Self-generation method for steady-state stable sample of electric power system

Abstract

The invention discloses a power system steady-state stable sample self-generation method, which is applied to the technical field of sample enhancement, and comprises the following steps: constructing a power system model based on topological information, equipment parameter information and operation scene information; determining a feasible region judgment rule based on the power system model; constructing a power flow correction model, a constraint soft cutting model and a stability margin correction model, and constructing a microprojectable operator based on the power flow correction model, the constraint soft cutting model and the stability margin correction model; constructing a sample generation model based on a preset constraint perception generation network; generating a first sample based on the sample generation model, correcting the first sample based on the microprojectable operator to obtain a second sample, and calculating a stability margin of the second sample based on a feasible region decision rule; and expanding the second sample based on the stability margin, the microprojectable operator and a preset correction rule to obtain a steady-state stable sample set of the power system.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of sample enhancement, in particular to a power system steady-state stability sample self-generation method. BACKGROUND

[0002] Power system steady-state operation samples are the basis for power grid analysis, dispatching and protection work. By recording key quantities such as voltage, phase angle, active or reactive power, power flow, distributed energy output and switch state under different loads, power generation, device topology and control settings, it provides measured or simulated evidence to describe the system operating point and behavior. High-quality and widely-covered steady-state samples are essential for parameter identification and calibration of physical mechanism models, training and verification of data-driven models, and robustness evaluation with uncertainty quantification; synchronous phase angle measurement and accurate time stamp can significantly improve the spatiotemporal consistency and diagnostic accuracy of the model. Therefore, building a systematic, well-labeled and covering the working domain steady-state operation sample library is a key prerequisite for improving the level of power grid simulation, operation decision and intelligent operation and maintenance.

[0003] Existing steady-state sample acquisition methods mainly rely on large-scale power flow simulation, optimization solution or random disturbance generation based on empirical distribution. These methods generally have high computational cost, uneven sample distribution, scarce boundary data and insufficient physical consistency. While using deep generation algorithms such as generative adversarial networks, variational autoencoders or diffusion models to improve sample coverage, they only fit the results at the data distribution level and fail to effectively embed physical laws and stability constraints, resulting in significant deficiencies in physical feasibility and engineering credibility. Another method introduces the idea of physical information neural network by incorporating the power flow equation residual into the loss function, but it is mainly aimed at power flow solution or parameter identification, and cannot generate rich, reasonably distributed and boundary-dense steady-state samples. At the same time, the non-differentiability of the power flow solution process makes it impossible for the neural network to achieve end-to-end optimization, limiting the learning depth and generalization ability of the model. SUMMARY

[0004] The present application provides a power system steady-state stability sample self-generation method to improve the efficiency of acquiring power system steady-state samples.

[0005] To solve the above technical problems, the present application provides a power system steady-state stability sample self-generation method, comprising:

[0006] Obtain the topology information, device parameter information and operation scene information of the power system, and construct a power system model based on the topology information, device parameter information and operation scene information; and determine the feasible region judgment rule based on the power system model;

[0007] a power flow correction model, a constraint soft clipping model and a stability margin correction model are constructed, and a differentiable projection operator is constructed based on the power flow correction model, the constraint soft clipping model and the stability margin correction model;

[0008] a conditional generation model is constructed based on a preset constraint perception generation network, and the conditional generation model is trained based on a preset loss function to obtain a sample generation model;

[0009] a first sample is generated based on the sample generation model, the first sample is corrected based on the differentiable projection operator to obtain a second sample, and a stability margin of the second sample is calculated based on the feasible region determination rule;

[0010] the second sample is expanded based on the stability margin, the differentiable projection operator and a preset correction rule to obtain a steady-state stability sample set of the power system.

[0011] The present application realizes comprehensive description of system structure, operation state and physical constraints by acquiring the topology information, equipment parameter information and operation scene information of the power system, constructing a power system model based on the information, and determining the feasible region judgment rule based on the model, which helps to clearly define the feasible boundary of steady-state stability constraints from the mechanism level, and improves the physical consistency and rationality of the sample generation process. By constructing a power flow correction model, a constraint soft clipping model and a stability margin correction model, and constructing a differentiable projection operator based on the three, the generated sample can realize end-to-end differentiable constraint mapping in the training and inference process, effectively avoiding the non-differentiable problem of traditional sample screening which relies on numerical iteration, thereby improving the convergence efficiency of the generation network and the sample physical constraint satisfaction rate. Further, by constructing a conditional generation model based on the preset constraint-aware generation network, and training the model based on the preset loss function, multiple constraints such as physical consistency loss, stability margin loss and constraint violation loss can be introduced in the generation process, realizing conditional perception modeling of the operation space of the complex power system, thereby generating high-quality samples that meet the multi-dimensional physical constraint and stability characteristic distribution, significantly improving the effectiveness and reliability of the generated data. Finally, by generating a first sample based on the sample generation model, and correcting the first sample to obtain a second sample using the differentiable projection operator, and calculating the stability margin of the second sample based on the feasible region judgment rule, the automatic physical correction and stability quantitative evaluation of the generated sample are realized, so that the generated sample satisfies the power balance constraint. Finally, by expanding the second sample based on the stability margin, the differentiable projection operator and the preset correction rule, the steady-state stability sample set of the power system is obtained, realizing the adaptive expansion of the sample in the feasible region boundary and the stability margin direction, which not only enhances the diversity and coverage of the sample set, but also ensures the physical effectiveness and interpretability of the generated sample, thereby efficiently constructing the steady-state stability sample library without large-scale real simulation calculation, improving the acquisition efficiency of the steady-state sample of the power system.

[0012] Further, the topology information, equipment parameter information and operation scene information of the power system are acquired, and a power system model is constructed based on the topology information, equipment parameter information and operation scene information; and a feasible region judgment rule is determined based on the power system model, comprising:

[0013] Acquiring the topology information, equipment parameter information and operation scene information of the power system;

[0014] Based on the topology information, a bus set and a line set of the power system are acquired, and based on the equipment parameter information, a generator set is acquired;

[0015] Based on the bus set, line set and generator set, a system power flow balance model is constructed, and based on the operation scene information, an operation constraint model is constructed;

[0016] construct a power system model based on the system power flow balance model and the operation constraint model;

[0017] determine a feasible region determination rule based on the power system model.

[0018] The present application forms a reproducible and structured system model input link through the processes of topology, device parameters, operation scene, bus set, line set and generator set, etc., ensures the consistency and traceability of the parameterization and numerical implementation of the subsequent power flow equation and constraint model, and the structured modeling makes the feasible region determination rule based on the explicit model source, facilitating engineering implementation, verification and cross-scene migration.

[0019] Further, the determination of the feasible region determination rule based on the power system model comprises:

[0020] construct a power flow Jacobian matrix based on the power system model, and take the minimum singular value of the power flow Jacobian matrix as a steady-state stability index;

[0021] and determine a feasible region determination rule based on the steady-state stability index.

[0022] The present application takes the minimum singular value of the power flow Jacobian matrix as a steady-state stability index and determines a feasible region determination rule accordingly, provides a quantitative and calculable stability margin measure, can convert the "steady-state feasibility" from an abstract concept into a testable numerical threshold, thereby realizing automatic labeling and grading of samples, facilitating accurate identification of instability critical states, directional generation of boundary samples, and risk assessment and control strategy verification based on the margin.

[0023] Further, the construction of the power flow correction model, the constraint soft clipping model and the stability margin correction model, the construction of the differentiable projection operator based on the power flow correction model, the constraint soft clipping model and the stability margin correction model comprises:

[0024] construct a power flow correction model based on a generalized inverse operator;

[0025] construct a constraint soft clipping model based on a differentiable function;

[0026] construct a stability margin correction model based on a singular vector corresponding to the minimum singular value and a preset fine-tuning step size;

[0027] splice the power flow correction model, the constraint soft clipping model and the stability margin correction model to construct a differentiable projection operator.

[0028] The application is based on a generalized inverse power flow correction model, a constraint soft clipping model based on a differentiable function, and a stability margin correction model based on a minimum singular vector, spliced to form an overall projection, realizing hierarchical processing of equality constraints, inequality constraints, and stability constraints, ensuring the stability of the numerical solution process, maintaining the differentiability of the overall operator to the generated network, facilitating the direct integration of physical constraints into the generated model training, thereby significantly reducing the proportion of physically infeasible samples during the generation stage, improving training efficiency and final sample quality.

[0029] Further, the constraint-aware generative network based on the preset constraint is used to construct a conditional generative model, and the conditional generative model is trained based on a preset loss function to obtain a sample generative model, including:

[0030] The constraint-aware generative network based on the preset constraint is used to construct a conditional generative model, which receives a preset random noise and a preset scene condition as input and generates a candidate sample;

[0031] A loss function is constructed based on a preset physical consistency loss, a stability margin loss, and a constraint violation loss, and the conditional generative model is iteratively trained based on the loss function to obtain a target generative model.

[0032] The constraint-aware generative network based on the preset constraint is used to construct a conditional generative model, which receives a preset random noise and a preset scene condition as input and generates a candidate sample;

[0033] Further, the constraint-aware generative network based on the preset constraint is used to construct a conditional generative model, and the conditional generative model is trained based on a preset loss function to obtain a sample generative model, including:

[0034] The preset random noise and the preset scene condition are input into the sample generative model to obtain a first sample;

[0035] The constraint-aware generative network based on the preset constraint is used to construct a conditional generative model, which receives a preset random noise and a preset scene condition as input and generates a candidate sample;

[0036] This invention enables seamless integration of statistical generation and physical correction by performing differentiable correction immediately after the generation stage, thereby maintaining the monitoring and repair of power flow balance and constraints throughout the sample flow. At the same time, by using stability margin as a quantitative indicator and calculating it at this step, it can be used to screen samples in real time and provide a judgment standard for subsequent boundary expansion, thereby improving the automation and reliability of sample screening.

[0037] Furthermore, the step of correcting the first sample based on the differentiable projection operator to obtain the second sample, and calculating the stability margin of the second sample based on the feasible region determination rule, includes:

[0038] The first sample is corrected based on the differentiable projection operator to obtain the second sample;

[0039] The minimum singular value of the second sample is calculated based on the feasible region determination rule, and the stability margin is calculated based on the minimum singular value and a preset margin threshold.

[0040] This invention calculates stability margin using minimum singular value and margin threshold, providing an objective and repeatable computational process for determining sample stability. It facilitates the unification of binary labels or continuous margin values ​​into the sample's metadata, enhancing the comparability of samples during training, validation, and evaluation. It also provides direct numerical evidence for robustness verification of margin-based risk grading, boundary enhancement strategies, and protection strategies.

[0041] Furthermore, the step of expanding the second sample based on the stability margin, differentiable projection operator, and preset correction rule to obtain a steady-state stable sample set of the power system includes:

[0042] Based on the stability margin and the preset stability threshold, the second sample is perturbed and expanded to obtain an initial sample set;

[0043] The initial sample set is corrected based on the differentiable projection operator to obtain the steady-state stable sample set of the power system.

[0044] This invention perturbs and expands the second sample based on stability margin and preset stability threshold, and corrects it with a differentiable projection operator to obtain the final sample set. It systematically creates high-density samples around the critical operating point, thereby addressing the scarcity of boundary states in the training data. This controlled expansion retains information about the stability-sensitive direction and ensures physical feasibility through projection.

[0045] Furthermore, the step of perturbating and expanding the second sample based on the stability margin and a preset stability threshold to obtain an initial sample set includes:

[0046] Obtain the absolute value of the stability margin. When the absolute value is less than a preset stability threshold, perturb and expand the second sample to obtain an initial sample set.

[0047] This invention limits the expansion trigger condition to perturbation expansion when the absolute value of the stability margin is less than a preset threshold, thereby achieving focused allocation and efficiency optimization of computing resources. Dense expansion is performed only on boundary and critical samples, avoiding redundant mutations on samples that are far from the critical region. This strategy saves the computational overhead of generation and correction, and maximizes the improvement of the model's discrimination and generalization performance in weak regions.

[0048] Furthermore, the perturbation amplification includes:

[0049] The second sample is perturbed and expanded based on the direction of the minimum singular vector of the second sample and a preset perturbation strategy.

[0050] This invention limits the perturbation expansion method to the direction of the minimum singular vector of the second sample and performs it according to a preset perturbation strategy. The generated expanded samples are rich in information in the "direction that has the greatest impact on system stability" and can effectively reveal the critical path of the system transitioning from steady state to instability. Therefore, this directional perturbation can improve the sensitivity of the boundary identifier and steady-state discrimination model to the weak direction of the system more than random expansion, thereby enhancing the overall sample set's support for steady-state security assessment and robust control strategy verification. Attached Figure Description

[0051] Figure 1 A flowchart illustrating a method for self-generating steady-state stability samples in a power system, provided by an embodiment of the present invention;

[0052] Figure 2 This is a schematic diagram of a power system steady-state stable sample self-generation system provided in an embodiment of the present invention. Detailed Implementation

[0053] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0054] The terms "first" and "second," etc., in the specification, claims, and drawings of this application are used to distinguish different objects, not to describe a specific order. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or apparatus that includes a series of steps or units is not limited to the listed steps or units, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to such processes, methods, products, or apparatus.

[0055] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0056] Example 1

[0057] See Figure 1 , Figure 1 This is a flowchart illustrating a method for self-generating steady-state stability samples in a power system, provided by an embodiment of the present invention. The method includes steps 101 to 105, as detailed below:

[0058] Step 101: Obtain the topology information, equipment parameter information, and operating scenario information of the power system; construct a power system model based on the topology information, equipment parameter information, and operating scenario information; and determine the feasible region determination rules based on the power system model.

[0059] In this embodiment, the steps of acquiring the topology information, equipment parameter information, and operating scenario information of the power system, constructing a power system model based on the topology information, equipment parameter information, and operating scenario information, and determining feasible region determination rules based on the power system model include:

[0060] Obtain topology information, equipment parameter information, and operating scenario information of the power system;

[0061] The set of busbars and lines of the power system are obtained based on the topology information, and the set of generators is obtained based on the equipment parameter information.

[0062] A system power flow balance model is constructed based on the bus set, line set, and generator set, and an operation constraint model is constructed based on the operation scenario information.

[0063] A power system model is constructed based on the system power flow balance model and the operation constraint model;

[0064] The feasible region determination rules are determined based on the power system model.

[0065] In this embodiment, firstly, the topology information, equipment parameter information, and operating scenario information of the power system are obtained through data sources such as the scheduling system, SCADA / EMS data, PMU, and equipment files. The topology information is used to identify the bus structure and branch connection relationships in the system. The equipment parameter information is used to determine the rated capacity, impedance, and regulation performance of each generator, transformer, and line. The operating scenario information includes load forecasting, renewable energy output, and standby configuration. Subsequently, based on the topology information, a bus set and a line set are extracted and constructed, and based on the equipment parameter information, a generator set is identified and established, clarifying the role and constraint boundaries of each component in the model.

[0066] In this embodiment, a system power flow balance model is constructed based on the aforementioned set, illustrating how to describe the supply and demand balance of active and reactive power from the perspectives of node power injection, bus voltage amplitude and phase angle, and branch admittance, and explaining how the power flow model adapts to different operating scenarios. Simultaneously, an operating constraint model is constructed based on operating scenario information, detailing how voltage upper and lower limits, generator active / reactive power upper and lower limits, branch thermal stability limits, reserve requirements, and necessary safety criteria are formalized into model constraints. Finally, a complete power system model is constructed based on the system power flow balance model and the operating constraint model to reflect the feasible operating set of the system under given scenarios and equipment parameters.

[0067] In this embodiment, let the bus set be B, the line set be ε, and the generator set be G. Define the bus voltage amplitude V. i With phase angle θ i Power generation P Gi Q Gi Load power P Li Q Li .

[0068] The system power flow balance model is as follows:

[0069]

[0070] In this embodiment, the system power flow balance model satisfies f P (i)=P Gi -P Li -P i =0,f Q (i)=Q Gi -Q Li -Q i =0.

[0071] In this embodiment, running the constraint model includes:

[0072]

[0073] Among them, Gi, Bij For the real and imaginary parts of the inter-bus admittance; S ij For the apparent power of the branch; V i min V i max These are the upper and lower limits of the bus voltage; These are the upper and lower limits of the generator's active power output. These are the upper and lower limits of the generator's reactive power output. For line thermal stability constraints.

[0074] In this embodiment, a reproducible and structured system model input link is formed through processes such as constructing bus sets, line sets, and generator sets based on topology, equipment parameters, and operating scenarios. This ensures that the parameterization and numerical implementation of subsequent power flow equations and constraint models are consistent and traceable. This structured modeling makes the feasible region determination rules based on a clear model source, which facilitates engineering implementation, verification, and cross-scenario migration.

[0075] In this embodiment, the step of determining the feasible region determination rule based on the power system model includes:

[0076] Based on the power system model, a power flow Jacobian matrix is ​​constructed, and the minimum singular value of the power flow Jacobian matrix is ​​used as a steady-state stability index.

[0077] The feasible region determination rule is then determined based on the steady-state stability index.

[0078] In this embodiment, based on the established power flow balance model and operation constraint model of the power system, a power flow Jacobian matrix is ​​constructed to characterize the sensitivity of the system power equation to changes in state variables, taking into account the coupling relationship between the system bus voltage magnitude and phase angle.

[0079] In this embodiment, the current flow Jacobian matrix is ​​constructed as follows:

[0080]

[0081] In this embodiment, the minimum singular value is obtained by performing singular value decomposition on the Jacobian matrix to reflect the steady-state stability of the power system under small disturbances at the current operating point. When the minimum singular value is large, the system has a strong recovery capability to disturbances and is in a stable and feasible operating state; when the minimum singular value approaches zero, the system operating point is close to the voltage collapse boundary or power flow limit, and can be considered infeasible. Therefore, the minimum singular value σ of the power flow Jacobian matrix is... min (J) Evaluate the steady-state stability of the system under small disturbances, i.e., the steady-state stability index.

[0082] In this embodiment, the steady-state stability index is combined with the system power flow equations and operational constraints to define the system's feasible region. This region is defined as the area where, under the premise of satisfying power balance and various operational constraints, the system's steady-state stability index is not lower than a set margin threshold. The resulting feasible region determination rule can be used to assess online whether the power system's operating point is within a safe and stable feasible region, providing a quantitative basis for dispatch optimization, safety margin analysis, and operational strategy adjustment, thereby ensuring the system's stability and safety under different operating scenarios.

[0083] In this embodiment, the feasible region determination rule is as follows:

[0084] Ω={x|f(x)=0,g(x)≤0,σ min (J(x))≥ε} (8)

[0085] Where x=[V,θ,P G Q G ,P L Q L [x] represents the system state vector; f(x) represents the power flow equation vector; g(x) represents the operating constraint vector; ε is the stability margin threshold, typically taken as 10. -3 ~10 -2 .

[0086] In this embodiment, the minimum singular value of the power flow Jacobian matrix is ​​used as the steady-state stability index, and the feasible region determination rule is determined accordingly. This provides a quantitative and computable stability margin measure, which can transform the "steady-state feasibility" from an abstract concept into a verifiable numerical threshold. This enables automatic labeling and classification of samples, which is beneficial for the accurate identification of instability critical states, the directional generation of boundary samples, and the verification of risk assessment and control strategies based on margin.

[0087] Step 102: Construct a power flow correction model, a constraint soft clipping model, and a stability margin correction model; and construct a differentiable projection operator based on the power flow correction model, the constraint soft clipping model, and the stability margin correction model.

[0088] In this embodiment, the construction of the power flow correction model, the constraint soft-pruning model, and the stability margin correction model, and the construction of a differentiable projection operator based on the power flow correction model, the constraint soft-pruning model, and the stability margin correction model, includes:

[0089] A power flow correction model is constructed based on generalized inverse operators;

[0090] Constructing a constrained soft clipping model based on differentiable functions;

[0091] A stability margin correction model is constructed based on the singular vector corresponding to the minimum singular value and the preset fine-tuning step size;

[0092] The power flow correction model, the constraint soft clipping model, and the stability margin correction model are spliced ​​together to construct a differentiable projection operator.

[0093] In this embodiment, for the generated candidate samples Construct a differentiable projection operator Π Ω (·) is used to map samples back to the physical feasible region.

[0094] In this embodiment, for the candidate samples to be mapped, a power flow correction model is first used to correct their physical consistency. This power flow correction model constructs a generalized inverse operator based on the Jacobian matrix of the power flow equation with respect to the state variables. An approximate Newton step is applied to the sample in the direction of the power balance residual to reduce power flow imbalance, thereby making the voltage magnitude and phase angle, and other state variables, closer to the solution that satisfies the power flow equation. In implementation, the generalized inverse can be numerically regularized to improve stability in near-singular cases, and upper limits are set on the correction step size and correction amplitude to avoid excessive instantaneous disturbances.

[0095] In this embodiment, the power flow correction model is:

[0096]

[0097] in, For the generalized inverse, Candidate samples; For candidate voltage magnitude vectors, This represents the voltage phase angle of all buses in the candidate sample. Let be the power flow residual vector, representing the state in the candidate state. The unbalance in the power flow equations is the set of residuals between active and reactive power injection and branch flow calculations. It is usually a 2n-dimensional vector (containing the active and reactive power residuals for each bus). is the generalized inverse of the Jacobian matrix J (e.g., the Moore–Penrose pseudo-inverse), used to map residuals to state corrections. This is the corrected voltage amplitude vector; This is the corrected voltage phase angle vector.

[0098] In this embodiment, a constrained soft-clipping model is then applied to smooth outbound variables. This constrained soft-clipping model uses a differentiable boundary function to perform a "soft" projection on the upper and lower limits of voltage, generator output, etc., which can strictly suppress outbounds while maintaining derivative continuity, making it easy to integrate seamlessly with gradient-based training or optimization processes. To balance clipping strength and differentiability, the clipping smoothness can be adjusted by the slope parameter of the differentiable function.

[0099] In this embodiment, taking voltage as an example, the clipping is achieved using a differentiable function:

[0100]

[0101] Where α V >0 controls the smoothness of the cut, V i + V represents the voltage amplitude obtained after "constrained soft trimming" of the i-th bus. i max V is the upper limit of the allowed voltage for the i-th bus. i min This is the lower limit of the allowed voltage for the i-th bus.

[0102] In this embodiment, the stability margin correction model fine-tunes key state variables such as voltage and phase angle along the sensitive direction corresponding to the minimum singular value to improve the minimum singular value of the Jacobian matrix, thereby expanding or restoring the steady-state margin of the system. In practice, the Jacobian matrix is ​​first decomposed into singular values ​​to obtain the most sensitive direction, and then the model moves in that direction with a limited amplitude at a preset fine-tuning step size. If necessary, it can be iterated multiple times until the margin threshold is met or the step limit is reached.

[0103] In this embodiment, the stability margin correction model is adjusted along the direction of the minimum singular value:

[0104]

[0105] Among them, v min For the corresponding singular vector, η σ To fine-tune the step size, η represents the feasible samples from the projection output; tanh(·) is the smoothing function used to implement differentiable boundary constraints; η σ Fine-tune the step size in the stability direction (typical value 10). -3 );v min V is the right singular vector corresponding to the minimum singular value; + The bus voltage magnitude vector is obtained after power flow correction and constraint soft clipping; θ + This is the voltage phase angle vector obtained after power flow correction and constraint soft clipping.

[0106] In this embodiment, a generalized reverse current correction model, a constraint soft pruning model based on differentiable functions, and a stability margin correction model based on minimum singular vectors are spliced ​​together to form an overall projection. This achieves hierarchical processing of equality constraints, inequality constraints, and stability constraints, ensuring the stability of the numerical solution process while maintaining the differentiability of the entire operator with respect to the generator network. This facilitates the direct incorporation of physical constraints into the generator model training, thereby significantly reducing the proportion of physically infeasible samples during the generation stage and improving training efficiency and final sample quality.

[0107] Step 103: Construct a conditional generation model based on a preset constraint-aware generative network, and train the conditional generation model based on a preset loss function to obtain a sample generation model;

[0108] In this embodiment, the construction of a conditional generation model based on a preset constraint-aware generative network, and the training of the conditional generation model based on a preset loss function to obtain a sample generation model, includes:

[0109] A conditional generation model is constructed based on a pre-defined constraint-aware generative network. The conditional generation model receives pre-defined random noise and pre-defined scene conditions as input and generates candidate samples.

[0110] A loss function is constructed based on preset physical consistency loss, stability margin loss, and constraint violation loss. The conditional generation model is then iteratively trained based on the loss function to obtain the target generation model.

[0111] In this embodiment, the conditional generation model G is constructed. θ (z,c), this model employs a conditional generative network architecture (such as a conditional GAN, conditional diffusion model, or conditional VAE, etc., which are alternative network structures) and receives random noise. The scenario conditions (c) (which may include load distribution, renewable energy output, topology configuration, and standby / failure assumptions) are used as inputs to output candidate samples. To ensure that the generated samples meet the physical and operational constraints of the power system, the generated samples are processed during the training process using the aforementioned differentiable projection operator Π. Ω The projected samples are obtained by mapping to the physical feasible region. Then, a composite training loss function is constructed based on the projected samples. The loss consists of four parts: physical consistency loss (used to measure the residual of the projected samples on the power flow equation, prompting the generator to learn to generate a sample distribution that satisfies power balance), constraint violation loss (using element-wise positive part operators to penalize out-of-bounds terms to suppress violations of operating constraints such as voltage, generator output and branch flow), stability margin loss (measuring the steady-state margin of the Jacobian matrix through the minimum singular value index, and applying penalties for cases below a preset threshold ε to improve the stability of the generated samples), and generator internal loss (such as reconstruction or noise prediction errors of the diffusion model, used to maintain the learning stability and sample diversity of the generator).

[0112] In this embodiment, the training loss function is:

[0113]

[0114] Where, λ f , λ g , λ σ , λ genFor the loss weight parameters; [·] + For element-wise positive part operators; This refers to the internal loss of the generator network (such as noise prediction error); This is the trainable parameter vector of the neural network.

[0115] In this embodiment, training employs an iterative gradient descent algorithm. Since both the projection operator and the steady-state margin index are designed to be differentiable, the loss can be backpropagated to the generator network parameters during training via the differentiable approximation of the projection operator and singular value decomposition. This allows the generative network to gradually converge between sample diversity and physical feasibility. To ensure numerical robustness and engineering usability, regularization or truncation of the Jacobian singular value decomposition can be applied during implementation, threshold saturation can be applied to the stability margin loss, and stepwise enhancement or curriculum learning can be applied to the constraint penalty. Furthermore, in scenarios where training is integrated into batch sampling, data augmentation and online fine-tuning can be combined to adapt to actual scheduling and operation scenarios. The trained target generation model can be used for high-quality, constrained candidate case generation, supporting engineering applications such as feasible domain coverage analysis, robust scheduling testing, data augmentation, and online safety assessment.

[0116] In this embodiment, a conditional generation model is constructed based on a constraint-aware generative network, and iteratively trained using a composite loss including physical consistency loss, stability margin loss, and constraint violation loss. Physical knowledge and stability criteria are embedded as training constraints into the generator's learning objective, enabling the generator to achieve a balance between sample diversity and physical feasibility. As a result, the generation model can more directly produce candidate samples that are close to the feasible region, reducing the burden of subsequent correction and improving the engineering applicability of the final sample set.

[0117] Step 104: Generate a first sample based on the sample generation model, correct the first sample based on the differentiable projection operator to obtain a second sample, and calculate the stability margin of the second sample based on the feasible region determination rule;

[0118] In this embodiment, the process of generating a first sample based on the sample generation model, correcting the first sample based on the differentiable projection operator to obtain a second sample, and calculating the stability margin of the second sample based on the feasible region determination rule includes:

[0119] The preset random noise and preset scene conditions are input into the sample generation model to obtain the first sample;

[0120] The first sample is corrected based on the differentiable projection operator to obtain the second sample, and the stability margin of the second sample is calculated based on the feasible region determination rule.

[0121] In this embodiment, during the generation stage, preset random noise and scene conditions are first input into the trained sample generation model to obtain original candidate samples (first samples); then, the candidate samples are input into the previously constructed differentiable projection operator to perform physical consistency correction and constraint recovery, thereby obtaining projection samples (second samples) that meet the formal requirements of power balance and operational constraints.

[0122] In this embodiment, by performing differentiable correction immediately after the generation stage, statistical generation and physical correction can be seamlessly integrated, thereby maintaining the monitoring and repair of power flow balance and constraints throughout the sample flow. At the same time, stability margin is used as a quantitative indicator and calculated in this step, which can be used to screen samples in real time and provide a judgment standard for subsequent boundary expansion, thereby improving the automation and reliability of sample screening.

[0123] In this embodiment, the step of correcting the first sample based on the differentiable projection operator to obtain the second sample, and calculating the stability margin of the second sample based on the feasible region determination rule, includes:

[0124] The first sample is corrected based on the differentiable projection operator to obtain the second sample;

[0125] The minimum singular value of the second sample is calculated based on the feasible region determination rule, and the stability margin is calculated based on the minimum singular value and a preset margin threshold.

[0126] In this embodiment, for the second sample, several operational constraint margin indices are calculated to quantify the margins from various constraint boundaries: these include voltage margin for each bus (i.e., the minimum difference between voltage and its upper and lower limits) and thermal stability margin for each branch (i.e., the difference between the branch's apparent power upper limit and the current actual flow amplitude). These margins are typically taken as the minimum values ​​for each bus or branch as global constraint margin indices to reflect the tightest bottlenecks. Simultaneously, the power flow Jacobian matrix is ​​reconstructed at the projected sample, and its minimum singular value is calculated to obtain the system's stability margin index d. σ This indicator represents the margin of the current operating point relative to the preset stability threshold ε.

[0127] In this embodiment, the physical constraint margin and stability margin are calculated:

[0128]

[0129] Where, ΔV, ΔS ij This refers to the operational constraint margin index.

[0130] In this embodiment, based on the above margin calculation rules, a binary stability label is defined: when the stability margin is non-negative (i.e., the minimum singular value is not lower than the threshold), it is labeled as "stable (1)", otherwise it is labeled as "instable (0)".

[0131]

[0132] Here, stable is the stability label, where 1 indicates stability and 0 indicates instability.

[0133] In this embodiment, the stability margin is calculated using the minimum singular value and the margin threshold, providing an objective and repeatable calculation process for determining the stability of samples. This facilitates the unification of binary labels or continuous margin values ​​into the sample's metadata, enhancing the comparability of samples during training, validation, and evaluation. It also provides direct numerical evidence for the robustness verification of margin-based risk grading, boundary enhancement strategies, and protection strategies.

[0134] Step 105: Expand the second sample based on the stability margin, differentiable projection operator and preset correction rule to obtain a steady-state stable sample set of the power system.

[0135] In this embodiment, the step of expanding the second sample based on the stability margin, differentiable projection operator, and preset correction rule to obtain a steady-state stable sample set of the power system includes:

[0136] Based on the stability margin and the preset stability threshold, the second sample is perturbed and expanded to obtain an initial sample set;

[0137] The initial sample set is corrected based on the differentiable projection operator to obtain the steady-state stable sample set of the power system.

[0138] In this embodiment, the second sample is perturbed and expanded based on the stability margin and a preset stability threshold, and then corrected with a differentiable projection operator to obtain the final sample set. High-density samples are systematically created around the critical operating point to compensate for the scarcity of boundary states in the training data. This controlled expansion retains information on the stability-sensitive direction and ensures physical feasibility through projection.

[0139] In this embodiment, the step of perturbating and expanding the second sample based on the stability margin and a preset stability threshold to obtain an initial sample set includes:

[0140] Obtain the absolute value of the stability margin. When the absolute value is less than a preset stability threshold, perturb and expand the second sample to obtain an initial sample set.

[0141] In this embodiment, based on the previously calculated stability margin d σSamples within the critical neighborhood (i.e., those satisfying (|d)) are selected based on a preset boundary threshold τ. σ Using samples of |<τ) as boundary seeds, perturbation expansion is performed to obtain an initial sample set. The obtained perturbation samples are then subjected to physical consistency correction and constraint recovery through differentiable projection operators, thereby mapping the perturbation points back to feasible samples that satisfy power flow balance and operational constraints and have improved stability margins.

[0142] In this embodiment, τ is the boundary sample threshold, typically set to 10. -3 ;

[0143] In this embodiment, the expansion trigger condition is limited to perturbation expansion when the absolute value of the stability margin is less than a preset threshold. This achieves focused allocation and efficiency optimization of computing resources, and intensive expansion is performed only on boundary and critical samples, avoiding redundant mutations on samples that are far from the critical region. This strategy saves the computational overhead of generation and correction, and maximizes the improvement of the model's discrimination and generalization performance in weak regions.

[0144] In this embodiment, the perturbation amplification includes:

[0145] The second sample is perturbed and expanded based on the direction of the minimum singular vector of the second sample and a preset perturbation strategy.

[0146] In this embodiment, for each boundary seed, along its corresponding minimum singular value direction vector v min A controlled perturbation is performed to generate augmented samples; the perturbation amplitude is controlled by a preset fine-tuning step size η (which can be set to a small amount to ensure that the samples remain close to the critical surface):

[0147] x aug =x * +ηv min (16)

[0148] Where η is the perturbation step size, typically 10. -4 ~10 -3 ;v min It is the direction vector corresponding to the minimum singular value, used to approximate the system's stable critical surface.

[0149] In this embodiment, the perturbation expansion method is limited to the direction of the minimum singular vector of the second sample and performed according to a preset perturbation strategy. The generated expanded sample is rich in information in the "direction that has the greatest impact on system stability" and can effectively reveal the critical path of the system transitioning from steady state to instability. Therefore, this directional perturbation can improve the sensitivity of the boundary identifier and steady-state discrimination model to the weak direction of the system more than random expansion, thereby enhancing the overall sample set's support for steady-state security assessment and robust control strategy verification.

[0150] In this embodiment, to obtain high-density critical boundary coverage, the expansion and projection loop can be executed iteratively in batches: in each round, perturbed samples are generated using the current boundary samples as seeds, projection corrections are made, and qualified samples are incorporated into the sample set until the predetermined boundary sample density or iteration limit is reached; during the iteration process, to avoid numerical instability or constraint violations, adaptive scaling or backtracking search should be used for the perturbation step size, and the constraint margin and changes in unfavorable directions should be checked and necessary backtracking performed after projection. This boundary self-filling and sample densification mechanism can generate rich training samples in the thin region near the stability limit to enhance the classifier or generative model's ability to identify the critical state, and ensure the feasibility of all expanded samples under physical and engineering constraints through differentiable projection, thereby providing a high-quality steady-state sample set for subsequent steady-state margin analysis, robust scheduling simulation, and data-based online safety assessment.

[0151] In this embodiment, training is performed again using the new scene condition c′:

[0152]

[0153] After discrimination and boundary enhancement, the parameters are updated.

[0154] Symbol explanation: The learning rate; c is the loss gradient; c′ is the new system condition parameters (such as load growth, topology reconstruction, output adjustment, etc.).

[0155] In this embodiment, candidate samples are first generated by a conditional generation network using random noise and current scene conditions as input. These candidate samples are then mapped to the physically feasible region using a differentiable projection operator to obtain projected samples. Next, discrimination and boundary reinforcement operations are performed on the projected samples, and a loss function for updating the generator is constructed accordingly. If the system topology or device parameters change, candidate samples are regenerated and projected using the new scene conditions as input. The loss gradient is calculated using the discriminator output and the boundary reinforcement strategy, and the generator parameters are updated according to gradient descent class rules, enabling the generation model to quickly adapt to the new operating environment. To ensure the stability and engineering usability of retraining, mini-batch updates, learning rate scheduling, regularization, and early stopping strategies can be employed during training. Historical samples are retained, or empirical replay is used to prevent catastrophic forgetting. Simultaneously, the differentiability and numerical regularization of the discriminator and projection operator are protected to ensure stable gradient calculation and effective update directions. This closed-loop method supports both offline batch training to obtain a globally convergent generative model and online, incremental fine-tuning to quickly restore or improve the physical feasibility and steady-state stability of sample generation in new scenarios such as load growth, topology reconfiguration, and power generation output adjustment. This provides continuous and reliable data support for subsequent steady-state margin assessment, robust scheduling, and online safety decision-making.

[0156] Please refer to Figure 2 , Figure 2 A schematic diagram of a power system steady-state stability sample self-generation system provided in an embodiment of the present invention includes: a system model construction module 201, a differentiable projection operator construction module 202, a sample generation model construction module 203, a sample generation module 204, and an expansion module 205;

[0157] The system model construction module is used to acquire the topology information, equipment parameter information, and operating scenario information of the power system, construct a power system model based on the topology information, equipment parameter information, and operating scenario information, and determine the feasible region determination rules based on the power system model.

[0158] The differentiable projection operator construction module is used to construct a power flow correction model, a constraint soft pruning model, and a stability margin correction model, and to construct a differentiable projection operator based on the power flow correction model, the constraint soft pruning model, and the stability margin correction model.

[0159] The sample generation model construction module is used to construct a conditional generation model based on a preset constraint-aware generation network, and to train the conditional generation model based on a preset loss function to obtain the sample generation model.

[0160] The sample generation module is used to generate a first sample based on the sample generation model, correct the first sample based on the differentiable projection operator to obtain a second sample, and calculate the stability margin of the second sample based on the feasible region determination rule.

[0161] The expansion module is used to expand the second sample based on the stability margin, differentiable projection operator and preset correction rule to obtain a steady-state stable sample set of the power system.

[0162] In this embodiment, the system model construction module is used to acquire the topology information, equipment parameter information, and operating scenario information of the power system; construct a power system model based on the topology information, equipment parameter information, and operating scenario information; and determine feasible region determination rules based on the power system model, including:

[0163] Obtain topology information, equipment parameter information, and operating scenario information of the power system;

[0164] The set of busbars and lines of the power system are obtained based on the topology information, and the set of generators is obtained based on the equipment parameter information.

[0165] A system power flow balance model is constructed based on the bus set, line set, and generator set, and an operation constraint model is constructed based on the operation scenario information.

[0166] A power system model is constructed based on the system power flow balance model and the operation constraint model;

[0167] The feasible region determination rules are determined based on the power system model.

[0168] In this embodiment, the system model construction module is used to determine the feasible region determination rules based on the power system model, including:

[0169] Based on the power system model, a power flow Jacobian matrix is ​​constructed, and the minimum singular value of the power flow Jacobian matrix is ​​used as a steady-state stability index.

[0170] The feasible region determination rule is then determined based on the steady-state stability index.

[0171] In this embodiment, the differentiable projection operator construction module is used to construct a power flow correction model, a constraint soft-pruning model, and a stability margin correction model. Based on the power flow correction model, the constraint soft-pruning model, and the stability margin correction model, a differentiable projection operator is constructed, including:

[0172] A power flow correction model is constructed based on generalized inverse operators;

[0173] Constructing a constrained soft clipping model based on differentiable functions;

[0174] A stability margin correction model is constructed based on the singular vector corresponding to the minimum singular value and the preset fine-tuning step size;

[0175] The power flow correction model, the constraint soft clipping model, and the stability margin correction model are spliced ​​together to construct a differentiable projection operator.

[0176] In this embodiment, the sample generation model construction module is used to construct a conditional generation model based on a preset constraint-aware generation network, and train the conditional generation model based on a preset loss function to obtain a sample generation model, including:

[0177] A conditional generation model is constructed based on a pre-defined constraint-aware generative network. The conditional generation model receives pre-defined random noise and pre-defined scene conditions as input and generates candidate samples.

[0178] A loss function is constructed based on preset physical consistency loss, stability margin loss, and constraint violation loss. The conditional generation model is then iteratively trained based on the loss function to obtain the target generation model.

[0179] In this embodiment, the sample generation module is used to generate a first sample based on the sample generation model, correct the first sample based on the differentiable projection operator to obtain a second sample, and calculate the stability margin of the second sample based on the feasible region determination rule, including:

[0180] The preset random noise and preset scene conditions are input into the sample generation model to obtain the first sample;

[0181] The first sample is corrected based on the differentiable projection operator to obtain the second sample, and the stability margin of the second sample is calculated based on the feasible region determination rule.

[0182] In this embodiment, the sample generation module is used to correct the first sample based on the differentiable projection operator to obtain a second sample, and to calculate the stability margin of the second sample based on the feasible region determination rule, including:

[0183] The first sample is corrected based on the differentiable projection operator to obtain the second sample;

[0184] The minimum singular value of the second sample is calculated based on the feasible region determination rule, and the stability margin is calculated based on the minimum singular value and a preset margin threshold.

[0185] In this embodiment, the expansion module is used to expand the second sample based on the stability margin, the differentiable projection operator, and the preset correction rule to obtain a steady-state stable sample set of the power system, including:

[0186] Based on the stability margin and the preset stability threshold, the second sample is perturbed and expanded to obtain an initial sample set;

[0187] The initial sample set is corrected based on the differentiable projection operator to obtain the steady-state stable sample set of the power system.

[0188] In this embodiment, the expansion module is used to perturb and expand the second sample based on the stability margin and a preset stability threshold to obtain an initial sample set, including:

[0189] Obtain the absolute value of the stability margin. When the absolute value is less than a preset stability threshold, perturb and expand the second sample to obtain an initial sample set.

[0190] In this embodiment, the perturbation amplification includes:

[0191] The second sample is perturbed and expanded based on the direction of the minimum singular vector of the second sample and a preset perturbation strategy.

[0192] This invention acquires topology, equipment parameters, and operational scenario information of a power system, constructs a power system model based on this information, and determines feasible region judgment rules based on this model. This achieves a comprehensive characterization of the system structure, operational state, and physical constraints, helping to clarify the feasible boundaries of steady-state stability constraints from a mechanistic perspective and improving the physical consistency and rationality of the sample generation process. Furthermore, by constructing a power flow correction model, a constraint soft-pruning model, and a stability margin correction model, and building a differentiable projection operator based on these three, the generated samples can achieve end-to-end differentiable constraint mapping during training and inference. This effectively avoids the non-differentiability problem of relying on numerical iteration in traditional sample selection, thereby improving the convergence efficiency of the generation network and the sample physical constraint satisfaction rate. Moreover, by constructing a conditional generation model based on a preset constraint-aware generation network and training this model based on a preset loss function, multiple constraints—physical consistency loss, stability margin loss, and constraint violation loss—can be introduced into the generation process. This enables conditional-aware modeling of the complex power system's operational space, generating high-quality samples that conform to multi-dimensional physical constraints and stability characteristic distributions, significantly improving the effectiveness and reliability of the generated data. Finally, a first sample is generated based on the sample generation model, and a second sample is obtained by correcting the first sample using a differentiable projection operator. Simultaneously, the stability margin of the second sample is calculated based on the feasible region determination rule, realizing automatic physical correction and quantitative stability assessment of the generated samples, ensuring that the generated samples satisfy power balance constraints. Finally, the second sample is expanded based on the stability margin, the differentiable projection operator, and preset correction rules to obtain a steady-state stable sample set of the power system. This achieves adaptive expansion of the samples in the feasible region boundary and stability margin directions, enhancing the diversity and coverage of the sample set while ensuring the physical validity and interpretability of the generated samples. Thus, a steady-state stable sample library can be efficiently constructed without large-scale real simulation calculations, improving the efficiency of obtaining steady-state samples for the power system.

[0193] In this embodiment of the invention, a terminal device is also provided, including a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor. When the processor executes the computer program, it implements the above-described method for self-generating steady-state samples of a power system.

[0194] In this embodiment of the invention, a computer-readable storage medium is also provided, which includes a stored computer program, wherein the computer program controls the device where the computer-readable storage medium is located to execute the above-described method for self-generating steady-state samples of a power system when it is running.

[0195] For example, a computer program can be divided into one or more modules, one or more of which are stored in memory and executed by a processor to perform the present invention. The one or more modules can be a series of computer program instruction segments capable of performing a specific function, which describe the execution process of the computer program in a terminal device.

[0196] The terminal device may be a desktop computer, laptop, handheld computer, or cloud server, etc. The terminal device may include, but is not limited to, a processor, memory, and display. Those skilled in the art will understand that the above components are merely examples of terminal devices and do not constitute a limitation on the terminal device. It may include more or fewer components, or combinations of certain components, or different components. For example, the terminal device may also include input / output devices, network access devices, buses, etc.

[0197] The processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor can be a microprocessor or any conventional processor. The processor is the control center of the terminal device, connecting all parts of the terminal device through various interfaces and lines.

[0198] Memory can be used to store computer programs and / or modules. The processor implements various functions of the terminal device by running or executing the computer programs and / or modules stored in the memory, and by accessing data stored in the memory. Memory can mainly include a program storage area and a data storage area. The program storage area can store the operating system, application programs required for at least one function (such as sound playback, text conversion, etc.), etc.; the data storage area can store data created based on the use of the mobile phone (such as audio data, text message data, etc.). In addition, memory can include high-speed random access memory, and can also include non-volatile memory, such as hard disks, RAM, plug-in hard disks, smart media cards (SMC), secure digital cards (SD cards), flash cards, at least one disk storage device, flash memory device, or other volatile solid-state storage devices.

[0199] The module based on the self-generated steady-state stability samples of the power system, if implemented as a software functional unit and sold or used as an independent product, can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the above embodiments of the present invention can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. Those skilled in the art can understand and implement this without any creative effort.

[0200] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the scope of protection of the present invention. In particular, it should be noted that any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention for those skilled in the art.

Claims

1. A method for self-generating steady-state stability samples in a power system, characterized in that, include: The system acquires topology information, equipment parameter information, and operating scenario information of the power system; constructs a power system model based on the topology information, equipment parameter information, and operating scenario information; and determines feasible region determination rules based on the power system model. Construct a power flow correction model, a constraint soft clipping model, and a stability margin correction model, and construct a differentiable projection operator based on the power flow correction model, the constraint soft clipping model, and the stability margin correction model; A conditional generation model is constructed based on a preset constraint-aware generative network, and the conditional generation model is trained based on a preset loss function to obtain a sample generation model. A first sample is generated based on the sample generation model, the first sample is corrected based on the differentiable projection operator to obtain a second sample, and the stability margin of the second sample is calculated based on the feasible region determination rule. The second sample is expanded based on the stability margin, differentiable projection operator, and preset correction rule to obtain a steady-state stable sample set of the power system.

2. The method for self-generating steady-state stability samples in a power system as described in claim 1, characterized in that, The process involves acquiring the topology information, equipment parameter information, and operating scenario information of the power system, and then constructing a power system model based on the topology information, equipment parameter information, and operating scenario information. And based on the power system model, the feasible region determination rules are determined, including: Obtain topology information, equipment parameter information, and operating scenario information of the power system; The set of busbars and lines of the power system are obtained based on the topology information, and the set of generators is obtained based on the equipment parameter information. A system power flow balance model is constructed based on the bus set, line set, and generator set, and an operation constraint model is constructed based on the operation scenario information. A power system model is constructed based on the system power flow balance model and the operation constraint model; The feasible region determination rules are determined based on the power system model.

3. The method for self-generating steady-state stability samples in a power system as described in claim 2, characterized in that, The rules for determining the feasible region based on the power system model include: Based on the power system model, a power flow Jacobian matrix is ​​constructed, and the minimum singular value of the power flow Jacobian matrix is ​​used as a steady-state stability index. The feasible region determination rule is then determined based on the steady-state stability index.

4. The method for self-generating steady-state stability samples in a power system as described in claim 3, characterized in that, The construction of the power flow correction model, the constraint soft-pruning model, and the stability margin correction model, and the construction of a differentiable projection operator based on the power flow correction model, the constraint soft-pruning model, and the stability margin correction model, includes: A power flow correction model is constructed based on generalized inverse operators; Constructing a constrained soft clipping model based on differentiable functions; A stability margin correction model is constructed based on the singular vector corresponding to the minimum singular value and the preset fine-tuning step size; The power flow correction model, the constraint soft clipping model, and the stability margin correction model are spliced ​​together to construct a differentiable projection operator.

5. The method for self-generating steady-state stability samples in a power system as described in claim 4, characterized in that, The process of constructing a conditional generation model based on a preset constraint-aware generative network and training the conditional generation model based on a preset loss function to obtain a sample generation model includes: A conditional generation model is constructed based on a pre-defined constraint-aware generative network. The conditional generation model receives pre-defined random noise and pre-defined scene conditions as input and generates candidate samples. A loss function is constructed based on preset physical consistency loss, stability margin loss, and constraint violation loss. The conditional generation model is then iteratively trained based on the loss function to obtain the target generation model.

6. The method for self-generating steady-state stability samples in a power system as described in claim 5, characterized in that, The process of generating a first sample based on the sample generation model, correcting the first sample based on the differentiable projection operator to obtain a second sample, and calculating the stability margin of the second sample based on the feasible region determination rule includes: The preset random noise and preset scene conditions are input into the sample generation model to obtain the first sample; The first sample is corrected based on the differentiable projection operator to obtain the second sample, and the stability margin of the second sample is calculated based on the feasible region determination rule.

7. The method for self-generating steady-state stability samples in a power system as described in claim 6, characterized in that, The step of correcting the first sample based on the differentiable projection operator to obtain the second sample, and calculating the stability margin of the second sample based on the feasible region determination rule, includes: The first sample is corrected based on the differentiable projection operator to obtain the second sample; The minimum singular value of the second sample is calculated based on the feasible region determination rule, and the stability margin is calculated based on the minimum singular value and a preset margin threshold.

8. The method for self-generating steady-state stability samples in a power system as described in claim 1, characterized in that, The expansion of the second sample based on the stability margin, differentiable projection operator, and preset correction rule to obtain a steady-state stable sample set of the power system includes: Based on the stability margin and the preset stability threshold, the second sample is perturbed and expanded to obtain an initial sample set; The initial sample set is corrected based on the differentiable projection operator to obtain the steady-state stable sample set of the power system.

9. The method for self-generating steady-state stability samples in a power system as described in claim 8, characterized in that, The step of perturbating and expanding the second sample based on the stability margin and a preset stability threshold to obtain an initial sample set includes: Obtain the absolute value of the stability margin. When the absolute value is less than a preset stability threshold, perturb and expand the second sample to obtain an initial sample set.

10. The method for self-generating steady-state stability samples in a power system as described in claim 1, characterized in that, The perturbation amplification includes: The second sample is perturbed and expanded based on the direction of the minimum singular vector of the second sample and a preset perturbation strategy.

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