Intra-day look-ahead scheduling rapid solving method considering large-scale new energy cluster power generation volatility

Abstract

The invention relates to the technical field of power system scheduling, and discloses an intra-day look-ahead scheduling rapid solving method considering large-scale new energy cluster power generation volatility. Comprising the following steps of S1, new energy cluster space-time fluctuation scene generation based on a neuron cellular automaton, S2, power grid dynamic security domain definition and simplification based on a physical information neural network, S3, scheduling rapid optimization solution based on model prediction path integration, and S4, scheduling scheme dynamic elasticity and stability evaluation based on a Kupman operator theory. The new energy cluster space-time fluctuation scene generation method based on the neuron cell automaton can effectively generate a space-time scene reflecting large-scale new energy cluster power generation volatility, supports uncertainty analysis, has the advantages of being high in calculation efficiency and scene authenticity, and is suitable for large-scale new energy cluster power generation. The problem that scene generation is inaccurate due to the fact that a traditional statistical model ignores space-time coupling is solved.

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: S1: New energy cluster spatiotemporal fluctuation scenario generation based on neural cellular automata: Integrate new energy cluster historical electrical data, preprocess and grid to build multi-channel grid, train neural cellular automata network to generate fluctuation scenario, and get spatiotemporal fluctuation scenario conforming to electrical and energy storage constraints after inverse normalization and verification; S2: Dynamic security domain definition and simplification of power grid based on physical information neural network: Based on S1 scenario, construct power grid state, control and disturbance vector, train physical information neural network to define dynamic security domain, and get low-dimensional simplified security domain after convex optimization simplification and verification; S3: Fast optimization solution of scheduling based on model predictive path integral: 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; S4: Dynamic flexibility and stability evaluation of scheduling scheme based on Koopman operator theory: 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, and output the final scheme.

[0007] Preferably, the specific steps of preprocessing and gridding in S1 are: filling missing data points in historical electrical data with bilinear interpolation, calculating the value of adjacent known data points and the weight based on distance during interpolation, and setting the distance measurement range to 0-1 and configuring the normalization factor; normalize the filled data with Z-score, 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 related channels, and the grid dimension is represented by the spatial dimension and the number of channels.

[0008] Preferably, the specific way of training neural cellular automata network in S1 is: initialize network parameters with Xavier initialization method, neural cellular automata network architecture includes convolution perception layer and multilayer perception update layer, convolution perception layer uses preset size convolution kernel, and multilayer perception update layer is a multilayer fully connected structure and is configured with an activation function; the training targets to minimize the loss function containing time series loss and 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 photovoltaic response and the power related parameters; use adaptive optimizer for training, and configure learning rate, batch size and iteration steps during training process.

[0009] Preferably, the specific way of training the physical information neural network in S2 is that the physical information neural network adopts a multi-layer perception 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 predicted safety value, the observed safety value and the number of data points, the PDE residual loss is associated with the PDE point number, the state derivative and the state vector, the control vector and the disturbance vector, the boundary condition loss is associated with the predicted boundary value and the constraint boundary value, and the stability loss is associated with the eigenvalue 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 stop condition.

[0010] Preferably, the specific steps of simplifying and verifying the power grid dynamic security domain in S2 by using the convex optimization method are that the power grid dynamic security domain is simplified 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 the mean 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 to re-fit until the volume error meets the preset requirement.

[0011] Preferably, the specific content of constructing the system state and the reference trajectory and preprocessing in S3 is that the system state contains 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.

[0012] Preferably, the specific way of calculating the total cost of each scheduling trajectory and weighting in S3 is that the total cost contains 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 scheduling 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 whose weights meet the preset conditions are preferentially selected.

[0013] Preferably, the specific steps of constructing a data matrix and a shift matrix, an approximate Krylov operator and spectral decomposition in S4 are as follows: the data matrix is composed of state snapshots, and the shift matrix is composed of adjacent state snapshots 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 Krylov operator approximation is solved based on the pseudo-inverse of the data matrix; characteristic decomposition is performed on the low-order Krylov 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.

[0014] Preferably, the specific way of calculating the stability index and the elasticity index in S4 is as follows: the stability index is calculated by spectral radius, the spectral radius is the maximum value of the modulus of the eigenvalues of the Krylov operator, and the stability index value is determined according to the relationship between the spectral radius and the preset stability threshold; the elasticity index is calculated by modal recovery time, the modal recovery time is related to the real part of the eigenvalue; the overall elasticity index is determined by combining the modal energy weight, the normalized recovery time and the number of modes, and the overall elasticity index value ranges from 0 to 1.

[0015] Preferably, the specific process of feedback iteration optimization in S4 is as follows: if the stability index or the elasticity index exceeds the preset qualified range, the stability index and the elasticity index are fed back to S3; S3 adjusts the cost penalty term weight according to the type of index exceeding the qualified range; a preset number of iterations are performed until the stability index and the elasticity index meet the preset qualified range, and the final scheduling scheme is output.

[0016] The application provides an intra-day forward scheduling fast solving method considering large-scale new energy cluster power generation fluctuation. 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 scene authenticity, and solves the problem of inaccurate scenario generation caused by ignoring space-time coupling in traditional statistical models.

[0017] 2. The power grid dynamic security domain fast definition and simplification method based on physical information neural network provided by the application can quickly define and simplify the security operation domain of the power grid under new energy fluctuation, avoid voltage / frequency instability, has the advantages of high precision and low calculation complexity, and solves the problem that high-dimensional security domain definition requires hourly simulation and cannot respond in real time.

[0018] 3. The scheduling fast optimization solving method based on model predictive path integral control provided by the application can quickly solve the intra-day scheduling optimization trajectory, balance economy and safety, has the advantages of strong robustness and fast parallel calculation, and solves the problem that traditional optimization algorithms are sensitive to non-convex constraints, slow to solve and prone to local optimum.

[0019] 4、The dynamic flexibility and stability evaluation method of the scheduling scheme based on the Koopman operator theory can evaluate the dynamic flexibility 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 the lack of closed-loop evaluation leads to poor flexibility of the scheduling scheme and instability under high penetration of new energy. BRIEF DESCRIPTION OF DRAWINGS

[0020] Figure 1 A schematic diagram of the intra-day forward scheduling fast solving method considering the intra-day fluctuation of large-scale new energy clusters; Figure 2 A product scheme diagram of the present application. DETAILED DESCRIPTION

[0021] The technical solutions in the embodiments of the present application will be described clearly and completely in conjunction with the drawings in the specification of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, not all the embodiments. 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.

[0022] Embodiment: 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 intra-day fluctuation of large-scale new energy clusters, comprising the following steps: The present application aims at the fluctuation of large-scale water-light-storage new energy clusters, such as the current-voltage (I-V) characteristic shift caused by the minute-level radiation variation of photovoltaic array due to cloud movement, or the uneven electrical output between panels caused by temperature gradient. The method of Neural Cellular Automata (NCA) is used for spatio-temporal fluctuation scenario generation. 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, current) in space and time are simulated through local neural network rules, thereby generating diversified extreme scenarios to support uncertainty analysis in intra-day 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 spatio-temporal fluctuation of new energy electrical quantities such as total solar radiation, which provides a solid foundation for simulating the real operating characteristics of photovoltaic clusters.

[0023] In new energy clusters, traditional models (such as statistical methods or GAN) often ignore the spatio-temporal coupled electrical quantity distribution, for example, the radiation gradient decay caused by local cloud shading in photovoltaic arrays affects the module current

[0024] (1) In the formula, the photovoltaic IV model, Photocurrent, Let q be the saturation current, q be the charge, k be the Boltzmann constant, and T be the temperature. The decrease in electrical output is due to parallel resistance or temperature gradient (power is affected by T). β is the temperature coefficient, and G is the radiation. (Referencing a reference temperature). NCA addresses this issue through a multi-channel grid representation (channels encode electrical quantities: power P, radiation G, temperature T, etc.), with its update rules parameterized as a neural network, combining new energy electrical dynamics. Cellular automata models can accurately simulate the IV curve and temperature effects of photovoltaic panels. NCA extends this to cluster-level spatiotemporal electrical variability, ensuring that the generated scenarios conform to actual electrical constraints, such as output limits, ramp rates, and energy storage status. In new energy clusters, traditional models (such as statistical methods or GANs) often neglect spatiotemporal coupling, such as the attenuation of radiation gradients caused by local cloud shading in photovoltaic clusters. NCA addresses this issue through a multi-channel grid representation (channels encode output, wind speed, radiation, temperature, etc.), with its update rules parameterized as a neural network, combining new energy physical dynamics:

[0025] in, It 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:

[0026] 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. , is the temperature loss term (d is the distance vector), describing the spatio-temporal evolution of temperature T in the cluster; (7) is the extension of is the short-circuit current, is the temperature coefficient, is the reference irradiance; (8) to (10) impose power constraints is the photovoltaic power, up / down is the ramp-up / ramp-down rate limit), ensuring the generated scenario avoids extreme fluctuations beyond the system's capacity; (11) to (13) integrate the energy storage model is the energy storage state, is the charge / discharge efficiency, min / max is the limit, to / tN is the initial / final state consistency), smoothing photovoltaic fluctuations in the water-light-storage base. This comprehensive model ensures that the scenarios generated by the NCA not only reflect the electrical characteristics of photovoltaic, but also couple with the energy storage scheduling requirements.

[0027] To address extreme electrical fluctuations of photovoltaic clusters in water-light-storage bases (such as voltage instability or risk of disconnection under high penetration, leading to electrical quantities exceeding limits such as ), the present invention incorporates a variational NCA (VNCA) by introducing a noise channel to simulate uncertainty:

[0028] wherein, quantifies the electrical fluctuation intensity is the scaling factor, based on the cluster variance of irradiance and temperature allows the generation of multiple extreme scenarios from a single instance state, such as the collapse of cluster electrical power under extreme cloud cover periods triggering low voltage. The loss function integrates reconstruction, diversity, and perception terms, and adds electrical and energy storage constraint penalties: L= 15

[0029]

[0030] wherein, is the VGG extractor, is the weight; the penalty ensures that the generated scenario complies with power balance is the generated quantity, is the consumption), voltage limits, ramp rates is the maximum allowed rate of change, typically and energy storage limits; the last term integrates the electrical divergence, ensuring that the scenario retains the influence of photovoltaic irradiance correlation and temperature gradient.

[0031] The core of NCA lies in its update rule, which is parameterized by a neural network, specifically a combination of multi-layer perceptron (MLP) and convolutional layers. This design allows NCA to learn local rules from data, leading to the emergence of global complex patterns. The MLP serves as the foundation for the NCA update rule.

[0032] An MLP is a feedforward artificial neural network composed of multiple layers: input, hidden, and output. Each layer consists of multiple neurons (nodes), each of which simulates 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 (a single-hidden-layer MLP can approximate any function according to Cybenko's universal approximation theorem). Key mechanisms include: Forward propagation: input signals propagate forward layer by layer from the input layer. Let the input vector be The output of the 1st layer is calculated as:

[0033] where is the weight matrix, is the bias vector, is the activation function. For example, ReLU: This simulates a neuron's "excitability": if the weighted sum exceeds a threshold, the activation output is activated. MLP learns hierarchical representations through multiple layers of stacking: shallow layers capture low-level features (e.g., edges), while deep layers capture high-level abstractions (e.g., patterns).

[0034] Activation function: the activation function introduces nonlinearity, otherwise the MLP degenerates into linear regression. ReLU prevents vanishing gradients, with a derivative of 1 (z>0) or 0 (z≤0). In NCA, ReLU allows nonlinear updates of cell states, simulating the threshold response of biological systems.

[0035] Backpropagation and learning: training uses gradient descent to minimize the loss function. The chain rule is used to calculate the gradient:

[0036] Parameter update: , is the learning rate. This allows the MLP to learn from errors, adjusting weights to better fit the data.

[0037] In NCA, the MLP parameterizes the update rule: the preliminary perception vector (which is calculated through convolution, containing states and gradients) serves as the basis, which is extended to the final perception vector Input MLP, output 16-dim delta s. Architecture typically 2-3 layers dense (1x1 conv equiv to fully connected), hidden units 128-dim, ReLU activation, final layer linear (no activation) to allow positive-negative updates. Initialize final layer weights to 0, ensuring initial "do-nothing" behavior, analogous to residual network skip connections, mitigating instability early in training. NCA also incorporates convolutional layer principles for perception step. Core of convolutional neural network (CNN) is shared weights and local receptive field: convolution kernel (e.g. 3x3 Sobel filter) slides over input, extracting local features:

[0038] In NCA, Sobel kernel computes gradient, capturing spatial variation, simulating biological gradient perception. Hierarchical feature extraction (edges at shallow layers, textures at deep layers) in CNN is achieved emergently in NCA through iterative updates: local MLP rules produce global patterns across multiple iterations, e.g. photovoltaic field fluctuations spreading from local turbulence to cluster-level output drops.

[0039] During training, Backpropagation Through Time (BPTT) unfolds iteration steps, computing gradients across T steps for updates, analogous to RNNs handling sequences. Loss includes reconstruction and diversity terms, optimizer like Adam handles high-dimensional grid, this MLP+CNN hybrid allows NCA to learn regenerative patterns: recovery from damage states, analogous to new energy cluster resilience.

[0040] 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. The training 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 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 a loss function including a time series loss and an 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: Scenario generation step: When generating the space-time fluctuation scenario of the water-light-storage new energy cluster by means of the NCA, first, historical electrical data (such as the 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.

[0041] 1. Data Preprocessing and Meshization: The original electrical sequences (such as current I caused by radiation G, power P caused by temperature T, and energy storage state S_{es}) are meshed into ^{HWC}, where HW represents the spatial dimension (e.g., 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.

[0042] in, Target grid location The interpolation result at the location; It is the value of the nearest known data point; These are weights, calculated based on distance, ensuring that neighboring points contribute more. The denominator is a normalization factor, making the sum of the weights equal to 1. Wherein, , A distance metric, ranging from [0,1], is used to ensure linear decay. Z-score normalization is then performed, and noise is added to simulate uncertainty.

[0043] Original data Mapping to a distribution with a mean of 0 and a standard deviation of 1 facilitates neural network training; then noise is added. Simulate uncertainty. It is the normalized value; It is the mean. It is the standard deviation; It is Gaussian noise, and its amplitude is controlled by the variance of photovoltaic power.

[0044] in, Extended electrical variance The gradient weights preserve the spatial impact of shading or temperature gradients on electrical quantities. The first term is the empirical variance, measuring the variability at discrete points; the second term is the gradient integral, capturing continuous spatial variations (such as 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 (such as radiation data from a database and temperature distributions measured in the field). This preprocessing method significantly improves the model's temporal consistency with photovoltaic fluctuations.

[0045] 2. NCA network initialization and training: NCA parameters θ are initialized 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 the electrical autocorrelation to verify the fluctuation capture effect. The initialization stage includes defining multi-channel hidden states (16-32 dimensions), encoding radiation, temperature, and energy storage states, and other features. The perception layer extracts local neighborhood information through a 3x3 convolution kernel. The training uses the Adam optimizer (learning rate 1e-3 to 1e-4), batch size 16-64, and the loss function is:

[0046]

[0047]

[0048] where, is the predicted grid state (electrical quantity distribution of the photovoltaic array, such as power matrix P) at time is the current state; is the MLP network, outputting the state increment; is the perception vector, providing local input. This formula represents the addition of a "small update" at each iteration step, similar to residual learning, avoiding drastic changes. The second formula is the objective function for training, finding the optimal parameters

[0049] to minimize the cumulative loss L and autocorrelation error. argmin represents the optimization solution; the first term is the time series loss and; the second term is the autocorrelation regularity, ensuring that the temporal and spatial correlation of the generated sequence matches the real data. is the cumulative loss, is the real state, is the prediction. is the regularization weight, balancing the loss and correlation.

[0050] The third formula is the spatio-temporal autocorrelation function, used to measure the correlation of power P at spatial offset and time delay . The first term is the Pearson correlation coefficient; the second term is the exponential decay, simulating the electrical propagation decay. close to 1 indicates high correlation (real fluctuations), used for regular training, indicates the decay time constant based on PV response. is the expected value, calculated by grid averaging. is the power value and mean, is the variance, calculated in training error, adjusting . ​

[0051] 3. Scenario generation and diversification: The transition phase of NCA model from training to practical application, whose core goal is to generate diversified photovoltaic electrical sequences from the initial seed state, simulating the temporal and spatial fluctuation scenarios in the water-light-storage base, such as the influence of cloud cover or temperature gradient. Through iterative updating 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 perturbations extend from local panels to power drops in the entire array. The entire step relies on trained parameters Iterate K steps (100-1000) to generate time-minute-level, facilitating intra-day rolling simulation.

[0052] Perception vector expansion and external driving terms:

[0053] This formula is used to inject conditional control in the generation process. is the final perception vector, obtained by connecting the preliminary perception Condition variable and external driving Implementation; External driving, balancing threshold difference ( , Power threshold such as ) and current rate of change , ensuring that the generation is biased towards a specific extreme. Time-varying weight, adjusting gradient influence. VNCA generates sequences:

[0054] This formula is used for sequence generation, is the K-step photovoltaic grid sequence, from seed generated by VNCA sampling, represents a variational stochastic process, trained parameters.

[0055] De-normalization formula:

[0056] Restore the standardized value to the original scale , is the standard deviation, is the mean. Convert (unitless) to real power for simulation input. Verification index calculation:

[0057] This is the extended Wasserstein distance, used to validate the generated distribution vs. the true distribution, plus a physical penalty term. inf is the optimal transport plan; expectation is the distance mean; the additional terms check energy, current, energy storage constraints. The distribution distance is <0.05 accepted. The joint distribution set is The transport plan is The energy integral difference is The current over-limit is The energy storage over-limit is As weights, the penalty terms balance the terms, restore the scale after validating the distribution and constraints, ensuring the scenario is physically valid, for dispatch.

[0058] The generated spatiotemporal fluctuation scenario serves as a key input, directly feeding into the physics-informed neural network (PINN)-based fast delineation and reduction method for power grid dynamic security domains. This scenario provides photovoltaic output distribution, radiation, and temperature data, helping the PINN model evaluate the safety boundaries of the power grid state space in real-time, optimizing dispatch decisions to avoid voltage / frequency instability; This method takes a computer as the execution subject, using the spatiotemporal fluctuation scenario generated by the first module as input, and uses a neural network to embed physical laws to approximate the "safety domain" (Safety Domain) in the power grid state space that maintains the stable operation of the system, thereby quickly evaluating the dynamic safety boundaries under photovoltaic output uncertainty, supporting dispatch decisions to avoid risks such as voltage collapse, frequency instability, or power angle out-of-step.

[0059] First, a complete power grid dynamic safety domain model is established. This model is based on power system dynamic equations and stability constraints, considering the fluctuation impact of high-penetration photovoltaic water-light storage clusters. The power grid dynamic model can be expressed as a system of nonlinear ordinary differential equations:

[0060] where is the state vector (known quantities, 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 changes caused by voltage deviation from the nominal value or mechanical vibration caused by speed fluctuations, 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 quantities, including standby power , energy storage charging and discharging rate, etc. m is the control dimension, the physical background is to intervene in the power grid physical process by adjusting the generator or energy storage device, such as increasing the standby power to balance the energy gap caused by photovoltaic fluctuation, the theoretical significance is to introduce the optimization degree of freedom, so that the model changes from description to controllability analysis, and supports to find the input strategy 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 cover cause radiation to drop or temperature rise to cause thermal effect to interfere with power grid balance, the theoretical significance is to quantify uncertainty, help the model evaluate robustness and simulate boundary behavior in real scenarios). Function includes swing equation and power flow constraints:

[0061] wherein, is the generator power angle, the phase offset of the generator rotor relative to the synchronous speed, reflecting the torque change caused by power imbalance under the action of 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, determined by mechanical inertia and electromagnetic force, dynamic response index, helping to analyze frequency fluctuation and evaluate system damping effect; is the synchronous speed 50Hz, reference point, used for normalized deviation calculation.

[0062]

[0063] wherein, is the inertia constant, the mechanical inertia of the generator rotor, resisting sudden changes in speed such as photovoltaic output drop causing frequency drop, quantifying the system's ability to buffer 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; 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.

[0064]

[0065] photovoltaic disturbance simultaneous equations:

[0066] where, is the photovoltaic current, is the photo current (dependent on G / T, known from the first module, photovoltaic effect base, environmental dependent for uncertainty modeling); is the saturation current, k is the Boltzmann constant, is the series resistance, is the parallel resistance. Energy storage constraints:

[0067] where, is the energy storage state, is the charge-discharge efficiency, is the charge-discharge power; the safety region is defined as a subset of states where there exists a control u that makes the trajectory always satisfy the constraints K (e.g. )

[0068] where g is the inequality constraint, PINNs approximate the safety region function u(x):

[0069] where, are the layer weights / biases, used for training solution, network parameters model the physical mapping, as a function approximator, provide high-dimensional nonlinear representation); is the activation, for introducing nonlinearity to match the actual grid behavior like voltage nonlinear response, universal approximation theorem support, allow the model to capture complex dynamics.

[0070] Loss function:

[0071] 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 summation: 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 the network output u(x) match both data, in the grid, from measurements (like voltage V), PDE describe dynamics (like power flow), BC are limits (like V<1.05pu), and stability prevent instability (like frequency oscillation). These correspond to real scenarios, like photovoltaic fluctuations leading to Ppv mutations, need to be ensured by loss penalty terms that the model simulates real physical processes, making it comply with grid physical laws. λ1, λ2, λ3 are weight coefficients, determined by tuning, used to balance the contribution of each loss.

[0072]

[0073] where, is the network predicted safety value, is the observed safety value, simulated or measured boundary. This equation is the mean squared error (MSE) loss for measuring the network prediction versus the observed difference. Averaged by normalization, avoiding scale impact. Data points come from actual measurements (e.g. SCADA system collects V / ω), reflecting grid operation, such as V drop under photovoltaic disturbance, loss method prediction deviation. Empirical risk minimization makes the model fit known scenarios, improving accuracy. Where MSE is sensitive to outliers, it is suitable for grid continuous variables. If data loss is high, it indicates mismatch with photovoltaic scenarios, training adjustment fit, such as cloud cover P_pv data.

[0074]

[0075] This is the PDE residual loss, measuring the difference between the predicted state derivative and the model f. L2 norm penalizes deviation, averaged normalization. Where is the number of PDE points, is the i-th point state derivative, automatically differentiated by the network. , , is the point state, control, disturbance. PDE points are internal "virtual" points, residual forces to comply with physical power flow conservation, simulating how photovoltaic disturbances propagate (e.g. P_pv drop leading to ω change). Meshless PDE solution, embedding physical knowledge through residual minimization, improves generalization, avoiding data scarcity problems. If PDE loss is high, it indicates that the model violates dynamics (e.g. photovoltaic injection imbalance), adjustment ensures physical consistency.

[0076]

[0077] This is the boundary condition loss, measuring the difference between the predicted u and the constraint g. L2 norm penalizes violation, averaged normalization. Boundary points represent limits (e.g. V upper limit), loss forces the model to comply at the edge, simulating photovoltaic over-limit induced collapse, ensuring solution uniqueness, improving model boundary accuracy. If BC loss is high, it indicates violation of limits (e.g. photovoltaic causes V>1.05), adjustment strengthens the boundary.

[0078]

[0079] This is the stability loss, penalizing the positive part of the largest eigenvalue of the Jacobian J ) is ReLU, ignoring negative values). Average Normalization. Positive spectrum indicates instability (e.g. PV-induced amplification of oscillations), penalize positive spectrum to ensure system damping PV fluctuations. If stability loss is high, it indicates Allowing instability points, adjust to avoid PV-induced frequency collapse. To cope with extreme fluctuations of PV clusters, the invention models disturbances using stochastic differential equations (SDEs):

[0080] 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 PV variability); is a Wiener process, a continuous disturbance simulation, such as Brownian motion, describing the noise path, a stochastic process framework, supporting Monte Carlo trajectory generation.

[0081] Domain simplification using convex optimization to fit an ellipsoid:

[0082] where Q is a positive definite matrix, optimized to solve, defining the shape of the ellipsoid to enclose the set of safe points, such as the elliptical boundary of voltage / power described by a quadratic form, convex approximation reducing computational complexity, ensuring that the boundary is mathematically differentiable and easy to optimize; 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 PV disturbances). Define and simplify steps: use a computer as the main execution body, describe the following steps: 1. Data input and preprocessing: the computer obtains the PV scenario (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:

[0083] 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).

[0084] 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 Adam optimizer (learning rate 1e-3 decay factor 0.95), iterating 1000-5000 steps, early stopping based on PDE residual <1e-4. Approximating the safety region function u(x), incorporating physics to improve generalization (key step, avoiding overfitting of purely data-driven, efficiently solving PDEs via automatic differentiation, enabling high-dimensional nonlinear approximation).

[0085] 3. Safety region bounding: computer evaluates u(x;0) < 0 to extract boundary points, samples 10^6 trajectories to simulate SDE, filters infeasible paths, computes level set gradient Verifying boundary continuity. Bounding the dynamic region, handling photovoltaic uncertainty (core output, providing decision basis, visualizing domain boundaries via level set method, supporting visual analysis).

[0086] 4. Safety region simplification and validation: computer fits ellipsoid from boundary points, solves Q and c using convex optimization (e.g., CVXPY library) (initializing Q as identity matrix, c as mean point, iterating until convergence), computes volume error:

[0087] where, is the volume integral (physical background: measuring domain capacity to quantify coverage, e.g., estimating multidimensional space volume via Monte Carlo sampling, theoretical significance: error evaluation, ensuring that simplification preserves the essence of the original domain); is the symmetric difference set (physical background: overlap deviation, representing the non-intersection part of the simplified domain and the original domain, theoretical significance: precision measurement, evaluating approximation loss). If ε > 5%, the computer increases sampling and refits. Simplifying high-dimensional domains supports scheduling, improves practicality, ensures computability through convex optimization, and reduces optimization variables; This method is derived from Feynman Path Integral Theory, taking the spatiotemporal wave scenario generated by the first module and the dynamic safety region bounded by the second module as input, and iteratively optimizing the scheduling trajectory through the feedback of the dynamic elasticity and stability evaluation results of the fourth module, quickly solving the intraday generation plan, energy storage charging and discharging strategy, and reserve allocation, supporting economic-safety balanced scheduling under high-penetration photovoltaic fluctuations. 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, efficiently handling nonlinear dynamics and uncertainties through parallel sampling under the MPPI framework.

[0088] 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 solutions. MPPI transforms the control problem into trajectory sampling through Feynman Path Integral, considering economic cost and safety penalty:

[0089] in, It is a trajectory The total cost is used as the total scheduling cost, and stochastic expectation optimization is performed. It is a penalty item for the terminal state (such as the deviation of SOC at the end of energy storage to make the cycle closed loop and long-term stability). This refers to operating costs (such as power generation costs + reserve penalties). MPPI sampling K-trajectory ( - ), weighted average optimization Compared to traditional MPC, this method has no derivative requirement and handles non-convex costs such as security region penalties. MPPI converges faster and is more robust in photovoltaic scenarios. Fluctuating scenarios are treated as perturbations. Security Domain As a cost item, to ensure the optimization trajectory is within the domain, the Koopman evaluation results are fed back (such as resilience metrics used for adjustment). (or penalty items), iterative refinement This achieves closed-loop optimization. MPPI, based on the Feynman path integral, expresses stochastic optimal control as a probability-weighted trajectory. Feynman theory was originally used for amplitude calculations in quantum mechanics.

[0090] in, It is the amplitude, the wave function, which is the superposition of all paths; It is the action (classical Lagrangian integral); It is the reduced Planck constant; It is a path metric. MPPI is extended to control, Replace with negative cost, exponentially weighted trajectory:

[0091] in, It is optimal control; For trajectory Weights (i.e., "probability density", soft maximization, choosing the low-cost path); It is a trajectory Cost (physical context: total scheduling cost; theoretical meaning: evaluation function); For temperature parameters, explore – utilize equilibrium, inverse temperature, and control sampling diversity; The system dynamics are SDE:

[0092] in, It is a dynamic determination; It is the diffusion matrix; It's a Wiener process. MPPI sampling perturbation. Simulated trajectory:

[0093] Costs include both economic and security aspects:

[0094] To minimize operating costs for economic purposes; For security reasons, penalties are imposed for violations of domain boundaries, which constitute soft constraints. For flexible penalties, feedback iteration is used to evaluate the flexibility of the solution; Terminal penalty (e.g., bias). For fast solution, MPPI parallel GPU sampling ( The trajectory (steps) is weighted and updated, with iterative feedback for evaluation in the fourth module. Theoretically, based on the Feynman-Kac formula, the PDE is transformed into a path integral, avoiding gridded calculations.

[0095] To further refine and optimize the core solution, this invention extends the MPPI framework to address specific challenges of large-scale renewable energy clusters, including high-dimensional state spaces (state vector dimensions can reach hundreds, such as multi-node voltage / power) and real-time requirements (intraday rolling optimization requires <1 minute). An adaptive sampling strategy is introduced: the sampling covariance Σ is dynamically adjusted based on the photovoltaic fluctuation intensity (variance obtained from the first module). For example, during periods of high uncertainty (cloud obstruction events), Σ is increased to explore more extreme trajectories and avoid local optimum traps. The formula is:

[0096] in, It is the basis covariance; It is a scaling factor (empirical value 0.1-0.5); This is the current variance of photovoltaic power output; It is the identity matrix. This adaptive approach enhances robustness by simulating the “diffusion” of the Feynman path to cover uncertain paths. Furthermore, it incorporates multi-stage rolling optimization: the MPPI is solved within each prediction window (T=15-60min), but updated rollingly via a sliding window (5min step), combining long-term economics (e.g., fuel costs) and short-term security (e.g., ramprates). The cost function is extended to a hierarchical form:

[0097] in, It is the fuel / reserve cost coefficient; It is the distance to the boundary of the safe region (L2 norm, close to instability); It is the fourth module, the Koopman resilience metric; is the weight (dynamically adjusted based on volatility level). This ensures that the optimization is not only economic but also resilient, 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.

[0098] Optimization solving step: With the computer as the execution subject, the following steps are described: 1. Data input and preprocessing: the computer obtains the volatility scenario and the safety domain from the first / second step, constructs the state and reference trajectory. Sample K=10^4 perturbations ε~N(0,Σ) (Σ is known, volatility covariance). Adaptively adjust Σ based on current Var(P_pv). Initialize MPPI input, ensure that the optimization considers real volatility, reduce sampling bias, and improve robustness. 2. Trajectory sampling and dynamic simulation: the computer simulates K trajectories in parallel:

[0099] Generate potential scheduling trajectories, simulate uncertainty, capture photovoltaic randomness through SDE, support Feynman integral approximation. Multi-stage rolling: update window T every 5 minutes.

[0100] 3. Cost calculation and quantification: the computer calculates

[0101] Weight Evaluate trajectories, select low-cost safe paths, weight Feynman path probability, and randomly optimal. Incorporate importance sampling: resample elite trajectories based on previous rounds.

[0102] 4. Control update and verification: the computer updates , verifies cost convergence <thresh or iteration <max_iter. Optimal scheduling, confirm economic-safety balance, converge to global near-optimal, verify energy storage / backup feasibility. Thresh takes 1e-3. Feedback fourth module evaluation, if resilience < threshold, re-optimize.

[0103] 5. Closed-loop iteration and output: the computer integrates fourth module feedback, adjusts penalty weight , iterates 2-5 rounds until resilience > 0.8. Output final scheduling: intra-day P_gen(t), SOC(t), P_res(t), ensure system stability under photovoltaic extreme scenarios, computation time; S4: Dynamic resilience and stability evaluation of scheduling scheme based on Kramers operator theory: The initial scheduling scheme obtained in S3 is obtained. The spatiotemporal fluctuation scenario that meets the electrical and energy storage constraints 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. The Koopman operator is approximated and spectral decomposition is performed on the Koopman operator. The stability index and the elasticity index are calculated. The stability index and the elasticity index are fed back to S3. S3 adjusts the cost penalty weight according to the feedback stability index and elasticity index. The optimization is iterated until the stability index and the elasticity index meet the preset requirements. The final scheduling scheme is then output. S4, "calculating stability and elasticity indices," includes: the stability index is calculated using the spectral radius, which is the maximum value of the modulus of the Koopman operator's eigenvalues. The stability index value is determined based on the relationship between the spectral radius and a preset stability threshold. The elasticity index is calculated using the modal recovery time, which is related to the real part of the eigenvalues. The overall elasticity index is determined by combining modal energy weights, normalized recovery time, and the number of modes. The overall elasticity index value ranges from 0 to 1. S4, "feeding back the stability and elasticity indices to S3; S3 adjusting the cost penalty weights based on the fed-back stability and elasticity indices, iteratively optimizing until the stability and elasticity indices meet the preset requirements," includes: if the stability or elasticity index exceeds the preset acceptable range, the stability and elasticity indices are fed back to S3; S3 adjusts the cost penalty weights based on the feedback results, with the adjustment direction related to the type of index exceeding the acceptable range; iterative optimization is performed, with the number of iterations configured as a preset number of rounds, until both the stability and elasticity indices meet the preset acceptable range, and the final scheduling scheme is output, including the following steps: This method takes the scheduling scheme optimized by the third module as input, linearizes the nonlinear power grid dynamics to a function space using Koopman operator theory, evaluates the dynamic resilience and stability of the scheme under photovoltaic fluctuations, and outputs quantitative indicators to feed back to the third module for iterative optimization, supporting closed-loop intraday look-ahead scheduling. Based on the Koopman operator theory proposed by Bernard Koopman, this method maps nonlinear dynamics to a linear infinite-dimensional Hilbert space, identifies dominant modes through spectral decomposition, and efficiently handles high-dimensional uncertainties in power system applications, such as transient stability analysis of high-penetration renewable energy clusters and coherent generator identification.

[0104] In hydro-solar-storage new energy clusters, traditional evaluation methods (such as time-domain simulation or Lyapunov functions) are computationally intensive and difficult to quantify resilience in real time, leading to scheduling schemes ignoring recovery capabilities or being sluggish in responding to minute-level fluctuations in photovoltaic power. The Koopman operator K is defined as a linear evolution operator:

[0105] in, It is the Koopman operator (theoretically, it is used to transform nonlinear dynamics). Linearization to observation function Evolution provides global linear representation, supports spectral analysis and prediction: is an observation function (known, such as power P, voltage V or frequency omega polynomial combinations of state vector x to lift dimensionality to capture nonlinearity); f is a nonlinear dynamic map (from third module input, including swing equation under photovoltaic perturbation). Spectral decomposition reveals system modes:

[0106] where, are eigenvalues; real part is a growth / decay rate, denotes stable mode decay; imaginary part denotes oscillation frequency, in Hz, to identify inter-cluster modes such as 0.1-2 Hz low frequency oscillations); is an eigenfunction, describing mode shape, such as spatial distribution of voltage gradient under photovoltaic perturbation; is a mode coefficient, quantifying mode amplitude. This decomposition allows identification of 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.

[0107] To achieve finite-dimensional approximation, the 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:

[0108] where, is a data matrix (columns are state snapshots, such as state vectors from an optimal trajectory , dimension , is state dimension voltage / power); is a shift matrix (from to ); is a pseudo-inverse (computed via singular value decomposition SVD). SVD decomposition :

[0109] where, are left singular vectors (known, , is a truncated rank, capturing dominant directions such as voltage modes of photovoltaic injection points); is a diagonal singular value matrix (known, , singular values denote 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:

[0110] right Eigenvalues ​​are obtained by performing eigenvalue decomposition, Λ(diag( )) and eigenvectors Koopman pattern:

[0111] 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:

[0112] 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:

[0113] 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.

[0114] 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. Used for classification mode (<0.1Hz is slow mode, susceptible to photovoltaic effects). If The marking is unstable, such as the collapse of photovoltaic power output leading to loss of power angle synchronization.

[0115] Resilience assessment: quantifying recovery capability based on modal recovery time Modal energy Overall elasticity index (Points to recovery time) If E < 0.8, it indicates poor elasticity, and the feedback adjustment schedule is reserved.

[0116] To handle uncertainty, the present invention incorporates noise-robust DMD (e.g., total least squares DMD) that minimizes the impact of disturbances:

[0117] where, is the Frobenius norm; is a regularization parameter (0.01-0.1, based on the noise level of photovoltaic). This improves the robustness to measurement noise, such as photovoltaic output error in SCADA data.

[0118] Evaluation steps: 1. Data input and preprocessing: the computer obtains the optimal scheduling trajectory (state sequence , N = 1000-10000 steps, x includes P_gen(t), SOC(t), V(t), etc.), injects the first module photovoltaic disturbance scenario (P_pv fluctuation, G / T sequence) to simulate extreme events, such as cloud cover causing a 20% output drop. Construct the lifting matrix Ψ if using EDMD (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 the capture of photovoltaic uncertainty (key step, reduce noise, improve pattern extraction accuracy); 2. Krylov approximation and spectral decomposition: the computer calculates SVD (X or ) to obtain U, Σ, V; solve low-order , characteristic decomposition to obtain , W. Calculate the mode (or equivalent). Identify the dominant mode (sort | descending, take top 10-20), extract photovoltaic-related modes such as cluster oscillation (core step, provide linear representation, support efficient spectral analysis, avoid non-linear simulation computational burden); 3. Stability and elasticity calculation: the computer calculates the spectral radius , if marking instability (considering a 5% margin); growth rate , threshold indicates insufficient damping. Elasticity , overall (normalized recovery score, s). Inject Monte Carlo perturbation (100-500 trajectories, from first module) to verify robustness, compute mean and variance, quantify scheme's immunity and recovery to photovoltaic fluctuations, support closed-loop optimization; 4. Evaluation and feedback: computer outputs indicators (stability S=1- , if 0; resilience , range 0-1). Visualize patterns (hotmap shows PV-affected areas). 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-accelerated), ensures real-time intra-day scheduling (final output provides basis for decision-making, improves system resilience).

[0119] While the embodiments of the application have been shown and described with reference to the Figs, it will be apparent that various modifications, changes, substitutions and alterations can be made to the embodiments without departing from the spirit and scope of the application as defined in the following claims and their equivalents.

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 scenario based on a neuron cellular automaton: Integrate historical electrical data of the new energy cluster, preprocess and grid to build a multi-channel grid, train the neuron cellular automaton network to generate a fluctuation scenario, and after inverse normalization and verification, obtain a space-time fluctuation scenario conforming to the electrical and energy storage constraints; S2: defining and simplifying the dynamic security domain of the power grid based on a physical information neural network: Based on the fluctuation scenario, construct the state, control and disturbance vector of the power grid, train the physical information neural network to define the 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 fluctuation scenario and the low-dimensional security domain of S2 to construct the system state and reference trajectory, sample the disturbance to simulate the scheduling trajectory, calculate the cost and weight, update the control strategy to obtain an initial scheme; S4: dynamic flexibility and stability evaluation of the scheduling scheme based on the theory of Koopman operator: Inject the fluctuation scenario into the initial scheme of S3, construct the matrix and approximate the Koopman operator, and perform spectral decomposition to calculate the stability and flexibility indicators; feedback to S3 to adjust the cost penalty weight, iterate until the indicators meet the standards, and output the final scheme. 2.The method of claim 1, wherein, The specific steps of preprocessing and gridding in S1 are: filling the missing data points in the historical electrical data by using bilinear interpolation, calculating the values of the adjacent known data points and the distance-based weight during interpolation, and setting the distance measurement range to 0-1 and configuring the normalization factor; 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 photovoltaic power variance; 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. 3.The method of claim 1, wherein, The specific way of training the neuron cellular automaton network in S1 is: the network parameters are initialized by using the Xavier initialization method, the neuron cellular automaton network architecture includes a convolution perception layer and a multilayer perception update layer, the convolution perception layer uses 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 the 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; the adaptive optimizer is used 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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