be obtained by actively applying or utilizing 10 to 20 naturally occurring perturbations. During actual model updates, 10 of these samples can be selected as the new topology samples.

[0081] With initial model parameters Starting from the aforementioned training loss function Under constraints, a few steps of gradient descent are performed to adjust the model parameters based on samples obtained under the changed topological mode, resulting in a feasible region evaluation meta-model suitable for the changed topological mode: In the formula, This represents the model parameters after online gradient update. This represents the feasible domain evaluation meta-model applicable to the changed topological modes after the update is completed.

[0082] In this embodiment, 10 new topological samples can be used, and with Starting from the first step, perform 5 steps of gradient descent to obtain... .

[0083] The above approach uses different topological modes as meta-learning tasks, enabling the model to form a parameter base that can be shared across different topological tasks during the offline training phase. When the distribution network topology changes, the model parameters are initialized using those corresponding to similar topologies, and then updated using a small number of samples obtained under the changed topology. This reduces the computational cost of retraining the model using all historical data for each topology change. Simultaneously, intra-task updates, inter-task optimizations, and model updates after topology changes are all subject to the combined effects of boundary classification loss and power flow mechanism residual constraints, ensuring that the model retains the power flow mechanism constraints provided by existing measurements when adjusting the synchronous stability boundary using new topology samples.

[0084] As a preferred embodiment, after obtaining the posterior probability distribution of the current synchronous feasible region boundary parameters, rolling forecasts can also be made for the synchronous feasible region at different future forecast time scales.

[0085] First, based on the forecast results and corresponding evaluation results of the synchronous feasible region during historical operation, forecast error samples are formed at different operating points and different forecast time scales. These forecast error samples are then used to train a Gaussian process error model. The Gaussian process error model is expressed as: ; In the formula, A Gaussian process model representing the forecast error distribution within the synchronous feasible region; This indicates the forecast timescale, that is, the time interval from the current time to the target forecast time. This indicates the current operating point, used to characterize the operating state of the distribution network when performing synchronous feasible domain forecasting.

[0086] At the current time t, the posterior probability distribution of the synchronization feasible region boundary parameters is obtained through the aforementioned particle filtering. This posterior probability distribution is recursively derived from the measurements of the current partial nodes and is used to characterize the probability of different synchronization feasible region boundary parameters under the existing measurement conditions.

[0087] Determine the forecast time scale Then, the target forecast time is expressed as: In the formula, t represents the current time. This indicates the forecast time scale; this formula is used to determine the target time position corresponding to a rolling forecast.

[0088] At any moment Based on the current running point and the selected forecast time scale The corresponding Gaussian process error model is invoked to obtain the forecast error distribution under the given operating conditions; then, the forecast error distribution is combined with the posterior probability distribution of the current synchronization feasible domain boundary parameters to determine... The probability distribution of the boundary parameters of the synchronous feasible region at each time point is obtained, and the probability distribution of the synchronous feasible region at that predicted time point is obtained accordingly.

[0089] When the above processing is used, the future synchronous feasible region is not directly extrapolated from the current single boundary value, but is based on the posterior distribution of the current boundary parameters, and historical forecast errors corresponding to the operating point and forecast time scale are introduced. In this way, the differences in boundary estimation formed under partial node measurement conditions, as well as the error changes caused by changes in the forecast time scale, can all be reflected in the probability distribution of the future synchronous feasible region.

[0090] In practical applications, different forecast time scales, such as minute-level and hour-level, can be set, and the probability distribution of the synchronization feasible region at the corresponding target time can be calculated for each. Based on the preset confidence level, the corresponding confidence interval is determined from the probability distribution to obtain the synchronization feasible region forecast results at different forecast time scales.

[0091] Once new real-time measurements of some nodes are obtained, the joint state posterior of the current topological mode and the boundary parameters of the synchronous feasible region is updated according to the aforementioned particle filtering method, and the updated boundary parameter posterior probability distribution is used as the starting point for the next forecast. As the measurement data is continuously updated, the forecast starting point and target time move forward accordingly, thus forming a rolling forecast of the synchronous feasible region.

[0092] To illustrate the impact of each processing step of the present invention on the evaluation results of the synchronous feasible domain, the following comparative examples are set under the same simulation scenario and data conditions as the above embodiments.

[0093] Comparative Example 1 employs a time-domain simulation method based on complete device parameters and a known network topology. This method requires complete model parameters and a defined network topology as computational conditions. In this embodiment, due to missing parameters and changes in network topology, the corresponding evaluation could not be completed, and therefore the relevant result is denoted as N / A.

[0094] Comparative Example 2 uses a purely data-driven approach, directly fitting the boundary of the synchronous feasible region through a standard neural network, without employing the aforementioned topology-dynamic joint embedding, meta-learning adaptation, and power flow mechanism residual constraints.

[0095] Comparative Example 3 adopts the simplified scheme A of the present invention. The rest of the processing is the same as in this embodiment, but the power flow mechanism residual constraint term is removed during the meta-learning training process, and only sample data is used for model training and parameter updates after topology changes.

[0096] Comparative Example 4 adopts the simplified scheme B of the present invention. The remaining processing procedures are the same as those in this embodiment, but Bayesian joint inference and particle filtering are not used. Instead, the updated feasible region evaluation meta-model directly outputs the deterministic feasible region evaluation result.

[0097] The complete technical solution adopted in this invention includes topology-dynamic joint embedding, physical fusion meta-learning, and Bayesian joint inference.

[0098] The test results for each scheme are shown in Table 1 below: Table 1 shows the test comparison results of each scheme under the corresponding evaluation indicators.

[0099] Among them, the evaluation accuracy is statistically analyzed using offline simulation results obtained based on complete information as a reference; the physical rationality verification is used to check whether the predicted synchronous feasible domain boundary satisfies basic electrical laws such as monotonicity.

[0100] The results in the table show that Comparative Example 2 requires model retraining after a topology change, with an adaptation time of approximately 30 minutes. Comparative Examples 3 and 4, and this embodiment, all use meta-learning updates, with adaptation times of less than 5 seconds. These results demonstrate that, under the full test conditions of this invention, using different topological modalities as meta-learning tasks and updating parameters using a small number of samples under the new topology can reduce the time required to retrain the model after a topology change.

[0101] With 10 new topology samples used in both cases, Comparative Example 3 achieved an evaluation accuracy of 91.8% and a physical rationality verification pass rate of 86.4%; the corresponding complete scheme of this invention achieved 94.5% and 98.1%. The main difference between Comparative Example 3 and this embodiment lies in whether or not a power flow mechanism residual constraint term is used. Therefore, the above results show that under this test condition, introducing the power flow equation residual information obtained from incomplete observation data into meta-learning training helps to limit the offset of the synchronous feasible domain boundary during few-sample updates and improves the consistency between the evaluation results and basic electrical laws.

[0102] Comparative Example 4 and the complete scheme of the present invention have similar few-sample evaluation accuracy. However, Comparative Example 4 directly outputs the point estimation results of the feasible region evaluation meta-model and cannot provide the topological identification uncertainty and probabilistic risk prediction results. The complete scheme of the present invention recursively derives the posterior probability distribution of the topological mode and the boundary parameters of the synchronous feasible region through Bayesian joint inference and particle filtering. Therefore, it can further output the probability information of the topological mode and the synchronous feasible region under the preset confidence level.

[0103] Therefore, in this embodiment, particle filtering is not used to replace the feasible region evaluation meta-model, but rather the updated feasible region evaluation meta-model is used as the dynamic basis of the state transition process. Combined with real-time partial node measurements, the candidate joint state is updated probabilistically, thereby preserving the uncertainty of topology identification and boundary estimation in the synchronous feasible region results.

[0104] The above test results show that, under the conditions of incomplete parameters in the complete scheme of this invention, partial node measurement, and topology changes, the method provided by this invention can complete the synchronous feasible region evaluation and update the feasible region evaluation meta-model with a small number of new samples after the topology changes.

[0105] Among them, the meta-learning mechanism is mainly used to improve the model adaptation efficiency after topology changes; the power flow mechanism residual constraint is used to constrain model updates using existing power flow information under incomplete observation conditions; and Bayesian joint inference and particle filtering are used to deduce the posterior probability distribution of the topological modes and the boundary parameters of the synchronous feasible region. The three act on the feature and model update, physical constraints, and uncertainty quantification stages, respectively, enabling this embodiment to output a synchronous feasible region with a pre-set confidence level under conditions of incomplete parameter information and dynamic topology changes.

[0106] To further illustrate the inventive concept and beneficial effects of the present invention, such as Figure 3 As shown, the physical fusion meta-learner used in this invention is compared with the control fine-tuning method in terms of few-shot adaptation performance under new topology tasks. Figure 3 In the graph, the horizontal axis represents the number of online update steps, and the vertical axis represents the accuracy of feasible region evaluation. As the number of online update steps increases, the evaluation accuracy of both methods improves. Specifically, the accuracy of the control fine-tuning method at the corresponding update steps is approximately 63.9%, 73.0%, 78.3%, and 80.5%, respectively. When the present invention uses a physical fusion meta-learner, the corresponding accuracies are approximately 79.7%, 89.8%, 91.8%, and 94.3%, respectively. It is evident that, at the same number of update steps, the evaluation accuracy of the present invention is higher than that of the traditional fine-tuning method, and gradually approaches that of the control fine-tuning method as the number of update steps increases. Figure 3 The target performance level is shown in the figure. This result indicates that after a topology change, using the existing feasible region evaluation meta-model parameters as the starting point for updates, and performing a small number of gradient updates under the combined effect of boundary classification loss and power flow mechanism residual constraints, can achieve a high feasible region evaluation accuracy with fewer update steps, which is beneficial to improving the online adaptability of the model under new topology conditions.

[0107] It should be noted that the control fine-tuning method uses the same basic network structure as the feasible domain evaluation meta-model in this embodiment. After detecting a new topology, it does not use the task adaptation parameters obtained by meta-learning, nor does it introduce power flow mechanism residual constraints. Instead, it uses a small number of control parameters - stability label samples obtained under the new topology to directly update the model parameters with gradients, thus serving as a control method for few-sample adaptation.

[0108] Example 2

[0109] The present invention also provides a time-varying distribution network synchronization feasible domain evaluation system with incomplete parameters, including a data acquisition module, a topology-dynamic joint embedding module, a physical fusion meta-learning module, and a Bayesian joint inference module.

[0110] The data acquisition module is used to acquire measurement sequences of some nodes in the distribution network and construct incomplete observation data. The measurement sequences include one or more of the following: node voltage amplitude, node injected active power, node injected reactive power, and frequency. For measurements for which no values ​​were obtained, a missing marker is set at the corresponding location. Therefore, the data required for subsequent evaluation can be directly generated using existing measurement conditions, without requiring all nodes to be observable.

[0111] The topology-dynamic joint embedding module is used to perform Koopman dimensionality upscaling on incomplete observation data and extract dynamic mode features of the distribution network. Specifically, the incomplete observation data is mapped to a high-dimensional feature space through an upscaling function, the finite-dimensional transition matrix of the Koopman operator is identified based on the time series data, and the dominant dynamic modes are extracted based on the spectral decomposition results of the matrix.

[0112] Furthermore, the electrical distances between nodes are estimated based on the historical voltage sensitivity matrix, and a prior graph structure is constructed using these electrical distances. A graph matching regularization term to preserve the prior graph structure is added to the cross-entropy loss of the uniform manifold approximate projection, and the dimensionality of the Koopman upscaling data is reduced to obtain low-dimensional embedding vectors. These low-dimensional embedding vectors simultaneously contain dynamic information reflected by the measurement sequences and electrical connection information between nodes, and can be used for subsequent topology mode identification.

[0113] The physical fusion meta-learning module is used to identify the current topological mode based on the low-dimensional embedding vector within the sliding time window, and to train the feasible region evaluation meta-model using different topological modes as meta-learning tasks. The feasible region evaluation meta-model takes the control parameter vector as input and outputs the probability that the corresponding combination of control parameters satisfies the synchronization stability condition.

[0114] The model training employs a training loss function consisting of a boundary classification loss term and a power flow mechanism residual constraint term. The boundary classification loss term is used to learn the synchronous stable boundary based on control parameters and their stability labels. The power flow mechanism residual constraint term uses a Gaussian process to probabilistically model the power flow equation residuals under incomplete observation conditions and is determined based on the expectation of the power flow equation residual norm. Therefore, even when equipment and network parameters are incomplete, the model can still be trained using the power flow relationships reflected by existing measurements.

[0115] When a topological modality change is detected, the physics fusion meta-learning module determines the initial model parameters for online updating based on the changed topological modality and obtains control parameter-stability label samples under the new topology. These samples can be generated by active perturbations or obtained using naturally occurring perturbations during operation. Starting with the initial model parameters, gradient updates are performed under the constraints of the training loss function to obtain a feasible region evaluation meta-model suitable for the changed topological modality. Using this approach, model updates can be completed using a small number of new topological samples based on an existing feasible region evaluation meta-model, without needing to retrain the model using all historical data for each topological change.

[0116] The Bayesian joint inference module is used to construct a state-space model with topological modes and synchronous feasible region boundary parameters as joint states, and uses the updated feasible region evaluation meta-model as the dynamic core of the state transition model to predict the changing trend of synchronous feasible region boundary parameters based on control input.

[0117] Given incomplete parameters and partial node measurements, both the current topological mode and the synchronous feasible region boundary may exhibit uncertainties. Therefore, the synchronous feasible region evaluation is constructed as a Bayesian filtering process. The Bayesian joint inference module sets up multiple weighted particles, each including a candidate topological mode and the corresponding synchronous feasible region boundary parameters.

[0118] Based on the updated feasible region evaluation meta-model and control input, the synchronous feasible region boundary parameters of each particle are predicted. Then, based on the corresponding topological mode of each particle, the predicted state is obtained through the Koopman linearization model, and the predicted measurement value is determined using the observation matrix. The predicted measurement value is compared with the real-time partial node measurement, and the observation likelihood of each particle is determined based on the difference between the two, and the particle weights are updated accordingly.

[0119] Based on the updated particles and their weights, the joint posterior probability distribution of the topological mode and the synchronous feasible region boundary parameters is recursively obtained. Using this method, when the current measurements are insufficient to uniquely determine the topological state or feasible region boundary, different candidate states and their corresponding probabilities can be retained, rather than directly determining a single result. For the control parameter vector to be evaluated, the Bayesian joint inference module calculates the probability that the control parameter vector belongs to the synchronous feasible region based on the synchronous feasible region boundary parameters and particle weights of each particle in the joint state posterior probability distribution, and determines the synchronous feasible region boundary according to a preset confidence level.

[0120] In one specific embodiment, the joint state is set to 7 dimensions, including a 1-dimensional topology indicator variable and a 6-dimensional synchronization feasible region boundary parameter, and outputs the synchronization feasible region at a 95% confidence level.

[0121] The system described above uses measurements from some nodes to extract joint dynamic and topological features, updates the feasible region evaluation meta-model when the topology changes, and performs probabilistic estimation of the topological modes and the boundaries of the synchronous feasible region through Bayesian joint inference. This allows for updating the synchronous feasible region under conditions of incomplete parameter information and time-varying topology, while retaining the uncertainty in the evaluation results.

[0122] Example 3

[0123] The present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein, when the program is executed, it controls the device on which the storage medium is located to perform some or all of the steps in Embodiment 1.

[0124] The storage medium may include high-speed RAM memory, and may also include nonvolatile memory, such as at least one disk storage device. It is understood that the storage medium can be any machine-readable medium capable of storing program code, such as random access memory (RAM), magnetic disk, hard disk, solid state disk (SSD), or nonvolatile memory.

[0125] Those skilled in the art will understand that embodiments of the present invention can be provided as methods or storage media. Therefore, embodiments of the present invention can take the form of entirely hardware embodiments, entirely software embodiments, or embodiments combining software and hardware aspects. Furthermore, embodiments of the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0126] The above are merely preferred embodiments of the present invention and do not limit the patent scope of the present invention. Any equivalent structural transformations made using the contents of the present invention's specification and drawings under the inventive concept of the present invention, or direct or indirect applications in other related technical fields, are within the patent protection scope of the present invention.

Claims

1. A method for evaluating the feasible region of synchronization in a time-varying distribution network with incomplete parameters, characterized in that, Includes the following steps: Obtain measurement sequences of some nodes in the distribution network to construct incomplete observation data; The incomplete observation data is subjected to Koopman dimensionality upscaling and dynamic modal features are extracted. The electrical distance between nodes is estimated based on historical voltage sensitivity. The electrical distance is used to construct a priori graph structure constraint. The upscaling data is subjected to uniform manifold approximate projection dimensionality reduction to obtain a low-dimensional embedding vector that simultaneously represents the dynamic mode of the cluster and the topological connection relationship of the distribution network. Topological modes are identified based on low-dimensional embedding vectors. A feasible region evaluation meta-model is trained using different topological modes as meta-learning tasks. The feasible region evaluation meta-model takes control parameter vectors as input and outputs synchronization stability probability. The training loss function includes a boundary classification loss term and a power flow mechanism residual constraint term determined by probabilistically modeling the power flow equation residuals under incomplete observations through a Gaussian process. When the topological mode changes, the feasible region evaluation meta-model is updated using samples containing control parameters and their corresponding stability labels under the changed topological mode. Bayesian joint inference is employed to construct a state-space model with topological modes and synchronous feasible region boundary parameters as the joint state. The updated feasible region evaluation meta-model is used as the dynamic core of the state transition model, and the changing trend of the synchronous feasible region boundary parameters is predicted according to the control input. Based on the joint state, the predicted state is obtained through a Koopman linearization model, and the predicted measurement value is determined according to the predicted state and the observation matrix. Particle filtering is used to update the particle weights according to the difference between the predicted measurement value and the real-time partial node measurement, and the posterior probability distribution of the joint state is obtained recursively. The probability that the control parameter vector belongs to the synchronization feasible region is determined based on the posterior probability distribution, and the synchronization feasible region under the preset confidence level is output.

2. The method for evaluating the synchronization feasible region of a time-varying distribution network with incomplete parameters according to claim 1, characterized in that, The Koopman dimensionality increase includes: mapping the incomplete observation data to a high-dimensional feature space through a dimensionality increase function, identifying the finite-dimensional transition matrix of the Koopman operator based on the time series data, and extracting the dynamic modal features based on the spectral decomposition results of the finite-dimensional transition matrix; The uniform manifold approximate projection dimensionality reduction includes: estimating the electrical distance between nodes based on the historical voltage sensitivity matrix, constructing a prior graph structure based on the electrical distance, adding a graph matching regularization term to the cross-entropy loss of the uniform manifold approximate projection to preserve the prior graph structure, and obtaining the low-dimensional embedding vector based on the objective function after adding the graph matching regularization term.

3. The method for evaluating the synchronization feasibility domain of a time-varying distribution network with incomplete parameters according to claim 1, characterized in that, The determination of the power flow mechanism residual constraint term includes: Taking the estimated operating state corresponding to the current control parameter vector as the center, the power flow equation residuals in the neighborhood of the corresponding operating point are obtained based on the incomplete observation data. The probability distribution of the power flow equation residuals is obtained by probabilistically modeling the residuals using a Gaussian process. The expected value of the residual norm of the power flow equation is determined based on the probability distribution, and the expected value is used to construct the residual constraint term of the power flow mechanism.

4. The method for evaluating the synchronization feasibility domain of a time-varying distribution network with incomplete parameters according to claim 3, characterized in that, Based on the low-dimensional embedding vector sequence within the sliding time window, the current topological mode is identified by a classifier; a model-independent meta-learning approach is adopted, with different topological modes as meta-learning tasks, and a training loss function composed of the boundary classification loss term and the power flow mechanism residual constraint term is used in the process of intra-task parameter update and inter-task parameter optimization to obtain the feasible region evaluation meta-model.

5. The method for evaluating the synchronization feasible region of a time-varying distribution network with incomplete parameters according to claim 4, characterized in that, After detecting a change in topological mode, the initial model parameters for online updating of the feasible domain evaluation meta-model are determined based on the changed topological mode. Samples generated by active or naturally occurring disturbances under the changed topological mode are obtained, and the samples include control parameters and their corresponding stability labels. Starting with the initial model parameters, gradient updates are performed under the constraints of the training loss function to obtain a feasible domain evaluation meta-model suitable for the changed topological modes.

6. The method for evaluating the synchronization feasible region of a time-varying distribution network with incomplete parameters according to claim 1, characterized in that, The steps for determining the posterior probability distribution of the joint state using particle filtering include: Multiple weighted particles containing topological modes and synchronous feasible region boundary parameters are set up, and the synchronous feasible region boundary parameters of each particle are predicted based on the feasible region evaluation meta-model and control input. Based on the topological modes and synchronous feasible domain boundary parameters corresponding to each particle, the predicted state is obtained through the Koopman linearization model, and the predicted measurement value is determined according to the predicted state and the observation matrix. The observation likelihood of each particle is determined based on the difference between the predicted measurement value and the real-time partial node measurement, and the particle weights are updated based on the observation likelihood. The posterior probability distribution of the joint state is recursively determined based on the updated particles and their weights.

7. The method for evaluating the synchronization feasible region of a time-varying distribution network with incomplete parameters according to claim 6, characterized in that, For the control parameter vector to be evaluated, the probability that the control parameter vector to be evaluated belongs to the synchronous feasible region is determined according to the synchronous feasible region boundary parameters and particle weights corresponding to each particle in the posterior probability distribution, and the synchronous feasible region boundary is determined according to the preset confidence level.

8. The method for evaluating the synchronization feasible region of a time-varying distribution network with incomplete parameters according to claim 7, characterized in that, It also includes a synchronous feasible region rolling forecast step: using historical forecast errors to train a Gaussian process error model related to the current running point and forecast time scale, combining the Gaussian process error model with the posterior probability distribution of the current synchronous feasible region boundary parameters, determining the synchronous feasible region probability distribution at future forecast times, and outputting synchronous feasible region forecast results with confidence intervals at different forecast time scales.

9. A time-varying distribution network synchronization feasibility domain evaluation system with incomplete parameters, characterized in that, It includes a data acquisition module, a topology-dynamic joint embedding module, a physical fusion meta-learning module, and a Bayesian joint inference module; The data acquisition module is used to acquire measurement sequences of some nodes in the distribution network and construct incomplete observation data; The topology-dynamic joint embedding module is used to perform Koopman dimensionality upscaling on the incomplete observation data and extract dynamic mode features, estimate the electrical distance between nodes based on historical voltage sensitivity, construct a prior graph structure constraint with the electrical distance, and perform uniform manifold approximate projection dimensionality reduction on the upscaled data to obtain a low-dimensional embedding vector that simultaneously represents the dynamic mode of the cluster and the topological connection relationship of the distribution network. The physical fusion meta-learning module is used to identify topological modes based on the low-dimensional embedding vector, train the feasible region evaluation meta-model with different topological modes as meta-learning tasks, construct the training loss function with the boundary classification loss term and the power flow mechanism residual constraint term determined by the Gaussian process, and update the feasible region evaluation meta-model with samples containing control parameters and their corresponding stability labels under the changed topological modes when the topological modes change. The Bayesian joint inference module is used to construct a state-space model with topological modes and synchronous feasible region boundary parameters as joint states. The updated feasible region evaluation meta-model is used as the dynamic core of the state transition model. The module predicts the changing trend of the synchronous feasible region boundary parameters according to the control input. Based on the joint state, the predicted state is obtained through the Koopman linearization model, and the predicted measurement value is determined according to the predicted state and the observation matrix. The particle weights are updated based on the difference between the predicted measurements and the real-time measurements of some nodes. The posterior probability distribution of the joint state is obtained by recursion through particle filtering, and the synchronization feasible region under the preset confidence level is output accordingly.

10. The time-varying distribution network synchronization feasibility domain evaluation system with incomplete parameters according to claim 9, characterized in that, The topology-dynamic joint embedding module is used to identify the finite-dimensional transition matrix of the Koopman operator based on time series data, extract dynamic mode features based on the spectral decomposition results of the finite-dimensional transition matrix, estimate the electrical distance between nodes based on the historical voltage sensitivity matrix, and add a graph matching regularization term to the cross-entropy loss of the uniform manifold approximate projection to preserve the prior graph structure. The physical fusion meta-learning module is used to perform probabilistic modeling of the power flow equation residuals obtained from incomplete observation data using a Gaussian process, with the estimated operating state corresponding to the current control parameter vector as the center. It forms power flow mechanism residual constraint terms based on the expectation of the power flow equation residual norm, and updates the feasible domain evaluation meta-model using samples containing control parameters and their corresponding stability labels under the changed topological modes when the topological modes change. The Bayesian joint inference module is used to set weighted particles containing topological modes and synchronous feasible region boundary parameters, predict the synchronous feasible region boundary parameters of each particle based on the updated feasible region evaluation meta-model and control input; obtain the predicted state through the Koopman linearization model, and determine the predicted measurement value based on the predicted state and the observation matrix; determine the observation likelihood of each particle based on the difference between the predicted measurement value and the real-time partial node measurement, update the particle weights based on the observation likelihood, and determine the posterior probability distribution of the joint state based on the updated particles and their weights.

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