Power Flow Calculation Model and Method Based on Trajectory Joint Optimization and Physical Information

Abstract

This invention discloses a power flow calculation model and method based on trajectory joint optimization and physical information, belonging to the field of power technology. The model includes a KAN-based physical information model and a trajectory joint optimization algorithm; it includes: applying interpretable KAN to power flow calculation; designing a physical constraint loss function to embed the physical mechanism; using the trajectory joint optimization algorithm to transform KAN training into a dynamic system evolution problem; the KAN-based physical information model has a two-layer architecture: the first layer calculates the node voltage magnitude, the second layer outputs the voltage phase angle, and the physical constraint network layer calculates the node power through the power flow network, using residual calculations to constrain the output results to satisfy the power balance equation; the trajectory joint optimization algorithm constructs a nonlinear dynamic system, guiding the parameters to evolve and converge to the optimal solution along the energy decrease direction. This invention can overcome the limitations of black-box networks and solve the challenge of training large-scale KAN networks, as well as improve accuracy.

Description

Technical Field

[0001] This invention belongs to the field of power technology, specifically relating to a power flow calculation model and method based on trajectory joint optimization and physical information. Background Technology

[0002] With the development of power systems, the proportion of renewable energy integration is continuously increasing, the power grid structure is becoming increasingly complex, and the interconnection between regions is becoming closer. The stochastic fluctuation characteristics of new energy sources lead to de-typical characteristics in system operation. Traditional power flow calculation methods suffer from problems such as long computation time and high resource consumption, limiting their application in distribution network modeling. The complexity of the relationship between system operating state and optimal power flow solution makes it difficult for traditional methods to quickly obtain the optimal solution. Currently, security analysis mainly relies on power flow solvers based on the Newton-Raphson optimization method. However, these solvers are relatively inefficient and may pose a potential risk to power grid security, leading to a continuously growing demand for high-precision, high-efficiency power flow solvers. With the development of artificial intelligence technology, data-driven methods combined with physical model constraints offer new possibilities for solving this challenge.

[0003] In recent years, artificial intelligence (AI) technology has made significant progress in the power system field, particularly in fault diagnosis, safety assessment, load forecasting, and economic dispatch. With the maturation of these technologies, researchers have begun to apply data-driven methods to power flow calculation, solving power flow problems by learning mapping rules from historical system operation data. Currently developed data-driven power flow calculation techniques mainly include: methods based on Kaufman operator theory; data-driven assisted linear power flow models for three-phase distribution networks; and deep neural network methods to address the inability of traditional power flow calculation methods to update the power system topology in real time. While these methods have advantages in computational speed, their accuracy is generally lower than that of traditional iterative numerical methods. However, in the context of new smart grids, the intermittency and uncertainty of generation and load are increasing, leading to potential deviations between the grid parameters stored in the power dispatch and control center database and actual values. This poses a challenge to the performance of data-driven methods. Furthermore, the scarcity of training sample data has also become a bottleneck restricting the further development of neural networks.

[0004] To address these challenges, Physical Information Neural Network (PINN) technology has emerged. This approach combines the advantages of data-driven methods with physical models, ensuring that the results meet the physical constraints of the power system while maintaining computational speed, and reducing reliance on training data. Compared to purely data-driven methods, power flow calculation methods based on physical information models have explicit physical meaning, ensuring that the calculation results satisfy the equality and inequality constraints required for system operation, making them more suitable for the operational needs of actual power systems.

[0005] Physical information models (PIMs) are machine learning frameworks that combine physical laws with deep learning techniques. They utilize scientific knowledge or physical laws to guide the optimization, architecture design, and implementation of neural networks. Currently, various physical model-assisted data-driven methods have been developed in the field of power system power flow calculation, such as physical model-assisted data-driven linear power flow models and physical-guided neural network power flow calculation methods. These methods improve computational efficiency while maintaining computational accuracy by integrating physical knowledge with data-driven techniques. However, their performance remains insufficient. Summary of the Invention

[0006] The present invention aims to at least partially solve one of the technical problems in the aforementioned related technologies.

[0007] Therefore, the purpose of this invention is to provide a power flow calculation model (TJU-PIKAN) and method based on the trajectory joint method that combines physical information and Kolmogorov-Arnold Networks. By combining the residuals of the power flow network calculation results with the loss function, the physical relationship of node power is better extracted, so that the model satisfies the node power balance equation. This can overcome the limitations of black box networks, solve the training challenges of large-scale KAN networks, and improve accuracy.

[0008] To solve the above-mentioned technical problems, the present invention is implemented as follows:

[0009] This invention provides a power flow calculation model based on joint trajectory optimization and physical information. The model consists of a KAN-based physical information model and a joint trajectory optimization algorithm, enabling data-driven power flow calculation guided by physical mechanisms. The implementation includes:

[0010] First, the interpretable KAN is applied to power flow calculation, overcoming the limitations of black-box networks, and the function fitting ability of KAN is used to approximate the calculation accuracy of numerical iterative methods. Then, considering the physical constraints of the power system, a physical loss function is designed to embed the physical mechanism. Finally, the trajectory joint optimization algorithm is used to transform the training of KAN into a dynamic system evolution problem, further improving the accuracy of the power flow solver.

[0011] In addition, the power flow calculation model based on joint trajectory optimization and physical information according to the present invention may also have the following additional technical features:

[0012] In some implementations, the KAN-based physical information model has a two-layer architecture:

[0013] The KAN layer is responsible for calculating node voltages;

[0014] The two-layer KAN network outputs the voltage amplitude and phase angle respectively. The physical constraint network layer uses the power flow network to calculate the node power, and the residual calculation constrains the output of the KAN layer to satisfy the power balance equation.

[0015] In some implementations, the KAN layer is based on the Kolmogorov-Arnold representation theorem, and achieves high-dimensional function fitting through a combination of univariate functions, thus overcoming the limitations of black-box networks.

[0016] In some implementations, the physical constraint network layer determines the physical loss function based on node power balance to ensure that the result satisfies physical laws.

[0017] In some implementations, the overall loss function of the KAN-based physical information model is: the sum of voltage loss and physical constraint loss by balancing weight parameters.

[0018] In some implementations, the trajectory joint optimization algorithm addresses the training challenge of large-scale KAN networks by constructing a nonlinear dynamic system that guides the parameters to evolve along the energy-decreasing direction and converge to the optimal solution.

[0019] In some implementations, the optimization process of the trajectory joint optimization algorithm includes: using a block diagonal pseudo-transient continuous method for numerical solution, and dynamically adjusting the step size and preprocessing matrix to improve training stability, convergence speed and accuracy.

[0020] In some implementations, the physical loss is obtained using an adaptive Huber function, which enhances the ability to adapt to anomalous data.

[0021] This invention also provides a power flow calculation method based on joint trajectory optimization and physical information, implemented using any of the power flow calculation models based on joint trajectory optimization and physical information described above; the method includes the following steps:

[0022] S1: Generate power flow samples: Generate samples by disturbing generators and load parameters, select convergent samples using the Newton-Raphson method, and divide them into training and test sets;

[0023] S2: Training the KAN-based physical information model: Standardize the training data, optimize the KAN using a trajectory joint optimization algorithm, calculate node voltages via forward propagation and evaluate the residuals with the Newton-Raphson results, obtain the power data of each node based on the power flow calculation results of the KAN through the power flow network, and calculate the degree of violation of the node power balance equation through residual calculation; optimize the model parameters via backpropagation to minimize the deviation between the model results and the results generated by the Newton-Raphson algorithm;

[0024] S3: Evaluate the performance of the KAN-based physical information model: Calculate the mean squared error (MSE) and mean absolute error (MAE) of the test power flow data to evaluate the model accuracy.

[0025] In addition, the power flow solver based on trajectory joint optimization and physical information model according to the present invention may also have the following additional technical features:

[0026] In some of these embodiments, step S1 includes the following detailed steps:

[0027] S1.1: Introduce generator disturbances by traversing each generator node in the power system network; randomly disturb the active power and voltage amplitude of unbalanced nodes; introduce load disturbances by traversing each load node in the network; limit the range of disturbance parameters to ensure the rationality of random disturbances;

[0028] S1.2: The Newton-Raphson algorithm is used to calculate and exclude non-convergent power flows. The calculated voltage magnitude and phase angle of each node are stored in the database to obtain a sample dataset.

[0029] S1.3: The dataset is then divided into training and test sets in a specific ratio.

[0030] Compared with the prior art, the present invention has at least the following beneficial effects:

[0031] In this embodiment of the invention, the power flow calculation model based on trajectory joint optimization and physical information can improve the interpretability of the model and overcome the limitations of the black box: by utilizing the characteristics of Kolmogorov-Arnold Networks (KAN), its interpretability is applied to power flow calculation; KAN is based on the Kolmogorov-Arnold representation theorem, and uses a combination of single-variable functions to represent high-dimensional functions. Its function fitting process has clear mathematical logic, which overcomes the limitation of traditional black box networks (such as some deep learning models) being difficult to interpret, and improves the reliability of the model in power system power flow calculation;

[0032] In this embodiment of the invention, the power flow calculation model based on trajectory joint optimization and physical information can guarantee calculation accuracy and approach the level of numerical iterative methods: KAN has a strong function fitting ability and can approach the calculation accuracy of numerical iterative methods (such as the Newton-Raphson method); experiments show that the best-performing PIKAN-TJU model in the IEEE 30-node system improves the mean absolute error of voltage amplitude (VM-MAE) by 0.0819 and the mean absolute error of voltage phase angle (VA-MAE) by 0.0221 compared to the Adam optimizer model, and the TJU optimization algorithm has the best training effect;

[0033] In this embodiment of the invention, the power flow calculation model based on trajectory joint optimization and physical information is embedded with physical mechanisms to ensure physical feasibility: considering the physical constraints of the power system (such as nodal power balance equations, Kirchhoff's laws, etc.), a special physical loss function is designed to explicitly embed the physical mechanism into the model training process; this makes the model calculation results satisfy the basic physical laws of the power system, avoids the problem of physical infeasibility in actual application that may occur with pure data-driven methods, and is more in line with the actual operation requirements of the power system;

[0034] In this embodiment of the invention, the power flow solver based on trajectory joint optimization and physical information model can optimize the training process and overcome the challenges of large-scale networks: the trajectory joint optimization algorithm (TJU) is used to overcome the training challenges of large-scale KAN networks; TJU transforms network training into a steady-state equilibrium point search problem by constructing a nonlinear dynamic system, and combines the block diagonal pseudo-transient continuous method (BD-PTC) for numerical solution, dynamically adjusting the step size and preprocessing matrix, thereby improving the stability, convergence speed and optimization accuracy of training, and enabling the model to better adapt to large-scale power system scenarios;

[0035] In this embodiment of the invention, the power flow calculation model based on trajectory joint optimization and physical information can balance computational efficiency with accuracy and speed: compared with traditional numerical-driven methods (such as the Newton-Raphson iterative method), the TJU-PIKAN model has a four-fold increase in computational speed, which greatly improves computational efficiency; at the same time, it is superior to pure data-driven methods in terms of accuracy, achieving a balance between accuracy and speed, and is suitable for the power flow calculation needs of modern power systems with high proportion of new energy access and complex structures.

[0036] In this embodiment of the invention, the power flow solver based on trajectory joint optimization and physical information model can enhance robustness and adapt to data quality fluctuations: the physical loss function adopts the adaptive Huber loss function, and the penalty intensity is adjusted according to the residual statistical characteristics through a dynamic threshold mechanism. While ensuring differential performance, it enhances the model's adaptability to abnormal data and reduces the impact of data quality on model performance.

[0037] The power flow calculation method based on trajectory joint optimization and physical information of the present invention adopts the power flow calculation model based on trajectory joint optimization and physical information, and therefore possesses at least all the features and advantages of the power flow calculation model based on trajectory joint optimization and physical information, which will not be repeated here. Additional aspects and advantages of the present invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0038] Figure 1 This is a general architecture of a power flow solver based on TJU-PIKAN disclosed in one embodiment of the present invention;

[0039] Figure 2 This invention discloses a KAN-based physical information model framework as an embodiment of the present invention.

[0040] Figure 3 This invention discloses the relationship between physical information and data quantity in one embodiment.

[0041] Figure 4 This is a flowchart of the TJU-PIKAN training steps disclosed in one embodiment of the present invention;

[0042] Figure 5 This is a performance index comparison chart disclosed in one embodiment of the present invention;

[0043] Figure 6 This is a comparison chart of the training losses of different models disclosed in one embodiment of the present invention;

[0044] Figure 7 This is a comparison chart of 30-node calculation results disclosed in one embodiment of the present invention.

[0045] Figure 8 This invention provides a comparison of the time consumption of 10,000 power flow calculations between the TJU-PIKAN model and the Newton-Raphson method, as disclosed in one embodiment of the invention. Detailed Implementation

[0046] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. 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.

[0047] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings and specific examples and application scenarios.

[0048] This invention combines the characteristics of KAN networks and physical information models to construct a novel physical information power flow calculation framework. This framework not only maintains the advantage of physical information models in reducing reliance on large datasets, but also enhances the reliability and application value of the model in power system power flow calculations through the interpretability features of KAN networks. This technical solution, by integrating the advantages of physical laws and KAN networks, effectively solves the problems faced by existing physical information neural networks in power system power flow calculations, such as gradient vanishing, complex parameter adjustment, high computational cost, and insufficient interpretability, providing more reliable technical support for the safe and stable operation of power systems. Furthermore, it proposes a power system power flow calculation model (TJU-PIKAN) based on the trajectory joint method, combining physical information and Kolmogorov–Arnold Networks. By combining the residuals of the power flow network calculation results with the loss function, the physical relationships of node power are better extracted, ensuring that the model calculation results satisfy the node power balance equations.

[0049] The following section describes the power flow solver based on TJU-PIKAN.

[0050] The TJU-PIKAN model enables data-driven power flow calculations guided by physical mechanisms. This method employs neural network technology to extract features from power flow samples. By constructing a power flow network, physical constraints are embedded into the training of the TJU-PIKAN model, thereby ensuring that the power flow calculation results are consistent with the feasibility of actual power systems. Figure 1 The overall system framework has been shown, and it will be explained in detail below.

[0051] The Physical Information Model Based on KAN (PIKAN) comprises a two-layer architecture: a KAN neural network and a physical constraint network. The KAN model primarily calculates the voltage information of each node, while the physical constraint network, based on the voltage values ​​output by the KAN, constrains the generator power parameters through a power flow network. The architecture diagram is shown below. Figure 2 As shown.

[0052] Power flow networks are built upon the physical laws of power grids, describing the intrinsic relationships between voltage magnitude, phase angle, and power. If the calculated results fail to satisfy these equations, the results are physically infeasible. To ensure the physical validity of the calculation results, this model introduces a residual calculation mechanism. This mechanism enforces physical constraints, ensuring that the power flow calculation results remain consistent with the fundamental physical laws of the power system, thereby improving the model's practical value and reliability.

[0053] In some embodiments of the present invention, physical information is incorporated into network training as a penalty term in the loss function, ensuring that the training results of the neural network satisfy specific physical constraints and possess physical interpretability, thereby improving generalization performance. The inclusion of a physical model provides a good direction for network training, preventing network parameters from reaching local optima, effectively increasing training speed. Furthermore, guided by physical knowledge, the neural network can reduce its dependence on data, achieving the same or even better results with less data. Figure 3 To understand the relationship between the amount of physical information and the amount of data in a neural network when the computational effect is the same, physical information can compensate for the lack of data to a certain extent.

[0054] The theoretical basis of KAN networks stems from the Kolmogorov-Arnold representation theorem (KAR), which is mathematically expressed as follows:

[0055] For any continuous function There exist continuous single-variable functions and Make:

[0056]

[0057] This theorem theoretically proves that any multivariate continuous function can be represented by a combination of a finite number of single-variable functions, providing a theoretical basis for the structured expression of high-dimensional functions.

[0058] KAN networks realize the practical application of this theorem through discretization and parameterization. In KAN networks, ψ p，q and φ q A parameterized, learnable univariate function is typically represented as:

[0059]

[0060] Where b(·) is a basis function (such as a B-spline function), w p，q，i These are learnable weights, μ i σ is the node position, σ is the smoothness parameter, and B is the number of basis functions.

[0061] The core idea of ​​Physical Information Neural Networks (PINNs) is to incorporate physical laws as constraints into the training process of the neural network. The loss function of PINNs can typically be expressed as:

[0062]

[0063] in, It is based on data loss. This represents the physical constraint loss, and λ is the trade-off parameter. For power flow calculations, Typically based on nodal power balance equations:

[0064]

[0065] Where, Δs i =s i，cal -s i，spec : Represents the difference between the calculated power of node i and the specified power, where N is the number of nodes. Specified power S i，spec The calculated power S is obtained by inputting generator and load power data. i，cal We obtain it through the following equation:

[0066]

[0067] Among them, V i Y is the complex voltage at node i. ij It is an element of the nodal admittance matrix, V j * It is the conjugate of the complex voltage at node j.

[0068] The present invention employs a five-layer KAN network for power flow calculation. This network receives power parameters from generators and loads as input, processes them, and outputs the voltage magnitude and phase angle of each node. The KAN output can be expressed as:

[0069] V = f KAN (P G Q G P L , Q L)

[0070] According to KAN's theory, this mapping can be expanded as follows:

[0071]

[0072] Where V = [V m V a ] represents voltage amplitude and phase angle, d is the input feature dimension, and n is the number of samples.

[0073] The PIKAN model explicitly embeds the physical laws of the power system into the KAN training process through a specially designed physical constraint network. This physical constraint network is based on the nodal power balance equations:

[0074] S cal =diag(V)·(Y·V) *

[0075] Where, S cal =[P cal +jQ cal] is the calculated complex power vector, V is the complex voltage vector, and Y is the nodal admittance matrix.

[0076] PIKAN implements a mapping model between power system state information and power flow calculation results. By using a power flow network, it ensures that the calculation results well satisfy physical mechanism constraints, such as node power balance in the power system. It utilizes the fundamental physical mechanism constraints in the power flow network to guide the training of KAN, ensuring adherence to constraints such as Kirchhoff's laws and Ohm's law. This approach helps prevent overfitting, improves model accuracy, and reduces violations of physical constraints. The overall loss function of PIKAN is designed as follows:

[0077]

[0078] Here, α and β are the balancing weight parameters.

[0079] To enhance the model's ability to adapt to outlier data, An adaptive Huber loss function is used to enhance robustness to outliers:

[0080]

[0081] Here, δ is an adaptive threshold parameter that is dynamically adjusted as the training process progresses. This function uses a dynamic threshold mechanism to automatically adjust the penalty strength based on the statistical characteristics of the residuals, thereby improving the ability to handle outliers while maintaining differential performance.

[0082] Trajectory Joint Optimization (TJU) technology combines the advantages of stochastic guidance and classical descent methods, overcoming the limitations of traditional optimization methods. The core design objectives of this method are to enhance the stability, accelerate convergence, and improve accuracy during neural network training.

[0083] In some embodiments of the present invention, the PIKAN model employs the Trajectory Joint Optimization (TJU) algorithm to transform the training of KAN into a dynamic system evolution problem:

[0084]

[0085] Here, the parameter vector x represents all the learnable parameters of the KAN network, and z represents the input dataset. It is worth noting that in the KAN architecture, traditional linear weights are replaced by spline-parameterized univariate functions, giving the optimization space unique characteristics.

[0086]

[0087] In some embodiments of the present invention, the following nonlinear dynamic system is constructed based on the above mapping relationship:

[0088]

[0089] in, Let be the Jacobian matrix, and α be the system response parameter. This dynamic equation guides the system state to evolve along the energy-decreasing direction, eventually converging to a stable equilibrium point.

[0090] In some embodiments of the present invention, the stable equilibrium point of the dynamic system corresponds to a local minimum of the following energy function:

[0091]

[0092] Through this mapping, the stable equilibrium point of the dynamic system corresponds precisely to the local optimum of the neural network optimization problem. The system trajectory evolves along the gradient descent direction of the energy function until it converges to a stable state, thus achieving the optimization objective.

[0093] The TJU algorithm numerically solves the above dynamic system using the block-diagonal pseudo-transient continuity method (BD-PTC):

[0094]

[0095] Where, η k It is an adaptive step size, dynamically adjusted according to changes in residuals; M k It is a preprocessed matrix, using a block diagonal structure to balance computational efficiency and convergence:

[0096]

[0097] Each block This corresponds to a subset of parameters for a specific layer or component in the network.

[0098] To address the challenges of high-dimensional network structures and massive parameter spaces, the TJU algorithm effectively reduces the dimensionality of the search space and the complexity of optimization through the synergistic effect of dynamic system mapping, pseudo-transient continuity techniques, and local optimizers. This mechanism significantly improves the optimization efficiency and convergence stability of interpretable KAN models in large-scale scenarios, overcoming the convergence barriers and inefficiencies faced by traditional methods.

[0099] In some embodiments of the present invention, the PI-KAN model employs a two-stage optimization strategy:

[0100] Dynamic system construction phase: A nonlinear dynamic mapping mechanism is established to transform the neural network optimization objective into a problem of finding a steady-state equilibrium point. Starting from the initial point in the state space, the block diagonal pseudo-transient continuous method (BD-PTC) is applied to perform numerical integration of the system.

[0101] Local fine optimization stage: Using the endpoint of the first stage BD-PTC iteration as the initial estimate, the optimal solution is accurately located through local solvers (such as SGD, Adam, etc.) to achieve high-precision convergence.

[0102] In some embodiments of the present invention Figure 4 The training process based on PIKAN has been explained. The following are the detailed steps for training the TJU-PIKAN model:

[0103] Phase 1: Generating trend samples

[0104] Step 1-1: Generate basic power flow samples by adding disturbance parameters to generators and loads in the power system. To ensure the diversity of the generated samples, generator disturbances are introduced by traversing each generator node in the power system network. Random disturbances are applied to the active power and voltage amplitude of unbalanced nodes. Similarly, load disturbances are introduced by traversing each load node in the network. To ensure the reasonableness of the random disturbances, the range of disturbance parameters is limited.

[0105] Steps 1-2: Use the Newton-Raphson algorithm to calculate and exclude non-convergent power flows, and save the calculated voltage magnitude and phase angle of each node in the database to obtain a sample dataset.

[0106] Steps 1-3: The dataset is then divided into training and test sets in a 7:3 ratio.

[0107] Phase 2: Training the PIKAN model

[0108] Step 2-1: Perform Z-score standardization on the training power flow data samples.

[0109] Step 2-2: Optimize KAN using the TJU algorithm, perform forward propagation to calculate node voltage magnitudes, and calculate the residuals compared to the results calculated by the Newton-Raphson algorithm. Obtain the power data for each node through the power flow network, and determine the degree of violation of the node power balance equations using the loss function.

[0110] Steps 2-3: Backpropagation is used to optimize model parameters to minimize the deviation between the model results and the results generated by the Newton-Raphson algorithm.

[0111] Phase 3: Evaluating the performance of the PIKAN model

[0112] Step 3-1: Standardize the test power flow data samples.

[0113] Step 3-2: Forward propagation and denormalization to compute the MAE and MSE of the model.

[0114] Step 3-3: Complete the assessment.

[0115] The following is an explanation of the experimental analysis.

[0116] Since its inception, the KAN model has been considered an effective alternative to the traditional fully connected network MLP. To test the actual performance of this KAN model, the PIKAN model will be tested. The specific network structure dimensions are shown in Table 1.

[0117] Table 1 shows the network size parameters used.

[0118]

[0119] In some embodiments of the present invention, performance metrics MAE and MSE are introduced to measure the power flow calculation accuracy of the two models. MAE is a metric used to quantify the mean absolute difference between model predictions and actual values. It directly reflects the deviation of the model during the prediction process. MSE is a metric used to measure the mean squared difference between model predictions and actual values. It assigns more weight to larger errors, making the objective function more sensitive to significant deviations during the optimization process.

[0120] Figure 5 This section presents a performance comparison of the deep learning model PIKAN under different optimization algorithms (TJU, Adam, AdamW, and SGD). The two top graphs show the VA-MAE and VA-MSE metrics, while the two bottom graphs show the VM-MAE and VM-MSE metrics. In all graphs, the x-axis represents the training epochs, and the y-axis displays the corresponding error values.

[0121] Experimental results show that curves of different colors represent various model-optimizer combinations, clearly demonstrating the convergence characteristics and error change trends of each combination over 1000 training rounds.

[0122] The specific data of the models after training for 1,000 epochs are shown in Table 2. The errors of VM and VA decreased continuously with the increase of training epochs, indicating that both models learned the mapping law between power flow calculations. Analysis shows that the TJU optimizer achieved the best performance, Adam and AdamW performed well but slightly worse, while SGD performed the worst with a slow convergence speed.

[0123] Table 2. Performance metrics of different models and algorithms trained 1000 times on IEEE 30 nodes.

[0124]

[0125] Figure 6The training loss trends of the Physical Information Model (PIKAN) combined with three different optimization algorithms (Adam, AdamW, SGD, and TJU) were compared. Five lines of different colors represent different model-optimizer combinations. Analysis shows that the PIKAN-SGD combination differs significantly from the others. Its initial loss value is as high as 55-65, fluctuating continuously for approximately the first 630 iterations before decreasing sharply and eventually stabilizing at around 4.8. In contrast, the other combinations (PIKAN-Adam, PIKAN-AdamW, and PIKAN-TJU) perform well, with a rapid decrease in loss within the first 25 iterations. All combinations converge to very low loss values ​​after 50 iterations. Among them, PIKAN-TJU (green line) achieved the fastest convergence and the lowest loss value. This further demonstrates that the combination of the PIKAN model and the TJU optimizer may be the optimal choice for this type of task.

[0126] Comparative analysis of the calculation accuracy and error of different power flow calculation models: Taking the IEEE 30-node model as an example, the power flow sample data was calculated using the PIKAN-TJU model. The specific results are shown in Table 3.

[0127] Table 3 Comparison of calculation results for nodes 5, 10, 15, 20, 25, and 30

[0128]

[0129] As shown in Figure 7, the blue solid line represents the actual voltage amplitude calculated by the Newton-Lambert method, and the green solid line represents the calculation result of the PIKAN model. It can be observed that when calculating power flow results based on the IEEE 30-node network, the PIKAN model's calculation results are closely consistent with the actual values, proving that the PIKAN model has high calculation accuracy. For the voltage phase angle, the actual value is still represented by the blue line, and the PIKAN model's calculation result is represented by the green solid line. The PIKAN model's results are closely related to the trend of the actual values, with minimal fluctuations, demonstrating high accuracy in power flow calculation.

[0130] To visually demonstrate the speed comparison between TJU-PIAKN's power flow calculation and Newton-Raphson's calculation, the computation time for each model or method processing 10,000 power flow data samples was statistically analyzed. The results are as follows: Figure 8 As shown, the power flow calculation speed of TJU-PIAKN is much faster than that of the Newton-Raphson method, about four times faster.

[0131] Any part of this invention not described in detail can be referred to in the prior art or in the art known to those skilled in the art. This embodiment does not limit such part and will not describe it in detail here.

[0132] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims, and all of these forms are within the protection scope of the present invention.

Claims

1. A trajectory-based joint optimization and physical information based power flow calculation model, characterized in that, The model is composed of a KAN-based physical information model and a trajectory joint optimization algorithm, realizing data-driven power flow calculation guided by physical mechanism; The implementation content includes: First, the KAN with interpretability is applied to power flow calculation, breaking through the limitations of black-box network, and using the function fitting capability of KAN to approximate the calculation accuracy of numerical iteration method; then, considering the physical constraints of the power system, a physical loss function is designed to realize the embedding of physical mechanism; finally, the trajectory joint optimization algorithm is adopted to convert the training of KAN into a dynamic system evolution problem, further improving the accuracy of the power flow solver; The KAN-based physical information model is a double-layer architecture: The KAN layer is responsible for calculating the node voltage; The double-layer KAN network outputs the amplitude and phase angle of the voltage respectively, and the physical constraint network layer calculates the node power by using the power flow network, and the output results of the KAN layer are constrained by the residual calculation to satisfy the power balance equation; The physical constraint network layer determines the physical loss function based on the node power balance to ensure that the power flow calculation results satisfy the physical law; The overall loss function of the KAN-based physical information model is: the voltage loss and the physical constraint loss are summed by balancing the weight parameters; The trajectory joint optimization algorithm guides the parameters to evolve along the energy descent direction by constructing a nonlinear dynamic system, and converges to the optimal solution to solve the training challenge of large-scale KAN network.

2. The trajectory-based joint optimization and physical information based power flow calculation model according to claim 1, wherein, The KAN layer is based on the Kolmogorov-Arnold representation theorem, which realizes high-dimensional function fitting through single-variable function combination, breaking through the limitations of black-box network. 3.The trajectory-based joint optimization and physical information based power flow calculation model according to claim 1, wherein, The optimization process of the trajectory joint optimization algorithm includes: using the block diagonal pseudo-transient continuation method for numerical solution, dynamically adjusting the step size and preprocessing matrix to improve the training stability, convergence speed and accuracy.

4. The trajectory-based joint optimization and physical information based power flow calculation model according to claim 1, wherein, The physical loss is obtained by using the adaptive Huber function, which can enhance the adaptability to abnormal data.

5. A method for power flow calculation based on trajectory joint optimization and physical information, characterized in that, The power flow calculation model based on trajectory joint optimization and physical information is realized according to any one of claims 1-4; the steps of the method include: S1: generating power flow samples: generating samples by perturbing generator and load parameters, selecting convergent samples by Newton-Raphson method, and dividing into training set and test set; S2: training KAN-based physical information model: standardizing the training data, optimizing KAN by trajectory joint optimization algorithm, forward propagating to calculate the node voltage amplitude and voltage phase angle and evaluating the residual error with Newton-Raphson result, obtaining the power data of each node through the power flow network based on the KAN-based power flow calculation result, and calculating the violation degree of node power balance equation through residual error; backward propagating to optimize model parameters to minimize the deviation between model calculation result and Newton-Raphson algorithm calculation result; S3: evaluating the performance of KAN-based physical information model: calculating the MAE and MSE of test power flow data to evaluate the model accuracy.

6. The trajectory-based joint optimization and physical information based power flow calculation method of claim 5, wherein, The detailed steps of step S1 include: S1.1: Introduce generator disturbance by traversing each generator node in the power system network; random disturbance is applied to the active power and voltage magnitude of non-balanced nodes; introduce load disturbance by traversing each load node in the network; S1.2: Calculate and exclude non-convergent power flow using Newton-Raphson algorithm to obtain a sample data set; S1.3: The data set is then divided into training and test sets at a certain ratio.

7. The trajectory-based joint optimization and physical information based power flow calculation method of claim 6, wherein, In S1.1, the range of disturbance parameters is limited to ensure the reasonableness of random disturbance. 8.The trajectory-based joint optimization and physical information based power flow calculation method of claim 6, wherein, In S1.2, the calculated voltage magnitude and phase angle of each node are saved in the database, thereby obtaining a sample data set.

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