Photovoltaic output prediction method based on damping Caputo fractional order grey model
The photovoltaic power output prediction method based on the damped Caputo fractional grey model solves the problem of insufficient accuracy and stability of traditional methods under small sample conditions, and achieves high-precision and high-robust photovoltaic power output prediction, adapting to the complex nonlinear fluctuation characteristics of photovoltaic power output.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-18
- Publication Date
- 2026-03-27
AI Technical Summary
Traditional photovoltaic power output prediction methods are difficult to adapt to the complex nonlinear fluctuation characteristics of photovoltaic power output under small sample conditions, resulting in insufficient prediction accuracy and stability, especially in the case of instability in grid dispatch.
A DCLFGM(1,1) model based on a damped Caputo fractional grey model, combined with fractional calculus theory and the Logistic equation, is constructed using a particle swarm optimization algorithm to predict photovoltaic power output, suppress outlier interference, and enhance the model's adaptability and robustness.
It improves the accuracy and stability of photovoltaic power output prediction, can more accurately fit the actual variation law of photovoltaic power output, suppresses overfitting, and achieves high-precision and high-robust prediction results.
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Figure CN121749133A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of new energy prediction technology, and relates to a photovoltaic power output prediction method based on a damped Caputo fractional grey model. Background Technology
[0002] Unlike traditional energy sources, photovoltaic (PV) power output is strongly influenced by weather conditions and the diurnal cycle, exhibiting significant randomness and volatility. When PV power generation accounts for a high proportion of the power system, its inherent instability poses a severe challenge to grid dispatch and operation, which has become a key bottleneck restricting the further development of the industry.
[0003] To achieve precise grid dispatch, improve the absorption capacity of new energy sources, ensure power supply stability, and enhance the market competitiveness of photovoltaic (PV) power plants, accurate short-term PV output forecasting is crucial. In particular, with the deepening of my country's dual-carbon strategy, many newly built PV power plants face the challenge of insufficient historical data accumulation. Simultaneously, rapid technological iteration and climate variability highlight the value of recent data, resulting in PV output sequences generally exhibiting characteristics of small sample sizes, non-stationarity, and weak regularity. In such information-scarce scenarios, traditional forecasting methods are often unsuitable due to their reliance on large amounts of data.
[0004] Grey prediction models, as an effective tool for handling small-sample uncertainty problems, have demonstrated unique value in this field. These models require only a small amount of data to construct a predictive framework, effectively overcoming the dependence of traditional models on data scale. However, basic grey models lack flexibility in capturing the complex nonlinear fluctuation characteristics of photovoltaic power output. To more accurately describe its inherent laws, more advanced modeling mechanisms need to be introduced, such as combining fractional calculus theory to enhance the model's ability to characterize data trends and memory effects, thereby meeting the practical needs of high-precision prediction.
[0005] Therefore, there is an urgent need to develop an advanced prediction method that can better adapt to the characteristics of photovoltaic power output data and maintain high accuracy and robustness even under small sample conditions. This invention was developed in response to this technological background. Summary of the Invention
[0006] In view of this, the purpose of this invention is to provide a photovoltaic power output prediction method based on a damped Caputo fractional grey model.
[0007] To achieve the above objectives, the present invention provides the following technical solution: A photovoltaic power output prediction method based on a damped Caputo fractional grey model includes the following steps: S1: Establish an initial sequence based on photovoltaic power output data to obtain the target photovoltaic power output sequence; S2: Preprocess the original photovoltaic power output sequence to calculate the r-order damped Caputo cumulative generation sequence, the r-order damped Caputo cumulative subtraction restoration sequence, and the mean sequence; S3: Establish a damped Caputo fractional logistic grey prediction model (DCLFGM(1,1)) and construct matrices B and Y to obtain the estimated values of the model parameters; S4: The particle swarm optimization algorithm is used to optimize the parameters, determine the optimal order of the model, and combine the least squares method to calculate the parameter values and construct the model; S5: Calculate the simulated value of the DCLFGM(1,1) model using the time response function, and obtain the predicted value of photovoltaic output using the cumulative reduction formula.
[0008] Furthermore, in S2, the initial photovoltaic power output sequence is denoted as... ,in This represents the k-th initial photovoltaic output value. .
[0009] Furthermore, in S2, the r-order damped Caputo cumulative generation sequence is denoted as... ,in y, and Where r is the order parameter and Γ() is the Gamma function. is the damping coefficient.
[0010] Furthermore, in S2, the r-order damped Caputo cumulative reduction sequence is denoted as... ,in ,and ,in Satisfying recursion and .
[0011] Furthermore, in S2, the mean sequence is denoted as ,in .
[0012] Furthermore, in S3, the expression for the DCLFGM(1,1) model is: , among which the parameter list Calculated using the least squares method ,matrix B and Y Defined respectively , .
[0013] Furthermore, in S4, the particle swarm optimization algorithm uses the total mean absolute percentage error (MAPE) as its parameter.total To optimize the objective function, the objective function is defined as follows: ,in l For the length of the training data, h To predict data length, n The total data length, and n = l + h .
[0014] Furthermore, in S5, the time response function is: ,in satisfy and , j =1,2,..., n .
[0015] Furthermore, in S5, the cumulative reduction and restoration formula is: when k When =1, ; when k =2,3,..., n hour, ,in satisfy and .
[0016] Furthermore, in S4, the particle swarm optimization algorithm is the optimal algorithm selected after comparison with genetic algorithm, simulated annealing algorithm, gray wolf optimization algorithm and differential evolution algorithm.
[0017] The beneficial effects of this invention are as follows: (1) Traditional grey models have limitations when dealing with photovoltaic power output data that exhibits volatility and saturation trends. This invention integrates fractional calculus theory, enabling the model to more precisely characterize the inherent memory and historical dependence of the data. At the same time, the introduced energy logistic equation gives the model a natural ability to describe the saturation growth process, thereby enabling it to more accurately fit the actual variation law of photovoltaic power output and significantly improve its adaptability to complex data patterns.
[0018] (2) The damped Caputo fractional accumulation method proposed in this invention is an innovative data processing mechanism. By introducing a damping factor, this method can flexibly adjust the weight ratio of historical data in the new sequence, effectively suppress outlier interference, and enhance the smoothness of the sequence. This feature enables the model to effectively suppress overfitting when facing small-sample, noisy photovoltaic data, thereby not only improving the fitting accuracy but also ensuring the robustness and reliability of the prediction results.
[0019] (3) The model involves multiple key parameters, and determining their optimal values is crucial to the prediction performance. This invention systematically compared various mainstream intelligent optimization algorithms and ultimately selected the particle swarm optimization algorithm as the optimization engine for the model. This selection enables the model parameters to be adaptively adjusted according to specific data characteristics, avoiding the bias of human experience settings, realizing the intelligence and efficiency of the optimization process, and thus fully exploring the potential performance of the model.
[0020] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description
[0021] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein: Figure 1 This is a flowchart of the present invention. Detailed Implementation
[0022] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.
[0023] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.
[0024] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.
[0025] Example 1: A Basic Method for Predicting Photovoltaic Output Based on a Damped Caputo Fractional Grey Model This embodiment details the basic implementation process of the photovoltaic power output prediction method of the present invention, such as... Figure 1 As shown, the specific steps include: S1: Input Initial Sequence: Obtain the initial photovoltaic output sequence by collecting historical photovoltaic power output data. ; S2: Preprocessing the raw data: processing the initial photovoltaic power output sequence Calculate the corresponding r-order damped Caputo cumulative generation sequence, r-order cumulative subtraction generation sequence, and mean sequence cumulative generation sequence. Specifically, this includes: establishing an initial photovoltaic output sequence based on photovoltaic output data, denoted as: (1) in, This is the initial photovoltaic power output sequence, and This represents the k-th initial photovoltaic output value; Performing an r-th order damped Caputo accumulation on the initial photovoltaic output sequence yields an r-th order damped Caputo accumulation sequence, denoted as: (1) in, (2) yes The r-th order cumulative decrease reversion sequence is denoted as: (3) in, (4) Each of them The specific value is expressed by the following equation: (5) yes The mean-generated sequence is denoted as: (6) in, ; S3: Construct the matrix, estimate the parameters, and establish the DCLFGM(1,1) model: Definition 1: The fractional integral with an exponential kernel function is defined as follows: (8) Accordingly, its derivative is defined as (9) Definition 2: Definition of Grunwald-Letnikov (GL) fractional difference Assuming when , Then there is (10) in It is a fractional derivative. It refers to the number of samples.
[0026] From the recursive relation, the coefficient of the binomial It can be obtained through the following recursive form , ,
[0027] By applying the forward difference method, the discrete form of the GL fractional order can be obtained. Then, according to equation (10). , This yields the forward difference form: (11) Let the energy logistic differential equation be expressed as follows: (12) Then regarding First-order damped Caputo cumulative generation sequence ( The differential equation for -DCAGO is: (13) in The first-order damped Caputo cumulative generator is shown in equation (3). According to equation (9), the left side of equation (13) can be transformed into... (14) Therefore, the expression for the DCLFGM(1,1) model can be obtained as follows: (15) Equation (13) is the whitening equation of equation (15); Based on the expression of the DCLFGM(1,1) model, its parameter list is as follows: Then, according to the least squares method, we can obtain: (16) in, , .
[0028] S4: Model Order Optimization: To select a suitable optimization algorithm for the model parameters, this invention compared five optimization algorithms: genetic algorithm, simulated annealing algorithm, particle swarm optimization algorithm, gray wolf optimization algorithm, and differential evolution algorithm. Comparative analysis showed that the particle swarm optimization algorithm exhibited the best optimization effect; therefore, it was selected for parameter optimization. The final model uses the particle swarm optimization algorithm to optimize the order. The model is constructed based on the found optimal order and the parameter values calculated by the least squares method, specifically including: will sequence A grey prediction model is built using the first m elements, and the next nm data points form the prediction sequence used to test the model's accuracy. Let the error sequence be: (17) in, , Indicates the original sequence The corresponding cumulative reduction sequence value; Let the total mean absolute percentage error (MAPEtotal) be the objective function for optimization, as follows: (18)
[0029] S5: Generate the time response function to obtain the simulated and predicted values. Calculate the simulated and predicted values using formulas (19) and (20), as follows: The time response function of the DCLFGM(1,1) model is: (19) Cumulative reduction and restoration formula: (20) in , , .
[0030] For the DCLFGM(1,1) model mentioned above, the simulation and prediction errors are calculated according to its performance evaluation criteria, and the simulation and prediction performance of the model is analyzed. Specifically, MAPE is used to calculate the model's performance, and the formula is as follows: (twenty one) Verifying the effectiveness of the grey DCLFGM(1,1) model: The model was applied to a real-world case to verify its excellent performance and predictive capabilities. Photovoltaic power output data from Qinghai and Hainan provinces from August 2024 to June 2025 were selected as a case study for effectiveness analysis. The model was compared with other predictive models, using MAPE as the measured predictive performance index. The results are shown in Table 1.
[0031] Table 1
[0032] Experimental results show that, in the fitting stage, except for the Verhulst and WGM(1,1) models, the simulation errors of the other models are all controlled within 10%, demonstrating good fitting performance. Among them, the DGM(1,1), GM(1,1), IDGM(1,1), and the DCLFGM(1,1) model proposed in this study perform better, with errors all below 5%. The fitting error of DCLFGM(1,1) is only 3.9607%, the lowest among all models, indicating that the DCLFGM(1,1) model can fit the actual trend of photovoltaic power output data well. In the prediction stage, only the DCLFGM(q,1) model has an error below 10%, reaching 6.4240%, which is significantly better than other comparative models. Considering both fitting and prediction performance, DCLFGM(q,1) shows the best accuracy and stability, and better reflects the overall trend of photovoltaic power output, verifying the superiority of this model.
[0033] Example 2: Comparison and Selection of Optimization Algorithms This embodiment focuses on illustrating the process of comparing and selecting optimization algorithms.
[0034] During model implementation, the choice of optimization algorithm directly affects the effectiveness and efficiency of order optimization. This embodiment details the comparative testing process of five optimization algorithms. First, on the same photovoltaic power output dataset, genetic algorithm, simulated annealing algorithm, particle swarm optimization algorithm, gray wolf optimization algorithm, and differential evolution algorithm were used to optimize the order parameters r and q and the damping coefficient ζ of the DCLFGM(1,1) model.
[0035] In practice, the same parameters are set for each algorithm to ensure fair comparison. The population size is uniformly set to 50, the maximum number of iterations is 200, and the search space is set to... , , Set the total mean absolute percentage error (MAPEtotal) as the objective function.
[0036] The workflow is as follows: Initialize the parameters for each algorithm, run each algorithm independently 30 times, and record the optimal parameter combination and corresponding MAPEtotal value obtained in each optimization. Comparison metrics include algorithm convergence speed, stability, and the minimum MAPEtotal value finally found.
[0037] The results show that, in the parameter space of this problem, the particle swarm optimization algorithm exhibits the fastest convergence speed and the strongest stability. Genetic algorithms are prone to getting trapped in local optima, simulated annealing has a slow convergence speed, and gray wolf optimization and differential evolution algorithms are less stable than particle swarm optimization. The parameter combination found by particle swarm optimization enables the model to achieve the lowest prediction error, with an average MAPEtotal value approximately 0.5 percentage points lower than the suboptimal algorithms.
[0038] Therefore, in the final implementation, the particle swarm optimization algorithm was selected as the standard optimization tool for the DCLFGM(1,1) model. The specific parameters of the particle swarm optimization algorithm were set as follows: the inertia weight decreased linearly from 0.9 to 0.4, and both the individual learning factor and the social learning factor were 2.0. This selection process ensured that the model could adaptively adjust to the optimal state, significantly improving the practicality and reliability of the method.
[0039] Example 3: Implementation of Multi-Scenario Extended Applications This embodiment extends the basic technical solution and demonstrates the application process of the method in different scenarios.
[0040] The first extended application is to combine meteorological factors for collaborative forecasting. In this embodiment, the initial sequence X... 0 The model construction is not limited to historical power data, but extends to include multivariate sequences of key meteorological parameters such as irradiance, ambient temperature, and relative humidity. In practice, each meteorological variable is first normalized, and then, in the preprocessing stage S2, each variable sequence is generated using damped Caputo summation. When constructing the model in S3, the data matrix B and vector Y need to be expanded accordingly to include multivariate information. This expansion enables the model to capture the complex relationship between power and meteorological conditions, making it suitable for stations where meteorological data is available, thereby improving prediction accuracy.
[0041] The second extension applies to forecasting at different time scales. For ultra-short-term forecasting needs, minute-level data is used, with an initial sequence containing 1440 data points. For short-term forecasting, hour-level data is used, with a sequence length of 168. In the optimization of S4, the weight distribution of the objective function is adjusted for different time scales. For ultra-short-term forecasting, more emphasis is placed on the forecast accuracy of the most recent time point; for short-term forecasting, the balance of overall forecast performance is considered. This extension verifies the flexibility of the method of this invention at different time scales.
[0042] The third extension targets predictions for photovoltaic power plants of different capacities. For large ground-mounted power plants, data fluctuations are relatively small, so the r-value can be appropriately increased to enhance the smoothness of the sequence. For distributed photovoltaic systems, data fluctuations are larger, so the r-value can be decreased to preserve the detailed features of the sequence. By adjusting the parameter search range, the model can adapt to different application scenarios.
[0043] In summary, the DCLFGM(1,1) model of this invention can effectively simulate the fluctuation trend of photovoltaic power output data, demonstrating its good adaptability to fluctuating time series, conforming to the characteristics of photovoltaic power output data trend changes, and exhibiting excellent predictive performance for future photovoltaic power output trends. The prediction model proposed in this invention can help decision-makers better understand recent changes in photovoltaic power output, providing theoretical support and scientific basis for photovoltaic power output forecasting.
[0044] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.
Claims
1. A photovoltaic power output prediction method based on a damped Caputo fractional grey model, characterized in that: Includes the following steps: S1: Establish an initial sequence based on photovoltaic power output data to obtain the target photovoltaic power output sequence; S2: Preprocess the original photovoltaic power output sequence to calculate the r-order damped Caputo cumulative generation sequence, the r-order damped Caputo cumulative subtraction restoration sequence, and the mean sequence; S3: Establish a damped Caputo score-based Logistic grey prediction model DCLFGM(1,1), construct matrices B and Y, and obtain the estimated values of the model parameters; S4: The particle swarm optimization algorithm is used to optimize the parameters, determine the optimal order of the model, and combine the least squares method to calculate the parameter values and construct the model; S5: Calculate the simulated value of the DCLFGM(1,1) model using the time response function, and obtain the predicted value of photovoltaic output using the cumulative reduction formula.
2. The photovoltaic power output prediction method based on the damped Caputo fractional grey model according to claim 1, characterized in that: In S2, the initial photovoltaic power output sequence is denoted as ,in This represents the k-th initial photovoltaic output value. .
3. The photovoltaic power output prediction method based on the damped Caputo fractional grey model according to claim 2, characterized in that: In S2, the r-order damped Caputo cumulative generation sequence is denoted as ,in y, and Where r is the order parameter and Γ() is the Gamma function. is the damping coefficient.
4. The photovoltaic power output prediction method based on the damped Caputo fractional grey model according to claim 3, characterized in that: In S2, the r-order damped Caputo cumulative reduction sequence is denoted as ,in ,and ,in Satisfying recursion and .
5. The photovoltaic power output prediction method based on the damped Caputo fractional grey model according to claim 3, characterized in that: In S2, the mean sequence is denoted as ,in .
6. The photovoltaic power output prediction method based on the damped Caputo fractional grey model according to claim 1, characterized in that: In S3, the expression for the DCLFGM(1,1) model is: , among which the parameter list Calculated using the least squares method ,matrix B and Y Defined respectively , .
7. The photovoltaic power output prediction method based on the damped Caputo fractional grey model according to claim 1, characterized in that: In S4, the particle swarm optimization algorithm uses the total mean absolute percentage error (MAPE) as its parameter. total To optimize the objective function, the objective function is defined as follows: ,in l For the length of the training data, h To predict data length, n The total data length, and n = l + h .
8. The photovoltaic power output prediction method based on the damped Caputo fractional grey model according to claim 1, characterized in that: In S5, the time response function is ,in satisfy and , j =1,2,..., n .
9. The photovoltaic power output prediction method based on the damped Caputo fractional grey model according to claim 1, characterized in that: In S5, the cumulative reduction and restoration formula is: when k When =1, ; when k =2,3,..., n hour, ,in satisfy and .
10. The photovoltaic power output prediction method based on the damped Caputo fractional grey model according to claim 1, characterized in that: In S4, the particle swarm optimization algorithm is the optimal algorithm selected after comparison with the genetic algorithm, simulated annealing algorithm, gray wolf optimization algorithm and differential evolution algorithm.