A Joint Estimation Method for Power System State and Parameters Based on Newton-Raphson Guided Machine Learning

Abstract

This invention discloses a joint estimation method for power system state and parameters based on Newton-Raphson guided machine learning, relating to the fields of smart grid optimization and power system analysis. The method includes: addressing the problems of low iteration efficiency and machine learning physical mapping distortion in traditional state estimation and parameter identification, embedding the fixed-step Newton-Raphson method as a differentiable module into the machine learning training framework to construct an end-to-end model for parameter and state co-optimization; establishing a PV / PQ node hybrid input-output mapping mechanism that conforms to actual measurement scenarios, using the admittance matrix as an optimizable parameter, and achieving gradient backpropagation under physical constraints through automatic differentiation; designing a node-level state estimation loss function, combined with physical regularization methods for conductance / susceptance, to ensure the feasibility and stability of parameter estimation; and balancing computational efficiency and accuracy by dynamically adjusting the number of Newton iteration steps, ultimately achieving high-precision state prediction and grid parameter reconstruction. Verified on the IEEE-118 node system, this method converges within three Newton iterations, with a state estimation error below 1.2e⁻³, an admittance reconstruction error reduced by 41% compared to the baseline, and strong generalization ability under multiple operating conditions. This invention can be applied to the construction of digital twins for power grids, online security assessment, and fault diagnosis, significantly improving the efficiency and accuracy of power system analysis.

Description

Technical Field

[0001] This invention relates to the field of power system optimization technology, and more specifically, to a method for joint estimation of power system state and parameters based on Newton-Raphson guided machine learning. Background Technology

[0002] With the widespread application of artificial intelligence technology in the power system field, machine learning (ML) has shown significant potential in state estimation and parameter identification tasks. Traditional data-driven methods, such as deep neural networks and support vector machines, can achieve rapid state prediction by mining the mapping relationship between measurement data and system state.

[0003] However, existing technologies still face three major bottlenecks: the mismatch between physical laws, lack of interpretability, and poor adaptability to small samples. Specifically, in the physical law mismatch problem, purely data-driven black-box models ignore the inherent physical constraints of power networks, such as Kirchhoff's laws and power balance equations, leading to estimation results that violate power flow equations and produce physically infeasible solutions. Existing methods cannot establish a mathematical relationship between parameter estimation and state estimation, requiring model retraining when the system topology changes, thus resulting in a lack of interpretability. In scenarios with sparse measurement data, traditional ML models suffer from overfitting due to a lack of prior physical knowledge, exhibiting poor adaptability to small samples.

[0004] To address the aforementioned issues, existing research proposes two improvement schemes: physical regularization methods and hybrid modeling methods. In physical regularization methods, introducing a power flow residual term into the loss function can improve physical consistency, but it may lead to fragmented derivative propagation and lag in dynamic response. Hybrid modeling methods use machine learning (ML) as a front-end preprocessing module for power flow calculations, achieving data-physical collaboration through a cascaded structure. However, this architecture has inherent limitations: error accumulation effects, amplification of parameter identification errors during power flow calculations, and increased latency due to the dual computation chains, resulting in insufficient real-time performance.

[0005] Existing methods have failed to organically integrate the core advantages of machine learning and physics models, and still have significant shortcomings:

[0006] Insufficient depth of mechanism embedding: Existing physical regularization only applies to the output layer and does not integrate the Newton-Raphson derivative mechanism into the gradient calculation of the neural network;

[0007] Parameter-state decoupling: Line parameter estimation and system state estimation are performed separately, ignoring the strong coupling between the two through the power flow equations;

[0008] Weak dynamic adaptability: Static constraints cannot respond to changes in system operating status, requiring manual adjustment of hyperparameters.

[0009] No effective solutions have yet been proposed to address the problems in the relevant technologies. Summary of the Invention

[0010] To address the problems in related technologies, this invention proposes a power system parameter and state estimation method that embeds power flow calculation into machine learning. This method, through deep integration of physical models and data-driven techniques, possesses advantages such as dynamically sensing system topology changes, efficiently identifying line parameters, and robustly estimating operating states. This solves the problems of existing technologies, such as physical models relying on complete topology information, data-driven methods lacking physical interpretability, and traditional methods having poor anti-interference capabilities.

[0011] Therefore, the specific technical solution adopted by the present invention is as follows:

[0012] A method for estimating power system parameters and state by embedding power flow calculation into machine learning includes the following steps:

[0013] S1. Construct a hybrid learning framework with physical constraints, embed the Newton-Raphson-Fajkobi matrix structure into the neural network, and design a two-stage training mechanism.

[0014] S2, Design parameter-state joint estimation module, construct dynamic parameter identification sub-network;

[0015] S3. Develop an online topology adaptive correction mechanism, which detects topology change events in real time based on graph convolutional networks, triggers local parameter recalibration, and constructs an impedance deviation compensation module.

[0016] Further, step S1 specifically includes:

[0017] S11. Establish a physical constraint layer with the power flow equation as the core, and embed the Newton-Raphson Fajokian matrix structure into the neural network.

[0018] S12. Design a two-stage training mechanism: the pre-training stage learns physical laws through theoretical data, and the fine-tuning stage optimizes parameter sensitivity by combining measured data.

[0019] S13. Define the mixed input vector and .

[0020] Furthermore, a physical constraint layer is established with the power flow equations at its core. This physical constraint layer is implemented by transforming the power flow equations into differentiable operators embedded in the network backpropagation process. The power flow equations are as follows:

[0021]

[0022] Furthermore, the two-stage training data generation method includes pre-training data, which generates 100,000 sets of noisy power flow samples based on the simulation of the standard IEEE node system; and fine-tuning data, which is connected to the SCADA / PMU measured data stream and subjected to Mahalanobis distance filtering.

[0023] Further, step S2 specifically includes:

[0024] S21. Construct a dynamic parameter identification subnetwork and fuse power flow equation deviation and measurement error through residual connection;

[0025] S22. An adaptive weight allocation mechanism is adopted to balance the coupling relationship between parameter estimation and state estimation.

[0026] Furthermore, the joint loss function is used to simultaneously optimize parameter estimation and state estimation, reconciling the contradiction between physical constraints and data fitting:

[0027]

[0028] in, represents the weighting coefficient, used to balance the constraint terms of the physical equations and the prediction error terms of the neural network, and its value ranges from [0,1]. Let g represent the gradient of the power flow equation g with respect to the state variable z, where The node power balance equation is represented by a vector function; z represents a vector of state variables, which typically include state quantities such as voltage magnitude and phase angle. The norm is usually calculated using the Euclidean norm; y represents the true output vector, which includes state estimates such as voltage phase angle and parameter estimates such as line resistance and reactance. This represents the predicted output of the neural network. This represents the trained neural network model. This represents the input feature vector, including node injected power, voltage measurements, etc.

[0029] Furthermore, the dynamic parameter identification subnetwork in S2 is characterized by its parallel dual-channel architecture and the design of a parameter-sensitivity loss function. In the parameter-state joint estimation module, it is ensured that the neural network's estimation of line parameters conforms to the power flow equations. The output state estimate of channel 1 is... Channel 2 output parameter estimate The parameter sensitivity loss function is:

[0030]

[0031] Where N represents the number of samples used for computation during training; k represents the index of the current sample in the batch. ; The Jacobian matrix represents the power flow equations g with respect to the line impedance parameter Z, indicating the rate of change of the power flow equations as the line impedance changes; Z represents the actual line impedance parameter vector. The line impedance parameter vector estimated by the neural network for the k-th sample; This represents the error vector between the true parameters and the estimated parameters of the k-th sample.

[0032] Furthermore, the triggering condition for the online topology adaptation mechanism in step S3 is:

[0033] S31, Circuit breaker status change event, detection accuracy >99.2%;

[0034] S32. The line impedance change exceeds the threshold, i.e. .

[0035] The beneficial effects of this invention are as follows:

[0036] (1) This invention proposes an innovative method for deeply embedding power flow equations of power systems into a machine learning framework. By integrating the power flow model of physical mechanisms as a core constraint or knowledge component into the machine learning process, a parameter and state estimation framework is established that can synergistically utilize the accuracy of the physical model and the generalization ability of the data-driven model. This method differs from the existing technology that relies solely on pure data-driven models or uses traditional numerical power flow calculations independently. Instead, it organically integrates the power flow equations or their Jacobian information into the neural network structure, loss function construction, or training process, achieving a significant improvement in model transparency, physical consistency, and estimation accuracy.

[0037] (2) The machine learning framework that integrates physical power flow equations proposed in this invention can effectively overcome the generalization bottleneck of pure data-driven models under conditions of insufficient training data, system topology changes, or noise interference, and significantly improve the joint estimation accuracy of system parameters and operating states. Especially in scenarios with a high proportion of renewable energy access and noise or missing measurement data, this method can correct physical model errors through learning while maintaining strong consistency constraints on physical laws, providing more robust and reliable estimation results.

[0038] (3) By designing a novel model architecture and training strategy, this invention successfully introduces nonlinear and complex power flow relationships into the machine learning optimization process. Compared with existing methods, the fusion strategy proposed in this invention can effectively inject physical prior knowledge while maintaining the fitting ability of machine learning, reduce the model's dependence on massive labeled data, improve the estimation stability and anti-interference ability under non-ideal measurement conditions, and has the interpretive potential to reveal potential physical laws.

[0039] Furthermore, this method is compatible with various power grid scenarios and measurement data sources, and has the potential to adapt to different system scales and topology changes. It provides a new generation of efficient, reliable, and physically interpretable core analysis tools for high-precision parameter identification, state awareness, data repair, and digital twin construction in modern power systems. Attached Figure Description

[0040] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0041] Figure 1 This is a schematic diagram of the overall process of a power system state and parameter joint estimation method based on Newton-Raphson guided machine learning according to an embodiment of the present invention.

[0042] Figure 2 This is a graph showing the change of the loss function with the number of training rounds in the IEEE-118 node system.

[0043] Figure 3 This is a graph showing the change in reconstruction error as a function of training rounds in the IEEE-118 node system.

[0044] Figure 4 This is a comparison chart of the reconstruction results of the line admittance parameters. Detailed Implementation

[0045] To further illustrate the various embodiments, the present invention provides accompanying drawings, which are part of the disclosure of the present invention. These drawings are mainly used to illustrate the embodiments and can be used in conjunction with the relevant descriptions in the specification to explain the operating principles of the embodiments. With reference to these drawings, those skilled in the art should be able to understand other possible implementation methods and the advantages of the present invention.

[0046] According to an embodiment of the present invention, a method for joint estimation of power system state and parameters based on Newton-Raphson guided machine learning is provided.

[0047] The present invention will now be further described in conjunction with the accompanying drawings and specific embodiments, such as... Figure 1 As shown, according to an embodiment of the present invention, a method for joint estimation of power system state and parameters based on Newton-Raphson guided machine learning is provided. The method includes the following steps:

[0048] S1. Data processing and input.

[0049] In this embodiment, measurement data from the power system synchronization phasor measurement unit (PMU) and the SCADA system are first collected. The PMU node provides the measurement data: voltage amplitude. Phase angle Active power reactive power SCADA nodes provide measurement data: active power reactive power The system has a reference node with a fixed voltage amplitude and phase angle; the collected raw data is normalized or standardized for each sample. The system input features are as follows:

[0050] ① For each PV node ( ): [ , ];

[0051] ②For each PQ node ( ): [ , ];

[0052] ③The value of a Slack node is implicitly set.

[0053] Generate N such sample datasets for training and validation.

[0054] S2, Newton-Raphson module embedding.

[0055] In this embodiment, a custom module layer is created within the selected machine learning framework.

[0056] Within this module, a finite number of Newton-Raphson iterative algorithms are implemented. The core inputs of this Newton-Raphson module include:

[0057] ① The currently estimated admittance matrix Y;

[0058] ② The voltage setting value of the generator node, i.e., the input... Measured value;

[0059] ③ The active power injection settings for all non-Slack nodes, i.e., the input values ​​for PV nodes. and PQ node ;

[0060] ④ The reactive power setpoint of the PQ node, i.e., the input of the PQ node. .

[0061] The core outputs of this NR module include:

[0062] ①Predicted phase angle vectors of all non-Slack nodes ;

[0063] ②Predicted voltage magnitude vector at PQ node ;

[0064] ③Predicted reactive power vector of PV nodes .

[0065] The Newton-Raphson module requires the following internal adjustments:

[0066] ① Initialization of node voltages and phases;

[0067] ② Calculate the active power mismatch in each iteration. With reactive power mismatch ;

[0068] ③ Calculate the Jacobian matrix in each iteration and its block submatrix ;

[0069] ④ Solve the linear system in each iteration ;

[0070] ⑤ Update the phase angle in each iteration and PQ node voltage ;

[0071] ⑥ After the iteration is completed, calculate the reactive power output of the PV node.

[0072] S3. Model building and loss function.

[0073] In this embodiment, the complete NR-ML model is based on one or more "embedded Newton-Raphson modules".

[0074] The output predicted by the model is the output of the Newton-Raphson module mentioned above. , , .

[0075] The loss function is defined as the mean square error between the predicted output value and the actual measured value of the PV node:

[0076]

[0077] Where Y is the admittance matrix parameter to be optimized; N is the batch size; This refers to the number of generator nodes; For node i in the sample The predicted voltage amplitude after n NR iterations; For node i in the sample The predicted phase angle after n NR iterations; For node i in the sample Predicted reactive power after n NR iterations; For node i in the sample The actual measured voltage amplitude below; For node i in the sample The actual measured phase angle; For node i in the sample The actual measured reactive power.

[0078] The loss function L(Y) is minimized during training. The optimization target is the elements in the admittance matrix Y.

[0079] S4, Model Training and Automatic Differentiation.

[0080] In this embodiment, gradient descent-type algorithms are used for model training. The key advantage lies in leveraging the automatic differentiation capabilities of machine learning frameworks.

[0081] ① In forward propagation, the input feature data and the current parameter Y are processed by the embedded Newton-Raphson iterative module to obtain the predicted output, and finally the loss L(Y) is calculated.

[0082] ② During backpropagation, the framework automatically calculates the gradient of the loss L(Y) with respect to the parameter Y. Even though the Newton-Raphson module involves multiple iterative steps and the solution of complex linear equations, automatic differentiation can accurately calculate this gradient;

[0083] ③ The optimizer utilizes gradients Update parameters ,in This is the learning rate.

[0084] S5, Output and Application.

[0085] After training, the model parameters Y represent the estimated line admittance parameters. In the prediction phase:

[0086] ① Input new hybrid PV-PQ measurement data;

[0087] ② The model is predicted and calculated using the embedded NR module;

[0088] ③ Output the state estimation results of all nodes, i.e., voltage amplitude. With phase angle .

[0089] This invention proposes a joint estimation method for power system state and parameters based on physical information machine learning. By embedding Newton-Raphson power flow calculation into a machine learning architecture, it achieves coordinated optimization of power system admittance parameters and global node voltage phase. This method directly uses hybrid PV-PQ measurement data from real-world engineering scenarios, such as generator voltage and power, and load power, as input. A finite-step Newton iteration is hard-coded into the training process, significantly improving the accuracy and generalization ability of state estimation. Through a unique loss function design that only supervises generator node output, this invention reduces the dependence on high-cost PMU deployment while ensuring the accuracy of transmission network parameter identification and the reliability of overall network state awareness, providing high-fidelity physical model support for dynamic optimization and scheduling of the power grid.

[0090] The present invention will be further described below with reference to a specific embodiment:

[0091] To verify the effectiveness of the above method, this invention employs a standard IEEE 118-node system, inputting the active power and voltage amplitude of the PV nodes, and the active power and reactive power of the PQ nodes. The admittance matrix Y is initialized using exponential parameterization. An NR-ML model is constructed, and a loss function is set before model training. Using the Adam optimizer, set the learning rate to... Minimize loss function The parameters of the admittance matrix Y are updated by automatically differentiating and backpropagating the gradient. The final output is the total node voltage magnitude. Phase angle With the admittance matrix Y.

[0092] Experimental results show that the loss function decreases exponentially with the number of training epochs, such as... Figure 2 As shown, the experimental results verify the stability of the NR-ML framework. All NR iterations achieved monotonically convergent. The curves for n=3 and n=4 almost overlap, indicating that performance saturation was reached after 3 iterations. The experimental results also demonstrate a low learning rate. Compared to a high learning rate The final loss is one order of magnitude lower. Figure 3 Revealed admittance reconstruction error A phased decline, when hour, The value drops sharply by 50% from 0.49 when n=1 to 0.28 when n=2. The system reaches its optimal state when n=3. The experimental results indicate that a high learning rate leads to Precocious puberty has ceased. Figure 4 By comparing the actual admittance parameters with the reconstructed values ​​of 186 lines, the parameter estimation capability of the NR-ML method was fully verified. In the conductance component ( Figure 4As shown in (a), 93% of the line reconstruction errors are below 0.01 pu, with only a small number of lines exhibiting significant deviations. However, all reconstruction values ​​remain strictly positive, satisfying the physical constraints. In the susceptance component ( Figure 4 As shown in (b), the 100% line reconfiguration value remains negative, perfectly conforming to the physical laws, with the maximum error concentrated in the weak electrical correlation region. It is worth noting that the susceptance reconfiguration accuracy is better than that of the conductance, and its error distribution is more concentrated near zero, indicating that NR-ML is more sensitive to inductive parameters.

[0093] In summary, by utilizing the technical solutions described above, the NR embedded training architecture proposed in this invention fundamentally solves the coupling problem between "high-precision state perception" and "network parameter uncertainty" in power systems. By reconstructing the propagation path of the automatic differentiation mechanism on the physical equations, the state estimation error was stabilized at the order of magnitude in the IEEE 118-node verification, the parameter identification accuracy was improved by two orders of magnitude compared to the initial value, and the estimation accuracy was maintained at 90%+ for operating conditions outside the training set. This technology provides a new paradigm for real-time dynamic perception of smart grids.

Claims

1. A method for joint estimation of state and parameters of power systems based on Newton-Raphson guided machine learning, characterized by: S1. Construct a joint training framework that integrates physical models and data-driven approaches, and integrate power system power flow equations as intrinsic constraints for machine learning models. S2. Design a physical constraint layer and embed the derivative of the Jacobian matrix of the Newton-Raphson power flow equation into the backpropagation process of the neural network. S3. Establish a multi-task learning architecture and simultaneously train the coupled objective function of parameter estimation and state estimation until convergence accuracy is achieved.

2. The machine learning parameter and state estimation method embedded in power flow calculation according to claim 1, characterized in that, Step S1 specifically includes: S11. Generate a hybrid training dataset: Use historical running data overlaid with perturbation data generated by the physical model; S12. Define the input feature vector: including node voltage magnitude, phase angle, line active and reactive power, and topology identifier; S13. Construct a dual-channel input structure: the first channel inputs real-time measurement data, and the second channel inputs physical residuals based on power flow equations.

3. The machine learning parameter and state estimation method embedded in power flow calculation according to claim 2, characterized in that, The method for generating the disturbance data in step S11 is to inject normally distributed noise into the reference power flow solution: ； in, , The measurement error standard is set at 2%-5%.

4. The machine learning parameter and state estimation method embedded in power flow calculation according to claim 1, characterized in that, The physical constraint layer in step S2 is implemented as follows: S21. Define the residual term of the power flow equation as the physical loss function: ； S22. Calculate the partial derivatives of the power flow equations during the back propagation process: ； in, These are the weight parameters of the neural network.

5. The machine learning parameter and state estimation method embedded in power flow calculation according to claim 1, characterized in that, The multi-task learning architecture in step S3 includes: S31, Parameter Estimation Branch: Output Line Impedance Parameter Matrix ; S32, State estimation branch: Output voltage amplitude With phase angle ; S33. Coupling constraint term: Connects the outputs of two branches through the power flow equations: 。 6. The machine learning parameter and state estimation method embedded in power flow calculation according to claim 1, characterized in that, The training process of the method employs an alternating optimization strategy: S41. Fix the weights of the neural network and solve the power flow equations to obtain a physically consistent output. S42. Fix the physical constraints and update the network parameters through gradient descent; S43. Dynamically adjust the physical loss weighting coefficient: ； in, These are the initial coefficients. This is the attenuation factor.

7. The machine learning parameter and state estimation method embedded in power flow calculation according to claim 1, characterized in that, The convergence accuracy determination criterion is as follows: S51, Physical residual satisfies ; S52, Parameter estimation error rate is less than 3%; S53, Root Mean Square Error of State Estimation Voltage .

8. The machine learning parameter and state estimation method embedded in power flow calculation according to claim 1, characterized in that, The method is applied in bad data detection, including: S61. Utilize the physical constraint layer to output residual constant values: ； S62. Define the detection threshold: when Time is marked as bad data, where ; S63. Enable adversarial training module: Retrain after injecting bad data samples to improve robustness.

9. The machine learning parameter and state estimation method embedded in power flow calculation according to claim 1, characterized in that, The application process of the method in real-time control is as follows: S71. Obtain SCADA / PMU measurement data stream; S72, Load the pre-trained dual-channel neural network model; S73. Parallel output of parameter estimation and state estimation results to the energy management system; S74. After the control command is adjusted, repeat steps S71-S73 to achieve closed-loop update.

10. The machine learning parameter and state estimation method embedded in power flow calculation according to claim 1, characterized in that, The deployment architecture of the neural network is as follows: S81, Cloud Training Platform: Uses GPU clusters to train physical constraint models; S82, Edge Inference Module: Deploy a lightweight TensorRT engine in substations; S83, Encrypted transmission channel: Secure transmission of measurement data and estimation results is achieved through IPSec VPN.

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