Wind power AC / DC system transient stability evaluation method based on positive definite structure neural Lyapunov function

Abstract

The invention discloses a wind power AC / DC system transient stability evaluation method based on a positive definite structure neural Lyapunov function. The method comprises the following steps: constructing a state space physical model containing a wind power AC / DC system, and collecting real-time operation data; determining a candidate Lyapunov function based on the neural network; updating parameters of the Lyapunov function based on a gradient method; generating a counter example set based on a projection gradient descent algorithm, and verifying a Lyapunov function based on an SMT solver; the method comprises the following steps: acquiring the operation state of a wind power-containing AC / DC system to obtain a training set, constructing a total training set based on the training set, a counter-example set and a verification set, and training based on the total training set to obtain a trained neural Lyapunov network; and evaluating the transient stability state of the wind power AC / DC system based on the trained neural Lyapunov network. According to the method, the local Lyapunov function of the complex power system can be effectively learned, and the transient stability of the alternating-current and direct-current hybrid system containing wind power can be quickly and accurately evaluated.

Description

Technical Field

[0001] This invention relates to the field of power system stability analysis technology, specifically to a transient stability assessment method for wind power AC / DC systems based on positive definite structural neural Lyapunov functions. Background Technology

[0002] With the large-scale integration of new energy sources into modern power systems, renewable energy and power electronic devices, represented by voltage source converters, are rapidly penetrating the power system landscape, profoundly changing its form. Simultaneously, the large-scale grid connection of power electronics has led to increasingly complex transient stability problems in power systems, giving them new dynamic characteristics, and causing the operating state of modern power systems to approach the stability boundary. Therefore, accurate and rapid transient stability assessment is crucial in the planning, operation, and control of power systems. However, finding the Lyapunov function for general complex power systems is a challenging task, urgently requiring a tool capable of calculating the Lyapunov function and rapidly and accurately assessing the transient stability of AC / DC hybrid systems including wind power. Summary of the Invention

[0003] To overcome the defects and shortcomings of existing technologies, this invention provides a transient stability assessment method for wind power AC / DC systems based on positive definite structure neural Lyapunov functions. This invention can effectively learn the local Lyapunov functions of complex power systems and can quickly and accurately assess the transient stability of AC / DC hybrid systems containing wind power. It applies positive definite structure neural Lyapunov functions to more complex systems with wind turbines and flexible DC renewable energy.

[0004] To achieve the above objectives, the present invention adopts the following technical solution:

[0005] This invention provides a transient stability assessment method for wind power AC / DC systems based on positive definite structural neural Lyapunov functions, comprising the following steps:

[0006] Construct a state-space physical model of an AC / DC system containing wind power and collect real-time operational data;

[0007] Candidate Lyapunov functions are determined based on neural networks;

[0008] Gradient-based methods for updating the parameters of the Lyapunov function;

[0009] A set of counterexamples is generated based on the projection gradient descent algorithm, and the Lyapunov function is verified based on the SMT solver.

[0010] The operating status of AC / DC systems including wind power is collected to obtain a training set. A total training set is constructed based on the training set, the counterexample set, and the validation set. The training is performed based on the total training set to obtain the trained neural Lyapunov network.

[0011] Evaluate the transient stability of wind power AC / DC systems based on trained neural Lyapunov networks.

[0012] As a preferred technical solution, candidate Lyapunov functions are determined based on neural networks, specifically including:

[0013] Construct a scalar function, represented as:

[0014] ;

[0015] in, for A connected set in a 3D real space. scalar function Along the vector field Lie's time derivative;

[0016] When collecting real-time running data The energy value obtained by substituting into the scalar function When the system is in a transiently stable state, it is determined that the system is in a transiently stable state. At that time, the system was determined to be in an unstable risk zone. Indicates the critical energy threshold;

[0017] Define the valid area: ,in, For state space; State vector The Euclidean norm, A pre-defined positive scalar is used to define the search boundary for the stability region estimation, allowing the neural network to operate within the effective region. We learned about candidate Lyapunov functions.

[0018] As a preferred technical solution, the gradient-based method for updating the parameters of the Lyapunov function specifically includes:

[0019] The Lyapunov function is expressed as:

[0020] ;

[0021] ;

[0022] in, It is a function that maps states to positive definite matrices. This indicates real-time running data. Represents a constant greater than zero. Represents the identity matrix;

[0023] Construct the loss function, expressed as:

[0024] ;

[0025] Where α is a positive hyperparameter;

[0026] Updating the parameters of the Lyapunov function based on minimizing the loss function

[0027] As a preferred technical solution, The positive definite property is transformed into a positive constraint on its diagonal elements, expressed as:

[0028] ;

[0029] in, and For the weights and biases of each layer of the neural network, Indicates the number of fully connected layers. This represents a monotonically non-decreasing nonlinear activation function. For the neural network The output vector of the layer, Represented by vector The elements are a diagonal matrix composed of diagonal elements.

[0030] As a preferred technical solution, a set of counterexamples is generated based on the projection gradient descent algorithm, specifically including:

[0031] Set the objective function, effective region, initial learning rate, and maximum number of iterations;

[0032] A set of initial state samples is randomly selected from the effective region, and each state sample is iteratively updated.

[0033] Calculate the gradient of the objective function at the current state, update it along the gradient descent direction according to the current learning rate, and use the projection operator to map the updated result back to the effective region to obtain the tentative state.

[0034] After all state samples have completed the iteration, the final state set is used as a potential set of counterexamples.

[0035] As a preferred technical solution, each state sample is iteratively updated, specifically including:

[0036] Calculate the gradient of the objective function at the current state, update it along the gradient descent direction according to the current learning rate, and use the projection operator to map the updated result back to the effective region to obtain the tentative state.

[0037] Calculate an index that measures the local curvature or gradient change rate, determine whether the current step size meets the preset convergence condition, output the tentative state if it meets the condition, and reduce the learning rate and recalculate the tentative state until the preset convergence condition is met.

[0038] Update the current state to a tentative state.

[0039] As a preferred technical solution, the Lyapunov function is verified based on the SMT solver, specifically as follows:

[0040] ;

[0041] in, , Indicates the valid area. This represents the critical energy threshold. This represents the Lyapunov function.

[0042] As a preferred technical solution, a total training set is constructed based on the training set, the negative example set, and the validation set, and training is performed based on the total training set, specifically including:

[0043] The operating status of AC / DC systems containing wind power is uniformly sampled within a preset effective area to obtain a training set;

[0044] Combine the training set, the current set of negative examples, and the validation set into a total training set;

[0045] Based on the total training set, calculate the current Lyapunov function and its derivative with respect to the system state, calculate the current loss value, and update the parameters of the neural network.

[0046] After the parameters are updated, multiple samples are randomly selected within the effective region, and an adversarial search is performed based on the adaptive projection gradient descent method to search for potential counterexamples.

[0047] Mathematical verification is performed based on the SMT solver. If the verification is successful, the neural Lyapunov function is considered to have been solved successfully, and the final function model is output for online evaluation.

[0048] The present invention also provides a computer-readable storage medium storing a program that, when executed by a processor, implements the transient stability assessment method for wind power AC / DC systems based on positive definite structured neural Lyapunov functions as described above.

[0049] The present invention also provides a computer device, including a processor and a memory for storing processor-executable programs, wherein when the processor executes the program stored in the memory, it implements the transient stability assessment method for wind power AC / DC systems based on positive definite structured neural Lyapunov functions as described above.

[0050] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0051] (1) Addressing the modeling and stability quantification issues of complex new energy power grids: This invention adopts a dynamic modeling and energy function mapping technique based on the motion equations of voltage amplitude / phase of doubly-fed wind turbines and flexible DC systems. This solves the technical problem that traditional energy function methods struggle to handle power electronic grids containing non-negligible transfer conductance and complex controller dynamics, leading to an inability to accurately describe the transient behavior of the system. It achieves the technical effect of accurately capturing and quantifying the dynamic characteristics of power systems with a high proportion of new energy after a fault, thus enabling precise assessment of the transient stability of wind power AC / DC hybrid systems.

[0052] (2) Addressing the conservative estimation problem of the stability boundary (attraction domain) of high-dimensional nonlinear systems: This invention adopts a technical solution based on positive definite structure neural Lyapunov function approximation and maximization of the attraction domain loss function training. This solves the technical problem that existing technologies (such as the sum of squares SOS method) are limited by polynomial degree and system dimension, resulting in the estimated stability domain (attraction domain ROA) being much smaller than the actual stability range of the system, leading to overly conservative evaluation results. This significantly expands the estimation range of the effective stability domain, making the evaluation results closer to the real physical boundary verified by time-domain simulation, thereby reducing unnecessary generator tripping or load shedding control in power grid operation.

[0053] (3) To address the problems of poor timeliness of online evaluation and difficulty in high-dimensional space verification: This invention adopts an adversarial training technical solution that combines projective gradient descent (PGD) to find counterexamples with strict verification by SMT solver. This solves the technical problem that directly finding state points that violate stability conditions (i.e. potential instability points) in high-dimensional nonlinear state space is computationally intensive and time-consuming, making it difficult to meet the timeliness of online power grid evaluation. This achieves the technical effect of accelerating model convergence speed, quickly screening out critical instability states in the power grid, and providing dispatchers with a fast and reliable transient stability auxiliary decision-making tool. Attached Figure Description

[0054] Figure 1 This is a schematic diagram of the overall process of the transient stability assessment method for wind power AC / DC systems based on positive definite structural neural Lyapunov functions of the present invention.

[0055] Figure 2 This is a flowchart of the neural network training process of the present invention;

[0056] Figure 3 This is a schematic diagram of the network framework of the neural Lyapunov function of this invention.

[0057] Figure 4 This is a flowchart illustrating the application of the present invention to the transient stability assessment of AC / DC systems with wind farms. Detailed Implementation

[0058] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0059] Example 1

[0060] like Figure 1 As shown, this embodiment provides a transient stability assessment method for wind power AC / DC systems based on positive definite structural neural Lyapunov functions. This method maps the physical state data of the power system to generalized energy values ​​and determines whether the system is stable by comparing the energy values ​​with a critical threshold. The method includes the following steps:

[0061] S1: Based on Lyapunov's stability theorem, the stability of AC / DC systems containing wind power is evaluated using scalar functions. A state-space physical model of the AC / DC system containing wind power is constructed, and real-time operational data is collected. Specifically, this includes:

[0062] (1) Real-time acquisition of wind power AC / DC system operation data through wide-area measurement systems or sensors, as system state variables. Based on the device type in the system, the state variables... Specifically, it includes:

[0063] Doubly fed induction generator (DFIG): Collects rotor speed Rotor current , and the controller's integral state variables; Flexible DC transmission system (VSC): acquiring active power. reactive power and DC side voltage Synchronous Generator (SG): Collects the generator's power angle. Angular velocity deviation and transient potential .

[0064] (2) Based on Kirchhoff's laws of the power system and the dynamic differential equations of each device, establish nonlinear state equations describing the dynamic changes of the above physical quantities. Based on Lyapunov's stability theorem, a scalar function is constructed. To assess stability. Physically, this function... It is considered a generalized transient energy function, and its evaluation logic is as follows: If there exists a continuously differentiable function that satisfies the following conditions... :

[0065] ;

[0066] In the formula, for A connected set in a 3D real space, containing the equilibrium points (i.e., the origin) of the system. ), A continuously differentiable scalar function Along the vector field The Lie time derivative.

[0067] The specific evaluation method is as follows: The estimated set of the attraction domain is defined as follows: ,in It is a positive constant (representing the critical energy threshold). This is based on the real-time system state data. The energy value obtained by substituting into the function When the system is in a transiently stable state, it is determined that it can automatically recover to the equilibrium point; when When the system is deemed to be in an unstable risk zone, control measures must be taken.

[0068] (2) By assuming that a correct Lyapunov function can be found by utilizing the powerful representational ability of neural networks. ,in, These are the parameters of the neural network, and this candidate Lyapunov function can evaluate the transient stability of the system.

[0069] To enhance the structure of the problem, consider a valid region of the following form, centered at the origin. The norm sphere is represented as: ,in, For state space; State vector The Euclidean norm; A pre-defined positive scalar is used to define the search boundary for stability region estimation. This strictly convex set will be very helpful for the subsequent PGD algorithm. Physically, this effective region defines the range of power grid operating conditions (such as the maximum allowable range of voltage and frequency fluctuations) that require stability search and verification. Furthermore, the goal of this embodiment is to maximize the effective region. Learn efficient local Lyapunov functions .

[0070] S2: Construct a learning module for updating Lyapunov function parameters based on gradient methods, and train a neural network to accurately fit the generalized energy distribution of the system, specifically including:

[0071] (1) In order to satisfy the conditions of the Lyapunov function as much as possible and reduce the optimization difficulty of the neural network, the neural Lyapunov function is designed and assumed to be expressed as:

[0072] ;

[0073] In the formula, It is a function that maps states to positive definite matrices, which is defined by parameters. Neural network construction; It is a positive definite matrix, and in this embodiment, we take... , It is the identity matrix. The constant, Physically, this represents the generalized transient energy of a power system. Since the degree to which a system deviates from its equilibrium point after a fault can be measured by the magnitude of its energy, this step constructs a positive definite neural network structure to ensure that the value of this energy function remains positive under any non-equilibrium state. This aligns with the non-negative energy characteristic of physical systems, thus solving the problem that traditional purely data-driven methods cannot guarantee physical constraints.

[0074] (2) The candidate neural Lyapunov function satisfies the first two conditions of the stability theorem for any parameter The neural network structure is constructed , It is positive definite, and only at the equilibrium point. The function disappears at the point. Similar to a quadratic function, the correlation matrix function... It enhances the flexibility of learning, determining different effective areas. The shape of the function in the equation. These properties define the shape of the function in the equation. It has the expressive power to describe the differences between different state quantities (safe state and unsafe state).

[0075] (3) By adding To enhance The lower bound, making ,in It is a type Function, upper bound function Based on The activation function of the output layer is used for construction; however, in neural learning, it is difficult to directly handle positive definite constraints, which are addressed through hypothesis functions or matrices. Since it is a diagonal matrix, the positive definite property of the matrix is ​​transformed into a positive constraint on its diagonal elements:

[0076] ;

[0077] In the formula, and For the weights and biases of each layer of the neural network, Indicates the number of fully connected layers. This represents a monotonically non-decreasing nonlinear activation function. For the neural network The output vector of the layer (i.e., the output layer). Represented by vector The elements are a diagonal matrix consisting of diagonal elements. A non-negative activation function is selected. It can be guaranteed The elements are non-negative, thus ensuring that... It is a positive definite (or semi-positive definite) diagonal matrix;

[0078] This invention will Select as The function is set up so that the one-dimensional tensor output by the neural network is the diagonal element of the positive definite matrix, and a squared activation function is connected after the output layer of the neural network. This activation function guarantees that the diagonal elements are positive, meaning that the diagonal matrix composed of the elements output by this neural network is positive. It is a positive definite matrix.

[0079] (4) To train the learning module to update θ and increase the likelihood of constraint satisfaction, the following loss function can be selected:

[0080] ;

[0081] The above equation can be approximated by using a subset of finite points sampled within the effective region R(γ):

[0082] ;

[0083] To accurately characterize the system's tolerance to disturbances, the attraction domain must be maximized. This is achieved by introducing the following loss term to maximize the system's performance within the effective region. The area of ​​attraction within:

[0084] ;

[0085] In the formula, α is a positive hyperparameter, and the first term represents the function. The degree to which the Lyapunov function condition is violated, the second term can effectively expand the size of the attraction field to a certain extent. By minimizing the expression, the learning module will return potential candidate neural Lyapunov functions.

[0086] The specific meaning and purpose of parameter updates: The first loss (stability constraint): aims to penalize... In this case, physically, by minimizing this term, the energy function learned by the neural network is forced to correctly reflect the physical law of energy decay over time, ensuring the accuracy of the evaluation. The second loss term (expanding the attraction domain) aims to maximize the system's energy within the effective region. The attraction domain within the grid. Physically, this means tapping into the grid's potential stability capabilities, avoiding overly conservative assessments (i.e., preventing a system that is clearly stable from being misjudged as unstable), thereby reducing unnecessary generator tripping operations.

[0087] By minimizing the above expression, the learning module will return an optimized candidate neural Lyapunov function.

[0088] S3: Construct a falsification module that uses the Projection Gradient Descent (PGD) algorithm to generate counterexamples and uses a Satisfiability Modulo Theories (SMT) solver to rigorously verify the neural Lyapunov function, in order to eliminate the safety blind spot in the evaluation model. Specifically, this includes:

[0089] (1) Verifying counterexamples can be approximated as the following optimization problem:

[0090] ;

[0091] The goal is to find the set of states (counterexamples) that violate the negative deterministic condition to the greatest extent within the effective region. Physically, counterexamples refer to those hidden high-risk operating state points that appear stable to the neural network at present but actually do not meet the energy decay condition (i.e., may lead to system instability).

[0092] (2) The solution to the problem is approximated using the PGD method. The role of the PGD algorithm is to quickly search for the power grid states most prone to misjudgment in the high-dimensional state space and feed them back as difficult samples to the training module. The projected gradient method is a continuous optimization algorithm for solving problems with simple constraints, mainly for solving the problem. ,in It is a convex set. The PGD method first moves one step along the descent direction, then determines whether it is within the feasible region. For Iterative updates :

[0093] ;

[0094] In the formula, Indicates passage Each dimension projects the gradient update step onto the domain. superior, It is the learning rate for PGD, a non-negative constant. The domain can be defined. Projection operator within for:

[0095] ;

[0096] In fact closest state The state, which guarantees that after each iteration All located in Internally. Specifically, for the selected valid region (a closed convex set). Hilbert's projection theorem demonstrates that any point not in the set... There exists a unique projection. For the selected valid region It is a standard norm ball, representing any point not in the set. The projection onto the convex set is:

[0097] ;

[0098] Step size during calculation The choice of step size significantly affects the convergence speed. The selection must meet the following Armijo line search criteria:

[0099] ;

[0100] In the formula, .

[0101] (3) After each gradient update of the neural network, from the closed convex set Take a random sample set As the initial running point for PGD, after K iterations of PGD, a set of samples that may violate the stability condition is returned. =PGD( Finally from Only the actual set of counterexamples is retained. These counterexamples High-risk states will be reintroduced into the training set for the next round of neural network parameter updates. The goal of this process is to continuously patch the defects in the energy function until no states violating stability conditions are found throughout the entire effective region. Finally, through rigorous verification using the SMT solver, a formally verified, blind-zone-free neural Lyapunov function model is obtained. .

[0102] Specifically, the process of generating counterexamples using the adaptive projective gradient descent (PGD) algorithm (i.e., the process of finding the set of states that violate the stability condition in step S3) includes the following sub-steps:

[0103] 1) Initialization settings:

[0104] Set the objective function (i.e., the negative value of the time derivative of the neural Lyapunov function) The aim is to find the violation point where the derivative is nonnegative and the effective region. (Allowable fluctuation range of physical state), initial learning rate and the maximum number of iterations A set of initial state samples is randomly selected from the effective region. .

[0105] 2) Sample iterative update:

[0106] For the initial sample set Each state sample in ,implement Updated in each iteration. ( Proceed according to the following logic:

[0107] A. Trial Step and Projection: Calculating the Current State gradient of the objective function Based on the current learning rate Update along the gradient descent direction and utilize the projection operator. Map the updated results back to the valid region. Inside, a tentative state was reached. Its physical meaning is to attempt to move in the direction most likely to cause system instability, while ensuring that the state does not exceed the operating boundaries allowed by the power grid.

[0108] B. Adaptive step size adjustment (While loop logic): Calculates an indicator that measures the rate of change of local curvature or gradient. (For example, calculated based on the ratio of gradient change to displacement). Determine if the current step size meets the preset convergence condition (i.e., determine...). Is it less than the threshold? If the conditions are not met ( This indicates that the current step size is too large, causing oscillations or out-of-bounds errors. In this case, reduce the learning rate (e.g., ...). ), and recalculate the trial state using the new learning rate. Continue until the condition is met. If the condition is met ( ): Accept this tentative state.

[0109] C. State Update and Step Expansion: Update the current state to a tentative state, i.e. At the same time, if the degree to which the conditions are met is high (indicating that the current search direction is flat and can be accelerated), the learning rate is increased before the next iteration (e.g., ( ), to speed up the search.

[0110] 3) Output results:

[0111] When all samples are completed After each iteration, the final set of states is collected as a potential set of counterexamples T', which is used for subsequent screening and network parameter correction.

[0112] PGD ​​can quickly find potential counterexamples, but it cannot guarantee the discovery of closed convex sets. The set of all counterexamples is insufficient, so the completeness of the recently developed SMT solver is still needed to verify the satisfiability of the following equations to validate the correctness of the neural Lyapunov:

[0113] ;

[0114] In the formula, , This is a numerical error parameter used to avoid numerical problems near the origin. It is selected by... , making This is several orders of magnitude smaller than the range of the state variables. Specifically, if the SMT module does not return any counterexamples, the completeness of the SMT solver parameters δ is guaranteed. In the effective area All states within the range satisfy the Lyapunov conditions.

[0115] like Figure 2 The diagram illustrates the learning process of the neural Lyapunov function. Overall, the falsification module consists of SMT and PGD. PGD is used to quickly find counterexamples, and SMT is used to verify the correctness of the neural Lyapunov function. To continuously update the set in each learning iteration... To reduce the effective area The loss function within the total training set. This invention will use the total training set... Divided into static fixed training sets and counterexample set and Partial. Through the effective area Uniform sampling within the fixed training set After each gradient update of the neural network, PGD iteration is used to quickly find the set of counterexamples. When PGD fails to find a set of counterexamples, the SMT solver is used to check whether the correct Lyapunov function has been successfully learned. If the verification is successful, training is complete. Otherwise, the counterexamples generated by the SMT solver are added to (or merged into) the set of counterexamples. Then, the above neural network training process is repeated based on the updated dataset.

[0116] like Figure 4 As shown, the process of solving the neural Lyapunov function (i.e., the complete iterative process of training and validation) includes the following steps:

[0117] (1) Initialization and Sampling: First, the set of counterexamples (i.e., the set of high-risk states) T'' used to store the set of counterexamples that violate the stability condition and the set of high-risk states T''. Initialize to an empty set. Within the preset valid region. (That is,) uniform sampling is performed within the range to generate a fixed training set containing several typical operating state points. .

[0118] (2) Constructing the total training set: Entering the iterative training loop. At the beginning of each iteration, the above fixed training set is... With the currently accumulated set of counterexamples T'' and The sets are merged to form the total training set. Physical meaning: To ensure that the model not only learns normal power grid conditions, but also focuses on learning difficult samples that have historically led to misjudgments.

[0119] (3) Neural network parameter update: based on the total training set Calculate the current neural Lyapunov function. The loss value is calculated based on its derivative with respect to the system state. The current loss value is then calculated according to the loss function defined in step S2, and the parameters of the neural network are updated using an optimization algorithm (Adam optimizer). This is to ensure that the properties of the function conform as closely as possible to the physical constraints of the generalized energy function (i.e., positive definiteness and negative definiteness of the derivative).

[0120] (4) Potential counterexample search: After the parameters are updated, random examples are selected within the valid region. For each sample, the aforementioned Adaptive Projective Gradient Descent (PGD) method is called to perform an adversarial search, seeking the method that maximally violates the negative definite condition (i.e., ...) under the current network parameters. The state set of T'' is defined. The search results are filtered, retaining only the actual counterexamples T'' confirmed to violate the stability condition.

[0121] (5) Rigorous validation and model output: Determine whether the PGD method has found counterexamples:

[0122] 1) If PGD finds a counterexample (T'' is not empty): it means that the current model has obvious flaws, so proceed directly to the next round of iteration and add T'' to the training set for targeted training.

[0123] 2) If PGD does not find any counterexamples (T'' is empty): This indicates that the model performs well at the numerical search level. In this case, a rigorous mathematical verification is performed using the Satisfiability Modular Theory (SMT) solver to check if the conditions are met. The solution (i.e., the verification set) ).

[0124] If SMT verification is successful ( (Empty): This proves that there are no instability-violation dead zones in the entire effective region, determines that the neural Lyapunov function has been successfully solved, and outputs the final function model. For online evaluation.

[0125] If SMT verification fails ( Not empty: This indicates that a hidden violation still exists. Update the set with new counterexamples discovered by SMT. Then return to step (2) and continue the next round of training and correction until it passes the verification.

[0126] Therefore, the Lyapunov function approximation based on neural networks can be learned using a training dataset. The overall framework of the neural Lyapunov function is similar to the Physical Information Neural Network (PINN). Figure 3 As shown, a neural Lyapunov network framework was obtained. The output of the designed positive definite network was regarded as a trial solution of the system stability scalar function. The known dynamic model was encoded into the neural network loss function for training.

[0127] S4: A positive-definite Lyapunov neural network consisting of a learner and a falsifier performs online assessment and early warning of transient stability of the power system. The specific steps are as follows:

[0128] (1) Online monitoring: The status data of the power grid after the fault is cleared, which was collected in real time in step S1. The input is fed into the neural Lyapunov network that has been trained in step S3.

[0129] (2) Energy calculation and discrimination: The network forward propagation calculates the generalized energy value of the system at the current moment. Compare this value with the critical energy threshold determined in step S1. Compare them.

[0130] (3) Stability determination: The calculated energy value With the preset attraction domain boundary threshold Comparison: If If the system is determined to be in a transient stable state, it will recover to the synchronous operating point by relying on its own damping; if The system is determined to be in a transient instability risk zone. At this point, the assessment system immediately sends an early warning signal to the dispatch center and triggers emergency control measures such as generator tripping, load shedding, or emergency DC power support to prevent the accident from escalating and to ensure the safety of the power grid.

[0131] Example 2

[0132] This embodiment provides a storage medium, which may be a ROM, RAM, disk, optical disk, or other storage medium. The storage medium stores one or more programs. When the program is executed by the processor, it implements the transient stability assessment method for wind power AC / DC systems based on positive definite structured neural Lyapunov functions as described in Embodiment 1.

[0133] Example 3

[0134] This embodiment provides a computing device, which may be a desktop computer, laptop computer, smartphone, PDA handheld terminal, tablet computer or other terminal device with display function. The computing device includes a processor and a memory. The memory stores one or more programs. When the processor executes the program stored in the memory, it implements the transient stability assessment method for wind power AC / DC systems based on positive definite structure neural Lyapunov functions of Embodiment 1.

[0135] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A transient stability assessment method for wind power AC / DC systems based on positive definite structural neural Lyapunov functions, characterized in that, Includes the following steps: Construct a state-space physical model of an AC / DC system containing wind power and collect real-time operational data; Candidate Lyapunov functions are determined based on neural networks; Gradient-based methods for updating the parameters of the Lyapunov function; A set of counterexamples is generated based on the projection gradient descent algorithm, and the Lyapunov function is verified based on the SMT solver. The operating status of AC / DC systems including wind power is collected to obtain a training set. A total training set is constructed based on the training set, the counterexample set, and the validation set. The training is performed based on the total training set to obtain the trained neural Lyapunov network. Evaluate the transient stability of wind power AC / DC systems based on trained neural Lyapunov networks.

2. The transient stability assessment method for wind power AC / DC systems based on positive definite structural neural Lyapunov functions according to claim 1, characterized in that, Candidate Lyapunov functions are determined based on neural networks, specifically including: Construct a scalar function, represented as: ； in, for A connected set in a 3D real space. scalar function Along the vector field Lie's time derivative; When collecting real-time running data The energy value obtained by substituting into the scalar function When the system is in a transiently stable state, it is determined that the system is in a transiently stable state. At that time, the system was determined to be in an unstable risk zone. Indicates the critical energy threshold; Define the valid area: ,in, For state space; State vector The Euclidean norm, A pre-defined positive scalar is used to define the search boundary for the stability region estimation, allowing the neural network to operate within the effective region. We learned about candidate Lyapunov functions.

3. The transient stability assessment method for wind power AC / DC systems based on positive definite structural neural Lyapunov functions according to claim 2, characterized in that, Gradient-based methods for updating the parameters of the Lyapunov function include: The Lyapunov function is expressed as: ； ； in, It is a function that maps states to positive definite matrices. This indicates real-time running data. Represents a constant greater than zero. Represents the identity matrix; Construct the loss function, expressed as: ； Where α is a positive hyperparameter; The parameters of the Lyapunov function are updated based on minimizing the loss function.

4. The transient stability assessment method for wind power AC / DC systems based on positive definite structural neural Lyapunov functions according to claim 3, characterized in that, Will The positive definite property is transformed into a positive constraint on its diagonal elements, expressed as: ； in, and For the weights and biases of each layer of the neural network, Indicates the number of fully connected layers. This represents a monotonically non-decreasing nonlinear activation function. For the neural network The output vector of the layer, Represented by vector The elements are a diagonal matrix composed of diagonal elements.

5. The transient stability assessment method for wind power AC / DC systems based on positive definite structural neural Lyapunov functions according to claim 1, characterized in that, A set of counterexamples is generated based on the projective gradient descent algorithm, specifically including: Set the objective function, effective region, initial learning rate, and maximum number of iterations; A set of initial state samples is randomly selected from the effective region, and each state sample is iteratively updated. Calculate the gradient of the objective function at the current state, update it along the gradient descent direction according to the current learning rate, and use the projection operator to map the updated result back to the effective region to obtain the tentative state. After all state samples have completed the iteration, the final state set is used as a potential set of counterexamples.

6. The transient stability assessment method for wind power AC / DC systems based on positive definite structural neural Lyapunov functions according to claim 5, characterized in that, For each state sample, iterative updates are performed, specifically including: Calculate the gradient of the objective function at the current state, update it along the gradient descent direction according to the current learning rate, and use the projection operator to map the updated result back to the effective region to obtain the tentative state. Calculate an index that measures the local curvature or gradient change rate, determine whether the current step size meets the preset convergence condition, output the tentative state if it meets the condition, and reduce the learning rate and recalculate the tentative state until the preset convergence condition is met. Update the current state to a tentative state.

7. The transient stability assessment method for wind power AC / DC systems based on positive definite structural neural Lyapunov functions according to claim 2, characterized in that, The Lyapunov function was verified based on the SMT solver, specifically expressed as follows: ； in, , Indicates the valid region. This represents the critical energy threshold. Let Lyapunov function be represented.

8. The transient stability assessment method for wind power AC / DC systems based on positive definite structural neural Lyapunov functions according to claim 1, characterized in that, A total training set is constructed based on the training set, negative example set, and validation set. Training is then performed based on this total training set, specifically including: The operating status of AC / DC systems containing wind power is uniformly sampled within a preset effective area to obtain a training set; Combine the training set, the current set of negative examples, and the validation set into a total training set; Based on the total training set, calculate the current Lyapunov function and its derivative with respect to the system state, calculate the current loss value, and update the parameters of the neural network. After the parameters are updated, multiple samples are randomly selected within the effective region, and an adversarial search is performed based on the adaptive projection gradient descent method to search for potential counterexamples. Mathematical verification is performed based on the SMT solver. If the verification is successful, the neural Lyapunov function is considered to have been solved successfully, and the final function model is output for online evaluation.

9. A computer-readable storage medium storing a program, characterized in that, When the program is executed by the processor, it implements the transient stability assessment method for wind power AC / DC systems based on positive definite structural neural Lyapunov functions as described in any one of claims 1-8.

10. A computer device comprising a processor and a memory for storing a processor-executable program, characterized in that, When the processor executes the program stored in the memory, it implements the transient stability assessment method for wind power AC / DC systems based on positive definite structural neural Lyapunov functions as described in any one of claims 1-8.

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