Robust optimization oriented physical guided diffusion model construction method and system

Abstract

This invention discloses a method and system for constructing a physically guided diffusion model for robust optimization, belonging to the technical field of power system optimization and scheduling. The method includes: constructing a wind farm topology information map and a topology-aware variational autoencoder (VAE). The VAE includes an encoder and a decoder. The encoder encodes the input wind power operation data into latent variables, and the decoder restores the latent variables to the wind power scenario. A diffusion model is constructed. The gradient of the predefined power system operating cost function onto the wind power scenario is projected onto the tangent space of the latent manifold to obtain a gradient-guided operator, which is then introduced into the diffusion model in the next round of solution. This method achieves dimensionality reduction mapping of high-dimensional wind power scenarios by constructing a topology-aware VAE that integrates wind farm topology information and introduces a gradient-guided diffusion process based on the power system operating cost gradient, thus solving the technical problem of low efficiency in solving traditional robust optimization subproblems.

Description

Technical Field

[0001] This invention belongs to the technical field of power system optimization and dispatching, specifically relating to a method and system for constructing a physical guided diffusion model for robust optimization. Background Technology

[0002] In power systems with high wind power penetration, the strong randomness and volatility of wind power output significantly increase the difficulty of system dispatching. Two-stage robust optimization is widely used in the combination and economic dispatch of units with a high proportion of wind power because it can ensure the feasibility of dispatching schemes under the worst-case scenario.

[0003] Traditional two-stage robust optimization subproblems are typically solved using mixed-integer linear programming and column constraint generation algorithms, which suffer from high computational complexity, slow solution speed, and difficulty in adapting to large-scale power grid scenarios. In recent years, diffusion models, due to their ability to generate high-dimensional data, have been attempted for wind power scenario generation. However, existing diffusion models are mostly unguided random generation, unable to target the worst-case wind power scenarios. Furthermore, these models do not effectively integrate the spatiotemporal correlation characteristics of wind power with the electrical topology information of the power grid, resulting in generated scenarios that easily deviate from physical laws and are difficult to directly use for solving robust optimization subproblems.

[0004] Therefore, it is urgent to construct a diffusion model that integrates topological embedding and physical guidance mechanisms to achieve directional, efficient, and compliant generation of the worst wind power scenarios, so as to improve the solution efficiency and practicality of the two-stage robust optimization. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of existing technologies by providing a method for constructing a physical guided diffusion model for robust optimization. This method achieves dimensionality reduction mapping of high-dimensional wind power scenarios by constructing a topology-aware variational autoencoder that integrates wind farm topology information, introduces a gradient-oriented guided diffusion process based on the power system operating cost, and utilizes the Jacobi transpose to achieve manifold constraints, thus solving the technical problem of low efficiency in solving traditional robust optimization subproblems.

[0006] To solve the above-mentioned technical problems, the present invention adopts the following technical solution: In a first aspect, the present invention provides a method for constructing a physically guided diffusion model for robust optimization, characterized by comprising the following steps: Construct a wind farm topology information map and a topology-aware variational autoencoder. The variational autoencoder includes an encoder and a decoder. The encoder uses the wind farm topology information map as a physical prior to encode the input wind power operation data into latent variables. The decoder restores the latent variables into a wind power scenario, so that all latent variables form a latent manifold in a low-dimensional space. A diffusion model is constructed and operates on the latent manifold. The diffusion model processes the latent variables and outputs them to the decoder. The gradient of the predefined power system operating cost function with respect to the wind power scenario is calculated, and the gradient is projected onto the tangent space of the potential manifold to obtain the gradient guiding operator. The gradient guiding operator is then introduced into the diffusion model in the next round of solution.

[0007] In one possible implementation, the wind farm topology information graph specifically includes a set of wind farm nodes, a set of interconnected edges between wind farms, and an adjacency matrix.

[0008] In one possible implementation, the encoder of the topology-aware variational autoencoder includes a one-dimensional convolutional layer, a graph attention network layer, a flattening layer, and a fully connected layer connected in series. The one-dimensional convolutional layer extracts the temporal features of wind power output at each node based on the input wind power operation data. The graph attention network layer performs topology aggregation based on the wind farm topology information graph and the temporal features to obtain a node feature matrix. The flattening layer flattens the node feature matrix into a one-dimensional vector. The fully connected layer maps the one-dimensional vector into latent parameters. The latent variables are obtained by reparameterizing the latent parameters.

[0009] In one possible implementation, the one-dimensional convolutional layer extracts the temporal features of wind power output based on the input wind power operation data, including: the one-dimensional convolutional layer of the encoder extracts the temporal features of wind power output through convolution kernel sliding operation and nonlinear activation.

[0010] In one possible implementation, the graph attention network layer performs topology aggregation based on the wind farm topology information graph and temporal features to obtain a node feature matrix, including: Step 1. Obtain the time-series features and wind farm topology information map; Step 2. For each node in the wind farm topology graph, calculate the attention score of all its neighboring nodes; Step 3. Perform Softmax normalization on the attention score of each node to obtain normalized attention weights; Step 4. Based on the normalized attention weights, the temporal features of all neighboring nodes are weighted and summed, and then processed by an activation function to obtain aggregated topological features; Step 5. Use the single-level topological aggregation feature output by the previous layer graph attention network as the sole input to the next layer graph attention network, and repeat steps 2 to 4 to complete the serial stacking of several layers of graph attention networks to obtain the node feature matrix.

[0011] In one possible implementation, projecting the gradient onto the tangent space of the latent manifold to obtain the gradient guiding operator includes: using the transpose of the Jacobian matrix as the manifold projection operator, projecting the gradient onto the tangent space of the latent manifold to obtain the gradient guiding operator. The Jacobian matrix is ​​the first-order partial derivative matrix of the high-dimensional output of the decoder with respect to the low-dimensional input, wherein the Jacobian matrix is ​​the first-order partial derivative matrix of the high-dimensional output of the decoder with respect to the low-dimensional input.

[0012] In one possible implementation, the diffusion model includes a forward fixed-noise Markov chain and a reverse parameterized denoising Markov chain equipped with a pre-trained neural network. The forward fixed-noise Markov chain is a parameterless pure mathematical calculation process. Based on a preset Gaussian noise scheduling rule, the latent variables are gradually noised to obtain pure Gaussian noise. The neural network is used to predict the noise values ​​added during the forward noise addition process based on the noisy latent variables and time steps. The inverse parameterized denoising Markov chain derives the denoising mean based on the noise prediction value, and then progressively reverses the denoising of pure Gaussian noise based on the denoising mean.

[0013] In one possible implementation, the inverse denoising process after introducing the gradient-guided operator includes: The basic denoised mean is calculated based on the noise prediction value output by the neural network. A gradient-guided operator is introduced to adjust the base denoising mean using an additive correction method, resulting in a fused gradient-guided denoising mean. The correction formula is as follows:

[0014] in, For gradient-guided operators; As a weighting factor, Based on the denoised mean; Based on the denoised mean, the latent variable z corresponding to the pure Gaussian noise is... T Initially, starting in reverse order of time steps from T to 1, process the noisy latent variable z at each step. t Perform noise reduction operation; After completing the inverse denoising for all time steps, the final denoised latent variables are output.

[0015] In one possible implementation, after each robust optimization subproblem is solved, the gradient of the power system operating cost function with respect to the current wind power scenario is recalculated, the gradient guidance operator is updated, and the updated gradient guidance operator is introduced into the next round of diffusion model.

[0016] Secondly, the present invention also provides a system for constructing a robustly optimized physical guided diffusion model, the system comprising: The manifold mapping module is used to construct a wind farm topology information map and a topology-aware variational autoencoder. The variational autoencoder includes an encoder and a decoder. The encoder uses the wind farm topology information map as a physical prior to encode the input wind power operation data into latent variables. The decoder restores the latent variables to the wind power scenario, so that all latent variables form a latent manifold in a low-dimensional space. A diffusion generation module is used to construct a diffusion model that runs on the latent manifold, and the diffusion model processes the latent variables and outputs them to the decoder; The physical guidance module is used to calculate the gradient of the predefined power system operating cost function with respect to the wind power scenario, project the gradient onto the tangent space of the potential manifold to obtain the gradient guidance operator, and introduce the gradient guidance operator into the diffusion model in the next round of solution.

[0017] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. By mapping high-dimensional wind power scenarios to low-dimensional latent manifolds through topology-aware variational autoencoders, the generation dimension of diffusion models is significantly reduced, and the solution speed is improved.

[0018] 2. By introducing a power system physical cost gradient as a guide, the diffusion model is transformed from random generation to targeted search of the worst-case scenario, thus adapting to robust optimization requirements. Attached Figure Description

[0019] Figure 1 This is a flowchart of a method for constructing a robustly optimized physical guided diffusion model according to an embodiment of the present invention; Figure 2 This is a flowchart illustrating the solution of subproblems using the physical-guided diffusion model in an embodiment of the present invention. Figure 3 This is a flowchart illustrating feature aggregation in the attention network layer according to an embodiment of the present invention; Figure 4 A flowchart illustrating the inverse denoising process following the introduction of a gradient-guided operator in an embodiment of the present invention; Figure 5 This is a structural diagram of the physical guided diffusion model construction system for robust optimization according to an embodiment of the present invention; Figure 6 This is a flowchart illustrating the solution of a two-stage robust optimization model for a power system with high wind power penetration, as described in an embodiment of the present invention. Detailed Implementation

[0020] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0021] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0022] The present invention will be further described below with reference to specific embodiments, but these are not intended to limit the scope of the invention.

[0023] This invention provides a method for constructing a physical guided diffusion model for robust optimization. This physical guided diffusion model is used to solve subproblems in a two-stage robust optimization model for look-ahead scheduling that takes into account reserve capacity. Before constructing this model, a two-stage robust optimization model for look-ahead scheduling that takes into account reserve capacity is first constructed. This invention first constructs a two-stage robust optimization model framework with a min-max-min structure.

[0024] The goal of the first phase is to minimize the baseline scheduling cost and reserve capacity reservation cost of the generating units. Decision variables This includes the unit's baseline output and reserve capacity.

[0025] (1.1) , (1.2) , , (1.3) , (1.4) , (1.5) , (1.6) , (1.7) , (1.8) , (1.9) in Let i be the output of thermal power unit i at time t; , These represent the upper and lower standby times for thermal power unit i at time t, respectively. The output cost of thermal power units; Costs reserved for reserve capacity of thermal power units; For the number of units, For the number of loads; Let i be the output of wind turbine i at time t; Let i be the output force of load i at time t; For forward scheduling time windows; , , These are the power transfer distribution factors of thermal power units, wind power units, and load-corresponding nodes on line l, respectively. This represents the active power flow transmission limit of line l; This represents the total number of power grid lines. This represents the maximum output of thermal power unit i. , Let represent the maximum power output of thermal power unit i during its uphill and downhill runs per unit time, respectively. Equation (1.2) represents the source-load power balance constraint. Equation (1.3) represents the line active power flow constraint based on DC power flow. Equations (1.4)-(1.9) represent the relevant constraints of thermal power units: Equations (1.4)-(1.5) represent the upper and lower limits of output considering reserve capacity; Equations (1.6)-(1.7) represent the reserve capacity constraint, indicating that the reserve capacity at time t cannot exceed the limit of the thermal power unit's ramp rate; Equations (1.8)-(1.9) represent the cross-time period ramp rate constraint of the unit, limiting the rate of change of thermal power output and reserve capacity in adjacent time periods.

[0026] The second stage, after the uncertainty of wind power is revealed, is to minimize the penalty cost incurred in maintaining system power balance and power flow security, the mathematical form of which is as follows: (2.1) , (2.2) , (2.3) , (2.4) , (2.5) , (2.6) , (2.7) , (2.8) , , (2.9) in Let be the amount of wind curtailed by the i-th wind turbine at time t; Let be the load shedding amount of the i-th load at time t; Let i be the cost of wind curtailment for the i-th wind turbine. The load shedding cost for the i-th load; , , Let i represent the output of the i-th thermal power unit, wind power unit, and the output after load adjustment, respectively. Equations (2.2)-(2.4) calculate the output of each type of unit after adjustment; Equations (2.5)-(2.7) indicate that the adjustment amount of each unit must be strictly limited within the reserve capacity reserved in the first stage; Equation (2.8) is the system power balance constraint after considering the adjustment amount; Equation (2.9) is the line active power flow constraint after considering the adjustment amount.

[0027] The mathematical form can be summarized as follows: (3) in , A, b, B, c, D, G, g, H, F, and C are the constraint coefficients for the compact form, respectively. For only with uncertainty The relevant deviation vector.

[0028] Understandably, the robust feasibility test of the sub-problems in the aforementioned two-stage robust optimization model aims to find the worst-case wind power scenario within a given set of uncertain wind power. The diffusion model proposed in this invention is used to replace traditional algorithms to solve this sub-problem.

[0029] Meanwhile, this application adopts the Bertsimas-Sim polyhedral uncertainty set. Describe the fluctuation range of wind power: (4) in, This refers to the ultra-short-term forecast value of wind power; , These represent the maximum permissible lower and upper deviations of wind power relative to the predicted value; The benchmark value used for normalizing the deviation magnitude is taken as... ; The uncertainty budget parameter is used to limit the total cumulative normalized bias of all wind farms over the entire time period, thereby adjusting the conservatism of the model's robustness.

[0030] After determining the application scenarios of this invention, such as Figure 1 As shown, this embodiment of the invention provides a method for constructing a physically guided diffusion model for robust optimization, including the following steps: S1. Construct a wind farm topology information map and a variational autoencoder capable of topology awareness.

[0031] In the second stage of robust optimization, costs are incurred. The main reason for the increase is that wind power fluctuations trigger the transmission limits of the power grid's lines or the ramp-up limits of the turbines, forcing the system to adopt load shedding or wind curtailment to maintain balance. When two wind farms have similar sensitivities to the same line or regulation constraints, they exhibit a high degree of correlation at the mathematical optimization level, tending to maximize system operational risk through fluctuations in the same direction.

[0032] In one possible implementation, a wind farm topology information map Specifically, this includes wind farm node sets. Set of inter-wind farm related edges and the adjacency matrix A, and the elements of the adjacency matrix. A ij Calculate using the following formula: (5) In equation (5), Represents the elements in the adjacency matrix. As a balance factor, The Pearson correlation coefficient is used to ensure that the generated severe scenarios are both high-risk and probabilistically reliable. This represents the wind power operation data at the i-th node; For the first Each wind farm is connected to the entire network. The power transfer distribution factor (PTDF) vector of each line; express and The cosine similarity is used; if the similarity is close to 1, it means that when nodes i and j increase their output simultaneously, the power flow change pattern of the entire network is almost identical. When a graph neural network aggregates, such nodes are given high weights, which helps the diffusion model automatically tend to make these nodes fluctuate in the same direction when generating severe scenarios, in order to find the most severe scenario. This represents the power transfer distribution factor of the unit at the i-th node.

[0033] For specific details, please refer to Figure 2The topology-aware variational autoencoder includes an encoder and a decoder. The encoder includes a one-dimensional convolutional layer, a graph attention network layer, a flattening layer and a fully connected layer connected in sequence. The network structure of the decoder is symmetrical to that of the encoder. The encoder uses the wind farm topology information graph as a physical prior to encode the input wind power operation data into latent variables. The decoder restores the latent variables into the wind power scene, so that all latent variables form a latent manifold in the low-dimensional space.

[0034] It should be noted that the one-dimensional convolutional layer is used to extract the temporal features of wind power output based on the input wind power operation data, and the graph attention network layer completes topology aggregation based on the wind farm topology information graph and the temporal features.

[0035] In one possible implementation, the encoder's one-dimensional convolutional layer extracts the temporal features of wind power output through a sliding operation of the convolution kernel and nonlinear activation. (6) In equation (6), For nodes i Feature vector after temporal compression; Indicates the first i Wind power operation data at each node; It is a one-dimensional convolution kernel; For bias terms; For pooling operations, This is the ReLU activation function.

[0036] In one possible implementation, such as Figure 3 The graph attention network layer performs topological aggregation of node features based on the wind farm topology information graph and temporal features, including: The graph attention network layer performs topology aggregation based on the wind farm topology information graph and temporal features to obtain a node feature matrix, including: S11. Obtain temporal characteristics and wind farm topology information map; S12. For each node in the wind farm topology graph, calculate the attention score of all its neighboring nodes; Specifically, with the first k Attention score of layer in a layered graph attention network For example, measuring nodes j For nodes i Importance: (7) In equation (7), For the first k The attention vector of the layer, Let be the learnable feature transformation matrix of the k-th layer. This represents a vector concatenation operation. For learnable scaling parameters, Represents the elements in the adjacency matrix. This represents the LeakyReLU activation function. For data-driven items; This means incorporating prior physical knowledge into the attention score formula; S13. Attention score for each node Perform Softmax normalization to obtain normalized attention weights. ; (8) In equation (8), Represents a node i The adjacency set; S14. Based on the normalized attention weights, the temporal features of all neighboring nodes are weighted and summed, and then processed by an activation function to obtain the aggregated topological features: (9) S15. Using the single-level topological aggregation feature output by the previous layer graph attention network as the sole input to the next layer graph attention network, repeat steps 12 to 14 to complete the serial stacking of several layers of graph attention networks, and obtain the node feature matrix. .

[0037] Complementarily, the flattening layer flattens the node feature matrix into a one-dimensional vector, and the fully connected layer maps the one-dimensional vector into latent parameters, where latent variables are obtained by reparameterizing the latent parameters.

[0038] It is understandable that the node feature matrix is ​​obtained after steps S11-S15. Then, it is flattened and mapped to the mean and variance of the latent distribution through a fully connected layer, and latent variables are obtained by sampling based on the reparameterization technique.

[0039] S2. Construct a diffusion model that runs on the latent manifold. The diffusion model processes the latent variables and outputs them to the decoder.

[0040] In one possible implementation, refer to Figure 2 The diffusion model includes a forward fixed-noise Markov chain and a reverse parameterized denoising Markov chain equipped with a pre-trained neural network. The forward fixed-noise Markov chain is a parameterless pure mathematical calculation process. Based on a preset Gaussian noise scheduling rule, the latent variables are gradually noised to obtain pure Gaussian noise.

[0041] Specifically, during the forward noise addition process, the ultra-short-term prediction data is fed into... Gaussian noise is gradually added until it becomes pure noise. For Noisy samples Can be derived from initial samples Obtained through reparameterized sampling: (11) In equation (11), , Indicates the first t The proportion of the original signal retained during the step; It is standard Gaussian noise.

[0042] Neural networks are used to predict noise values ​​added during the forward noise generation process, based on noisy latent variables and time steps. ,Depend on Figure 2 It can be seen that the neural network consists of at least one input fusion layer, two residual blocks, and one output layer; the inverse parameterized denoising Markov chain is based on noise prediction values. Derivation of the denoised mean And based on the denoised mean The pure Gaussian noise is gradually denoised in reverse.

[0043] Understandably, this invention utilizes the inverse generation process of a diffusion model as the search mechanism for the worst-case scenario. The problem of finding the worst-case scenario is reconstructed as a conditional probability sampling problem. The inverse process aims to extract the worst-case scenario from pure noise. The noise is gradually removed to recover samples that conform to the data distribution. The process is modeled as another parameterized Markov chain with transition probabilities. Follows a Gaussian distribution: (12) In equation (12), The mean value is used to predict the noise component in the current sample by a trained neural network. get; The variance is usually fixed.

[0044] S3. Calculate the gradient of the predefined power system operating cost function with respect to the wind power scenario, project the gradient onto the tangent space of the potential manifold to obtain the gradient guiding operator, and introduce the gradient guiding operator into the diffusion model in the next round of solving.

[0045] Preferably, the power system operating cost function includes the risks of load shedding, wind curtailment, and line overload.

[0046] In one possible implementation, in order to achieve adversarial conditional generation, the present invention introduces a gradient guidance mechanism in the mean equation of the reverse process, while ensuring that the generated perturbation always moves along the surface of the physical manifold.

[0047] It should be noted that the reference Figure 2 Each round of physical guidance model construction is accompanied by an iterative solution process for robust optimization. In the iterative solution process of robust optimization, the gradient guidance operator comes from the gradient of the power system operating cost function relative to the wind power scenario generated by the diffusion model in the previous round and restored by the decoder. If it is the first round of robust optimization (no historical wind power scenario generated), the diffusion model first performs pure random reverse denoising without gradient guidance to generate an initial wind power scenario. After calculating the gradient guidance operator based on the initial wind power scenario, it is introduced into the diffusion model reverse denoising process in the next round of robust optimization. In each subsequent round of robust optimization, the gradient guidance operator is updated based on the wind power scenario generated in the previous round, and then the diffusion model is driven to generate the worst wind power scenario that adapts to the current scheduling decision. This cycle continues until the robust optimization converges. The decoded scenario satisfies the continuity of wind power and grid topology constraints. This invention uses the transpose of the Jacobian matrix as a manifold projection operator to project the gradient onto the tangent space of the latent manifold, obtaining a gradient-guided operator. The Jacobian matrix is ​​the first-order partial derivative matrix of the decoder's high-dimensional output with respect to the low-dimensional input. The expression for the Jacobian matrix is: (13) In equation (13), Let be the Jacobian matrix of the decoder. Indicates high-dimensional output. This indicates a low-dimensional input.

[0048] In one possible implementation, the formula for calculating the gradient guiding operator includes: (14) In equation (14), This represents the gradient-guided operator. The transpose of the Jacobian matrix represents the gradient in high-dimensional space. The projection onto the tangent space of the latent manifold theoretically guarantees the generation of perturbations. Always moving along the surface of the physical manifold, the decoded scene It can satisfy the continuity of wind power and grid topology constraints; The gradient of the power system operating cost function with respect to a high-dimensional wind power scenario. Theoretically, this guarantees the generation of perturbations. It always moves along the surface of the physical manifold.

[0049] It is worth noting that in actual calculations, it is not necessary to explicitly construct the high-dimensional Jacobian matrix; it is only necessary to... The error signal can be obtained by backpropagating it to the decoder once, thus avoiding the huge overhead of high-dimensional matrix operations.

[0050] It is understood that the gradient guidance operator of this invention is essentially a gradient guidance mechanism based on an affine strategy. It can be parsed as follows: (15) (16) (17) (18) (19) In equations (15)-(19), For the Sigmoid function, It is a symbolic function; ; As an indicator function, if the wind farm Connected to the node If the value is above the given value, the function value is 1; otherwise, it is 0. The net power deficit in the system caused by wind power forecasting errors during time period t; , These represent the sum of the upper and lower reserve capacities of thermal power units, respectively. for Time Node The change in net injected power, For connecting nodes A collection of generator units, for Timetable The meritorious trend, The path calculated for the main problem The benchmark value for current flow; The wind power forecast value used during the pre-scheduling of the main problem. The uncertainty scenario value of wind power generated by the diffusion model.

[0051] like Figure 4 In one possible implementation, the inverse denoising process after introducing the gradient-guided operator includes: S31. The basic denoised mean is calculated based on the noise prediction value output by the neural network. The calculation formula is as follows: (20) In equation (20), , Indicates the first t The proportion of the original signal retained during the step. Indicates the first t The latent variables after adding noise at each step, S32. Introduce a gradient-guided operator to adjust the base denoising mean using an additive correction method, resulting in a fused gradient-guided denoising mean. The correction formula is as follows: (twenty one) In equation (21), For gradient-guided operators; As a weighting factor, Based on the denoised mean, The noise component in the current sample predicted by the neural network; S33. Based on the denoised mean, from the latent variable z corresponding to pure Gaussian noise T Initially, starting in reverse order of time steps from T to 1, process the noisy latent variable z at each step. t Perform noise reduction operation; Preferably, the calculation formula for inverse denoising includes: (twenty two) In equation (22), , Indicates the first t The proportion of the original signal retained during the step. Indicates the first t The latent variables after adding noise at each step, Indicates noise components, The diffusion model is represented by the first... t The output of the reverse reasoning step, This is the transpose of the Jacobian matrix. Indicates the trade-off coefficient. Indicates the first t Gradient guidance operator for step, This represents the random noise term.

[0052] S34. After completing the inverse denoising for all time steps, output the final denoised potential variables.

[0053] Secondly, such as Figure 5 The present invention also provides a physical guided diffusion model construction system 50 for robust optimization, the system 50 comprising: The manifold mapping module 510 is used to construct a wind farm topology information map and a topology-aware variational autoencoder. The variational autoencoder includes an encoder and a decoder. The encoder uses the wind farm topology information map as a physical prior to encode the input wind power operation data into latent variables. The decoder restores the latent variables into a wind power scenario, so that all latent variables form a latent manifold in a low-dimensional space. The diffusion generation module 520 is used to construct a diffusion model that runs on the latent manifold. The diffusion model processes the latent variables and outputs them to the decoder. The physical guidance module 530 is used to calculate the gradient of the predefined power system operating cost function with respect to the wind power scenario, project the gradient onto the tangent space of the potential manifold to obtain the gradient guidance operator, and introduce the gradient guidance operator into the diffusion model in the next round of solution.

[0054] Figure 6 The applicant provides the following explanation of the process for solving the two-stage robust optimization model of a power system with high wind power penetration after constructing the physically guided diffusion model using the construction method of this invention: (1) Initialization: Set the lower bound of the main problem Upper Realm Initialize the scene set.

[0055] (2) Solve the main problem: Solve the first-stage problem under the current scenario set to obtain the optimal decision. .

[0056] (3) Use this model to generate adverse scenarios: First, the decision-making process will be... The data is input into the physical guided diffusion model. Then, using the method described in step 4, a batch of candidate wind power scenarios is generated through multiple reverse iterations. Finally, the scenario that results in the highest cost for the second stage is selected from these. .

[0057] (4) Update the limits and add the cutting plane: First calculate The precise second-stage cost is used to update UB. Then, if UB-LB is greater than the convergence threshold, the process is... Add the scene to the scene set and return to step (2). Otherwise, stop the iteration and output the result. This is the optimal scheduling scheme.

[0058] The above are merely preferred embodiments of the present invention and are not intended to limit the implementation methods and protection scope of the present invention. Those skilled in the art should recognize that any equivalent substitutions and obvious changes made based on the content of this specification should be included within the protection scope of the present invention.

Claims

1. A method for constructing a physical-guided diffusion model for robust optimization, wherein the model is used to solve subproblems of a two-stage robust optimization model for a power system with high wind power penetration, characterized in that... The steps include the following: Construct a wind farm topology information map and a topology-aware variational autoencoder. The variational autoencoder includes an encoder and a decoder. The encoder uses the wind farm topology information map as a physical prior to encode the input wind power operation data into latent variables. The decoder restores the latent variables into a wind power scenario, so that all latent variables form a latent manifold in a low-dimensional space. A diffusion model is constructed and operates on the latent manifold. The diffusion model processes the latent variables and outputs them to the decoder. The gradient of the predefined power system operating cost function with respect to the wind power scenario is calculated, and the gradient is projected onto the tangent space of the potential manifold to obtain the gradient guiding operator. The gradient guiding operator is then introduced into the diffusion model in the next round of solution.

2. The method for constructing a robust optimization-oriented physical guided diffusion model according to claim 1, characterized in that, The wind farm topology information graph specifically includes a set of wind farm nodes, a set of edges connecting wind farms, and an adjacency matrix.

3. The method for constructing a robust optimization-oriented physical guided diffusion model according to claim 1, characterized in that, The encoder of the topology-aware variational autoencoder includes a one-dimensional convolutional layer, a graph attention network layer, a flattening layer, and a fully connected layer connected in series. The one-dimensional convolutional layer extracts the temporal features of wind power output at each node based on the input wind power operation data. The graph attention network layer performs topology aggregation based on the wind farm topology information graph and the temporal features to obtain a node feature matrix. The flattening layer flattens the node feature matrix into a one-dimensional vector. The fully connected layer maps the one-dimensional vector into latent parameters. The latent variables are obtained by reparameterizing the latent parameters.

4. The method for constructing a robust optimization-oriented physical guided diffusion model according to claim 3, characterized in that, The one-dimensional convolutional layer extracts the temporal features of wind power output based on the input wind power operation data, including: the one-dimensional convolutional layer of the encoder extracts the temporal features of wind power output through convolution kernel sliding operation and nonlinear activation.

5. The method for constructing a robust optimization-oriented physical guided diffusion model according to claim 3, characterized in that, The graph attention network layer performs topology aggregation based on the wind farm topology information graph and temporal features to obtain a node feature matrix, including: Step 1. Obtain the time-series features and wind farm topology information map; Step 2. For each node in the wind farm topology graph, calculate the attention score of all its neighboring nodes; Step 3. Perform Softmax normalization on the attention score of each node to obtain normalized attention weights; Step 4. Based on the normalized attention weights, the temporal features of all neighboring nodes are weighted and summed, and then processed by an activation function to obtain aggregated topological features; Step 5. Use the single-level topological aggregation feature output by the previous layer graph attention network as the sole input to the next layer graph attention network, and repeat steps 2 to 4 to complete the serial stacking of several layers of graph attention networks to obtain the node feature matrix.

6. The method for constructing a robust optimization-oriented physical guided diffusion model according to claim 1, characterized in that, The step of projecting the gradient onto the tangent space of the latent manifold to obtain the gradient guiding operator includes: using the transpose of the Jacobian matrix as the manifold projection operator, projecting the gradient onto the tangent space of the latent manifold to obtain the gradient guiding operator. The Jacobian matrix is ​​the first-order partial derivative matrix of the high-dimensional output of the decoder with respect to the low-dimensional input, wherein the Jacobian matrix is ​​the first-order partial derivative matrix of the high-dimensional output of the decoder with respect to the low-dimensional input.

7. The method for constructing a robust optimization-oriented physical guided diffusion model according to claim 1, characterized in that, The diffusion model includes a forward fixed-noise Markov chain and a reverse parameterized denoising Markov chain equipped with a pre-trained neural network. The forward fixed-noise Markov chain is a parameterless pure mathematical calculation process. Based on a preset Gaussian noise scheduling rule, the latent variables are gradually noised to obtain pure Gaussian noise. The neural network is used to predict the noise values ​​added during the forward noise addition process based on the noisy latent variables and time steps. The inverse parameterized denoising Markov chain derives the denoising mean based on the noise prediction value, and then progressively reverses the denoising of pure Gaussian noise based on the denoising mean.

8. The method for constructing a robust optimization-oriented physical guided diffusion model according to claim 7, characterized in that, The inverse denoising process after introducing the gradient-guided operator includes: The basic denoised mean is calculated based on the noise prediction value output by the neural network. A gradient-guided operator is introduced to adjust the base denoising mean using an additive correction method, resulting in a fused gradient-guided denoising mean. The correction formula is as follows: in, For gradient-guided operators; As a weighting factor, Based on the denoised mean; Based on the denoised mean, the latent variable z corresponding to the pure Gaussian noise is... T Initially, starting in reverse order of time steps from T to 1, process the noisy latent variable z at each step. t Perform noise reduction operation; After completing the inverse denoising for all time steps, the final denoised latent variables are output.

9. The method for constructing a robust optimization-oriented physical guided diffusion model according to claim 1, characterized in that, After solving each robust optimization subproblem, the gradient of the power system operating cost function with respect to the current wind power scenario is recalculated, the gradient guidance operator is updated, and the updated gradient guidance operator is introduced into the next round of diffusion model.

10. A system for constructing a physically guided diffusion model for robust optimization, characterized in that, The system includes: The manifold mapping module is used to construct a wind farm topology information map and a topology-aware variational autoencoder. The variational autoencoder includes an encoder and a decoder. The encoder uses the wind farm topology information map as a physical prior to encode the input wind power operation data into latent variables. The decoder restores the latent variables to the wind power scenario, so that all latent variables form a latent manifold in a low-dimensional space. A diffusion generation module is used to construct a diffusion model that runs on the latent manifold, and the diffusion model processes the latent variables and outputs them to the decoder; The physical guidance module is used to calculate the gradient of the predefined power system operating cost function with respect to the wind power scenario, project the gradient onto the tangent space of the potential manifold to obtain the gradient guidance operator, and introduce the gradient guidance operator into the diffusion model in the next round of solution.

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