A fast solution method for day-ahead scheduling considering large-scale new energy cluster generation fluctuation

Abstract

The application relates to the technical field of power system dispatching, and discloses an intra-day forward-looking dispatching fast solving method considering large-scale new energy cluster power generation fluctuation, which comprises the following steps: S1: new energy cluster space-time fluctuation scene generation based on neuron cellular automata, S2: power grid dynamic security domain definition and simplification based on physical information neural network, S3: dispatching fast optimization solving based on model prediction path integral, and S4: dispatching scheme dynamic elasticity and stability evaluation based on the theory of Koopman operator. The new energy cluster space-time fluctuation scene generation method based on neuron cellular automata can effectively generate a space-time scene reflecting the large-scale new energy cluster power generation fluctuation, support uncertainty analysis, has the advantages of high calculation efficiency and scene authenticity, and solves the problem that the traditional statistical model ignores space-time coupling, thereby causing inaccurate scene generation.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of power system dispatching, in particular to a fast solution method for day-ahead forward scheduling considering the generation fluctuation of large-scale new energy cluster. BACKGROUND

[0002] With the continuous increase of the penetration rate of new energy in the power system, the generation characteristics of large-scale new energy clusters (such as water-light-storage clusters) show significant fluctuation, which poses new challenges to the power grid dispatching link. As a key link to ensure the stable operation of the power grid in the day-ahead period and balance the power supply and demand, the core goal of the day-ahead forward scheduling of the power grid is to cope with the changes in the operating variables of the power system caused by the generation fluctuation of new energy, to ensure that the power grid meets the electricity demand while maintaining a safe and stable state, and is an important support for the efficient operation of the power system under the background of high proportion of new energy access.

[0003] In the current power grid environment with high proportion of new energy access, the existing day-ahead forward scheduling method mainly takes statistical models and traditional optimization algorithms as the core technical support. Among them, the statistical model is often used to analyze and predict the key operating parameters such as new energy generation power and load demand, providing basic data reference for dispatching decision; the traditional optimization algorithm is based on the results output by the statistical model, combined with the basic constraints of power grid operation (such as unit output limit, network transmission capacity limit, etc.), to calculate and formulate the scheduling scheme, to realize the preliminary allocation and scheduling of power resources in the day-ahead period.

[0004] The most critical deficiency of the existing day-ahead forward scheduling method is the weak processing ability of the uncertainty brought by the generation fluctuation of large-scale new energy clusters. This weak processing ability is due to the fact that the method itself does not fully consider the uncertainty factors related to the generation fluctuation of new energy, and cannot effectively capture the complex spatio-temporal correlation and dynamic change characteristics behind the fluctuation, thus leading to the difficulty of accurately adapting the real-time fluctuation of new energy generation for the scheduling decision, and burying potential risks for the operation of the power grid. In view of this, we propose a fast solution method for day-ahead forward scheduling considering the generation fluctuation of large-scale new energy cluster. SUMMARY

[0005] In view of the deficiencies of the prior art, the present application provides a fast solution method for day-ahead forward scheduling considering the generation fluctuation of large-scale new energy cluster, which solves the problem of weak processing ability of uncertainty brought by the generation fluctuation of large-scale new energy cluster, which is caused by the fact that it does not fully consider the related uncertainty factors and cannot effectively capture the complex spatio-temporal correlation and dynamic change characteristics behind the fluctuation.

[0006] To achieve the above purpose, the present application is implemented by the following technical scheme: a fast solution method for day-ahead forward scheduling considering the generation fluctuation of large-scale new energy cluster, comprising the following steps:

[0007] S1: New energy cluster spatio-temporal fluctuation scenario generation based on neuron cellular automata:

[0008] Integrate new energy cluster historical electrical data, preprocess and grid to build multi-channel grid, train neuron cellular automata network to generate fluctuation scenario, and verify after inverse normalization, get spatio-temporal fluctuation scenario conforming to electrical and energy storage constraints;

[0009] S2: Power grid dynamic security domain definition and simplification based on physical information neural network:

[0010] Based on S1 scenario, construct power grid state, control and disturbance vector, train physical information neural network to define dynamic security domain, and simplify and verify by convex optimization to get low-dimensional simplified security domain;

[0011] S3: Fast optimization solution of scheduling based on model predictive path integral:

[0012] Combine S1 scenario and S2 low-dimensional security domain to construct system state and reference trajectory, sample disturbance to simulate scheduling trajectory, calculate cost and weight, update control strategy to get initial scheme;

[0013] S4: Dynamic flexibility and stability evaluation of scheduling scheme based on Koopman operator theory:

[0014] Inject S1 scenario into S3 initial scheme, construct matrix and approximate Koopman operator, spectral decomposition, calculate stability and flexibility index; feedback to S3 to adjust cost penalty weight, iterate until index meets the standard, output final scheme.

[0015] Preferably, the specific steps of preprocessing and gridding in S1 are: adopt bilinear interpolation to fill in missing data points in historical electrical data, calculate the value of adjacent known data points and the weight based on distance during interpolation, the distance measurement range is set to 0 to 1 and a normalization factor is configured; Z-score normalization is performed on the filled data, and the original data mean and standard deviation are combined during normalization; Gaussian noise is added to the normalized data, and the noise amplitude is controlled by the variance of photovoltaic power; the constructed multi-channel grid includes power, radiation, temperature and energy storage state related channels, and the grid dimension is represented by the spatial dimension and the number of channels.

[0016] Preferably, the specific way of training the neural cellular automaton network in S1 is: initializing network parameters by Xavier initialization method, the neural cellular automaton network architecture comprises a convolutional perception layer and a multilayer perceptron update layer, the convolutional perception layer uses a preset size of convolution kernel, and the multilayer perceptron update layer is a multilayer fully connected structure and is configured with an activation function; training is performed to minimize a loss function comprising a time series loss and an autocorrelation regular term, the time series loss is related to a predicted grid state, a current state and a state increment output by the multilayer perceptron, and the autocorrelation regular term is related to a Pearson correlation coefficient, a decay time constant based on a photovoltaic response and a power-related parameter; adaptive optimizer is used for training, and the training process is configured with a learning rate, a batch size and an iteration step number.

[0017] Preferably, the specific way of training the physical information neural network in S2 is: the physical information neural network adopts a multilayer perceptron structure, and is configured with a preset number of layers, a number of hidden units and an activation function; training is performed to minimize a total loss function comprising a data loss, a PDE residual loss, a boundary condition loss and a stability loss, and the total loss function is balanced by weights of the loss terms; the data loss is related to a network predicted safety value, an observed safety value and a data point number, the PDE residual loss is related to a PDE point number, a state derivative and a state vector, a control vector and a disturbance vector, the boundary condition loss is related to a predicted boundary value and a constraint boundary value, and the stability loss is related to eigenvalues of a Koopman operator Jacobian matrix and a ReLU function; adaptive optimizer is used for training, and the training process is configured with a learning rate, a decay factor, an iteration step number and an early stop condition.

[0018] Preferably, the specific steps of simplifying and verifying the power grid dynamic security domain by using the convex optimization method in S2 are: simplifying the power grid dynamic security domain by fitting a geometric figure by using the convex optimization method, and the geometric figure is characterized by a positive definite matrix and a center vector; the positive definite matrix and the center vector are solved by using a numerical calculation library, the positive definite matrix is initialized as an identity matrix, and the center vector is initialized as a mean point of the power grid state; the simplification effect is verified by calculating a volume error, and the volume error is related to a volume of the simplified geometric figure, a volume of the original power grid dynamic security domain and a symmetric difference set; if the volume error exceeds a preset threshold, the sampling points are increased for re-fitting until the volume error meets a preset requirement.

[0019] Preferably, the specific content of constructing the system state and the reference trajectory and preprocessing in S3 is: the system state comprises power generation related parameters, energy storage related parameters and backup related parameters; the reference trajectory is a benchmark trajectory determined based on an economic target; during preprocessing, the sampling covariance is adaptively adjusted based on a current photovoltaic output variance, and the adjustment is combined with a base covariance, a scaling factor and the current photovoltaic output variance, and the sampling covariance is characterized in a matrix form.

[0020] Preferably, the specific manner of calculating the total cost of each scheduling trajectory and weighting in S3 is that the total cost comprises an economic related cost, a safety related penalty, an elasticity related penalty and a terminal related penalty, the economic related cost is associated with a fuel / backup cost coefficient, the safety related penalty is associated with the distance to the boundary of a low-dimensional simplified safety domain, the elasticity related penalty is associated with a Kuppman elasticity indicator, and the terminal related penalty is associated with a deviation of the energy storage end state; the weight of each scheduling trajectory is calculated based on the Feynman path integral theory, and the weight is associated with the trajectory cost, a temperature parameter and an exponential sum of all trajectory costs; and an importance sampling strategy is adopted to preferentially select trajectories whose weights meet preset conditions.

[0021] Preferably, the specific steps of constructing the data matrix, the shift matrix, the approximate Kuppman operator and the spectral decomposition in S4 are that the data matrix is composed of state snapshots, and the shift matrix is composed of state snapshots adjacent in time sequence; singular value decomposition is performed on the data matrix to obtain left singular vectors, a diagonal singular value matrix and right singular vector transpose conjugate; a low-order Kuppman operator approximation is solved based on the pseudo-inverse of the data matrix; characteristic decomposition is performed on the low-order Kuppman operator to obtain eigenvalues and eigenvectors; a preset number of eigenvalues and eigenvectors are selected in descending order of singular values as dominant disturbance modes.

[0022] Preferably, the specific manner of calculating the stability indicator and the elasticity indicator in S4 is that the stability indicator is calculated by a spectral radius, the spectral radius is the maximum value of the modulus of the eigenvalues of the Kuppman operator, and the stability indicator value is determined according to the relationship between the spectral radius and a preset stability threshold; the elasticity indicator is calculated by a modal recovery time, the modal recovery time is associated with the real part of the eigenvalue; and the overall elasticity indicator is determined in combination with a modal energy weight, a normalized recovery time and a modal number, and the overall elasticity indicator value ranges from 0 to 1.

[0023] Preferably, the specific process of feedback iteration optimization in S4 is that if the stability indicator or the elasticity indicator exceeds a preset qualified range, the stability indicator and the elasticity indicator are fed back to S3; S3 adjusts the cost penalty weight according to the type of the indicator exceeding the qualified range; a preset number of iterations are performed until the stability indicator and the elasticity indicator both meet the preset qualified range, and a final scheduling scheme is output.

[0024] The application provides an intra-day forward-looking scheduling fast solving method considering large-scale new energy cluster power generation fluctuation.

[0025] 1. The new energy cluster space-time fluctuation scenario generation method based on neuron cellular automata provided by the application can effectively generate a space-time scenario reflecting the large-scale new energy cluster power generation fluctuation, support uncertainty analysis, has the advantages of high calculation efficiency and scenario authenticity, and solves the problem that the traditional statistical model ignores space-time coupling, resulting in inaccurate scenario generation.

[0026] 2. The method for quickly defining and simplifying the dynamic security domain of the power grid based on the physical information neural network can quickly define and simplify the safe operation domain of the power grid under new energy fluctuation, avoids voltage / frequency instability, has the advantages of high precision and low computational complexity, and solves the problem that high-dimensional security domain definition requires short-time simulation and cannot respond in real time.

[0027] 3. The scheduling fast optimization solving method based on the model predictive path integral control can quickly solve the intra-day scheduling optimization trajectory, balance economy and safety, has the advantages of strong robustness and fast parallel computing, and solves the problem that traditional optimization algorithms are sensitive to non-convex constraints, slow to solve, and prone to local optimum.

[0028] 4. The scheduling scheme dynamic elasticity and stability evaluation method based on the theory of the Koopman operator can evaluate the dynamic elasticity and stability of the scheduling scheme, provide quantitative feedback, has the advantages of accurate evaluation and closed-loop optimization support, and solves the problem that lack of closed-loop evaluation leads to poor scheduling scheme flexibility and instability under high-penetration new energy. BRIEF DESCRIPTION OF DRAWINGS

[0029] Figure 1 The figure is a schematic diagram of the intra-day forward scheduling fast solving method considering the fluctuation of large-scale new energy cluster power generation.

[0030] Figure 2 The figure is a product scheme of the present application. DETAILED DESCRIPTION

[0031] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the specification of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, not all. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0032] Embodiment:

[0033] Please refer to the drawings in the specification of the present application Figure 1 - the drawings in the specification of the present application Figure 2 The embodiment of the present application provides an intra-day forward scheduling fast solving method considering the fluctuation of large-scale new energy cluster power generation, which comprises the following steps:

[0034] The present application is directed to large-scale water-light-storage new energy cluster power generation volatility, such as the current-voltage (I-V) characteristic shift caused by the minute-level radiation variation of photovoltaic array caused by cloud movement, or the uneven electrical output between panels caused by temperature gradient. The method of neural cellular automata (NCA) is used to generate space-time fluctuation scenarios. This method regards the new energy cluster as a dynamic grid system, and each "cell" represents the state of a single photovoltaic panel. The propagation and emergence of electrical quantities (such as power output, voltage, and current) in space and time are simulated through local neural network rules, thereby generating diversified extreme scenarios to support uncertainty analysis in intraday forward scheduling. NCA can learn complex dynamic patterns from time series images and partial differential equation (PDE) trajectories, and is particularly suitable for capturing the space-time fluctuations of new energy electrical quantities such as total solar radiation, which provides a solid foundation for simulating the real operating characteristics of photovoltaic clusters.

[0035] In new energy clusters, traditional models (such as statistical methods or GAN) often ignore the space-time coupled electrical quantity distribution, such as the radiation gradient decay caused by local cloud shading in photovoltaic arrays affecting module current

[0036]

[0037] (1) In the formula, the photovoltaic I-V model, is the photocurrent, is the saturation current, q is the charge, k is the Boltzmann constant, T is the temperature, is the parallel resistance, or the electrical output drop caused by temperature gradient (power is affected by T , β is the temperature coefficient, G is the radiation, is the reference temperature). NCA solves this problem through multi-channel grid representation (channels encode electrical quantities: power P, radiation G, temperature T, etc.), and its update rule is parameterized as a neural network, coupled with new energy electrical dynamics. The cellular automaton model can accurately simulate the I-V curve and temperature effect of photovoltaic panels. NCA extends to cluster-level space-time electrical variation on this basis, ensuring that the generated scenarios meet the actual electrical constraints, such as output upper and lower limits, ramping rate, and energy storage state. In new energy clusters, traditional models (such as statistical methods or GAN) often ignore space-time coupling, such as the radiation gradient decay caused by local cloud shading in photovoltaic clusters. NCA solves this problem through multi-channel grid representation (channels encode output, wind speed, radiation, temperature, etc.), and its update rule is parameterized as a neural network, coupled with new energy physical dynamics:

[0038]

[0039] wherein, is the grid position Electrical state at time t (e.g., normalized power output) , (Rated power); These are MLP parameterization rules, responsible for capturing local electrical interactions; This is the perception vector, which includes the current electrical state, spatial gradients (such as the power gradient extracted by the Sobel filter, simulating the impact of shading or temperature gradients on downstream electrical quantities), and meteorological variables (such as radiation and temperature). This rule further integrates the photovoltaic electrical model with energy storage constraints:

[0040]

[0041] Here, equation (3) defines the perception vector. Capture spatial gradients ( Simulate the diffusion of electrical quantities, such as power loss caused by voltage gradient); (4) is extended to the final sensing vector. Incorporating photovoltaic-specific variables such as radiation and temperature; (5) modeling photovoltaic current Joint photocurrent (Depending on radiation G and temperature T) and diode equations, reflecting the impact of minute-level cloud shading on electrical quantities; (6) Equation calculates photovoltaic power. , The temperature loss term (d is the distance vector) describes the spatiotemporal evolution of temperature T in the cluster; (7) extended This is the short-circuit current. For temperature coefficient, For reference radiation; Equations (8) to (10) apply output force constraints ( For photovoltaic power output, up / down is the limit of ramp / deceleration rate), to ensure that the generated scenario avoids extreme fluctuations that exceed the system's capacity; (11) to (13) integrate energy storage models ( In energy storage state, For charging and discharging efficiency, (min / max are limits, to / tN are consistent with the initial / final states) to smooth photovoltaic fluctuations in the hydro-solar-storage base. This comprehensive model ensures that the scenarios generated by NCA not only reflect the electrical characteristics of photovoltaics, but also are coupled with energy storage dispatch requirements.

[0042] To address extreme electrical fluctuations in photovoltaic clusters within hydro-solar-storage bases (such as voltage instability or grid disconnection risks under high penetration rates, leading to electrical quantities exceeding limits, etc.), This invention incorporates variational NCA (VNCA) to simulate uncertainty by introducing a noise channel:

[0043]

[0044] in, Quantifying the electrical volatility intensity is the scaling factor, based on the radiation and temperature cluster variance), allowing to generate multiple extreme scenarios from a single seed state, like cluster electrical output collapse under extreme cloud shadow periods triggering low voltage. The training loss function combines reconstruction, diversity, perception terms, and adds electrical and energy storage constraint penalties:

[0045] L= 15

[0046]

[0047] where, is the VGG extractor, is the weight; penalties ensure that generated scenarios respect power balance as generation, as consumption), voltage limits, ramp rates as maximum allowed variation rate, typically and energy storage limits; the last term integrates electrical divergence, ensuring that scenarios preserve photovoltaic radiation correlation and temperature gradient influence.

[0048] The core of NCA lies in its update rule, which is parameterized by a neural network, specifically a combination of multilayer perceptron (MLP) and convolutional layers. This design allows NCA to learn local rules from data, thereby emerging global complex patterns. The MLP serves as the foundation of the NCA update rule.

[0049] MLP is a feedforward artificial neural network composed of multiple layers: input, hidden, and output. Each layer consists of multiple neurons (nodes), each simulating the behavior of a biological neuron by processing input through weighted summation and a nonlinear activation function. The principle of MLP is inspired by biological heuristics: it approximates any continuous function by learning input-output mappings (according to Cybenko's universal approximation theorem, a single-hidden-layer MLP can approximate any function). Key mechanisms include:

[0050] Forward propagation: input signals propagate forward from the input layer to the output layer. Assuming the input vector , the output of the 1st layer is calculated as:

[0051]

[0052] where, is the weight matrix, is the bias vector, is an activation function. Like ReLU: This models the neuron's "excitement": if the weighted sum exceeds the threshold, the activation output is fired. MLPs learn hierarchical representations by stacking multiple layers: shallow layers capture low-level features (like edges), deep layers capture high-level abstractions (like patterns).

[0053] Activation function: Activation functions introduce nonlinearity, otherwise MLPs degenerate into linear regression. ReLU prevents vanishing gradients, with derivative 1 (z > 0) or 0 (z ≤ 0). In NCA, ReLU allows nonlinear updates of cell states, modeling the threshold response of biological systems.

[0054] Backpropagation (Backprop) and learning: Training uses gradient descent by minimizing the loss function. Chain rule computes the gradient:

[0055]

[0056] Parameter update: , is the learning rate. This allows the MLP to learn from errors, adjusting weights to better fit the data.

[0057] In NCA, the MLP parameterizes the update rule: preliminary perception vector (computed via convolution, incorporating states and gradients) as a basis, extended to the final perception vector inputs the MLP, outputting a 16-dimensional increment ds. The architecture is typically 2-3 layers of dense (1x1 convolution equivalent to fully connected), with 128-dimensional hidden units, ReLU activation, and the final layer linear (no activation) to allow positive and negative updates. The final layer weights are initialized to 0, ensuring an initial "do-nothing" behavior, similar to the skip connections of residual networks, mitigating instability during early training. NCA also incorporates convolutional layer principles for the perception step. The core of Convolutional Neural Networks (CNNs) is shared weights and local receptive fields: convolution kernels (like the 3x3 Sobel filter) slide over the input, extracting local features:

[0058]

[0059] In NCA, the Sobel kernel computes gradients, capturing spatial variations, modeling biological gradient perception. The hierarchical feature extraction of CNNs (edges in shallow layers, textures in deep layers) is achieved in NCA through emergent updates: local MLP rules, iterated multiple times, produce global patterns, like how local turbulence in a photovoltaic field diffuses to a cluster-level output drop.

[0060] In training, Backpropagation Through Time (BPTT) unfolds the iterative steps, computing gradients to update across T steps, similar to how RNNs process sequences. The loss includes reconstruction and diversity terms, and the optimizer like Adam handles the high-dimensional grid. This MLP+CNN hybrid allows NCA to learn regenerative patterns: recovery from damage states, analogous to the elastic recovery of new energy clusters.

[0061] The constructed multi-channel grid contains power, radiation, temperature, and energy storage state-related channels, and the grid dimension is represented by the spatial dimension and the number of channels. The training of the neural cellular automaton network in S1 includes: initializing the neural cellular automaton parameters using the Xavier initialization method, the neural cellular automaton network architecture includes a convolutional perception layer and a multilayer perception update layer, the convolutional perception layer uses a preset size of convolution kernel, and the multilayer perception update layer is a multilayer fully connected structure and is configured with an activation function; the training process aims to minimize the loss function including the time series loss and the autocorrelation regularization term, the time series loss is related to the predicted grid state, the current state and the state increment output by the multilayer perception, and the autocorrelation regularization term is related to the Pearson correlation coefficient, the decay time constant based on the photovoltaic response and the power-related parameters; an adaptive optimizer is used for training, and the training process is configured with a learning rate, a batch size and an iteration step number, including the following steps:

[0062] The scene generation step is:

[0063] When generating a space-time fluctuation scene of a water-light-storage new energy cluster by means of NCA, first, historical electrical data (such as NREL photovoltaic data set, including multi-site power, voltage, current and energy storage state) are integrated, a grid is constructed and preprocessed to ensure that the cluster-level electrical variation is captured.

[0064] 1. Data preprocessing and gridding: The original electrical sequence (such as current I caused by radiation G, power P caused by temperature T, and energy storage state S_{es}) is gridded into^{HWC}, where HW represents the spatial dimension (such as photovoltaic array layout), and C is the number of channels (power, radiation, temperature, energy storage state, etc.). Missing data points are filled using bilinear interpolation:

[0065]

[0066] where, is the interpolation result at the target grid position ; and is the value of the adjacent known data point; is the weight, which is calculated based on the distance to ensure that the adjacent points contribute more. The denominator is a normalization factor to make the weights sum to 1. Where, , Distance metric, range [0,1], ensures linear decay. Z-score normalization is then applied and noise is added to simulate uncertainty:

[0067]

[0068] Raw data is mapped to a distribution with mean 0 and standard deviation 1 for neural network training; noise is then added to simulate uncertainty. is the normalized value; is the mean, is the standard deviation; is Gaussian noise with amplitude controlled by the photovoltaic power variance.

[0069] where, extends the electrical variance, is the gradient weight, preserving the spatial influence of shading or temperature gradients on electrical quantities. The first term is the empirical variance, measuring the variability of discrete points; the second term is the gradient integral, capturing spatially continuous variations (e.g., power gradients caused by temperature gradients). This step ensures that the grid reflects the actual spatiotemporal characteristics of the photovoltaic cluster by integrating historical data (e.g., radiation data from the database and on-site measured temperature distribution). This preprocessing method can significantly improve the model's temporal consistency in capturing photovoltaic fluctuations.

[0070] 2. NCA network initialization and training: Initialize NCA parameters θ using the Xavier initialization method, and the architecture combines convolutional perception layers and MLP update layers. The training process minimizes the loss function through T iterations while monitoring electrical autocorrelation to verify the fluctuation capture effect. The initialization stage includes defining multi-channel hidden states (16-32 dimensions), encoding features such as radiation, temperature, and energy storage states, and the perception layer extracts local neighborhood information through 3x3 convolution kernels. Training uses the Adam optimizer (learning rate 1e-3 to 1e-4), batch size 16-64, and the loss function is:

[0071]

[0072]

[0073]

[0074] where, is the predicted grid state at time (t, t+1,...); t is the current state; is the current state; is the MLP network, outputting the state increment; is the perception vector, providing local input. The formula indicates that a "small update" is added at each iteration step, similar to residual learning, avoiding drastic changes.

[0075] The second formula is the objective function for training, finding the optimal parameters to minimize the cumulative loss L and autocorrelation error. argmin represents optimization solution; the first term is the temporal loss and; the second term is the autocorrelation regularizer, ensuring that the spatiotemporal correlation of the generated sequence matches the real data. is the cumulative loss, is the real state, is the prediction. is the regularizer weight, balancing loss and correlation.

[0076] The third formula is the spatiotemporal autocorrelation function, used to measure the correlation of power P at spatial offset and temporal delay . The first term is the Pearson correlation coefficient; the second term is the exponential decay, simulating electrical propagation attenuation. Close to 1 indicates high correlation (real fluctuations), used for regular training, represents the decay time constant based on PV response. is the expected value, calculated by grid average. is the power value and mean, is the variance, calculated in training error, adjusting .

[0077] 3. Scenario generation and diversification: The transition phase from training to practical application of the NCA model, its core goal is to generate diversified photovoltaic electrical sequences from the initial seed state, simulating the spatiotemporal fluctuation scenarios in the water-light-storage base, such as the influence of cloud cover or temperature gradient. Through iterative updates and conditional injection, NCA can produce multiple extreme variants, supporting uncertainty analysis in scheduling decisions. The generation phase utilizes the principle of emergence, evolving complex patterns from simple seeds; in photovoltaic applications, such irradiance disturbances extend from local panels to power drops in the entire array. The entire step relies on the trained parameters iterating K steps (100-1000), generating time minutes, facilitating intra-day rolling simulation.

[0078] Perception vector expansion and external driving terms:

[0079]

[0080] This formula is used to inject conditional control in the generation process. is the final perception vector, obtained by connecting the preliminary perception conditional variables and external driving Implementation; External driving, balance threshold difference (T , For power threshold such as ) and current rate of change , ensure the generation of bias to a particular extreme. Time-varying weights, adjust gradient impact. VNCA generates sequence:

[0081]

[0082] This formula is sequence generation, K-step photovoltaic grid sequence from seed Generated by VNCA sampling, Indicates a variational stochastic process, Training parameters.

[0083] Denormalization formula:

[0084]

[0085] The normalized value Restored to the original scale , Is the standard deviation, For the mean. Convert (No unit) to real power , used for simulation input. Validation index calculation:

[0086]

[0087] This is an extended Wasserstein distance, used to verify the similarity of the generated distribution With the real , plus a physical penalty term. Inf is the optimal transport plan; Expectation is the average distance; Additional terms check energy, current, and energy storage constraints. Distribution distance, <0.05 accepted. As a joint distribution set; As a transport plan. As the energy integral difference, As the current overrun, As the energy storage overrun. As a weight, balance terms, verify the distribution and constraints after restoring the scale, ensure the physical validity of the scenario, used for scheduling.

[0088] The generated spatiotemporal fluctuation scenario, as a key input, is directly connected to the power grid dynamic safety domain fast definition and simplification method based on the physical information neural network (PINNs). This scenario provides photovoltaic output distribution, radiation and temperature data to help the PINNs model evaluate the safety boundary of the power grid state space in real time, and optimize scheduling decisions to avoid voltage / frequency instability;

[0089] The method takes the computer as the execution subject, takes the spatiotemporal fluctuation scenario generated by the first module as the input, and uses the neural network to embed the physical law to approximate the "safety domain" (Safety Domain) in the power grid state space to maintain the stable operation of the system, thereby quickly evaluating the dynamic safety boundary under the uncertainty of photovoltaic output, and supporting scheduling decisions to avoid risks such as voltage collapse, frequency instability or power angle out-of-step.

[0090] First, a complete power grid dynamic safety domain model is established. The model is based on power system dynamic equations and stability constraints, and considers the fluctuation influence of high-penetration photovoltaic water-light storage clusters. The power grid dynamic model can be expressed as a system of nonlinear ordinary differential equations:

[0091]

[0092] wherein, is the state vector (known quantity, including generator power angle , speed , voltage , current , etc., n is the system dimension, such as 100-1000, the physical background is to describe the physical process of the power grid from steady state to transient state, such as electromagnetic field change caused by voltage deviation from the nominal value or mechanical vibration caused by speed fluctuation, and the theoretical significance is to provide a mathematical framework for system evolution, which is used to analyze stability and predict potential instability points); is the control vector (unknown quantity, including standby power , energy storage charge / discharge rate, etc., m is the control dimension, the physical background is to intervene in the physical process of the power grid by adjusting the generator or energy storage device, such as increasing standby power to balance the energy gap caused by photovoltaic fluctuation, and the theoretical significance is to introduce optimization freedom to make the model from descriptive to controllable analysis, supporting the search for input strategies to maintain stability); is the disturbance vector (input from the first module, known, including photovoltaic output fluctuation, radiation change, temperature gradient, etc., p is the disturbance dimension, the physical background is that external environmental factors such as cloud shadow cause radiation to drop suddenly or temperature rise causes thermal effect to interfere with power grid balance, and the theoretical significance is to quantify uncertainty to help the model evaluate robustness and simulate boundary behavior under real scenarios). The function includes swing equations and power flow constraints:

[0093]

[0094] where, is the generator is the power angle, the phase shift of the generator rotor relative to the synchronous speed, reflecting the torque variation caused by power imbalance under the action of the electromagnetic field, capturing the angle stability between synchronous machines, used to predict the risk of power angle out-of-step; is the speed deviation, the deviation of the generator speed from the reference, jointly determined by mechanical inertia and electromagnetic force, dynamic response indicator, helping to analyze frequency fluctuations and evaluate system damping effect; is the synchronous speed 50Hz, reference point, used for normalized deviation calculation.

[0095]

[0096] where, is the inertia constant, the mechanical inertia of the generator rotor, resisting sudden changes in speed such as frequency drop caused by photovoltaic output drop, quantifying the system's buffering capacity for disturbances, used for small disturbance stability analysis; is the damping coefficient energy dissipation mechanism, damping winding absorbs oscillation energy, damping factor to slow down system oscillation, helping to evaluate the convergence speed of transient process;

[0097] is the mechanical power, control u part, input mechanical energy such as torque provided by water turbine or standby unit, control source, used to balance electrical load; is the electrical power, electromagnetic energy exchange, transmitted through the line, output load reflection, used for power imbalance diagnosis.

[0098]

[0099] Photovoltaic disturbance simultaneous:

[0100]

[0101] where, is the photovoltaic current, is the photo current (dependent on G / T, known from the first module, photovoltaic effect basis, environmental dependent term, used for uncertainty modeling); is the saturation current, k is the Boltzmann constant, is the series resistance, is the parallel resistance. Energy storage constraints:

[0102]

[0103] where, is the energy storage state, For charging and discharging efficiency, For charging and discharging power; safety domain is defined as a subset of states where there exists a control u such that the trajectory always satisfies the constraints K (e.g. )

[0104]

[0105] where g is inequality constraint, PINNs approximate safety domain function u(x):

[0106]

[0107] where, are layer weights / biases, used to train the solution, network parameters model the physical mapping, as a function approximator, provide high-dimensional nonlinear representation); is activation, to introduce nonlinearity to match actual grid behavior such as voltage nonlinear response, universal approximation theorem supports, allow the model to capture complex dynamics.

[0108] Loss function:

[0109]

[0110] This is the total loss function of PINNs, used to optimize network parameters θ, including weights W and biases b, updated during training. It integrates four parts by weighted sum: data loss (fit observations), PDE loss (comply with physical equations), BC loss (meet boundary conditions) and stability loss (ensure system stability). Minimizing L(θ) makes network output u(x) match both data, in grid, from measurements (e.g. voltage V), PDE describe dynamics (e.g. power flow), BC are limits (e.g. V<1.05pu), and stability prevent instability (e.g. frequency oscillation). These correspond to actual scenarios, such as photovoltaic fluctuations leading to Ppv mutations, need to be ensured by loss penalty to make the model simulate real physical process, make it comply with the physical law of grid. λ1, λ2, λ3 are weight coefficients, determined by tuning, used to balance the contribution of each loss.

[0111]

[0112] where, is network predicted safety value, is observed safety value, simulated or measured boundary. This formula is mean square error (MSE) loss used to measure the difference between network predicted and observed . Averaged divided by Normalization, avoid scale effects. Data points come from actual measurements (e.g. SCADA system collects V / ω), reflect grid operation, like V drop under photovoltaic disturbance, loss-based prediction deviates. Empirical risk minimization, make model fit known scenarios, improve accuracy. MSE is sensitive to outliers, suitable for grid continuous variables. If data loss is high, it indicates Mismatched photovoltaic scenarios, adjust training Fit, like cloud shadow P_pv data.

[0113]

[0114] This is PDE residual loss, measures difference between predicted state derivative and model f. L2 norm penalizes deviation, average normalization. Where is number of PDE points, is the i-th point state derivative, automatically differentiated by network. , , is point state, control, disturbance. PDE points are internal "virtual" points, residual enforces physical power flow conservation, simulate how photovoltaic disturbance propagates (e.g. P_pv drop causes ω change). Meshless PDE solution, embeds physical knowledge through residual minimization, improves generalization, avoids data scarcity issues. If PDE loss is high, it indicates model violates dynamics (e.g. photovoltaic injection imbalance), adjust to ensure physical consistency.

[0115]

[0116] This is boundary condition loss, measures difference between predicted u and constraints g. L2 norm penalizes violation, average normalization. Boundary points represent limits (e.g. V upper bound), loss enforces model respects limits at edges, simulate photovoltaic over-limit induced collapse, ensure solution uniqueness, improve model boundary accuracy. If BC loss is high, it indicates violation of limits (e.g. photovoltaic causes V>1.05), adjust to strengthen boundaries.

[0117]

[0118] This is stability loss, penalizes positive part of maximum eigenvalue of Jacobian J (ReLU, ignores negative values). Average normalization. Spectral >0 indicates instability (e.g. photovoltaic disturbance amplifies oscillations), loss penalizes positive spectrum, ensures system damps photovoltaic fluctuations. If stability loss is high, it indicates Allowing instability points, adjusting to avoid photovoltaic-induced frequency collapse. To cope with extreme fluctuations of photovoltaic clusters, the invention models disturbances by solving stochastic differential equations (SDEs):

[0119]

[0120] Where A / B / C are linearization matrices; is the standard deviation of fluctuations, is the intensity of random noise in the first module, quantifying uncertainty, representing the statistical characteristics of photovoltaic variability; is a Wiener process, a continuous disturbance simulation, such as Brownian motion, describing noise paths in a stochastic process framework, supporting Monte Carlo trajectory generation.

[0121] Domain simplification using convex optimization to fit an ellipsoid:

[0122]

[0123] Where Q is a positive definite matrix, optimized to define the shape of the ellipsoid to enclose the set of safe points, such as an elliptical boundary describing voltage / power through a quadratic form, reducing computational complexity with convex approximation, ensuring mathematical differentiability of the boundary and facilitating optimization; c is the center vector, the geometric center of the safety domain, such as the average offset point in the state space, adjusting the offset to fit asymmetric domains, such as skewed distributions caused by photovoltaic disturbances. Define and simplify steps: use a computer as the main execution body, describe the following steps:

[0124] 1. Data input and preprocessing: the computer obtains photovoltaic scenarios (P_pv sequence, G, T) from the first module, constructs the state space x and disturbance d. Sample collocation points N=10^5, calculate the Jacobian J to evaluate sensitivity:

[0125]

[0126] Initialize PINNs input, ensure that the disturbance reflects the true fluctuations (key step, reduce subsequent computational burden, filter irrelevant variables through sensitivity analysis, improve training efficiency).

[0127] 2. PINNs network construction and training: the computer initializes the MLP (5-10 layers, hidden units 200-500, Tanh activation), inputs the sampling points and minimizes L(θ) training using the Adam optimizer (learning rate 1e-3, decay factor 0.95), iterating 1000-5000 steps, early stopping based on PDE residual <1e-4. Approximate the safety domain function u(x), integrate physics to improve generalization (key step, avoid overfitting of pure data-driven, efficiently solve PDEs through automatic differentiation, achieve high-dimensional nonlinear approximation).

[0128] 3. Safety region definition: computer extracts boundary points by evaluating u(x; θ)≤0, filters infeasible paths by sampling 10^6 trajectories from SDE, computes level set gradient Confirms boundary continuity. Defines dynamic region, handles photovoltaic uncertainty (core output, provides decision basis, visualizes region boundary through level set method, supports visual analysis).

[0129] 4. Safety region simplification and verification: computer fits ellipsoid from boundary points, solves Q and c using convex optimization (such as CVXPY library) (initialize Q as identity matrix, c as mean point, iterate until convergence), computes volume error:

[0130]

[0131] where, is the volume integral (physical background is the measurement domain capacity to quantify coverage, such as estimating the volume of multi-dimensional space through Monte Carlo sampling, theoretical significance is error evaluation, ensuring that simplification retains the essence of the original domain); is the symmetric difference set (physical background is the overlap deviation, representing the non-intersection part of the simplified domain and the original domain, theoretical significance is precision measurement, evaluating the loss of approximation). If ε>5%, the computer increases sampling and re-fitting. Simplifies high-dimensional domain, supports scheduling, improves practicality, ensures computability through convex optimization, reduces optimization variables;

[0132] This method is derived from Feynman Path Integral Theory, which takes the time-space wave field scenario generated by the first module and the dynamic safety region defined by the second module as input, and iteratively optimizes the scheduling trajectory through the feedback of the dynamic elasticity and stability evaluation results of the fourth module. It quickly solves the daily power generation plan, energy storage charging and discharging strategy and standby allocation, and supports economic-safety balanced scheduling under high-penetration photovoltaic fluctuation. According to the Path Integral Theory proposed by Richard Feynman, this method extends the concept of quantum mechanics probability amplitude to the field of stochastic optimal control, and efficiently handles nonlinear dynamics and uncertainty through parallel sampling under the MPPI framework.

[0133] In a water-light-storage new energy cluster, traditional scheduling optimization (such as mixed integer linear programming MILP) is difficult to handle photovoltaic minute-level fluctuations and safety region constraints in real time, resulting in slow calculation or suboptimal solution. MPPI converts the control problem into trajectory sampling through Feynman Path Integral, and simultaneously optimizes economic cost and safety penalty:

[0134]

[0135] where, is the total cost of trajectory , which is the total cost of scheduling, optimized by stochastic expectation; is terminal state penalty (e.g. SOC deviation at end of storage, periodic closed loop, long term stability); is operational cost (e.g. generation cost + reserve penalty). MPPI samples K trajectories ( - ), weighted average optimizes . Compared with traditional MPC, this method has no derivative requirement, and can handle non-convex costs such as safety domain penalty. MPPI converges faster and is more robust in photovoltaic scenarios. Fluctuating scenarios as disturbances ; safety domain as a cost item, ensures that the optimized trajectory is within the domain, and the Koopman evaluation result is fed back (e.g. elasticity index is used to adjust or penalty), iterative refinement , closed loop optimization. MPPI is based on Feynman path integral, which expresses stochastic optimal control as trajectory probability weighted. Feynman theory is originally used for amplitude calculation in quantum mechanics:

[0136]

[0137] where, is amplitude, a wave function that superimposes all paths; is the action (classical Lagrangian integral); is the reduced Planck constant; is the path measure. MPPI is extended to control, replacing with negative cost, exponentially weighting trajectories:

[0138]

[0139] where, is optimal control; is trajectory weight (i.e. "probability density", soft-maximization, selects low-cost path); is trajectory cost (physical background is total fee for scheduling, theoretical significance is evaluation function); is temperature parameter, exploration-exploitation balance, inverse temperature, controls sampling diversity;

[0140] System dynamics is SDE:

[0141]

[0142] where, is deterministic dynamics; is diffusion matrix; is Wiener process. MPPI samples disturbance , simulates trajectory:

[0143]

[0144] Costs include economic + safety:

[0145]

[0146] For economic cost, minimize operating cost; For safety penalty, domain boundary violation, soft constraint; For flexibility penalty, assess flexibility of scheme, feedback iteration; Terminal penalty (e.g., deviation). For fast solution, MPPI parallel GPU sampling (trajectory / step), weighted update, iterative feedback fourth module assessment. In theory, derived from the Feynman-Kac formula, convert PDE to path integral, avoid grid calculation.

[0147] To further improve the core content of optimization solution, the application extends the MPPI framework to process the specific challenges of large-scale new energy clusters, including high-dimensional state space (state vector dimension can reach hundreds, such as multi-node voltage / power) and real-time requirement (intra-day rolling optimization needs <1min). Introduce adaptive sampling strategy: dynamically adjust the sampling covariance based on the volatility of photovoltaic (variance obtained from the first module), such as increasing in high uncertainty period (cloud cover event) to explore more extreme trajectories and avoid local optimal trap. The formula is:

[0148]

[0149] Wherein, is the base covariance; is the scaling factor (empirical value 0.1-0.5); is the current photovoltaic output variance; is the unit matrix. This adaptive improves robustness, simulates the "diffusion" of Feynman path to cover uncertain paths. In addition, multi-stage rolling optimization is integrated: MPPI solves within each prediction window (T=15-60min), but through sliding window (step 5min) rolling update, long-term economic (such as fuel cost) and short-term safety (such as ramp rates) are solved. The cost function is extended to a hierarchical form:

[0150]

[0151] Wherein, is the fuel / backup cost coefficient; is the distance to the safety domain boundary (L2 norm, close to instability); is the fourth module Koopman flexibility index; ​is the weight (dynamically adjusted based on volatility level). This ensures that the optimization is not only economic but also flexible, handling scenarios with photovoltaic penetration > 50%. To speed up the computation, importance sampling is employed: low-cost trajectories are sampled preferentially, resampled through an elite subset (top-10%), reducing invalid paths.

[0152] Optimization solving step:

[0153] With computer as the execution subject, the following steps are described:

[0154] 1. Data input and preprocessing: the computer obtains the volatility scenario and the safety domain from the first / second step, and constructs the state and reference trajectory. K=10^4 perturbations ε~N(0,Σ) are sampled (Σ is known, volatility covariance). Adjust Σ adaptively based on the current Var(P_pv). Initialize MPPI input to ensure that the optimization considers real volatility, reduces sampling bias, and improves robustness. 2. Trajectory sampling and dynamic simulation: the computer simulates K trajectories in parallel:

[0155]

[0156] Generate potential scheduling trajectories, simulate uncertainty, capture photovoltaic randomness through SDE, and support Feynman integral approximation. Multi-stage rolling: update the window T every 5 minutes.

[0157] 3. Cost calculation and quantification: the computer calculates

[0158]

[0159] Weight Evaluate trajectories, select low-cost safe paths, weight Feynman path probability, and randomly optimize. Integrate importance sampling: based on the previous Resample elite trajectories.

[0160] 4. Control update and verification: the computer updates , verifies that the cost converges <thresh or the iteration <max_iter. Optimize scheduling, confirm economic-safety balance, converge to global near-optimal, and verify the feasibility of energy storage / back-up. Thresh takes 1e-3. Feedback to the fourth module evaluation, and if the flexibility < threshold, re-optimize.

[0161] 5. Closed-loop iteration and output: the computer integrates the fourth module feedback, adjusts the penalty weight , iterates 2-5 rounds until the flexibility > 0.8. Output the final schedule: intra-day P_gen(t), SOC(t), P_res(t), ensure system stability under extreme photovoltaic scenarios, and calculate time;

[0162] S4: Dynamic flexibility and stability evaluation of the scheduling scheme based on the theory of the Koopman operator:

[0163] The initial scheduling scheme obtained in S3 is obtained, the time and space fluctuation scenario conforming to the electrical constraint and the energy storage constraint obtained in S1 is injected into the initial scheduling scheme and preprocessed, a data matrix and a shift matrix are constructed based on the preprocessed data, a Kramers- Kronig operator is approximated and spectrum decomposition is performed on the Kramers-Kronig operator, a stability index and a flexibility index are calculated, the stability index and the flexibility index are fed back to S3, S3 adjusts the cost penalty term weight according to the fed back stability index and flexibility index, and iterative optimization is performed until the stability index and the flexibility index meet preset requirements, and a final scheduling scheme is output;

[0164] The "calculating the stability index and the flexibility index" in S4 includes that the stability index is calculated by a spectral radius, the spectral radius is the maximum value of the modulus of the eigenvalue of the Kramers-Kronig operator, and the stability index value is determined according to the relationship between the spectral radius and a preset stability threshold; the flexibility index is calculated by a modal recovery time, the modal recovery time is related to the real part of the eigenvalue; and the overall flexibility index is determined by combining the modal energy weight, the normalized recovery time and the modal number, and the overall flexibility index value ranges from 0 to 1. The "feeding back the stability index and the flexibility index to S3; S3 adjusts the cost penalty term weight according to the fed back stability index and flexibility index, and iterative optimization is performed until the stability index and the flexibility index meet preset requirements" in S4 includes that if the stability index or the flexibility index exceeds a preset qualified range, the stability index and the flexibility index are fed back to S3; S3 adjusts the cost penalty term weight according to the feedback result, the adjustment direction of the cost penalty term weight is related to the type of the index exceeding the qualified range; iterative optimization is performed, the number of iterations is configured as a preset number of rounds, until the stability index and the flexibility index both meet the preset qualified range, and a final scheduling scheme is output, including the following steps:

[0165] The method takes the scheduling scheme optimized by the third module as input, linearizes the nonlinear power grid dynamics into a function space through the Kramers-Kronig operator theory, evaluates the dynamic flexibility and stability of the scheme under photovoltaic fluctuation, outputs quantitative indexes to feedback the third module for iterative optimization, and supports closed-loop intra-day forward scheduling. According to the Kramers-Kronig operator theory proposed by Bernard Koopman, the method maps nonlinear dynamics to a linear infinite-dimensional Hilbert space, identifies dominant modes through spectrum decomposition, and efficiently handles high-dimensional uncertainty in power system applications, such as transient stability analysis of high-penetration new energy clusters and coherent generator identification.

[0166] In a water-light-storage new energy cluster, traditional evaluation methods (such as time-domain simulation or Lyapunov function) are computationally intensive and difficult to quantify flexibility in real time, resulting in scheduling schemes that ignore recovery capabilities or respond sluggishly to photovoltaic minute-level fluctuations. The Kramers-Kronig operator K is defined as a linear evolution operator:

[0167]

[0168] where, is the Koopman operator (theoretical sense of linearizing the nonlinear dynamics to the observation function provides a global linear representation, supports spectral analysis and prediction on the evolution of the system): is the observation function (known, such as polynomial combinations of the power P, voltage V or frequency ω of the state vector x, used to lift the dimension to capture nonlinearity); f is the nonlinear dynamic map (input from the third module, including the swing equation under photovoltaic perturbation). Spectral decomposition reveals the system modes:

[0169]

[0170] where, are the eigenvalues; the real part is the growth / decay rate, denotes stable mode decay; the imaginary part denotes oscillation frequency, in Hz, used to identify inter-cluster modes at low frequencies such as 0.1-2 Hz); are the eigenfunctions, describing the mode shape, such as the spatial distribution of voltage gradient under photovoltaic perturbation; are the mode coefficients, quantifying the mode amplitude. This decomposition allows to identify photovoltaic perturbation modes, such as frequency oscillations caused by radiation gradient, elasticity assessment based on decay rate and recovery time, stability based on spectral radius.

[0171] To achieve a finite-dimensional approximation, the present invention employs dynamic mode decomposition as a numerical proxy for the Koopman operator, particularly in power systems for transient stability prediction and coherence analysis. DMD constructs an approximate operator from a time-series data matrix:

[0172]

[0173] where, is the data matrix (columns are state snapshots, such as state vectors from the optimized trajectory , dimension , is the state dimension voltage / power); is the shift matrix (from to ); is the pseudo-inverse (computed via singular value decomposition, SVD). SVD decomposition :

[0174]

[0175] where, are the left singular vectors (known, , To truncate the rank and capture the dominant direction, such as the voltage mode at the photovoltaic injection point. diagonal singular value matrix (given, Singularity Indicates mode energy, Large corresponds to strong mode); It is the transpose and conjugate of the right singular vector (given, (Time evolution). Then, low-order approximation:

[0176]

[0177] right Eigenvalues ​​are obtained by performing eigenvalue decomposition, Λ(diag( )) and eigenvectors Koopman pattern:

[0178]

[0179] These patterns This describes the spatial structure, such as how local disturbances in a photovoltaic cluster propagate to global frequency instability. In photovoltaic applications, X is constructed from an optimized trajectory (state sequences such as V(t), ω(t), Ppv(t)) to capture disturbance modes such as subsynchronous oscillations of 0.5–1 Hz or voltage collapse under high photovoltaic penetration. To improve the capture of nonlinear photovoltaic dynamics (such as IV curve bending or the nonlinear effects of temperature gradients), this invention extends to extended dynamic mode decomposition, using dictionary functions to elevate the observation space:

[0180]

[0181] in, These are dictionary vectors; polynomials are used to capture quadratic nonlinearities such as power flow equations; the RBF Gaussian kernel... Local photovoltaic disturbances are captured around center c; trigonometric functions simulate oscillations. EDMD matrix:

[0182]

[0183] in, It is the matrix that lifts X (d×(N-1)). This improves the accuracy of the Koopman approximation and supports high-dimensional power grids such as clusters with 1000+ nodes.

[0184] Stability assessment: Calculation of spectral radius (<1 indicates asymptotic stability; all modes are considered); Modal growth rate This indicates good damping (threshold -0.05 indicates sufficient damping to prevent amplification of photovoltaic fluctuations); oscillation frequency. For classification mode (<0.1 Hz for slow mode, vulnerable to PV) , instability in the form of power angle instability due to PV output collapse.

[0185] Elasticity assessment: quantify resilience, based on modal recovery time , modal energy , overall elasticity index (integrated to recovery time , e.g. 1-5 min), simulated trajectory recovery curve after disturbance. If E<0.8, indicate poor elasticity, feedback adjustment to dispatch reserve.

[0186] To handle uncertainty, the invention incorporates noise-robust DMD (e.g. total least squares DMD) that minimizes the impact of disturbance:

[0187]

[0188] where, is the Frobenius norm; is the regularization parameter (0.01-0.1, based on PV noise level). This improves robustness to measurement noise, e.g. PV output error in SCADA data.

[0189] Assessment steps:

[0190] 1. Data input and preprocessing: computer obtains the optimal dispatch trajectory (state sequence , N=1000-10000 steps, x includes P_gen(t), SOC(t), V(t), etc.) from the third module, injects the first module PV disturbance scenario (P_pv fluctuation, G / T sequence) to simulate extreme events, e.g. 20% output drop due to cloud shadow. Construct the lifting matrix Ψ if EDMD is used (select dictionary: polynomial order 2-3, RBF kernel 10-20 centers, filter irrelevant observations based on sensitivity analysis). Preprocessing includes Z-score normalization and singular value truncation (retain σ j >0.01) to ensure capturing PV uncertainty (key step, reduce noise, improve mode extraction accuracy);

[0191] 2. Koopman approximation and spectral decomposition: computer computes SVD (X or ) to get U, Σ, V; solve for low-order , eigen decomposition to get , W. Compute modes (or equivalent). Identify dominant modes (sort |descending, take top 10-20), extract PV-related modes like cluster oscillation (core step, provide linear representation, support efficient spectral analysis, avoid nonlinear simulation computational burden);

[0192] 3. Stability and elasticity computation: computer computes spectral radius , if flagged unstable (consider 5% margin); growth rate , threshold indicates under-damped. Elasticity , overall (normalized recovery fraction, s). Inject Monte Carlo perturbation (100-500 trajectories, from first module) to verify robustness, compute mean and variance, quantify scheme's immunity and recovery against photovoltaic fluctuations, support closed-loop optimization;

[0193] 4. Evaluation and feedback: computer outputs indicators (stability S=1- if 0 otherwise; elasticity , range 0-1). Visualize patterns (hotmap shows photovoltaic impact area). If S<0.95 or E<0.8, feedback third module to adjust cost penalty (e.g. increase ), iterate 2-5 rounds. Computation time <1s / evaluation (GPU acceleration), ensure real-time intra-day scheduling (final output, provide decision basis, boost system elasticity).

[0194] While the embodiments of the application have been shown and described, it is to be understood that the embodiments proposed are only by way of example and that many modifications, substitutions, alternatives, and variations can be suggested to one skilled in the art and that the scope of the present application is to be limited only by the appended claims and equivalents thereof.

Claims

1. A method for fast solving day-ahead scheduling considering large-scale new energy cluster generation fluctuation, characterized in that, The method comprises the following steps: S1: generating a new energy cluster space-time fluctuation scene based on a neuron cellular automaton: Integrate historical electrical data of the new energy cluster, preprocess and grid to construct a multi-channel grid, train a neuron cellular automaton network to generate a space-time fluctuation scene, and after inverse normalization and verification, obtain a space-time fluctuation scene conforming to the electrical and energy storage constraints; S2: defining and simplifying a dynamic security domain of a power grid based on a physical information neural network: Based on the space-time fluctuation scene, construct three vectors of grid state, control and disturbance, train a physical information neural network to define a dynamic security domain, and after convex optimization simplification and verification, obtain a low-dimensional simplified security domain; S3: fast optimization solution of scheduling based on model predictive path integral: Combine the space-time fluctuation scene and the low-dimensional simplified security domain of S2 to construct system state and reference trajectory, sample disturbance to simulate scheduling trajectory, calculate cost and weight, update control strategy to obtain an initial scheme; S4: dynamic flexibility and stability evaluation of scheduling scheme based on Koopman operator theory: Inject the space-time fluctuation scene into the initial scheme of S3, construct a matrix and approximate the Koopman operator, and perform spectral decomposition to calculate stability and flexibility indexes; feedback to S3 to adjust the cost penalty weight, iterate until the indexes meet the standard, and output the final scheme. 2.The method of claim 1, wherein, The specific steps of preprocessing and gridding in S1 are as follows: adopt bilinear interpolation to fill in missing data points in historical electrical data, calculate the values of adjacent known data points and the weight based on distance during interpolation, and set the distance measurement range to 0-1 and configure a normalization factor; perform Z-score normalization on the filled data, and combine the original data mean and standard deviation during normalization; add Gaussian noise to the normalized data, and the noise amplitude is controlled by the photovoltaic power variance; the constructed multi-channel grid includes power, radiation, temperature and energy storage state channels, and the grid dimension is represented by the spatial dimension and the number of channels. 3.The method of claim 1, wherein, The specific way of training the neuron cellular automaton network in S1 is as follows: adopt Xavier initialization method to initialize network parameters, the neuron cellular automaton network architecture includes convolution perception layer and multilayer perception update layer, the convolution perception layer adopts a preset size convolution kernel, and the multilayer perception update layer is a multilayer fully connected structure and is configured with an activation function; the training targets to minimize a loss function containing a time series loss and an autocorrelation regular term, the time series loss is related to the predicted grid state, the current state and the state increment output by the multilayer perception, and the autocorrelation regular term is related to the Pearson correlation coefficient, the decay time constant based on the photovoltaic response and the power related parameters; adopt an adaptive optimizer for training, and the training process is configured with a learning rate, a batch size and an iteration step number. 4.The method of claim 1, wherein, The specific way of training the physical information neural network in S2 is that the physical information neural network adopts a multi-layer perceptron structure, and is configured with a preset number of layers, a number of hidden units and an activation function; training is targeted at minimizing a total loss function containing data loss, PDE residual loss, boundary condition loss and stability loss, and the total loss function is balanced by the weights of each loss term; the data loss is associated with the network's predicted safety value, observed safety value and data point number, the PDE residual loss is associated with PDE point number, state derivative and state vector, control vector and disturbance vector, the boundary condition loss is associated with predicted boundary value and constraint boundary value, and the stability loss is associated with eigenvalues of the Koopman operator Jacobian matrix and the ReLU function; an adaptive optimizer is used for training, and the training process is configured with a learning rate, a reduction factor, a number of iteration steps and an early stopping condition.

5. The method of claim 1, wherein, The specific steps of simplifying and verifying the power grid dynamic security domain by using the convex optimization method in S2 are: fitting a geometric figure to simplify the power grid dynamic security domain by using the convex optimization method, and the geometric figure is characterized by a positive definite matrix and a center vector; solving the positive definite matrix and the center vector by using a numerical calculation library, and the positive definite matrix is initialized as an identity matrix and the center vector is initialized as the average point of the power grid state; The volume error is calculated to verify the simplification effect, and the volume error is associated with the volume of the simplified geometric figure, the volume of the original power grid dynamic security domain and the symmetric difference set; if the volume error exceeds a preset threshold, the sampling points are increased for re-fitting until the volume error meets the preset requirement.

6. The method of claim 1, wherein, The specific contents of constructing the system state and the reference trajectory and preprocessing in S3 are: the system state includes power generation related parameters, energy storage related parameters and backup related parameters; the reference trajectory is a benchmark trajectory determined based on an economic target; during preprocessing, the sampling covariance is adaptively adjusted based on the current photovoltaic output variance, and the adjustment is combined with the base covariance, a scaling factor and the current photovoltaic output variance, and the sampling covariance is characterized in the form of a matrix. 7.The method of claim 1, wherein, The specific way of calculating the total cost of each dispatch trajectory and weighting in S3 is that the total cost includes economic related cost, safety related penalty, elasticity related penalty and terminal related penalty, the economic related cost is associated with a fuel / backup cost coefficient, the safety related penalty is associated with the distance to the boundary of the low-dimensional simplified security domain, the elasticity related penalty is associated with the Koopman elasticity index, and the terminal related penalty is associated with the deviation of the energy storage end state; The weight of each dispatch trajectory is calculated based on the Feynman path integral theory, and the weight is associated with the trajectory cost, a temperature parameter and the exponential sum of all trajectory costs; an importance sampling strategy is adopted, and the trajectories with weights meeting a preset condition are preferentially selected. 8.The method of claim 1, wherein, The specific steps of constructing a data matrix and a shift matrix, an approximate Koopman operator and spectral decomposition in S4 are: the data matrix is composed of state snapshots, and the shift matrix is composed of state snapshots adjacent in time sequence; singular value decomposition is performed on the data matrix to obtain left singular vectors, a diagonal singular value matrix and right singular vector transpose conjugate; the pseudo-inverse of the data matrix is used to solve a low-order Koopman operator approximation; Characteristic decomposition is performed on the low-order Koopman operator to obtain eigenvalues and eigenvectors; a preset number of eigenvalues and eigenvectors are selected in descending order of singular values as dominant disturbance modes. 9.The method of claim 1, wherein, The specific manner of calculating the stability index and the elasticity index in the S4 is as follows: the stability index is calculated by a spectral radius, the spectral radius is the maximum value of the modulus of the eigenvalue of the Koopman operator, and the stability index value is determined according to the relationship between the spectral radius and a preset stability threshold; the elasticity index is calculated by a modal recovery time, the modal recovery time is related to the real part of the eigenvalue; and the overall elasticity index is determined in combination with a modal energy weight, a normalized recovery time and a modal number, and the overall elasticity index value ranges from 0 to 1. 10.The method of claim 1, wherein, The specific process of the feedback iteration optimization in the S4 is as follows: if the stability index or the elasticity index exceeds a preset qualified range, the stability index and the elasticity index are fed back to the S3; the S3 adjusts the cost penalty term weight according to the type of the index exceeding the qualified range; The iteration optimization is performed for a preset number of rounds until the stability index and the elasticity index both meet the preset qualified range, and a final scheduling scheme is output.

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