A transient stability evaluation method based on topological structure and closed-form neural network

Abstract

A transient stability evaluation method based on topology and closed neural network, which utilizes differential equations to establish the nonlinear relationship between the transient power angle stability state and the power dynamic variables, and introduces an adjacency matrix to represent the topology of the power system, solves the long-standing problems of explainable and targeted modeling of complex continuous-time nonlinear dynamics of the power grid. Specifically, the present application combines differential equations, closed continuous-time neural networks and neural circuit strategies, wherein the closed continuous-time neural network greatly simplifies the modeling of continuous-time dynamics and avoids the limitations of numerical solutions of differential equations; and the neural circuit strategy ingeniously combines the adjacency matrix of the power system to simulate the adjacency relationship between buses, so that the model structure is highly sparse, which is conducive to improving the calculation efficiency. At the same time, when the topology of the power system changes, the method can quickly update the model to meet the accuracy requirements under the new topology.

Description

Technical Field

[0001] This invention relates to the fields of new energy and power system technology, and in particular to transient power angle stability analysis technology for power systems, specifically to a transient stability assessment method based on topology and closed neural network. Background Technology

[0002] With energy shortages and environmental pollution becoming increasingly prominent, countries worldwide are promoting the construction of low-carbon energy systems. The integration of large amounts of renewable energy into the power grid places new demands on its security and stability. Failure to detect transient instability and implement timely countermeasures can lead to power system collapse, resulting in widespread blackouts and potential damage to critical equipment such as generators, transformers, and transmission lines. Therefore, rapidly and accurately assessing the transient power angle stability of the power system to prevent and reduce transient power angle stability problems caused by system faults, and to improve the safety and stability of system operation, is becoming increasingly important.

[0003] Traditional methods for transient power angle stability assessment include time-domain simulation and direct methods. Time-domain simulation offers the highest accuracy, but its computational process is complex and time-consuming, making it unsuitable for real-time transient power angle stability assessment. Direct methods include the transient energy function method and the limiting equal-area method. While direct methods are faster, they require simplification of the power system model, leading to less than ideal accuracy and overly conservative assessment results. Therefore, data-driven models based on machine learning are currently widely used in transient power angle stability assessment. However, these machine learning models, such as "Stability analysis of discrete-time recurrent neural networks," use an improved RNN network to achieve transient stability assessment. Although it considers the temporal characteristics of the power system, it is still a discrete-time step. In addition, models such as CNN, GRU, and Transformer are also used for transient stability assessment, but most of the above models are end-to-end discrete-time models and were originally designed for non-electrical problems. The reasons for using such neural networks, the number of neurons, and the number of network layers have always been unclear, making the process of power system network dynamics modeling ambiguous and difficult to interpret. How to model and learn the continuous-time nonlinear dynamics and structural dependencies of power systems is a problem that has not been fully studied.

[0004] Therefore, this invention proposes a transient stability assessment method based on topology and closed neural network. It uses a system of differential equations to establish the nonlinear relationship between transient power angle stability and power dynamic variables, and introduces an adjacency matrix to characterize the topology of the power system, thereby solving the problems of fuzzy modeling and computational complexity in power system network dynamics. Summary of the Invention

[0005] This invention aims to address the technical problems of existing machine learning models' inability to accurately capture the continuous-time dynamic characteristics of power systems in transient stability assessment, and the decline in model accuracy after topology changes. Specifically, most existing machine learning transient power angle stability assessment methods adopt end-to-end discrete-time step training, which makes it difficult to accurately capture the continuous-time dynamic characteristics of power systems and has weak interpretability. After the power system topology changes, the model's accuracy often drops significantly. To address the above technical problems, this invention is proposed.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0007] A transient stability evaluation method based on topology and closed neural networks includes the following steps:

[0008] Step S1: An objective differential equation is introduced to simulate the continuous-time nonlinear dynamics on the complex topology of the power system;

[0009] Step S2: Use a closed-loop continuous-time neural network to solve the differential equation in step S1;

[0010] Step S3: Utilize machine learning to continuously learn and improve the evaluation method, and parameterize the transient power angle steady-state variables of the solution in step S2;

[0011] Step S4: Introduce a neural circuit strategy to simulate the connection structure of whole neurons, explicitly model the topology by simulating the adjacency relationship of the bus, and improve computational efficiency;

[0012] Step S5: Use the steady-state criteria of the power system to determine the transient power angle stability of the power system, and form a dataset based on the criteria to train the neural network;

[0013] Step S6: Combine offline training, practical application, and online updates;

[0014] The above steps enable a comprehensive assessment of transient power angle stability.

[0015] In step S1, the transient stability process of the power system can be regarded as a continuous-time nonlinear dynamic on a complex topology. A specific differential equation is introduced to simulate this nonlinear process. Under a given power system topology, its dynamics can be simply described as follows: the state variables of each bus change continuously according to certain dynamic laws under the influence of adjacent buses, and there is a nonlinear relationship between these state variables and the transient power angle stability state of the power system.

[0016] The nonlinear relationship is expressed by the differential equation as follows:

[0017] (1);

[0018] In the formula, yes t The set of transient power angle steady-state variables of the power system at any given time. Indicates the first i The busbar at time t State variables, It is a collection of them. For dynamic management parameters, It is the first i Electrical dynamic variables of a busbar This corresponds to the adjacency matrix of the power system topology. f This represents a neural network;

[0019] The first expression in this formula represents the set of state variables through each bus. To solve the transient power angle stability state of the power system The second formula represents the electrical dynamic variables through each bus. Its corresponding topology To solve for the state variables of each bus .

[0020] To enhance the expressiveness of continuous-time dynamics, an improved form, called the Liquid Time Constant Recurrent Neural Network (LTC), was introduced, mimicking the synaptic interactions of neurons. This structure has been proven to be robust, bounded, and stable. Taking the transient work angle as an example of the stable state variable, the improved equation form is as follows:

[0021] (2);

[0022] In the formula, This helps the system reach an equilibrium state with a time constant τ, and nonlinear synapses are introduced to represent the hidden state flow of the network as a system of linear differential equations. Neurons are activated through nonlinear synapses. It is the sum of all synaptic inputs that receive external stimuli and input them into the cell (the sum of all variables input into the electrical system). It depends on the state of all neurons (the nodes of the power system). It is the external input (the sum of the state variables of all buses input to the power system); This refers to the system parameter vector of the power system.

[0023] In step S2, the differential equation that originally required iterative solution is transformed into an approximately closed form, so that under given initial conditions, the analytical solution or high-precision approximate solution of the network state can be obtained directly or through a finite number of steps.

[0024] The specific solution result is as follows:

[0025] (3);

[0026] This is the initial state of the power system;

[0027] The formula introduces a second time constant. Subsequently, the formula for calculating the transient work angle steady state at each time step is:

[0028] (4);

[0029] In the formula replace It becomes a parameter vector. and （D） It is a system parameter vector. f It is a neural network, and its neural network parameters are: , represent and The weights between them represent and The weights between them Represents bias, It is each time step t m-dimensional input, It is each time step t The D-dimensional output.

[0030] In step S3, to make the training process of the neural network more controllable and efficient, the solution obtained in step S2 is parameterized as a transient power angle stable state variable. By adjusting the parameters, different types of activation functions and layer structures can be used to optimize the convergence speed, stability and generalization ability of the model, improve the expressive power of the model, and ultimately enhance the performance of the model.

[0031] The parameterized formula for the transient work angle steady-state variable is shown below:

[0032] (5);

[0033] In order to enhance the flexibility of the model, a trainable neural network is introduced. and Replace the parameters in equation (4) respectively and To avoid gradient vanishing during neural network training, the exponential decay term... By an inverse s-shaped nonlinear variable (.) will replace With (1- The product of (.)) is a time-decaying sigmoid term, which acts as a gate control; finally, , and The first few layers of the neural network are shared in the form of a backbone to accelerate and stabilize the learning process. In step S4, a neural circuit strategy is introduced to explicitly model the topology, specifically:

[0034] By employing an end-to-end input-output approach, and observing the output of each neuron (or the state variables of each node in a power system), a unique, generalizable, and interpretable RNN structure is established through the cooperation between neurons. This allows for the observation of the model's entire learning state, which is reflected in the state variables of each bus. Not only by the dynamic variables on this bus line The decision also relates to the dynamic variables on the remaining busbars. With its own state variables The specific details, represented by neural network parameters, are shown in the following formula:

[0035] (6);

[0036] The directional transmission between neurons, i.e., between individual neurons, is achieved by multiplying the weight parameters by the sparse mask matrix. The weight parameters are modified as follows: ,in represent and The weights between them represent and The weights between them Represents bias. It is a non-trainable sparse mask matrix that reflects the connection relationships between neurons, i.e., between various buses. In a power system, this connection relationship corresponds to the bus connection relationship. The zero parameter corresponding to The parameter will be initialized to zero.

[0037] The improved RNN network exhibits better model interpretability and stability. Traditional RNN networks only consider the sufficiency of the number of neurons to fit the target data, rarely taking into account the interactions between neurons. In contrast, the neural circuit strategy classifies neurons into four categories: sensory neurons, interneurons, command neurons, and motor neurons. Its characteristics include high sparsity. Sensory neurons are responsible for acquiring information from the external environment, internal and command neurons make decisions, and finally, motor neurons control muscles. Different neurons are connected through synapses to form a meaningful topological structure. Secondly, utilizing the structure of RNNs can make the model more robust, effectively resist noise, and has a greater ability to prioritize learning from recent scenes.

[0038] In step S5, a criterion for transient power angle stability is given to evaluate whether the system is stable. The criterion for transient power angle stability is mainly based on the behavior of the power system after being subjected to a large disturbance. The classification label for stability evaluation is defined by the transient power angle stability index (TSI), as shown in the following formula:

[0039] (7);

[0040] (8);

[0041] in, This represents the maximum power angle difference between any two generators. Greater than ,Right now If <0, the system is considered unstable, and the sample is labeled as 1; if Less than If the system is stable, the sample label is 0.

[0042] Before importing past data into a neural network for training, if the data volume varies greatly, the gradients of different features may differ significantly, leading to slower convergence during model training. Normalization can unify the scale of all features, thereby accelerating convergence. The specific formula is shown below:

[0043] (9);

[0044] in, and The mean and standard deviation of a single feature.

[0045] In step S6, a transient power angle stability evaluation method is constructed to realize transient power angle stability evaluation, which includes three parts: offline training, practical application, and online update.

[0046] During the offline training phase, the length of the selected samples is crucial, as it significantly impacts the training process. Therefore, introducing a training set with dynamically adjustable sample lengths is essential. In the practical application phase, a time-adaptive strategy is employed, avoiding the use of fixed observation windows and saving considerable time. For the online update phase, the topology of the monitored power system may change due to factors such as system maintenance, expansion, and generator shutdown. Therefore, it is necessary to adjust the internal parameters and update the data and neural network parameters continuously.

[0047] Step S6 includes the following steps:

[0048] Step 6-1) Generate a training dataset based on the transient power angle stability evaluation criteria in step S5, and normalize the variables according to formula (9) to unify the variable scale;

[0049] Step 6-2) Select an appropriate sample length to train the model and obtain the trained model to generate a transient power angle stability evaluation model;

[0050] Step 6-3) This invention uses Accuracy (ACC), Average Response Time (ART) after fault clearing, False Alarm Rate (FAL), and False Alarm Rate (MIS) as transient power angle stability evaluation indicators to determine whether the offline training results meet the accuracy requirements of the power system; if they meet the requirements, proceed to Step 6-4); otherwise, proceed to Step 6-5. The expressions for each indicator are:

[0051] (10)

[0052] (11)

[0053] (12)

[0054] (13)

[0055] and These refer to the number of stable samples assessed as unstable and the number of unstable samples assessed as stable, respectively. Represents the total number of samples. represent cycle, represent Number of samples in a period Represents the maximum evaluation period;

[0056] Step 6-4) The trained model is deployed to the power system and receives system data in real time. When a fault occurs, the PMU measurement unit measures the input data into the transient power angle stability assessment model. Then, the data from the fault clearing time to each assessment cycle is input sequentially to solve the transient power angle stability prediction probability. If the prediction probability of the cycle is greater than the assessment threshold, it is output as the result. If the threshold is not met, the assessment of the next cycle is performed. This process continues until the maximum assessment cycle is reached.

[0057] Step 6-5) Adjust the parameters inside the transient power angle stability assessment model. The transient power angle stability assessment model will be verified again to ensure that its assessment accuracy meets the requirements. Then, proceed to step 6-4.

[0058] Step 6-6) When the power grid topology changes, fine-tune the structure of the first layer of synapses and neurons to match the actual topology change. If the model fails to restore the original evaluation level, jump to step 6-5.

[0059] Through the above steps, we can continuously iterate and optimize.

[0060] Compared with the prior art, the present invention has the following technical effects:

[0061] 1) Previous machine learning models mostly used discrete time step training, which made it difficult to accurately capture the continuous time dynamic characteristics of power systems. This invention proposes a data-driven method that combines differential equations and neural networks. This method can accurately characterize the dynamic characteristics of power systems through differential equations, enhancing the interpretability of the model. It can also use data-driven methods to achieve efficient training and improve computational efficiency.

[0062] 2) Most previous machine learning evaluation methods did not explicitly model the power system topology. This invention uses a neural circuit strategy to adjust the connection structure of neurons to simulate the bus adjacency relationship, enhance the model's ability to represent the system topology, and can quickly update the model to meet the evaluation accuracy of transient power angle stability after the topology change when the power grid topology changes.

[0063] 3) This invention introduces a training set with variable sample length, a time-adaptive strategy, and a topology update strategy to achieve an efficient transient power angle stability evaluation method. This customized method significantly improves the prediction accuracy and update efficiency of the model. Attached Figure Description

[0064] The present invention will be further described below with reference to the accompanying drawings and embodiments:

[0065] Figure 1 Overall flowchart of the present invention;

[0066] Figure 2The closed continuous neural structure of the present invention;

[0067] Figure 3 Neural circuit strategy structure diagram of the present invention;

[0068] Figure 4 Model structure diagram of the present invention;

[0069] Figure 5 Transient power angle stability assessment flowchart;

[0070] Figure 6 Time-adaptive strategy diagram for online applications;

[0071] Figure 7 Model structure validity verification diagram;

[0072] Figure 8 Visualization of state variables;

[0073] Figure 9 Parameter sensitivity verification graph. Detailed Implementation

[0074] like Figure 1 As shown, a transient stability evaluation method based on topology and closed neural networks includes the following steps:

[0075] S1 introduces specific differential equations to simulate continuous-time nonlinear dynamics on complex power system topologies;

[0076] S2, using a closed continuous-time neural network to solve the differential equation in step S1;

[0077] S3, use machine learning to continuously learn and improve the evaluation method, and parameterize the transient power angle steady state variables of the solution in step S2;

[0078] S4 introduces a neural circuit strategy to improve this transient power angle stability assessment method, explicitly modeling the topology and improving computational efficiency;

[0079] S5 uses the criteria for steady-state power system to determine the transient power angle stability of the power system, and forms a dataset based on the criteria to train the neural network.

[0080] S6 combines offline training, practical applications, and online updates to construct a comprehensive transient power angle stability evaluation method. ； ;

[0081] Specifically:

[0082] First, we formulate the neural network-like ordinary differential equations (NDEs) to model the power system as a neural network. In this framework, each bus in the power system is considered a neuron node in the neural network, carrying key state information. Branch lines in the power system are analogized to synaptic connections between neurons, not only transmitting information but also influencing the dynamic characteristics of the entire network. We map the relationship between neurons and synapses to the transient power angle steady state and the state variables of each bus in the power system, using specific differential equations to simulate the continuous-time nonlinear dynamics of the complex topology of the power system. We formulate the neural network-like NDEs, with buses corresponding to neurons as nodes and branches corresponding to neuron synapses as edges.

[0083] Next, differential equations were used as the core tool for modeling. By adjusting these equations, the performance of continuous-time dynamics was enhanced, thereby optimizing its descriptive power. This optimization process focused on constructing a special neural network model—a liquid time constant recurrent neural network. Inspired by a deep understanding of continuous-time dynamic systems, this network incorporates a time constant as a key parameter, enabling it to more flexibly capture and simulate complex time-series data. After establishing the basic architecture of the liquid time constant recurrent neural network, the solution strategy of closed-loop continuous-time neural networks was adopted, but not directly applied. Instead, its closed-loop solution concept was creatively integrated into the model. This is a more efficient and accurate solution method, avoiding the computational complexity and error accumulation problems that traditional numerical methods may cause by constructing an approximately closed neural network mathematical model.

[0084] Next, the network structure is optimized to further improve the training efficiency and performance of the neural network. To achieve this goal, the previously solved approximate closed-form mathematical model is first parameterized by the neural network. This not only accurately characterizes the dynamic characteristics of the system through differential equations, enhancing the model's interpretability, but also enables efficient training through data-driven methods, improving computational efficiency. This allows the model to automatically adjust parameters during training to better adapt to complex data distributions and dynamic changes. Subsequently, a neural circuit strategy is used to guide this optimization process. As the basic unit of information transmission and processing in a neural network, the design and optimization of neural circuits directly affect the performance of the entire network. Through a carefully designed neural circuit strategy, the connection structure of neurons is adjusted to simulate the adjacency relationship of bus lines, enhancing the model's ability to represent the system topology and promoting effective cooperation and interaction between neurons (each bus line), enabling the network to learn more complex and useful feature representations.

[0085] Building upon this foundation, a unique, generalizable, and highly interpretable RNN (Recurrent Neural Network) structure was successfully constructed. This structure not only inherits the inherent advantages of RNNs in processing sequential data but also overcomes problems such as vanishing or exploding gradients that traditional RNNs may encounter during training through optimization strategies. More importantly, the design of this RNN structure fully considers the practical application needs of power systems or similar fields, enabling a clear explanation of the network's internal working mechanism and greatly facilitating subsequent model debugging, improvement, and practical applications.

[0086] Ultimately, a comprehensive and systematic framework for transient power angle stability assessment was constructed. This framework is carefully divided into three closely linked and mutually supportive components: offline training, practical application, and online updating. The design of this framework aims to ensure the accuracy, practicality, and sustainability of transient power angle stability assessment.

[0087] First, during the offline training phase, historical data, simulated data, and professional knowledge were used to thoroughly train and validate the previously optimized model. Throughout the training process, close attention was paid to improving the evaluation accuracy, ensuring it met or exceeded the accuracy standards required for transient power angle stability assessment in power systems. The successful completion of this phase laid a solid foundation for subsequent practical applications.

[0088] Subsequently, if the offline training results meet the accuracy requirements of the power system, the system enters the practical application stage. In this stage, the trained model is deployed to the power system, receiving system data in real time and outputting accurate transient power angle stability assessment results. These assessment results are crucial for the stable operation, fault early warning, and rapid response of the power system.

[0089] However, considering the complexity and dynamism of power systems, as well as the continuous introduction of new technologies and equipment, the framework also needs to be equipped with online update capabilities. Once a decrease in evaluation accuracy or a change in topology renders the model unsuitable for practical applications, the online update process should be initiated immediately. This process includes modifying the model structure to adapt to new data characteristics, adjusting model parameters to optimize performance, or introducing new training data to enhance the model's generalization ability. The updated model will then undergo further validation to ensure its evaluation accuracy meets requirements before being deployed in practical applications, forming a continuously iterating and optimizing closed-loop system.

[0090] In step S1, the transient power angle stability of the power system can be reduced to a continuous-time nonlinear dynamics problem with a complex topology. While traditional differential equation-based neural network models (such as neural ODEs) have shown strong modeling potential, their practical applications are limited by low training and inference efficiency, especially as data volume and task complexity increase, leading to exponentially higher computational costs. To address this challenge more effectively, a closed-loop continuous-time neural network is introduced. This network directly solves the differential equations describing the interaction between neurons and synapses, and significantly improves processing efficiency by employing a closed-form approximation strategy, effectively avoiding the performance bottlenecks of traditional methods. In the context of the power system, this neuron-synapse relationship corresponds to the transient power angle stability state and the state variables of each bus. Specifically, under a given power system topology, its dynamics can be concisely described as follows: the state variables of each bus change continuously according to certain dynamic laws under the influence of adjacent buses, and there is a nonlinear relationship between these state variables and the transient power angle stability state of the power system.

[0091] By writing differential equations, under a given power system topology, its dynamics can be concisely described as follows: the state variables of each bus change continuously according to certain dynamic laws under the influence of adjacent buses, and there is a nonlinear relationship between these state variables and the transient power angle steady state of the power system. This can be expressed by a system of differential equations:

[0092] (1); where, It is the set of transient power angle steady-state variables of the power system at time t. The state variable of the i-th bus at time t It is a collection of them. For dynamic management parameters, It is the electrical dynamic variable of the i-th bus. This corresponds to the adjacency matrix of the power system topology, where f represents the neural network. The first expression in this formula represents the set of state variables through each bus. To solve the transient power angle stability state of the power system The second formula represents the electrical dynamic variables through each bus. Its corresponding topology To solve for the state variables of each bus .

[0093] Secondly, differential equations are used to construct the model. Based on the neural network's constant differential equations, in order to enhance the expressiveness of continuous-time dynamics, an improved form is introduced, mimicking the synaptic interaction of neurons, called the Liquid Time Constant Recurrent Neural Network (LTC). This structure has been proven to be robust, bounded, and stable. Taking the transient work angle stable state variable as an example, an improved differential equation form is introduced:

[0094] (2);

[0095] In the formula, This helps the system reach an equilibrium state with a time constant τ; nonlinearity is introduced so that the hidden state flow of the network can be represented by a linear system of differential equations. Neurons are activated through nonlinear synapses. It is the sum of all synaptic inputs that receive external stimuli and input them into the cell (the sum of all state variables input into the power system). It depends on the state of all neurons (the nodes of the power system). It is the external input (the sum of the state variables of all buses input to the power system). This refers to the system parameter vector of the power system.

[0096] In step S2, the interaction between neurons and synapses is constructed in a closed form, similar to a closed continuous-time neural network. The depth dimension of the static neural network and the time dimension of the recurrent neural network are transformed into a continuous vector field. The derivation of the approximate closed-form solution of the continuous neural network with explicit simulation of time is then performed.

[0097] From a mathematical perspective, we need to find the solution. It is difficult because X(s) is a positive, continuous, monotonically increasing, bounded nonlinear function, which is difficult to solve in closed-form because it depends on an arbitrarily defined input signal X(s) (e.g., real-world sensory readings). To solve this problem, X(s) is discretized into piecewise constant segments, and a discrete approximation of the integral is obtained in the form of the sum of piecewise constant segments over the interval, thus solving the formula in step S1; the specific solution is as follows:

[0098] (3);

[0099] Representing the initial state of the power system, a second time constant is introduced. Adding parameter B makes the formula more flexible, and thus, the formula for calculating the transient power angle steady state at each time step is:

[0100] (4);

[0101] In the formula replace It becomes a parameter vector. and It is a system parameter vector. It is a neural network, and its neural network parameters are: , It is the m-dimensional input at each time step t. It is each time step t The D-dimensional output. In the neural network parameters, represent and The weights between them represent and The weights between them Represents the bias of the neural network;

[0102] In step S3, to make the training process of the neural network more controllable and efficient, the solution obtained in step S2 is parameterized. This allows for the adjustment of parameters to use different types of activation functions and layer structures, thereby optimizing the model's convergence speed, stability, and generalization ability, improving its expressive power, and ultimately enhancing its performance. The meanings of the variables in the formula are consistent with those described in step S1, with the introduction of a second time constant. Adding parameter B makes the formula more flexible. Therefore, the parameterized formula for the transient work angle steady-state variable is shown below:

[0103] (5);

[0104] See Figure 2 The closed-loop continuous neural network structure of the present invention is given, which can better illustrate the structure of the closed-loop neural network and better explain the above formula, replacing the exponential term in step S2 with... This is because the exponential term derives the first part of the system (exponentially fast) as 0, and the entire hidden state as A. This problem becomes more pronounced when recurrent connections are present, and leads to vanishing gradient factors when training with gradient descent. To mitigate this effect, the exponential decay term is replaced with an inverse sigmoid nonlinearity. This nonlinear function approximates 1 at t = 0, and in the limit... It approaches 0. However, unlike exponential decay, its transition occurs more smoothly and works better in training neural networks.

[0105] Meanwhile, to enhance the model's flexibility, the backbone neural network layer feeds the input signals into the three head networks. , and f is the liquid time constant for the network's sigmoid time-gated system. and The nonlinearity of the entire closed neural network was constructed. Then... and Replace parameters B and A in equation S2 respectively, and then... and Multiplying them together allows the sigmoid term representing time decay to act as a gate. Thus, the time-decaying sigmoid function represents the time decay of t at... and A gating mechanism for interpolation between two limits.

[0106] exist Figure 2 This paper demonstrates a multi-branch shared network structure. In this structure, it's unnecessary to design completely different network structures for each neural network instance f, g, and h. This is because power systems have complex topologies where multiple nodes share real-time operational data. These connections are largely unchanging, so a shared backbone network is chosen. This backbone typically contains several shared first layers, which are high-level feature extractors in deep neural networks, learning common features in the input data, such as edges, textures, and shapes. Sharing these layers effectively reduces the number of network parameters, lowers the risk of overfitting, and improves training efficiency and generalization performance. Next, the output of the backbone network is branched into three branches, each corresponding to a neural network instance f, g, and h. These branch networks typically contain independent layers designed according to specific task requirements. During training, different task data can be fed into the corresponding branch networks for training, while the parameters of the backbone and branch networks are updated using backpropagation. This allows for simultaneous learning of multiple tasks, improving training efficiency and generalization performance while maintaining model accuracy.

[0107] In step S4, a neural circuit strategy is introduced to explicitly model the topology. Specifically, this involves drawing inspiration from the neural cell structure of *Caenorhabditis elegans*, employing an end-to-end input-output approach. By observing the output of each neuron (or the state variables of each node in a power system), and through the cooperation between neurons, a unique, generalizable, and interpretable RNN structure is established. This allows for the observation of the model's entire learning state, which is reflected in the state variables of each bus. Not only by the dynamic variables on this bus line The decision also relates to the dynamic variables on the remaining busbars. With its own state variables The specific neural network parameters are represented by the following formula:

[0108] (6);

[0109] The parameters in the formula are the same as those in step S1. Directional transmission between neurons (i.e., each parent neuron) is achieved by multiplying the weight parameters by the sparse mask matrix. The weight parameters are modified as follows: ,in It is a non-trainable sparse mask matrix that reflects the connectivity between neurons (i.e., individual neurons), and The zero parameter corresponding to The parameter will be initialized to zero. represent and The relationship between them represent and The relationship between them This represents the bias of the neural network.

[0110] See Figure 3 This diagram illustrates the specific neural circuit strategy structure, which categorizes neurons into four types: sensory neurons, interneurons, command neurons, and motor neurons. Inspired by the wiring diagram of the Caenorhabditis elegans worm, it is characterized by high sparsity. The model consists of a first layer, a multi-layered CNN network; a second layer, an intermediate layer, a sparse neural network; a third layer, a control layer, a self-connected RNN network; and an output layer, which outputs commands. The connections primarily involve feedforward connections from sensors to interneurons, highly recurrent connections between interneurons and command neurons, and feedforward connections from command neurons to motor neurons. This end-to-end input-output structure provides good interpretability, allowing observation of the model's overall learning process by monitoring the output of each neuron. Furthermore, the command neuron layer utilizes the concept of RNN sequence networks, enabling short-term memory of previous network states and achieving a degree of stability.

[0111] Complex topologies in power systems can also be modeled after this neuron-like connection structure, where the state variables of different buses are determined by the dynamic variables of the other buses and their own state variables. Secondly, utilizing the RNN structure makes the model more robust, effectively combating noise and prioritizing the learning of recent scenarios.

[0112] In step S5, a criterion for transient power angle stability is given to assess whether the system is stable. The criterion for transient power angle stability is mainly based on the behavior of the power system after being subjected to a large disturbance. The classification label for stability evaluation is defined by the Transient Power Angle Stability Index (TSI), as shown in the following formula:

[0113] (7); (8);

[0114] in, This represents the maximum power angle difference between any two generators. Greater than ,Right now If <0, the system is considered unstable, and the sample is labeled as 1; if Less than If the system is stable, the sample label is 0.

[0115] In this method, active power, reactive power, voltage, and frequency are selected as dynamic variable inputs of the power system to obtain state variables. Then, the transient power angle stability of the power system is determined using the state variables of each bus. These parameters, input into the neural network for learning, are indispensable in determining the transient power angle stability of power systems. They each reflect different aspects of the system's stability and performance, and can effectively predict the transient power angle stability of the power system. Simultaneously, during model learning, the loss value is calculated based on the cross-entropy loss function.

[0116] (9);

[0117] Where p and y are the predicted value and the true label, respectively, when p and y are equal, The value is 0 when p and y are different. The result is not 0. This function can effectively reflect the error between the predicted value and the actual value.

[0118] Before importing past data into the neural network for training, the different units of measurement for various features lead to significant differences in the feature data, which is detrimental to model training. Therefore, it is necessary to normalize the original dataset beforehand, which slows down the convergence speed during model training. Normalization can unify the scale of all features, thereby speeding up the convergence speed. The specific formula is shown below:

[0119] (10);

[0120] in, and The mean and standard deviation of a single feature;

[0121] See Figure 4 The diagram shows the model structure of the present invention. Figure 4 The model structure is visualized, and its workflow is clearly explained. The first layer contains the same number of neurons as the power system bus; the number of synapses and connections relate to branching. Figure 4 In the equation, bus A is connected to bus B, C, and D via branches. Correspondingly, the dynamic variables on buses A, B, C, and D will be input to neuron A as synaptic inputs. These feature sets constitute the parameterized differential equation. The solution value of neuron A is the state variable. This allows for the full capture of structure-dynamic dependencies by structurally solving the state variables of all buses. Extracting spatial correlations through adjacency relationships is a common method in graph neural networks (GNNs), and the structure proposed in this invention is inspired by it.

[0122] The second layer consists of only two neurons and is used to solve for the transient power angle steady-state variables of the power system. . The solution is obtained using the formula in step S3. The next step is to merge these values ​​into two single values ​​using average time pooling. Finally, these single values ​​are mapped to [0,1] through a SoftMax layer, representing the stable and unstable prediction probabilities.

[0123] In step S6, a transient power angle stability evaluation framework is constructed to train and apply this method, which includes three parts: offline training, practical application, and online update.

[0124] See Figure 5This paper demonstrates the specific content of the transient power angle stability assessment framework. First, offline training is performed. A training dataset is generated based on the transient power angle stability evaluation criteria in step S5. Then, modeling training is conducted based on the method proposed in this invention to generate a transient power angle stability assessment model. If the offline training results meet the accuracy requirements of the power system, the model proceeds to the practical application stage. In the practical application stage, the trained model is deployed to the power system, receiving system data in real time. When a fault occurs, the PMU measurement unit measures the input data into the transient power angle stability assessment model. Then, data from the fault clearing time to each assessment cycle is input sequentially to solve for the predicted values ​​of state variables and the transient power angle stability probability. If the measurement accuracy of a cycle is greater than the assessment accuracy, it is output as the result. If the accuracy assessment is not met, the assessment for the next cycle is performed. This process continues until the maximum assessment cycle is reached. If the power system topology changes, online updates are performed. First, it is determined whether the assessment model after the topology change meets the requirements. If it does, the model continues to be applied; otherwise, the model structure is modified or the parameters are adjusted. The model, after being updated online, will be validated again to ensure that its evaluation accuracy meets the requirements before it can be put into practical application, forming a closed-loop system that is continuously iterated and optimized.

[0125] At the same time, corresponding improvement methods were proposed at each stage to make the framework more accurate and faster.

[0126] In the offline training phase, the selection of sample length has a significant impact on offline training. Excessively long samples can lead to unreliable predictions of transient dynamic angle steady-state variables, while excessively short samples can result in insufficient fitting of continuous-time dynamics. Therefore, the sampling can be terminated at the moment of system instability to avoid learning unstable dynamic behaviors. For stable systems, the samples can be cut when the system reaches a certain steady state (such as maximum swing angle) to ensure that the samples contain sufficient stable dynamic information. Therefore, introducing a training set with variable sample length is crucial for the offline training phase.

[0127] In the online update section, the topology of the monitored power system may change due to factors such as system maintenance, expansion, and generator shutdown. Therefore, it is necessary to adjust its internal parameters at any time. First, the synaptic and neuron structures can be adjusted to ensure the effectiveness of the dynamic topology over continuous time. At the same time, a dataset matching the new topology scenario is established through time-domain simulation. If the model cannot restore the original evaluation level, all parameters are fine-tuned or even retrained.

[0128] In practical applications, the transient power angle steady state is predicted using real-time data. (See also...) Figure 6When a fault is detected and cleared, the PMU's real-time data is transmitted to the control center. At the control center, the proposed model receives selected data using a time-adaptive strategy. Data from the fault clearing time to each evaluation cycle is used sequentially to solve for the predicted values ​​of state variables and the transient power angle stability probability. The evaluation cycle is 1 / 60 of a second, thus avoiding the drawbacks of fixed observation windows, saving considerable time, and balancing the speed and accuracy of transient power angle stability evaluation. During the evaluation process, once either the stable or unstable predicted probability exceeds a reliability threshold, that probability is considered reliable and output as the evaluation result. Otherwise, the system waits for the latest real-time data before entering the next evaluation cycle. This process continues until the maximum evaluation cycle is reached. Then, the larger probability value is directly output as the result, completing the system evaluation, as shown in the following formula:

[0129] (11);

[0130] This represents the probability of a stable state due to transient work angle. This represents the probability of a transient unstable state. This represents the maximum evaluation period.

[0131] Example:

[0132] 1. Data Generation

[0133] The model and method proposed in this invention were demonstrated on an IEEE 39-node system and a real-world 1648-node system. All programs were run on a computer equipped with a 2.50GHz Intel Core i5-12500H CPU and 16GB of RAM. An NVIDIA RTX-3080 GPU was configured to support efficient deep learning in Python.

[0134] Three datasets were generated in the IEEE 39-line system for performance testing, each with a different specific topology scheme. It is the standard sample set. This indicates that branches 2-3 and 16-21 are disconnected. This indicates that bus 14 is disconnected. To further test the method, this invention used a larger-scale 1648 bus system, comprising 1648 buses, 313 generators, 182 shunts, and 2294 transmission lines. For the standard sample set, This indicates that branches 25-30 and 16-83 are disconnected. This indicates that busbar 102 is disconnected. All samples of the transient processes of both systems were simulated using the PSS / E platform. The simulation time after fault clearance was set to 10 seconds to ensure correct labeling. The specific configuration is as follows: the fault duration was set to a random value between 0.05s and 0.25s. Most of the load was a random load, set between 80% and 120% of the system's basic load level, and other loads were set between 70% and 130%. It was assumed that a three-phase short-circuit fault would occur on each transmission line and busbar. The data sampling frequency was 120Hz. After simulation and labeling, a dataset was formed from the sampled data of different lengths after fault clearance. The ratio of training, validation, and test datasets was 6:2:2, and the specific quantities are shown in Table 1.

[0135] Table 1

[0136]

[0137] This invention uses accuracy (ACC), average response time (ART) after fault clearing, false alarm rate (FAL), and false alarm rate (MIS) as evaluation indicators for transient power angle stability. The formulas for each indicator are as follows:

[0138] (12);

[0139] (13);

[0140] (14);

[0141] (15);

[0142] and These refer to the number of stable samples assessed as unstable and the number of unstable samples assessed as stable, respectively. Represents the total number of samples. represent cycle, represent Number of samples in a period This represents the maximum evaluation period.

[0143] 2. Model Performance Comparison

[0144] Dataset and Normal operation scenarios from the IEEE 39 bus system and 1648 bus system were used to verify the performance of transient stability power angle state prediction. Figure 2As shown, Model 1 and Model 2 represent models compared with and without a training set of variable sample length. The results show that the model using a training set of variable sample length performs better. Compared with other classic data-driven models, the time-adaptive strategy is validated using Deep Forest (DF) and Convolutional Neural Network (CNN) with a fixed observation window, demonstrating its superiority and faster response time. RNN, LSTM, and GRU, as discrete-time models, are introduced for comparison with continuous-time models. These models have structures similar to the proposed model, consisting of two densely stacked layers. The first layer uses 39 and 1648 neurons, respectively, corresponding to the two systems. The hyperparameters and online application settings are the same as recommended. The results, shown in Table 2, demonstrate that the proposed model achieves both speed and accuracy, and obtains the best evaluation performance. In particular, it maintains 98.87% accuracy and a response time of 1.43 even with a 1648-bus system, thanks to the powerful modeling capabilities of differential equations and the fast response of the data-driven approach.

[0145] Table 2

[0146]

[0147] 3. Validation of Model Structure

[0148] This invention employs a neural circuit strategy to encode the topological information of a power system, enabling differential equations to simulate the topological relationships between buses. The invention is validated using a 39-bus system as an example. Figure 7 As shown, compared to the complex 1648 bus system, the 39 bus system has a clearer topology. While retaining core topological characteristics, it avoids overly complex topological relationships, thus better showcasing the relationship between the model structure and the topology. Specifically, the connection method between neurons in the model mimics the bus connection method of the IEEE 39 system to better represent the topology of the power system. To compare the topology connection schemes between different neurons, this invention introduces a visualization of the sparse matrix and the sparse connectivity of the model (i.e., the proportion of 0-value parameters to total parameters) to describe the range of different topologies. First, the connections between nodes are gradually adjusted. During the topology expansion process, the connection range between neurons and the model structure gradually increases, and the connection density continuously increases until all values ​​of the sparse matrix are 1. Experimental results (e.g.) Figure 7As shown in the figure, the overall performance of the model is most reliable when the sparsity of the proposed topology modeling scheme is the same as that of the bus sparsity of the IEEE 39 system. Furthermore, this invention also employs two random topologies with the same neuron sparsity as the IEEE 39 system bus, but the connections between neurons are random and not connected according to the IEEE 39 system bus connection method. Through comparative experiments with these random topologies, we demonstrate that, under the same sparsity, the topology with ordered connections (consistent with the IEEE 39 bus system) achieves the best performance. Therefore, the proposed topology modeling scheme simulates the topology structure in a power system and exhibits the most reliable performance.

[0149] 4. Process visualization

[0150] Because the dataset's state is high-dimensional, it's difficult to describe the model's reasoning process using intuitive images. This hinders the model's interpretability. To enhance the transparency of classification results, this invention employs the t-SNE nonlinear dimensionality reduction algorithm to map the original features to a two-dimensional plane, enabling visualization of the data before and after classification. Since the 1648 bus system has a large number of features and samples, this invention uses the 1648 bus system as an example, which is more representative. Figure 8 As shown, the initial input features Stable and unstable samples are mixed together, making them difficult to distinguish. After the first layer of model training (output) When the distributions of the two types of samples form an initial boundary, some overlapping areas still exist that are difficult to distinguish. After training the second layer of CFC (output...), At this point, a clear boundary exists between stable and unstable samples, with no overlap. These results validate the effectiveness of the proposed hierarchical feature extraction architecture. Through two-layer feature extraction, the model can progressively strengthen category discrimination information. Furthermore, the data augmentation strategy of introducing a variable-length temporal window effectively learns sample features and improves the model's classification ability.

[0151] 5. Parameter sensitivity analysis

[0152] Obviously, due to the adoption of a time-adaptive strategy, i.e., according to formula (11) the reliable threshold, and maximum evaluation period This significantly affects evaluation performance. Under fixed conditions, it is necessary to determine this through sensitivity analysis. and The result is as follows Figure 9 As shown in (a)(b). The range is [1, 10] and the step size is 1. The range is [0.5, 0.99] and the step size is 0.01. When selecting a reliable threshold... At the same time, the ART should be as small as possible while ensuring the accuracy of the assessment (ACC). Figure 9 (b) indicates that when two systems Even when a certain period is reached, Adding more won't bring significant performance improvements. In fact, the model's computation time will increase with... The computation time for each evaluation in online applications should ideally be shorter than the evaluation cycle. Taking all factors into consideration, the 39-bus system... and The values ​​are set to 4 cycles and 0.62. The 1648 bus system... and The value is set to 5 periods and 0.67.

[0153] 6. Online updates for usability verification

[0154] Dataset and Represents the branch topology changes of two systems, dataset and These datasets represent changes in the bus topology of two systems. They are used to evaluate the online update capability of the transient evaluation method in this invention. To address the performance degradation under the new topology, this invention compares two update strategies: fine-tuning some parameters (the method adopted in this invention) and retraining the entire model. Before updating, the model structure is adjusted according to the topology change, such as deleting invalid synapses, neurons, and related parameters. The results are shown in Table 3.

[0155] Table 3

[0156]

[0157] After implementing the fine-tuning strategy, the model's evaluation accuracy recovered to over 98%. Furthermore, compared to the retraining strategy, this method significantly reduces time costs, as the retraining strategy requires at least twice the number of iterations to restore accuracy to over 98%. It can be seen that the online update method proposed in this invention can achieve fast and efficient online updates, and its interpretable model structure facilitates the customization of simpler and more effective online update strategies.

Claims

1. A transient stability evaluation method based on topological structure and closed neural network, characterized in that, Includes the following steps: Step S1: Introduce the objective differential equation to simulate the continuous-time nonlinear dynamics on the complex topology of the power system; Step S2: Use a closed-loop continuous-time neural network to solve the differential equation in step S1; Step S3: Utilize machine learning to continuously learn and improve the evaluation method, and parameterize the transient power angle steady-state variables of the solution in step S2; Step S4: Introduce a neural circuit strategy to simulate the connection structure of whole neurons, explicitly model the topology by simulating the adjacency relationship of the bus, and improve computational efficiency; Step S5: Use the steady-state criteria of the power system to determine the transient power angle stability of the power system, and form a dataset based on the criteria to train the neural network; Step S6: Combine offline training, practical application, and online updates; The above steps enable a comprehensive transient power angle stability assessment. The nonlinear relationship is expressed by the differential equation as follows: （1）； In the formula, yes t The set of transient power angle steady-state variables of the power system at any given time. Indicates the first i The busbar at time t State variables, It is a collection of them. For dynamic management parameters, It is the first i Electrical dynamic variables of a busbar This corresponds to the adjacency matrix of the power system topology. f This represents a neural network; The first expression in this formula represents the set of state variables through each bus. To solve the transient power angle stability state of the power system The second formula represents the electrical dynamic variables through each bus. Its corresponding topology To solve for the state variables of each bus ; To enhance the expressiveness of continuous-time dynamics, an improved form is introduced, mimicking the interaction between neurons via synapses. The improved equation is as follows: （2）； In the formula, This helps the system reach an equilibrium state with a time constant τ, and nonlinear synapses are introduced to represent the hidden state flow of the network as a system of linear differential equations. Activating neurons through nonlinear synapses It is the sum of all synaptic inputs that receive external stimuli and input them into the cell; It depends on the state of all neurons. It is an external input; This refers to the system parameter vector of the power system; The specific solution result is as follows: （3）； This is the initial state of the power system; The formula introduces a second time constant. Subsequently, the formula for calculating the transient power angle steady state at each time step is: （4）； In the formula replace It becomes a parameter vector. and （D） It is a system parameter vector. f It is a neural network, and its neural network parameters are: , represent and The weights between them represent and The weights between them Represents bias, It is each time step t m-dimensional input, It is each time step t The D-dimensional output.

2. The method according to claim 1, characterized in that, In step S1, the transient stability process of the power system can be regarded as a continuous-time nonlinear dynamic on a complex topology. A specific differential equation is introduced to simulate this nonlinear process. Under a given power system topology, its dynamics can be simply described as follows: the state variables of each bus change continuously according to certain dynamic laws under the influence of adjacent buses, and there is a nonlinear relationship between these state variables and the transient power angle stability state of the power system.

3. The method according to claim 1 or 2, characterized in that, In step S2, the differential equation that originally required iterative solution is transformed into an approximately closed form, so that under given initial conditions, the analytical solution or high-precision approximate solution of the network state can be obtained directly or through a finite number of steps.

4. The method according to claim 1, characterized in that, In step S3, to make the training process of the neural network more controllable and efficient, the solution obtained in step S2 is parameterized as a transient power angle stable state variable. By adjusting the parameters, different types of activation functions and layer structures can be used to optimize the convergence speed, stability and generalization ability of the model, improve the expressive power of the model, and ultimately enhance the performance of the model.

5. The method according to claim 4, characterized in that, The parameterized formula for the transient work angle steady-state variable is shown below: （5）； In order to enhance the flexibility of the model, a trainable neural network is introduced. and Replace the parameters in equation (4) respectively and To avoid gradient vanishing during neural network training, the exponential decay term... By an inverse s-shaped nonlinear variable (.) will replace With (1- The product of (.)) is a time-decaying sigmoid term, which acts as a gate control; finally, , and The first few layers of the neural network are shared in the form of a backbone to accelerate and stabilize the learning process.

6. The method according to claim 1, 2, 4, or 5, characterized in that, In step S4, a neural circuit strategy is introduced to explicitly model the topology, specifically as follows: By employing an end-to-end input-output approach and observing the output of each neuron, a unique, generalizable, and interpretable RNN structure is established through the cooperation between neurons. This allows for the observation of the model's entire learning state, which is reflected in the state variables of each bus. Not only by the dynamic variables on this bus line The decision also relates to the dynamic variables on the remaining busbars. With its own state variables The specific details, represented by neural network parameters, are shown in the following formula: （6）； The directional transmission between neurons, i.e., between individual neurons, is achieved by multiplying the weight parameters by the sparse mask matrix. The weight parameters are modified as follows: ,in represent and The weights between them represent and The weights between them Represents bias. It is a non-trainable sparse mask matrix that reflects the connection relationships between neurons, i.e., between various buses. In a power system, this connection relationship corresponds to the bus connection relationship. The zero parameter corresponding to The parameter will be initialized to zero.

7. The method according to claim 6, characterized in that, The improved RNN network exhibits better model interpretability and stability. Traditional RNN networks only consider the sufficiency of the number of neurons to fit the target data, rarely taking into account the interactions between neurons. In contrast, the neural circuit strategy classifies neurons into four categories: sensory neurons, interneurons, command neurons, and motor neurons. Its characteristics include high sparsity. Sensory neurons are responsible for acquiring information from the external environment, internal and command neurons make decisions, and finally, motor neurons control muscles. Different neurons are connected through synapses to form a meaningful topological structure. Secondly, utilizing the structure of RNNs can make the model more robust, effectively resist noise, and has a greater ability to prioritize learning from recent scenes.

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