Photovoltaic scene generation method and system based on random matrix theory enhancement

Abstract

The invention discloses a photovoltaic scene generation method and system based on random matrix theory enhancement, and the method comprises the steps: constructing a training sample set based on historical data, and constructing a generative adversarial network framework comprising a generator and a discriminator; on the basis of a random matrix theory, time sequence data of a generated photovoltaic power time sequence scene and a real photovoltaic power time sequence scene are constructed into an augmented matrix, spectral distribution of the augmented matrix is calculated, the spectral distribution is converted into a correlation measurement index, and the correlation measurement index serves as an additional loss item to be introduced into a loss function of a discriminator; adopting an alternate training strategy to perform joint training on the generator and the discriminator into which the correlation loss item is introduced, and optimizing a generative adversarial network framework; and inputting the random noise vector to the generator, and generating a photovoltaic power time sequence scene. Spectral distribution analysis is carried out on a generated scene and a real scene through a random matrix theory, a correlation index is used as a discriminator loss item, and the problems of insufficient interpretability, lack of correlation evaluation and the like of the generative adversarial network in photovoltaic scene generation are solved.

Description

Technical Field

[0001] This invention relates to the field of electronic digital data processing, and in particular to a photovoltaic scene generation method and system based on random matrix theory. Background Technology

[0002] As the penetration rate of photovoltaic (PV) power generation in the power system continues to increase, its impact on power grid planning, dispatching, and risk assessment is becoming increasingly significant. PV power output is affected by various factors such as irradiance and weather conditions, exhibiting significant randomness and volatility. Therefore, generating time-series scenarios that accurately reflect its statistical characteristics is crucial for ensuring the safe and stable operation of high-proportion renewable energy power systems.

[0003] Currently, methods for generating photovoltaic power scenarios can be mainly divided into two categories: statistical modeling-based methods and deep learning-based methods. Statistical modeling-based methods, such as autoregressive moving average models and Gaussian mixture models, generate scenarios by fitting the probability distribution of historical data. However, these methods require prior assumptions about the data distribution and struggle to accurately describe the complex nonlinear characteristics of photovoltaic power. Deep learning-based methods, especially generative adversarial networks (GANs), can automatically learn the distribution characteristics of high-dimensional time-series data, generating more realistic samples. However, existing GAN-based methods have a significant drawback: the model discrimination process is black-boxed, lacking clear and quantifiable metrics to assess the correlation between the generated scenario and the real scenario. This results in insufficient model interpretability and makes it difficult to effectively evaluate and validate the generated results.

[0004] Furthermore, as the role of new energy scenario analysis becomes increasingly important in system scheduling and energy storage configuration, higher demands are placed on the statistical realism of generated scenarios and the interpretability of models. While traditional generative adversarial networks (GANs) have advantages in generation accuracy, their model training process is unstable, and they cannot provide quantitative proof of the statistical structural similarity between generated and real scenarios. This limits their application in power system analysis where reliability is critical. Summary of the Invention

[0005] The purpose of this invention is to provide a photovoltaic scene generation method and system based on random matrix theory. By introducing random matrix theory to perform spectral distribution analysis on the generated scene and the real scene, and using the correlation index quantified by the single-loop theorem as the discriminator loss term, the problem of insufficient interpretability and lack of correlation evaluation in photovoltaic scene generation by generative adversarial networks is effectively solved.

[0006] To address the aforementioned technical problems, a first aspect of this invention provides a photovoltaic scene generation method enhanced by random matrix theory, comprising the following steps: A training sample set is constructed based on the historical power output data of photovoltaic power plants, and a generative adversarial network framework including a generator and a discriminator is built. Based on the theory of random matrices, the time series data of the generated photovoltaic power time series scene output by the generator and the real photovoltaic power time series scene in the training sample set are used to construct an augmented matrix. The spectral distribution of the augmented matrix is ​​calculated, and the spectral distribution is transformed into a correlation metric according to the single-loop theorem. The correlation metric is then introduced as an additional loss term into the loss function of the discriminator. An alternating training strategy is adopted to jointly train the generator and the discriminator with the correlation loss term to optimize the generative adversarial network framework. A random noise vector is input into the generator to generate a photovoltaic power time series scenario.

[0007] Furthermore, based on stochastic matrix theory, an augmented matrix is ​​constructed from the time-series data of the generated photovoltaic power time-series scenario and the actual photovoltaic power time-series scenario. The spectral distribution of the augmented matrix is ​​calculated, and the spectral distribution is transformed into a correlation metric according to the one-ring theorem, including: Using a sliding time window method, an augmented matrix is ​​constructed by combining the time series data of the generated photovoltaic power time series scenario and the real photovoltaic power time series scenario. The augmented matrix is ​​then standardized. Multiplying the standardized augmented matrix by the corresponding western adjoint matrix yields the spectral distribution matrix; Singular value decomposition is performed on the spectral distribution matrix to obtain the spectral distribution of the spectral distribution matrix in the complex plane; Based on the single-ring theorem in random matrix theory, the average spectral radius of the spectral distribution is calculated as the correlation metric.

[0008] Furthermore, the step of employing a sliding time window method to construct an augmented matrix from the time-series data of the generated photovoltaic power time-series scenario and the actual photovoltaic power time-series scenario includes: A fixed-length sliding time window is used to slide on the generated photovoltaic power time series scenario and the real photovoltaic power time series scenario in a non-overlapping manner to capture multiple local sequence segments; The local sequence segments of the generated photovoltaic power time series scenario from the same time window are paired with the local sequence segments of the real photovoltaic power time series scenario to form time-aligned sample pairs. The local sequence fragments of the generated photovoltaic power time series scene in all sample pairs are concatenated row by row into a first matrix block, and the local sequence fragments of the real photovoltaic power time series scene in all sample pairs are concatenated row by row into a second matrix block; The augmented matrix is ​​constructed by concatenating the first matrix block and the second matrix block column by column.

[0009] Furthermore, prior to the step of performing singular value decomposition on the spectral distribution matrix, the method further includes: During the iterative process of model training, the spectral distribution matrix generated by the current iteration step and multiple previous iteration steps is cached; The multiple cached spectral distribution matrices are weighted and averaged to obtain a smoothed spectral distribution matrix, which is then used for subsequent singular value decomposition processing.

[0010] Furthermore, the step of introducing the correlation metric as an additional loss term into the loss function of the discriminator includes: Using the average spectral radius as a correlation metric, a random matrix theoretical correlation loss term is constructed. Obtain the initial loss function of the discriminator, which is a Wasserstein distance loss including a gradient penalty term; The trainable hyperparameters are set as weighting coefficients, and the theoretical correlation loss term of the random matrix and the initial loss function are linearly weighted and summed through the weighting coefficients to obtain the total loss function of the discriminator. During training, the weighting coefficients are dynamically adjusted based on the convergence of the spectral distribution in the complex plane. When the spectral distribution tends to be concentrated, the value of the weighting coefficients is increased; when the spectral distribution shows divergence, the value of the weighting coefficients is decreased.

[0011] Furthermore, the method of jointly training the generator and the discriminator with the introduced correlation loss term using an alternating training strategy includes: Within each training iteration, the network parameters of the generator are kept constant. Based on the current batch training data, the discriminator is updated multiple times consecutively. Each update calculates the total loss function including the additional loss term and performs backpropagation. After multiple updates of the discriminator are completed, the network parameters of the discriminator are kept unchanged. Perform a parameter update on the generator, wherein the optimization objective of the generator is to minimize the discriminator's discriminative output for its generated scene; Repeat the alternating training process described above until the preset training cycle is reached; The ratio of the number of updates of the discriminator to the number of updates of the generator is maintained at a preset ratio value.

[0012] Furthermore, after generating the photovoltaic power time-series scenario, the method further includes: The generated photovoltaic power time series scene is combined with the real photovoltaic power time series scene from the training sample set to construct an augmented matrix; The augmented matrix is ​​standardized, and the standardized augmented matrix is ​​multiplied by the corresponding Western adjoint matrix to obtain the sample covariance matrix. Calculate the eigenvalues ​​of the sample covariance matrix to obtain the eigenvalue distribution in the complex plane; Based on the single-ring theorem in random matrix theory, the average spectral radius of the eigenvalue distribution is calculated as a quality evaluation index for the generated scene. The calculated average spectral radius is compared with a preset threshold, wherein the preset threshold is determined based on the average spectral radius value in the discriminator loss function after the model training converges; When the average spectral radius is less than the preset threshold, it is determined that the currently generated photovoltaic power time series scene is strongly correlated with the real scene. Output the generated photovoltaic power time series scenario and its corresponding average spectral radius evaluation index.

[0013] Furthermore, before constructing the augmented matrix from the time-series data of the generated photovoltaic power time-series scenario and the actual photovoltaic power time-series scenario, the method further includes: Calculate the average sunrise time and average sunset time based on the historical power output data; Based on the average sunrise time and the average sunset time, define the effective sunshine interval and the no-sunlight interval; A time-gated function is constructed such that when the input time is within the effective sunshine interval, the output value of the time-gated function is 1; when the input time is within the no-sunshine interval, the output value of the time-gated function is 0. The photovoltaic power time series scene directly output by the generator is multiplied point by point with the time gating function to generate a photovoltaic power time series scene corrected by physical constraints. At the boundary between the effective sunshine interval and the no-sunshine interval, the output value of the time-gated function is smoothly transitioned between 0 and 1 using the Sigmoid function, thereby eliminating the step change of the power curve at sunrise and sunset.

[0014] Furthermore, at the boundary between the effective sunshine interval and the no-sunshine interval, the output value of the time gating function is smoothly transitioned between 0 and 1 using the Sigmoid function, which includes: Based on the historical power output data, the average rate of change of the photovoltaic power sequence with respect to time is calculated within a preset time range near sunrise and sunset. Based on the absolute value of the average rate of change, the time width of the sunrise transition interval and the sunset transition interval are determined by a preset mapping relationship, wherein the larger the absolute value of the average rate of change, the narrower the time width of the corresponding transition interval. For each time point within the sunrise transition interval, the time difference between the time point and the average sunrise time is calculated. The result of dividing the time difference by the first scaling factor is passed as input to the Sigmoid function to obtain the first smoothing gate value. The first smoothing gate value continuously transitions from 0 to 1 as the input value changes from negative to positive. For each time point within the sunset transition interval, the time difference between the time point and the average sunset time is calculated. The result of dividing the time difference by the second scaling factor is passed as input to the Sigmoid function to obtain the second smoothing gate value. The second smoothing gate value transitions continuously from 1 to 0 as the input value changes from negative to positive. The first smoothing gate value corresponding to the sunrise transition interval and the second smoothing gate value corresponding to the sunset transition interval are integrated into the time gating function, replacing the step output of the time gating function at the boundary, to obtain a continuously smooth time gating function.

[0015] Accordingly, a second aspect of the present invention provides a photovoltaic scene generation system based on stochastic matrix theory enhancement, which generates a photovoltaic power time series scene based on the above-described photovoltaic scene generation method based on stochastic matrix theory enhancement, including: The model building module is used to construct a training sample set based on the historical power output data of photovoltaic power plants, and to build a generative adversarial network framework including a generator and a discriminator. The matrix construction module is used to construct an augmented matrix based on the time series data of the generated photovoltaic power time series scene output by the generator and the real photovoltaic power time series scene in the training sample set, based on the random matrix theory. The module calculates the spectral distribution of the augmented matrix and transforms the spectral distribution into a correlation metric according to the single-loop theorem. The correlation metric is then introduced as an additional loss term into the loss function of the discriminator. The model optimization module is used to jointly train the generator and the discriminator with the correlation loss term introduced by adopting an alternating training strategy to optimize the generative adversarial network framework. The scene generation module is used to input a random noise vector into the generator to generate a photovoltaic power time series scene.

[0016] Accordingly, a third aspect of the present invention provides an electronic device, including: at least one processor; and a memory connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to cause the at least one processor to perform the above-described photovoltaic scene generation method based on random matrix theory enhancement.

[0017] Accordingly, a fourth aspect of the present invention provides a computer-readable storage medium having computer instructions stored thereon, which, when executed by a processor, implement the above-described photovoltaic scene generation method based on random matrix theory enhancement.

[0018] The above-described technical solutions of the embodiments of the present invention have the following beneficial technical effects: 1. By introducing the single-loop theorem from random matrix theory into the discriminator of generative adversarial networks, a quantifiable correlation evaluation and constraint mechanism is constructed. By constructing an augmented matrix between the generated scene and the real scene and analyzing its spectral distribution, the originally black-box, qualitative "similarity" judgment can be transformed into a precise and computable mathematical index based on the average spectral radius. This index is not only incorporated into the model training as a correlation loss term to guide the generator to optimize towards more realistic statistical characteristics, but also serves as an objective criterion for scene quality in the final evaluation stage. This achieves full-process interpretability from the internal mechanism of the model to the external output evaluation, breaking through the bottleneck of traditional generative models lacking clear correlation measurement indicators. 2. By integrating a physical constraint generator, an interpretable discriminator, a stable alternating training strategy, and a post-generation evaluation process into a complete collaborative system, this invention significantly improves the overall efficiency and engineering practicality of photovoltaic scene generation models. Dynamic gating ensures the physical baseline, random matrix theory constraints drive statistical realism, and specific training strategies guarantee the convergence stability of complex model training. The final quality evaluation step provides credible certification for the reliability of the generated results. This enables the model to efficiently generate large-scale and diverse photovoltaic scenes with physical correctness, statistical realism, and clear quality indicators, directly meeting the urgent needs of high-requirement engineering applications such as new energy system planning, energy storage optimization configuration, and operational risk assessment for input data quality and reliability. 3. By introducing a dynamic gating function based on average sunrise and sunset times and structurally embedding it into the generator's output, the physical rationality of the generated photovoltaic power scenario is fundamentally ensured. The generator's output power sequence can be constrained and corrected point by point, forcing the power output during periods without sunlight to be set to zero. This completely solves the core flaw of traditional deep generation models—generating non-zero power at night, which violates physical laws. Simultaneously, combined with smooth transition processing at the boundaries, the generated power curve is not only numerically correct but also morphologically continuous and smooth, significantly improving the simulation fidelity of the generated scenario to the real-world diurnal variation of photovoltaic power generation, providing a reliable data foundation for subsequent power system analysis. Attached Figure Description

[0019] Figure 1 This is a flowchart of a photovoltaic scene generation method based on random matrix theory enhancement provided in an embodiment of the present invention; Figure 2a This is a schematic diagram illustrating the single-ring theorem for measuring the weak correlation of elements in a random matrix, provided in an embodiment of the present invention. Figure 2b This is a schematic diagram illustrating how the single-ring theorem measures the strong correlation between elements of a random matrix, as provided in an embodiment of the present invention. Figure 3 This invention provides a comparison curve of power output from scenarios generated using different models, as provided in this embodiment. Figure 4 This is a block diagram of a photovoltaic scene generation system module based on random matrix theory, provided in an embodiment of the present invention.

[0020] Figure label: 1. Model building module, 2. Matrix building module, 3. Model optimization module, 4. Scene generation module. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments and the accompanying drawings. It should be understood that these descriptions are merely exemplary and not intended to limit the scope of the invention. Furthermore, descriptions of well-known structures and techniques are omitted in the following description to avoid unnecessarily obscuring the concept of the invention.

[0022] Please refer to Figure 1 The first aspect of this invention provides a photovoltaic scene generation method based on random matrix theory, comprising the following steps: Step S100: Construct a training sample set based on historical power output data of photovoltaic power plants, and build a generative adversarial network framework including a generator and a discriminator. The generator is used to generate photovoltaic power time-series scenarios through random noise vectors; the discriminator is used to distinguish the generated photovoltaic power time-series scenarios output by the generator from the real photovoltaic power time-series scenarios in the training sample set.

[0023] Historical power data for at least one full year was acquired from the monitoring system of the target photovoltaic power plant, with a data sampling interval of 15 minutes to fully capture power fluctuation details. The raw data underwent rigorous preprocessing, including outlier identification and removal based on statistical distribution, filling in missing data segments caused by equipment failures using linear interpolation, and mapping power values ​​to a standard numerical range through maximum-minimum normalization. A training sample set was constructed based on the processed data, ensuring it included typical daily power curves under different seasons and weather conditions. Simultaneously, a generative adversarial network (GAN) framework was constructed. The generator employed a deep neural network structure with four fully connected layers. The input was a random noise vector following a 100-dimensional standard normal distribution, which underwent a nonlinear transformation through three hidden layers with LeakyReLU activation functions, ultimately outputting a 96-dimensional photovoltaic power time-series scene. The discriminator used a one-dimensional convolutional neural network architecture, extracting the spatiotemporal features of the power sequence through three convolutional layers, and finally outputting a scalar score to evaluate the authenticity of the input data.

[0024] Specifically, the WGAN framework consists of two parts: a generator and a discriminator. The generator is responsible for generating photovoltaic power curves from random noise, while the discriminator is used to judge the difference between the generated data and the real data. The two parts learn and generate the photovoltaic power sequence distribution through adversarial training. Generator A multi-layer neural network structure is used, with the input being a low-dimensional random vector, as shown below: ; in, Represents the noise vector. For the noise dimension, It follows a standard normal distribution.

[0025] Based on this, the generator outputs time-series data with the same dimension as the real power curve through nonlinear mapping.

[0026] in, This represents the generated photovoltaic power sequence. This represents the length of the time series.

[0027] Discriminator The system receives both real and generated power curves and employs a one-dimensional convolutional structure to capture the time dependence and statistical features of the power sequence. During model initialization, initial parameter values ​​and learning rates are set for both the generator and discriminator, and a gradient penalty mechanism is introduced to avoid training instability. Through an adversarial game approach, the generator continuously optimizes the realism of the generated samples, while the discriminator improves its discrimination ability, thereby achieving distribution fitting and generation of photovoltaic power scenarios.

[0028] WGAN is an improvement on GAN. The optimization objective of GAN is: ; in, Let represent the discriminator function space that satisfies the 1-Lipschitz continuity constraint. The core idea of ​​WGAN is to use the Wasserstein distance (also known as Earth's distance) to measure the distribution of real-world data. With the distribution of generated data The Wasserstein distance offers advantages over the JS divergence of traditional GANs in terms of training stability and gradient propagation. To satisfy the Lipschitz constraint, a gradient penalty (GP) term is introduced, resulting in the improved discriminator loss function: in, , The gradient penalty coefficient is used to ensure that the gradient norm of the discriminator is close to 1, thereby improving training stability.

[0029] The optimization objective of the generator is: During the model initialization phase, initial parameter values ​​are set for both the generator and the discriminator. , and learning rate During training, the discriminator typically performs a certain number of iterations per cycle. The generator is then updated once more to ensure that the discriminator can accurately assess the quality of the generated samples.

[0030] The iterative update rules for adversarial games are as follows: As training progresses, the generator gradually improves the realism of the generated samples, making their distribution... Approximating the true distribution Ultimately, this achieves high-fidelity generation and distribution fitting of photovoltaic power scenarios.

[0031] Step S200: Based on the theory of random matrices, the generated photovoltaic power time series scene output by the generator and the time series data of the real photovoltaic power time series scene in the training sample set are used to construct an augmented matrix. The spectral distribution of the augmented matrix is ​​calculated, and the spectral distribution is transformed into a correlation metric according to the single-loop theorem. The correlation metric is introduced as an additional loss term into the loss function of the discriminator.

[0032] During discriminator training, a correlation constraint mechanism is constructed using random matrix theory. First, a fixed-length, non-overlapping sliding time window with 32 sampling points is used to extract multiple local sequence fragments from both the generated and real scenes. Generated and real fragments from the same time window are then concatenated row-wise to form sample pairs. Generated scene fragments from all sample pairs are concatenated row-wise to form the first matrix block, and real scene fragments are concatenated row-wise to form the second matrix block. These two matrix blocks are then concatenated column-wise to construct a non-Hermitian augmented matrix. This matrix is ​​standardized so that the mean of each row and column is zero and the variance is one. The product of the standardized matrix and its adjoint matrix is ​​then calculated to obtain the sample covariance matrix. Eigenvalue decomposition of this matrix yields the eigenvalue distribution in the complex plane. Based on the one-loop theorem in random matrix theory, the arithmetic mean of the magnitudes of all eigenvalues ​​is calculated as the average spectral radius. This index is then used as a correlation loss term and introduced into the discriminator's loss function in a linearly weighted manner.

[0033] Specifically, the generated and real scenes are constructed into an augmented matrix using a sliding time window method. This matrix is ​​then standardized and subjected to singular value decomposition to obtain the distribution of eigenvalues ​​in the complex plane. According to the one-ring theorem, when the matrix elements are independent, their eigenvalue distribution should exhibit randomness; if the eigenvalues ​​are concentrated at the center, it indicates a strong correlation between the generated and real samples. By calculating the average spectral radius, the consistency of the statistical structure between the two classes of samples can be quantitatively measured. This metric is introduced into the discriminator loss function, forming an optimization objective together with the Wasserstein distance, allowing the model to consider both data authenticity and relevance during training. As shown below: This method not only improves the model's discrimination accuracy, but also provides a visual and interpretable mathematical basis for the generation process.

[0034] Step S300: An alternating training strategy is adopted to jointly train the generator and the discriminator with a relevant loss term to optimize the generative adversarial network framework.

[0035] A discriminator-first, alternating training strategy is employed to optimize the network. Within each training iteration, the generator parameters are first frozen, and a batch of random noise vectors are sampled from the latent space to generate scenes. These scenes are then input into the discriminator along with a batch of real scene data. The discriminator performs five parameter updates based on a total loss function that includes Wasserstein distance loss, gradient penalty terms, and random matrix theoretical correlation loss to improve its discriminative ability. Subsequently, the discriminator parameters are frozen again, and the generator parameters are updated once. The optimization objective is to minimize the discriminator's output score for the generated scenes. The entire training process lasts for 8000 iterations, using the Adam optimizer with a learning rate ratio of 5:1 between the discriminator and generator.

[0036] Step S400: Input a random noise vector into the generator to generate a photovoltaic power time series scenario.

[0037] After model training, a large number of random noise vectors are sampled from a standard normal distribution and input into the trained generator to output diverse photovoltaic power time-series scenarios in batches. To ensure generation quality, an evaluation augmented matrix is ​​constructed by comparing the generated scenarios with real historical scenarios, and its average spectral radius is calculated. A scenario is considered qualified when this value is lower than a threshold determined during the training convergence phase. These validated high-fidelity scenarios can be directly applied to practical engineering scenarios such as renewable energy power prediction, energy storage system capacity optimization, and power system operation risk analysis, providing reliable data support for power system planning and operation under high-proportion renewable energy access.

[0038] To verify the model performance, the generated results were comprehensively evaluated using multiple indicators, including mean absolute error (MAE), structural similarity index (SSIM), autocorrelation coefficient (ACC), and mean spectral radius, as shown below: ; in, For the actual photovoltaic power sequence at time points The value; The generator output at time point The power value; This refers to the sample length (number of time steps or number of samples). Let be the mean of the real sequence and the variance of the generated sequence, respectively. Let be the covariance of the two. The stability constant (to prevent the denominator from being zero, it is usually taken as 0) , (for the dynamic range of data) The time lag step.

[0039] The smaller the MAE, the closer the generated result is to the actual data in terms of value. MAE is not sensitive to outliers and is suitable for assessing the overall error level; the closer SSIM is to 1, the more similar the shape, fluctuation trend and amplitude characteristics of the two curves are; the higher the ACC is, the more consistent the fluctuation pattern of the generated sequence is with the actual sequence in time, and it can reflect the dynamic trend of photovoltaic output.

[0040] This invention systematically constructs a generative adversarial network framework and innovatively introduces stochastic matrix theory. It constructs augmented matrices from the time-series data of generated and real-world scenarios for spectral analysis. Based on the single-loop theorem, the spectral distribution is transformed into a quantifiable correlation metric and incorporated as an additional loss term into the discriminator's optimization objective. Combined with a discriminator-priority alternating training strategy, it effectively establishes a mathematical representation and optimization mechanism for the statistical correlation between generated and real-world scenarios. This significantly improves the statistical fidelity of the generated scenarios and the interpretability of the model. Simultaneously, a stable training process ensures the model's convergence reliability. The resulting photovoltaic power time-series scenario exhibits high consistency with real data in terms of fluctuation characteristics, statistical distribution, and time-series structure, providing a data foundation with clear quality assurance for the planning and operation analysis of new energy power systems.

[0041] Furthermore, before constructing the augmented matrix from the time-series data of the generated photovoltaic power time-series scenario and the actual photovoltaic power time-series scenario in step S200, the following steps are also included: Step S110: Calculate the average sunrise time and average sunset time based on historical power output data.

[0042] Based on the preprocessed historical data, the start and end times corresponding to the first continuous non-zero power interval in the daily power sequence are extracted and used as the sunrise and sunset times of that day, respectively. Then, the arithmetic mean of the corresponding times for all dates in the entire dataset is calculated to obtain the static parameters characterizing the illumination pattern of the power station, namely the average sunrise time and the average sunset time, which provide a benchmark for subsequent physical constraints.

[0043] Specifically, the average sunrise and sunset times are calculated as follows: in, Total number of days and For the first The sunrise and sunset times of the day.

[0044] No. The sunrise and sunset times for a day are calculated using the following formula: in, for Photovoltaic power generation at any given time Determined by time resolution: .

[0045] Step S120: Define the effective sunshine interval and the no-sunshine interval based on the average sunrise time and average sunset time.

[0046] Based on the two key time-series parameters of average sunrise and average sunset obtained from the aforementioned calculations, the typical solar cycle of a photovoltaic (PV) power plant is clearly defined. The continuous period between the average sunrise and average sunset is divided into the effective sunshine interval, which characterizes the theoretical time range within which PV modules can generate output power. The period between sunset and the sunrise of the following day is uniformly defined as the no-sunlight interval, corresponding to the nighttime period when the PV power plant's power output should theoretically be zero. This division establishes a time benchmark for the physical laws of PV power generation, providing a clear basis for subsequent power constraints. In practical implementation, if the calculated average sunrise time is 6:00 AM and the average sunset time is 6:00 PM, then the effective sunshine interval is from 6:00 AM to 6:00 PM each day, and the remaining time periods are considered the no-sunlight interval.

[0047] Step S130: Construct a time-gated function. When the input time is within the effective sunshine interval, the output value of the time-gated function is 1. When the input time is within the no-sunshine interval, the output value of the time-gated function is 0.

[0048] Based on defined effective sunshine intervals and no sunshine intervals, a deterministic time-gated function is constructed. This function uses the specific time corresponding to each data point in the power sequence as the unique input variable. Its output logic is as follows: when the input time falls within the effective sunshine interval, the function outputs a discrete value of 1; when the input time is within the no sunshine interval, the function outputs a discrete value of 0. Essentially, this function is a time-based binary switch, and its output pattern strictly follows the predefined sunshine interval rules. In engineering implementation, this function is implemented by traversing the timestamps of the power sequence and comparing them with the interval boundaries, ensuring that each time point obtains the correct gating state identifier.

[0049] Step S140: The original photovoltaic power time series scene directly output by the generator is multiplied point by point with the time gating function to generate a photovoltaic power time series scene corrected by physical constraints.

[0050] The original photovoltaic power time series scene directly output by the generator network (which may include non-zero power at night) is multiplied element-wise with the time gating function constructed in step S320. The mathematical significance of this operation is that within the effective sunshine interval, the gating value is 1, and the generator's original power output is fully preserved; within the no-sunlight interval, the gating value is 0, and any non-zero output of the generator is forcibly set to zero. Through this point-by-point filtering mechanism, the physical laws of the generator's original output are corrected, ensuring that the final output power sequence strictly satisfies the fundamental physical constraint of "zero power at night," thus generating a photovoltaic power time series scene corrected by physical constraints.

[0051] Following the final output layer of the generator network, a time-based dynamic gating function is cascaded. This function takes the sequence time points as input and defines a binary gating signal based on the average sunrise and sunset times calculated in step S100: the gating value is 1 within the interval between the average sunrise and sunset times, allowing the generator's raw power output to pass; outside this interval, the gating value is 0, forcibly setting the power output to zero at the corresponding time. To achieve a smooth transition of the power curve at sunrise and sunset times, a 30-minute transition band is set before and after the boundary of the gating interval. Within the transition band, the gating value is smoothly interpolated using the Sigmoid function, thereby generating a photovoltaic power time series scenario that strictly conforms to the diurnal characteristics of photovoltaic power generation and has a continuous curve.

[0052] Average sunrise time calculated from historical data With sunset time Construct time-gated functions Used to depict Real-time photovoltaic output status: When the time is during daylight hours, the gate value is 1, and the generator output is retained; when the time is during nighttime, the gate value is 0, and the generated result is forcibly set to zero. This gate function effectively avoids the problem of traditional generation models still outputting non-zero power under no-light conditions, thus ensuring the physical consistency of the generated curve. In the generator output layer, let the original generated output be... The power output after dynamic gating correction Defined as: ; In this way, the generator can learn the power distribution characteristics during end-to-end training while always adhering to the temporal physical constraints of photovoltaic power generation.

[0053] Step S150: At the boundary between the effective sunshine interval and the no-sunshine interval, the Sigmoid function is used to smooth the output value of the time-gated function between 0 and 1, eliminating the step change of the power curve at sunrise and sunset.

[0054] To address the power curve step problem caused by abrupt output changes in the gating function at the boundary between the effective sunshine interval and the no-sunshine interval, a smooth transition mechanism based on the Sigmoid function is introduced at the interval boundary. Specifically, a transition band of a certain width (e.g., 30 minutes each) is symmetrically extended to both sides of the average sunrise and average sunset times. Within the sunrise transition band, the time difference between the current time and the sunrise time is used as input, and a smooth gating value continuously varying from 0 to 1 is calculated using the Sigmoid function. Similarly, within the sunset transition band, a smooth gating value continuously varying from 1 to 0 is calculated based on the time difference. By adjusting the slope parameter of the Sigmoid function, the steepness of the transition can be controlled, allowing the power value to smoothly rise from zero at sunrise and smoothly fall from its normal value to zero at sunset, thereby eliminating the power curve step phenomenon and generating a continuous and smooth power curve that conforms to the start-up and shutdown characteristics of actual photovoltaic power plants.

[0055] The above process establishes a complete constraint mechanism for the physical laws of photovoltaic power generation by embedding a time-based dynamic gating function at the generator output. It not only ensures the basic physical requirement of zero power at night through binary gating, but also eliminates the non-physical step of the power curve at sunrise and sunset through sigmoid smooth transition. This makes the generated power scenario strictly follow the diurnal pattern of photovoltaic power generation and maintain the temporal continuity of the curve, which significantly improves the physical rationality and engineering practicality of the generated scenario and provides a data foundation that is closer to the real operating characteristics for subsequent analysis of new energy systems.

[0056] Furthermore, in step S150, at the boundary between the effective sunshine interval and the no-sunshine interval, the output value of the time gating function is smoothly transitioned between 0 and 1 using the Sigmoid function, including: Step S151: Based on historical power output data, calculate the average rate of change of photovoltaic power sequence with respect to time within a preset time range near sunrise and sunset.

[0057] Based on preprocessed historical power output data, a quantitative analysis of photovoltaic power variation characteristics around sunrise and sunset times is conducted. Specifically, within a preset time range of 30 minutes before and after the average sunrise time, the first difference of the photovoltaic power sequence with respect to time is calculated, and the average of its absolute values ​​is obtained to obtain the average rate of change of power increase during sunrise. Similarly, within a preset time range of 30 minutes before and after the average sunset time, the average rate of change of power decrease is calculated. These two rate of change indicators objectively reflect the typical rate of power start-up and shutdown of the photovoltaic power station under natural conditions, providing data support for the adaptive determination of the subsequent transition range.

[0058] Step S152: Based on the absolute value of the average rate of change, determine the time width of the sunrise transition interval and the sunset transition interval through a preset mapping relationship. The larger the absolute value of the average rate of change, the narrower the time width of the corresponding transition interval.

[0059] Based on the absolute value of the average rate of change calculated in step S151, the time widths of the sunrise and sunset transition intervals are determined through a preset linear mapping relationship. This mapping relationship is set as an inverse proportional function; that is, the larger the absolute value of the average rate of change, the more drastic the power change per unit time, and the narrower the corresponding transition interval time width is set; conversely, the smaller the absolute value of the average rate of change, the wider the transition interval time width is set. For example, when a power plant is detected to have a rapid power increase rate at sunrise, its sunrise transition interval is set to 20 minutes; while for a power plant with a slower power increase, a 40-minute transition interval is set. This adaptive mechanism ensures that the transition interval settings match the actual operating characteristics of the power plant.

[0060] Step S153: For each time point within the sunrise transition interval, calculate the time difference between the time point and the average sunrise time, and pass the result of dividing the time difference by the first scaling factor as input to the Sigmoid function to obtain the first smoothing gate value. The first smoothing gate value continuously transitions from 0 to 1 as the input value changes from negative to positive.

[0061] For each time point within the sunrise transition interval, calculate the time difference between that time point and the average sunrise time (negative values ​​for times earlier than sunrise, positive values ​​for times later than sunrise). Divide this time difference by the first scaling factor to adjust the time scale, ensuring the value input to the Sigmoid function is on an appropriate order of magnitude. Input the scaled time difference into the standard Sigmoid function to obtain the corresponding first smoothing gate value. As the input value changes from negative to positive, the Sigmoid function output monotonically increases from 0 to 1, forming a smooth transition curve. The value of the first scaling factor affects the steepness of the transition curve and needs to be adjusted and optimized according to the specific application scenario.

[0062] Step S154: For each time point within the sunset transition interval, calculate the time difference between the time point and the average sunset time, and pass the result of dividing the time difference by the second scaling factor as input to the Sigmoid function to obtain the second smoothing gate value. The second smoothing gate value continuously transitions from 1 to 0 as the input value changes from negative to positive.

[0063] For each time point within the sunset transition interval, calculate the time difference between that time point and the average sunset time (negative values ​​for times earlier than sunset, positive values ​​for times later than sunset). Divide this time difference by the second scaling factor and input it into the Sigmoid function to obtain the corresponding second smoothing gate value. As the input value changes from negative to positive, the Sigmoid function output continuously and monotonically decreases from 1 to 0, forming a smooth decay curve symmetrical to the sunrise transition. The second scaling factor can be the same as the first scaling factor to ensure symmetry, or it can be set separately according to the actual sunset characteristics of the power plant to more accurately simulate the power decline process at sunset.

[0064] Step S155: Integrate the first smoothing gate value corresponding to the sunrise transition interval and the second smoothing gate value corresponding to the sunset transition interval into the time gate function, and replace the step output of the time gate function at the boundary to obtain a continuous and smooth time gate function.

[0065] The first smoothing gate value obtained in step S153 and the second smoothing gate value obtained in step S154 are integrated into the corresponding transition intervals of the original time-gated function, completely replacing the step output of the original function at the boundary. In the core segments of the effective sunshine interval and the core segments of the no-sunlight interval, the original gate function's 1 and 0 outputs are maintained. Through this piecewise function reconstruction, a new, continuously smooth time-gated function is obtained. This function remains 1 in the sunshine interval, 0 in the night interval, and smoothly transitions within the sunrise-sunset transition interval, thus providing the generator output with physically consistent and smoothly curved constraints.

[0066] By analyzing the variation characteristics of historical power data, the transition interval parameters are adaptively determined, and the Sigmoid function is used to achieve a smooth transition of the gate value. This ensures that the generated photovoltaic power curve not only strictly meets the diurnal power variation law, but also presents a smooth transition that conforms to the actual power plant operation characteristics during sunrise and sunset. This effectively eliminates the power step problem caused by traditional hard gates, significantly improves the physical realism and engineering applicability of the generated scenario, and provides a higher quality data foundation for the refined analysis of power systems.

[0067] Based on the above, the alternating training strategy in step S300 involves jointly training the generator containing the time-gated function and the discriminator with a correlation loss term to optimize the generative adversarial network framework.

[0068] Specifically, in step S200, based on stochastic matrix theory, an augmented matrix is ​​constructed from the time-series data of the original photovoltaic power time-series scenario and the actual photovoltaic power time-series scenario. The spectral distribution of the augmented matrix is ​​calculated, and the spectral distribution is transformed into a correlation metric according to the one-ring theorem, including: Step S210: Using the sliding time window method, an augmented matrix is ​​constructed from the time series data of the original photovoltaic power time series scenario and the real photovoltaic power time series scenario.

[0069] A fixed-length sliding time window method was used to synchronize the original photovoltaic power time-series scenario with the actual photovoltaic power time-series scenario. The time window length was set to 32 sampling points (corresponding to 8 hours of data), sliding along the time axis in a non-overlapping manner to extract multiple local sequence fragments from both scenarios. Local sequence fragments from the generated scenario and the actual scenario from the same time window were combined row-wise to form time-aligned sample pairs. The generated scenario fragments from all sample pairs were concatenated row-wise to form the first matrix block, and the actual scenario fragments were concatenated row-wise to form the second matrix block. Finally, these two matrix blocks were concatenated column-wise to construct a non-Hermitian augmented matrix. The row dimension of this matrix is ​​equal to the number of sample pairs multiplied by 2, and the column dimension is equal to the time window length, thus preserving the temporal structure characteristics of both generated and actual data.

[0070] Step S220: Standardize the augmented matrix.

[0071] The constructed augmented matrix undergoes standardization preprocessing to eliminate the influence of data dimensions and satisfy the analytical premises of random matrix theory. Specifically, the arithmetic mean and standard deviation of each column of the augmented matrix are calculated. Then, each element is subtracted from the mean of the corresponding column and divided by the standard deviation of that column. This process ensures that the mean of each column is 0 and the variance is 1, making the power data at different time points comparable while maintaining the correlation structure between rows of the matrix. The standardized augmented matrix elements follow a zero-mean, unit-variance distribution, creating suitable mathematical conditions for subsequent spectral analysis.

[0072] Step S230: Multiply the standardized augmented matrix with the corresponding western adjoint matrix to obtain the spectral distribution matrix.

[0073] The standardized augmented matrix is ​​multiplied by its western adjoint matrix (i.e., the conjugate transpose) to obtain the sample covariance matrix. The mathematical significance of this operation lies in calculating the inner product relationship between different row vectors of the original data matrix, forming a square matrix. This sample covariance matrix contains all the second-order statistical information within and between the generated and real scenes, and its eigenvalue distribution reflects the correlation structure of the two types of data in high-dimensional space. In actual calculations, this step is implemented through basic matrix transpose and multiplication operations, serving as a bridge connecting the original data with the theoretical analysis of random matrices.

[0074] Step S240: Perform singular value decomposition on the spectral distribution matrix to obtain the spectral distribution of the spectral distribution matrix in the complex plane.

[0075] The sample covariance matrix obtained in step S230 is subjected to singular value decomposition (SVD), which decomposes it into a product of three specific matrices. SVD yields all the singular values ​​of the sample covariance matrix, and the square roots of these singular values ​​correspond to the singular values ​​of the original augmented matrix. Mapping these singular values ​​onto the complex plane yields the spectral distribution of the matrix. The characteristics of the spectral distribution directly reflect the degree of similarity in statistical structure between the generated scene and the real scene: when the two scenes are strongly correlated, the spectral distribution exhibits a specific clustering pattern; while when the correlation is weak, the spectral distribution is more dispersed.

[0076] Step S250: Calculate the average spectral radius of the spectral distribution as a correlation metric based on the single-ring theorem in random matrix theory.

[0077] According to the single-ring theorem in random matrix theory, the average spectral radius of the spectral distribution is calculated as a measure of correlation. The average spectral radius is defined as the arithmetic mean of the distances from all eigenvalues ​​to the origin of the complex plane. A smaller value indicates that the eigenvalues ​​are more concentrated near the center of the circle. Figure 2a and Figure 2b As shown. According to the single-ring theorem, when the generated scene has a strong statistical correlation with the real scene, its eigenvalue distribution will be tightly clustered around the center, resulting in a decrease in the average spectral radius; conversely, when the correlation is weak, the eigenvalue distribution tends to be dispersed, and the average spectral radius increases. This quantifiable indicator provides an objective mathematical basis for evaluating the quality of generated scenes.

[0078] By systematically applying the theory of random matrices, the correlation assessment between generated scenes and real scenes is transformed from subjective qualitative judgment to objective quantitative analysis. An interpretability assessment system based on spectral distribution characteristics is established, which not only provides a clear correlation optimization target for the training of generative adversarial networks, but also provides a reliable mathematical basis for the quality certification of the final generated scenes, significantly improving the transparency and credibility of photovoltaic scene generation methods.

[0079] Furthermore, in step S210, the sliding time window method is used to construct an augmented matrix from the time series data of the original photovoltaic power time series scenario and the actual photovoltaic power time series scenario, including: Step S211: Using a fixed-length sliding time window, slide it in a non-overlapping manner on the original photovoltaic power time series scenario and the real photovoltaic power time series scenario respectively to capture multiple local sequence fragments.

[0080] A fixed-length sliding time window was used to synchronously segment the original photovoltaic power time-series scenario and the actual photovoltaic power time-series scenario. The time window length was set to 32 consecutive sampling points, corresponding to an eight-hour observation period with a sampling interval of 15 minutes. This time window was slid across both types of power time-series scenarios in a non-overlapping manner; that is, after data extraction for one window, the window's starting position was moved directly to the beginning of the next unsampled region, ensuring that each local sequence segment came from a different time interval. Using this sampling method, three local sequence segments could be obtained from the generated 96-point daily power scenario, and a corresponding number of segments could also be obtained from the actual scenario. This non-overlapping sampling strategy ensured the statistical independence between the various local sequence segments, providing a theoretically sound sample basis for subsequent random matrix analysis.

[0081] Step S212: Pair local sequence fragments of the original photovoltaic power time series scenario from the same time window with local sequence fragments of the real photovoltaic power time series scenario to form time-aligned sample pairs.

[0082] The local sequence fragments obtained in step S211 are precisely paired according to their temporal correspondence. Specifically, a local sequence fragment from the first time window of the original photovoltaic power time series scenario is paired with a local sequence fragment from the same time window of the real photovoltaic power time series scenario; similarly, fragments from the second time window of both scenarios are paired, and so on, until all time windows are paired. This strict temporal alignment ensures that the two local sequence fragments in each sample pair represent the power generation behavior under the same solar irradiance conditions, enabling subsequent correlation analysis to accurately reflect the differences in statistical characteristics between the generated scenario and the real scenario within the same time period, thus laying the foundation for meaningful comparisons.

[0083] Step S213: Concatenate the local sequence fragments of the original photovoltaic power time series scene in all sample pairs into a first matrix block by row, and concatenate the local sequence fragments of the real photovoltaic power time series scene in all sample pairs into a second matrix block by row.

[0084] Local sequence fragments of the original photovoltaic power time-series scenarios from all sample pairs are extracted and concatenated along the row direction of the matrix according to the order of the sample pairs to form the first matrix block. The number of rows in this matrix block is equal to the total number of sample pairs, and the number of columns is equal to the length of each local sequence fragment (32 sampling points). Similarly, local sequence fragments of the real photovoltaic power time-series scenarios from all sample pairs are concatenated along the row direction in the same order to form the second matrix block. These two matrix blocks have the same size in the row dimension, and the matrix rows indexed in the same row come from paired data in the same time window, maintaining a strict correspondence between the generated data and the real data in the sample dimension, and providing a structured data organization method for subsequent joint analysis.

[0085] Step S214: Concatenate the first matrix block and the second matrix block column by column to construct an augmented matrix.

[0086] The first and second matrix blocks obtained in step S213 are concatenated along the column direction of the matrix, keeping the number of rows unchanged. The columns of the second matrix block are then appended to the right side of the first matrix block, ultimately constructing a complete augmented matrix. The total number of rows in this augmented matrix equals the number of sample pairs, and the total number of columns equals the sum of the lengths of the two local sequence segments (64 sampling points). This concatenation method ensures that the left side of the augmented matrix is ​​entirely from the generated scene, and the right side is entirely from the real scene, while preserving the temporal structure information within each local sequence segment. This matrix construction method integrates data from the generated and real scenes into the same mathematical structure, providing a suitable data foundation for subsequent analysis of the correlation between the two types of data using random matrix theory.

[0087] Through systematic sliding time window sampling, time-series alignment and pairing, and matrix block splicing operations, the augmented matrix constructed by this invention retains both the short-term fluctuation characteristics and long-term statistical properties of photovoltaic power data. It reflects the local correspondence between the generated scenario and the real scenario in the time dimension, and provides sufficient data dimensions to meet the analysis requirements of random matrix theory. This lays a solid structural foundation for subsequent quantification of the correlation between the two types of scenarios through spectral distribution analysis.

[0088] Furthermore, step S240, prior to the step of performing singular value decomposition on the spectral distribution matrix, also includes: Step S2401: During the iterative process of model training, cache the spectral distribution matrix generated by the current iteration step and multiple previous iteration steps.

[0089] During the iterative training of the model, a dedicated caching mechanism is established to store historical data of the spectral distribution matrix. Specifically, a fixed-capacity first-in, first-out queue is set up, with a capacity of five training iterations. After the spectral distribution matrix is ​​calculated in each training iteration, the matrix is ​​stored in the cache queue. If the queue is full, the oldest stored matrix is ​​automatically removed. In this way, the system always retains the spectral distribution matrices generated by the current iteration step and its four preceding iteration steps, forming a continuous matrix sequence. This caching mechanism provides the necessary data foundation for subsequent smoothing processes, enabling the model to consider the evolution of the spectral distribution over time during training, rather than relying solely on the instantaneous state of a single iteration.

[0090] In step S2402, the multiple cached spectral distribution matrices are weighted and averaged to obtain a smoothed spectral distribution matrix, which is used for subsequent singular value decomposition processing.

[0091] All five spectral distribution matrices are extracted from the cache queue and smoothed using an exponentially decaying weighted average algorithm. Specifically, each matrix is ​​assigned a different weight coefficient, with the matrix in the current iteration having the highest weight (0.4); the matrix in the previous iteration has a weight of 0.3; and the weights of earlier iterations decrease sequentially to 0.2, 0.1, and 0.05, respectively. Each matrix is ​​multiplied by its corresponding weight and then summed to obtain the smoothed spectral distribution matrix. This weighting strategy gives higher importance to recent data while retaining the trend information of historical data, effectively filtering out instantaneous fluctuations in the spectral distribution caused by the randomness of batch data during training, making the trend of the spectral distribution more stable and reliable.

[0092] By introducing a caching and weighted average smoothing mechanism for the spectral distribution matrix, the fluctuations in evaluation metrics caused by the randomness of mini-batch sampling during the training of generative adversarial networks are effectively suppressed. This makes the correlation measurement based on random matrix theory more stable and reliable, providing a smoother optimization path for model training, significantly enhancing the stability and convergence of the training process, and improving the consistency and credibility of the final generated scene quality evaluation results.

[0093] Furthermore, step S200, which introduces the correlation metric as an additional loss term into the discriminator's loss function, includes: Step S261: Using the average spectral radius as a correlation metric, construct the theoretical correlation loss term for the random matrix.

[0094] The calculated average spectral radius is used as the core correlation metric, and a correlation loss term based on random matrix theory is constructed based on this. The design principle of this loss term is that a smaller average spectral radius indicates a stronger correlation between the generated scene and the real scene; therefore, the loss term is directly proportional to the average spectral radius. In the specific implementation, the value of the average spectral radius is directly used as the base value of the correlation loss term. When the statistical structures of the generated scene and the real scene are highly consistent, this loss term approaches 0; while when there are differences in the statistical characteristics of the two types of scenes, this loss term increases accordingly. This allows the correlation quantification results of random matrix theory to be directly transformed into guiding signals for model optimization.

[0095] Step S262: Obtain the initial loss function of the discriminator, which is the Wasserstein distance loss including a gradient penalty term.

[0096] The initial loss function for the discriminator is obtained, which adopts the Wasserstein distance loss form including a gradient penalty term. Specifically, it consists of three components: the discriminator's expectation of the generated scene output value, the discriminator's negative expectation of the real scene output value, and the gradient penalty term. The gradient penalty term is implemented by calculating the degree to which the gradient norm of the discriminator deviates from 1 at the midpoint of the line connecting the generated and real scenes; the penalty coefficient is typically set to 10. This initial loss function ensures the basic stability of the generative adversarial network training and provides the basic framework for subsequently introducing relevance constraints.

[0097] Step S263: Set trainable hyperparameters as weighting coefficients, and linearly sum the random matrix theoretical correlation loss term and the initial loss function using weighting coefficients to obtain the total loss function of the discriminator.

[0098] A trainable hyperparameter is set as a weighting coefficient to balance the relative importance of the random matrix theoretical correlation loss term and the initial loss function. This weighting coefficient is initially set to 0.1 and can be adjusted during training. The random matrix theoretical correlation loss term and the initial loss function are linearly summed using this weighting coefficient to obtain the discriminator's total loss function. The linear weighting preserves the differentiability of the loss function, allowing errors to propagate smoothly to each layer of the network. Furthermore, the introduction of the weighting coefficient provides a flexible balancing mechanism between the two types of losses.

[0099] Step S264: During the training process, the weighting coefficients are dynamically adjusted according to the convergence of the spectral distribution on the complex plane. When the spectral distribution tends to be concentrated, the weighting coefficients are increased; when the spectral distribution diverges, the weighting coefficients are decreased.

[0100] A dynamic adjustment mechanism for the weighting coefficients is established during training, making decisions based on the convergence of the spectral distribution in the complex plane. Specifically, after every 100 training iterations, the concentration of the spectral distribution is evaluated: when the distribution of eigenvalues ​​in the complex plane tends to be concentrated and the average spectral radius continues to decrease, the weighting coefficients are increased by 5% to strengthen the effect of correlation constraints; when the distribution of eigenvalues ​​shows a divergent trend and the average spectral radius fluctuates more, the weighting coefficients are decreased by 5% to reduce the impact of correlation constraints. This adaptive adjustment strategy ensures a balance between different loss terms during training, enabling the model to effectively optimize the relevance quality of the generated scene while maintaining training stability.

[0101] During model training, the discriminator calculates the average spectral radius for both generated and real samples, and provides a correlation metric based on the one-loop theorem to represent the correlation difference between the two. This metric is incorporated into the discriminator's loss function using the following formula.

[0102] ; in For the correlation constraint of the single-ring theorem, Let the initial loss function of the discriminator be , This is a hyperparameter.

[0103] By systematically incorporating the correlation metric of random matrix theory into the loss function of the discriminator and establishing an adaptive weighted adjustment mechanism, this invention achieves quantifiable optimization of the statistical correlation of generated scenes. This enables the model to maintain the basic training stability of generative adversarial networks while specifically improving the consistency of the statistical structure between generated scenes and real scenes, significantly enhancing the reliability and practicality of the generated results. It provides a training paradigm for photovoltaic power scene generation that combines stability and interpretability.

[0104] Furthermore, step S300 employs an alternating training strategy to jointly train the generator embedded with a dynamic gating function and the discriminator with a correlation loss term, including: Step S310: In each training iteration cycle, the network parameters of the generator are kept unchanged.

[0105] At the start of each training iteration, all trainable parameters in the generator network, including the weight matrices and bias vectors of the fully connected layers, are locked to remain constant during the discriminator optimization phase of the current iteration. This parameter freezing operation cuts off the path for generator parameter updates, ensuring that the photovoltaic power scene distribution output by the generator remains unchanged during discriminator training, providing a stable learning environment for the discriminator. Parameter freezing is achieved by setting the gradient flags of all generator parameters to an uncomputable state, thereby preventing gradients from flowing to the generator during backpropagation and creating the necessary conditions for focused optimization of the subsequent discriminator.

[0106] Step S320: Based on the current batch of training data, perform multiple consecutive parameter updates on the discriminator. Each update calculates the total loss function including the additional loss term and performs backpropagation.

[0107] Based on a batch size of 128 samples, the discriminator network undergoes five consecutive parameter update cycles. In each update, a batch of random vectors is sampled from the latent space and input into the generator to obtain generated scenes. Simultaneously, an equal number of real scenes are extracted from the training set and input into the discriminator. The total loss function, including Wasserstein distance loss, gradient penalty term, and random matrix theoretical correlation loss, is calculated. The gradients of the discriminator's layer parameters are calculated using backpropagation. The Adam optimizer is used to update the discriminator's convolutional kernel weights and bias parameters with a learning rate of 0.0001. This multiple consecutive update strategy ensures that the discriminator can fully learn to distinguish between real and fake samples when the generator parameters are fixed.

[0108] Step S330: After completing multiple updates of the discriminator, the network parameters of the fixed discriminator remain unchanged.

[0109] After five parameter updates of the discriminator, the parameter freezing state is switched to fix the network parameters of all layers of the discriminator, including the filters of the convolutional layers and the weights of the fully connected layers. At this point, the discriminator acts as a fixed evaluation function, and its parameters remain unchanged, providing a stable evaluation benchmark for the generator optimization. The parameter freezing operation is achieved by disabling the gradient calculation flag of the discriminator parameters, ensuring that the evaluation criteria of the discriminator remain consistent during subsequent generator updates.

[0110] Step S340: Perform a parameter update on the generator, where the optimization objective of the generator is to minimize the discriminator's discrimination output for its generated scene. The ratio of the number of discriminator updates to the number of generator updates remains at a preset ratio.

[0111] The generator undergoes a parameter update, with its optimization objective defined as minimizing the discriminator's output score for the generated scene. Specifically, a batch of random vectors is sampled from the latent space, passed through the generator network to obtain a photovoltaic power scene, and input to a discriminator with fixed parameters to obtain output scores. The negative mean of these scores is calculated as the generator's loss function. The gradient of each layer's parameters is calculated using the backpropagation algorithm, and the Adam optimizer is used to update the generator's fully connected layer weights and bias parameters with a learning rate of 0.0005. Optionally, the ratio of discriminator to generator update times is maintained at a preset value of 5:1 to ensure that the discriminator has sufficient capability to guide the generator's learning direction.

[0112] Step S350: Repeat the above alternating training process until the preset training cycle is reached.

[0113] The alternating training process described above was repeated for 8000 training iterations. Each training iteration strictly followed the order of updating the discriminator 5 times followed by the generator 1 time, using the same batch size and optimizer parameters. During training, the model performance was periodically evaluated on the validation set. When the Wasserstein distance and average spectral radius between the generated scene and the real scene no longer significantly improved within 100 consecutive iterations, the model was considered to have converged, the training process was terminated, and the final usable photovoltaic scene generation model was obtained.

[0114] Specifically, after generating the photovoltaic power time-series scenario in step S400, the following steps are also included: Step S510: Combine the generated photovoltaic power time series scene with the real photovoltaic power time series scene from the training sample set to construct an augmented matrix.

[0115] After the model completes training and generates photovoltaic power time-series scenarios, a quality assessment process is initiated. First, 100 generated scenario samples are extracted from the generator, and the same number of real photovoltaic power time-series scenarios are randomly selected from the training sample set as a reference. Using the same sliding time window processing method as in the training phase, with a window length of 32 sampling points, the two types of scenarios are simultaneously segmented in a non-overlapping manner to obtain multiple local sequence fragments. Generated scenario fragments from the same time interval are combined with real scenario fragments row-wise to form time-aligned sample pairs. Finally, all sample pairs are concatenated according to generated scenario blocks and real scenario blocks respectively, and merged into a complete augmented matrix. The number of rows in this matrix is ​​the total number of sample pairs, and the number of columns is twice the length of a single fragment, providing a structured data foundation for subsequent spectral analysis.

[0116] Step S520: Standardize the augmented matrix and multiply the standardized augmented matrix with the corresponding adjoint matrix to obtain the sample covariance matrix.

[0117] The constructed augmented matrix undergoes standardization preprocessing. The arithmetic mean and standard deviation of each column are calculated. Each element is subtracted from the mean of its corresponding column and then divided by the standard deviation of that column, ensuring that the data in each column are transformed into a distribution with zero mean and unit variance. The standardized augmented matrix is ​​then multiplied by its adjoint matrix (i.e., the conjugate transpose) to obtain the sample covariance matrix. This square matrix, with dimensions equal to the number of rows in the augmented matrix, contains all second-order statistical information between the generated and real scenes, providing a suitable mathematical object for eigenvalue analysis.

[0118] Step S530: Calculate the eigenvalues ​​of the sample covariance matrix to obtain the eigenvalue distribution in the complex plane.

[0119] Eigenvalue decomposition is performed on the sample covariance matrix to solve for all eigenvalues. After obtaining the eigenvalues ​​through numerical calculation methods, these eigenvalues ​​are mapped onto the complex plane to form an eigenvalue distribution graph. This distribution graph visually demonstrates the similarity in statistical structure between the generated scene and the real scene: when the two types of scenes are highly correlated, the eigenvalues ​​are tightly clustered near the center; when the correlation is weak, the eigenvalues ​​are dispersed over a wider range. The eigenvalue distribution pattern provides an intuitive visual basis and quantitative analysis foundation for subsequent quality assessment.

[0120] Step S540: Based on the single-ring theorem in random matrix theory, calculate the average spectral radius of the eigenvalue distribution as a quality evaluation index for the generated scene.

[0121] Based on the single-ring theorem in random matrix theory, the average spectral radius of the eigenvalue distribution is calculated as a quality assessment metric for the generated scene. The average spectral radius is defined as the arithmetic mean of the distances from all eigenvalues ​​to the origin of the complex plane; this metric quantifies the concentration of the eigenvalue distribution. The calculation process involves first determining the magnitude of each eigenvalue, then calculating the arithmetic mean of these magnitudes to obtain the final average spectral radius. A smaller value indicates that the eigenvalue distribution is more concentrated around the center, meaning a stronger statistical correlation between the generated scene and the real scene.

[0122] Step S550: The calculated average spectral radius is compared with a preset threshold, wherein the preset threshold is determined based on the average spectral radius value in the discriminator loss function after the model training converges.

[0123] The calculated average spectral radius is compared with a preset quality threshold, which is determined based on the average spectral radius value in the discriminator loss function during the model training convergence phase. Specifically, the moving average of the average spectral radius in the discriminator loss function over the last 100 training epochs is taken as the threshold benchmark, and then multiplied by a leniency factor of 1.2 to obtain the final threshold. This threshold determination method considers both the actual training level of the model and provides a moderately lenient tolerance for the quality assessment of the generated scene, ensuring that the evaluation criteria match the model's capabilities.

[0124] Step S560: When the average spectral radius is less than a preset threshold, it is determined that the currently generated photovoltaic power time series scene has a strong correlation with the real scene.

[0125] A quality assessment mechanism based on the average spectral radius is established. When the average spectral radius of the generated scene is less than a preset threshold, the generated scene is determined to have a strong correlation with the real scene and meet the quality requirements; otherwise, it is determined to be of unacceptable quality. This judgment logic is based on the core principle of random matrix theory: the more concentrated the eigenvalue distribution, the stronger the correlation between matrix elements. In this application scenario, it means that the generated scene is highly consistent with the real scene in terms of statistical characteristics. The judgment result assigns a clear quality label to each generated scene, providing a screening basis for subsequent applications.

[0126] Step S570: Output the generated photovoltaic power time series scenario and its corresponding average spectral radius evaluation index.

[0127] The system outputs quality-verified photovoltaic power time-series scenarios and their corresponding average spectral radius evaluation metrics. Each generated scenario data file includes metadata recording its average spectral radius value and quality judgment result. A quality assessment report is also generated, summarizing the average spectral radius distribution of all tested scenarios, pass rate statistics, and comparative analysis with historical generated quality data. These quality-certified scenario data can be directly delivered to power system planners for practical engineering applications such as renewable energy absorption capacity analysis, energy storage capacity configuration optimization, and operational risk assessment.

[0128] By introducing a quality assessment process after scenario generation, an objective quality certification system based on random matrix theory was established. This ensures that the generated photovoltaic power scenarios not only have physical rationality but also maintain a high degree of consistency with real scenarios in terms of statistical characteristics. At the same time, quantifiable quality indicators are provided for each generated scenario, which greatly enhances the reliability and credibility of the generated results in the actual application of the power system and provides data quality assurance for the accurate analysis of the power system under high proportion of new energy access.

[0129] Experimental results show that the photovoltaic scene generated by the method of this invention is highly consistent with the real data in terms of volatility, diurnal characteristics, and statistical regularity. Figure 3As shown, the average spectral radius is significantly better than that of the traditional WGAN model. The generated power curve can be freely adjusted according to meteorological conditions and time scale, exhibiting good generalization ability. This model can be directly applied to new energy power prediction, energy storage optimization scheduling, and power system operation risk analysis, providing reliable time-series data support for the planning and operation of new energy systems, and achieving accurate modeling and simulation in scenarios with a high proportion of renewable energy.

[0130] Accordingly, please refer to Figure 4 A second aspect of this invention provides a photovoltaic scene generation system based on random matrix theory enhancement, which generates a photovoltaic power time-series scene based on the aforementioned photovoltaic scene generation method based on random matrix theory enhancement, including: Model building module 1 is used to build a training sample set based on the historical power output data of photovoltaic power plants and to build a generative adversarial network framework including a generator and a discriminator. Matrix construction module 2 is used to construct an augmented matrix based on the random matrix theory, by combining the time series data of the generated photovoltaic power time series scene output by the generator with the real photovoltaic power time series scene in the training sample set, to calculate the spectral distribution of the augmented matrix, and transform the spectral distribution into a correlation metric according to the single-loop theorem, and introduce the correlation metric as an additional loss term into the loss function of the discriminator. Model optimization module 3 is used to jointly train the generator and the discriminator with a relevant loss term using an alternating training strategy to optimize the generative adversarial network framework. Scene generation module 4 is used to input random noise vectors into the generator to generate photovoltaic power time series scenes.

[0131] Accordingly, a third aspect of the present invention provides an electronic device, including: at least one processor and a memory connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to cause the at least one processor to perform the above-described photovoltaic scene generation method based on random matrix theory enhancement.

[0132] Accordingly, a fourth aspect of the present invention provides a computer-readable storage medium having computer instructions stored thereon, which, when executed by a processor, implement the above-described photovoltaic scene generation method based on random matrix theory enhancement.

[0133] The embodiments of the present invention aim to protect a photovoltaic scene generation method and system based on random matrix theory, which has the following effects: 1. By introducing the single-loop theorem from random matrix theory into the discriminator of generative adversarial networks, a quantifiable correlation evaluation and constraint mechanism is constructed. By constructing an augmented matrix between the generated scene and the real scene and analyzing its spectral distribution, the originally black-box, qualitative "similarity" judgment can be transformed into a precise and computable mathematical index based on the average spectral radius. This index is not only incorporated into the model training as a correlation loss term to guide the generator to optimize towards more realistic statistical characteristics, but also serves as an objective criterion for scene quality in the final evaluation stage. This achieves full-process interpretability from the internal mechanism of the model to the external output evaluation, breaking through the bottleneck of traditional generative models lacking clear correlation measurement indicators. 2. By integrating a physical constraint generator, an interpretable discriminator, a stable alternating training strategy, and a post-generation evaluation process into a complete collaborative system, this invention significantly improves the overall efficiency and engineering practicality of photovoltaic scene generation models. Dynamic gating ensures the physical baseline, random matrix theory constraints drive statistical realism, and specific training strategies guarantee the convergence stability of complex model training. The final quality evaluation step provides credible certification for the reliability of the generated results. This enables the model to efficiently generate large-scale and diverse photovoltaic scenes with physical correctness, statistical realism, and clear quality indicators, directly meeting the urgent needs of high-requirement engineering applications such as new energy system planning, energy storage optimization configuration, and operational risk assessment for input data quality and reliability. 3. By introducing a dynamic gating function based on average sunrise and sunset times and structurally embedding it into the generator's output, the physical rationality of the generated photovoltaic power scenario is fundamentally ensured. The generator's output power sequence can be constrained and corrected point by point, forcing the power output during periods without sunlight to be set to zero. This completely solves the core flaw of traditional deep generation models—generating non-zero power at night, which violates physical laws. Simultaneously, combined with smooth transition processing at the boundaries, the generated power curve is not only numerically correct but also morphologically continuous and smooth, significantly improving the simulation fidelity of the generated scenario to the real-world diurnal variation of photovoltaic power generation, providing a reliable data foundation for subsequent power system analysis.

[0134] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A photovoltaic scene generation method based on random matrix theory enhancement, characterized in that, The method comprises the following steps: constructing a training sample set based on historical power output data of a photovoltaic power station, and constructing a generative adversarial network framework comprising a generator and a discriminator; based on random matrix theory, constructing an augmented matrix from the generated photovoltaic power time series scenario output by the generator and the time series data of the real photovoltaic power time series scenario in the training sample set, calculating the spectral distribution of the augmented matrix, and converting the spectral distribution into a correlation measurement index according to the single ring theorem, and introducing the correlation measurement index as an additional loss term into the loss function of the discriminator; adopting an alternating training strategy to jointly train the generator and the discriminator with the additional correlation loss term, and optimizing the generative adversarial network framework; inputting a random noise vector into the generator to generate a photovoltaic power time series scenario.

2. The photovoltaic scene generation method enhanced based on random matrix theory according to claim 1, characterized in that, The step of constructing an augmented matrix from the generated photovoltaic power time series scenario and the time series data of the real photovoltaic power time series scenario based on random matrix theory, calculating the spectral distribution of the augmented matrix, and converting the spectral distribution into a correlation measurement index according to the single ring theorem comprises: adopting a sliding time window method to construct an augmented matrix from the generated photovoltaic power time series scenario and the time series data of the real photovoltaic power time series scenario; standardizing the augmented matrix; multiplying the standardized augmented matrix and the corresponding coprime matrix to obtain a spectral distribution matrix; singular value decomposition of the spectral distribution matrix to obtain the spectral distribution of the spectral distribution matrix on the complex plane; according to the single ring theorem in the random matrix theory, calculating the average spectral radius of the spectral distribution as the correlation measurement index.

3. The photovoltaic scene generation method enhanced based on random matrix theory according to claim 2, characterized in that, The step of adopting a sliding time window method to construct an augmented matrix from the generated photovoltaic power time series scenario and the time series data of the real photovoltaic power time series scenario comprises: adopting a sliding time window of fixed length to slide on the generated photovoltaic power time series scenario and the real photovoltaic power time series scenario in a non-overlapping manner to obtain multiple local sequence segments; pairing the local sequence segments of the generated photovoltaic power time series scenario and the real photovoltaic power time series scenario from the same time window to form time series aligned sample pairs; splicing the local sequence segments of the generated photovoltaic power time series scenario in all sample pairs into a first matrix block and splicing the local sequence segments of the real photovoltaic power time series scenario in all sample pairs into a second matrix block; splicing the first matrix block and the second matrix block by column to construct the augmented matrix.

4. The photovoltaic scene generation method enhanced based on random matrix theory according to claim 3, characterized in that, Before the step of singular value decomposition of the spectral distribution matrix, the method further comprises: in the iteration process of model training, caching the spectral distribution matrices generated by the current iteration step and a plurality of previous iteration steps; weighting and averaging the cached spectral distribution matrices to obtain a smoothed spectral distribution matrix for subsequent singular value decomposition processing.

5. The photovoltaic scene generation method enhanced based on random matrix theory according to claim 2, characterized in that, The step of introducing the correlation measurement index as an additional loss term into the loss function of the discriminator comprises: constructing a random matrix theory correlation loss term by taking the average spectral radius as the correlation measurement index. obtaining an initial loss function of the discriminator, the initial loss function being a Wasserstein distance loss containing a gradient penalty term; setting a trainable hyper-parameter as a weighting coefficient, linearly weighting and summing the random matrix theory correlation loss term and the initial loss function by the weighting coefficient to obtain a total loss function of the discriminator; in the training process, dynamically adjusting the size of the weighting coefficient according to the convergence of the spectral distribution on the complex plane, increasing the value of the weighting coefficient when the spectral distribution tends to concentrate, and decreasing the value of the weighting coefficient when the spectral distribution diverges.

6. The photovoltaic scene generation method enhanced based on random matrix theory according to claim 2, characterized in that, After generating the photovoltaic power time series scene, the method further comprises: combining the generated photovoltaic power time series scene with the real photovoltaic power time series scene from the training sample set to construct an augmented matrix; standardizing the augmented matrix and multiplying the standardized augmented matrix by the corresponding coprime matrix to obtain a sample covariance matrix; calculating the eigenvalues of the sample covariance matrix to obtain an eigenvalue distribution on the complex plane; calculating the average spectral radius of the eigenvalue distribution as a quality evaluation index of the generated scene according to the single ring theorem in the random matrix theory; comparing the calculated average spectral radius with a preset threshold, wherein the preset threshold is determined based on the average spectral radius value in the discriminator loss function after model training converges; when the average spectral radius is less than the preset threshold, it is determined that the currently generated photovoltaic power time series scene has strong correlation with the real scene; outputting the generated photovoltaic power time series scene and its corresponding average spectral radius evaluation index.

7. The random matrix theory enhanced photovoltaic scene generation method of claim 1, wherein, The joint training of the generator and the discriminator with the correlation loss term is performed by using an alternating training strategy, comprising: fixing the network parameters of the generator unchanged in each training iteration period; based on the current batch of training data, performing continuous multiple parameter updates on the discriminator, each update calculating the total loss function containing the additional loss term and performing back propagation; after completing multiple updates of the discriminator, fixing the network parameters of the discriminator unchanged; performing a parameter update on the generator, wherein the optimization target of the generator is to minimize the discrimination output of the discriminator on the generated scene; repeating the above alternating training process until a preset training period is reached; wherein the ratio of the number of updates of the discriminator to the number of updates of the generator remains a preset proportion value.

8. The photovoltaic scene generation method based on random matrix theory enhancement according to any one of claims 1-7, characterized in that, Before constructing the augmented matrix from the time series data of the generated photovoltaic power time series scene and the real photovoltaic power time series scene, the method further comprises: calculating the average sunrise time and the average sunset time based on the historical power output data; defining the effective sunshine interval and the non-sunshine interval based on the average sunrise time and the average sunset time; constructing a time gating function, the output value of the time gating function being 1 when the input time is within the effective sunshine interval, and the output value of the time gating function being 0 when the input time is within the non-sunshine interval; The generated photovoltaic power time sequence scene directly output by the generator is point-by-point multiplied with the time gating function to generate a physically constrained corrected photovoltaic power time sequence scene; At the boundary between the effective sunshine interval and the no-sunshine interval, a Sigmoid function is used to perform a smooth transition processing on the output value of the time gating function between 0 and 1, so as to eliminate the step change of the power curve at sunrise and sunset.

9. The photovoltaic scene generation method enhanced based on random matrix theory according to claim 8, characterized in that, The smooth transition processing on the output value of the time gating function between 0 and 1 at the boundary between the effective sunshine interval and the no-sunshine interval includes: Based on the historical power output data, the average change rate of the photovoltaic power sequence with respect to time within a preset time range near the sunrise time and the sunset time is calculated respectively; Based on the absolute value of the average change rate, the time width of the sunrise transition interval and the sunset transition interval is determined through a preset mapping relationship, wherein the greater the absolute value of the average change rate, the narrower the time width of the corresponding transition interval determined; For each time point in the sunrise transition interval, the time difference between the time point and the average sunrise time is calculated, and the result obtained by dividing the time difference by a first scaling factor is taken as the input of a Sigmoid function to obtain a first smooth gating value, which continuously transitions from 0 to 1 as the input value changes from a negative value to a positive value; For each time point in the sunset transition interval, the time difference between the time point and the average sunset time is calculated, and the result obtained by dividing the time difference by a second scaling factor is taken as the input of a Sigmoid function to obtain a second smooth gating value, which continuously transitions from 1 to 0 as the input value changes from a negative value to a positive value; The first smooth gating value corresponding to the sunrise transition interval and the second smooth gating value corresponding to the sunset transition interval are integrated into the time gating function to replace the step output of the time gating function at the boundary, so as to obtain a continuous and smooth time gating function.

10. A photovoltaic scene generation system enhanced based on random matrix theory, characterized in that, The photovoltaic power time sequence scene is generated based on the random matrix theory enhanced photovoltaic scene generation method according to any one of claims 1-9, comprising: A model construction module is configured to construct a training sample set based on historical power output data of a photovoltaic power station, and construct a generative adversarial network framework including a generator and a discriminator; A matrix construction module is configured to construct an augmented matrix by constructing the generated photovoltaic power time sequence scene output by the generator and the time sequence data of the real photovoltaic power time sequence scene in the training sample set based on the random matrix theory, calculate the spectral distribution of the augmented matrix, and convert the spectral distribution into a correlation measurement index according to the single ring theorem, and introduce the correlation measurement index as an additional loss term into the loss function of the discriminator; A model optimization module is configured to use an alternating training strategy to jointly train the generator and the discriminator with the additional correlation loss term introduced, and optimize the generative adversarial network framework; A scene generation module is configured to input a random noise vector to the generator to generate a photovoltaic power time sequence scene.

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