A Method and System for Generating Wind and Solar Power Prediction Models Based on Elliptic Curves

Abstract

This application provides a method and system for generating a wind and solar power prediction model based on elliptic curves. The method includes: spatiotemporal matching and fusion of acquired multi-source meteorological data to construct a wind and solar power prediction feature matrix; mapping the hyperparameter vectors of the LightGBM algorithm to the elliptic curve parameter space, and constructing an optimization objective function based on the geometric constraint regularization term of the elliptic curve, the prediction loss, the LightGBM native regularization term, and the feature matrix; iteratively updating the hyperparameter vectors according to the optimization objective function, the L-function of the elliptic curve, the rational point group structure, the tangent space projection, and group operations to determine the target hyperparameter vector; and generating a wind and solar power prediction model based on the target hyperparameter vector. This application utilizes the group operation rules of elliptic curves, the L-function, and the mathematical properties of rank to determine the search path and update step size of the LightGBM hyperparameters, solving the problems of slow convergence and insufficient generalization ability in existing technologies for wind and solar power prediction.

Description

Technical Field

[0001] This invention relates to the field of renewable energy power generation prediction technology, and in particular to a method and system for generating wind and solar power prediction models based on elliptic curves. Background Technology

[0002] As renewable energy continues to account for an increasing proportion of the energy mix, the large-scale application of wind and solar power is becoming increasingly widespread. Wind and solar power forecasting technology is crucial for grid dispatch and energy management.

[0003] In the field of machine learning, gradient boosting decision tree algorithms are widely used due to their high prediction accuracy and adaptability to various data types. LightGBM, as an efficient implementation of gradient boosting decision trees, significantly improves training speed and memory efficiency while maintaining high accuracy through techniques such as gradient-based one-sided sampling and mutually exclusive feature binding.

[0004] However, existing LightGBM algorithms face challenges in parameter tuning, slow convergence, and overfitting when dealing with high-dimensional sparse data and complex nonlinear relationships in wind and solar power forecasting. The lack of mathematical guidance in parameter tuning further hinders their ability to converge on complex meteorological datasets and generalize effectively, failing to meet the refined requirements of grid energy management. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a method and system for generating wind and solar power prediction models based on elliptic curves, so as to improve the convergence speed and generalization ability in the process of generating wind and solar power prediction models.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows: A method for generating a wind and solar power prediction model based on elliptic curves, comprising: Spatiotemporal matching and fusion of the acquired multi-source meteorological data are performed to obtain spatiotemporal multi-source meteorological data, and a wind and solar power prediction feature matrix is ​​constructed based on the spatiotemporal multi-source meteorological data. The hyperparameter vectors of the LightGBM algorithm are mapped to the parameter space of the elliptic curve, and an optimization objective function is constructed based on the geometric constraint regularization term of the elliptic curve, the prediction loss, the LightGBM native regularization term, and the wind and solar power prediction feature matrix. Based on the optimization objective function, the L-function of the parameter space of the elliptic curve, the rational point group structure, the tangent space projection, and group operations, the hyperparameter vector is iteratively updated to determine the target hyperparameter vector corresponding to the multi-source meteorological data. A wind and solar power prediction model is generated based on the target hyperparameter vector.

[0007] To solve the above-mentioned technical problems, another technical solution adopted by the present invention is as follows: A wind and solar power prediction model generation system based on elliptic curves includes a memory, a processor, and a computer program stored in the memory and running on the processor. When the processor executes the computer program, it implements the various steps of the wind and solar power prediction model generation method based on elliptic curves as described above.

[0008] The beneficial effects of this invention are as follows: By performing spatiotemporal matching and fusion of acquired multi-source meteorological data and constructing a wind and solar power prediction feature matrix, the quality and feature representation capabilities of the input data are improved. By mapping the hyperparameter vectors of the LightGBM algorithm to the parameter space of an elliptic curve and constructing an optimization objective function, the geometric constraint regularization term of the elliptic curve is used to constrain the parameter search path, avoiding blind parameter search. By iteratively updating the hyperparameter vectors according to the optimization objective function, the L-function of the elliptic curve, the rational point group structure, tangent space projection, and group operations, and by using the L-function of the elliptic curve and rank adaptive adjustment of the update step size, the convergence speed is accelerated. By generating a wind and solar power prediction model based on the target hyperparameter vector, the generalization ability and prediction accuracy of the model are improved. In this way, this invention solves the problems of existing technologies lacking mathematical theoretical guidance, slow convergence speed, and insufficient generalization ability when dealing with high-dimensional sparse data and complex nonlinear relationships in wind and solar power prediction scenarios. Attached Figure Description

[0009] Figure 1 This is a flowchart illustrating a method for generating a wind and solar power prediction model based on elliptic curves, according to an embodiment of the present invention. Figure 2 This is a flowchart illustrating a method for generating a wind and solar power prediction model based on elliptic curves, according to an embodiment of the present invention. Figure 3 This is a schematic diagram of a wind and solar power prediction model generation system based on elliptic curves, according to an embodiment of the present invention. Detailed Implementation

[0010] Definitions:

[0011] To explain in detail the technical content, objectives, and effects of the present invention, the following description is provided in conjunction with the embodiments and accompanying drawings.

[0012] With the increasing large-scale application of wind and solar power generation, wind and solar power prediction technology is crucial for grid dispatch and energy management. LightGBM, as an efficient implementation of gradient boosting decision trees, has been widely used in wind and solar power prediction. However, wind and solar power prediction data are characterized by high dimensionality, sparsity, and complex nonlinear relationships, making the hyperparameter settings of the LightGBM algorithm significantly impact model performance. Existing technologies primarily rely on grid search, random search, or Bayesian optimization methods for hyperparameter tuning, lacking mathematical theoretical guidance. These methods suffer from slow convergence, susceptibility to local optima, and insufficient generalization ability, making it difficult to meet the needs of refined grid dispatch.

[0013] To at least address the aforementioned problems, this invention provides a method for generating a wind and solar power prediction model based on elliptic curves. By mapping the hyperparameter vectors of the LightGBM algorithm to the parameter space of an elliptic curve, the hyperparameter vectors are iteratively updated using the L-function of the elliptic curve, the rational point group structure, the tangent space projection, and group operations to determine the target hyperparameter vector, and a wind and solar power prediction model is generated based on the target hyperparameter vector.

[0014] In this way, the mathematical properties of elliptic curves can be used to effectively constrain and guide the hyperparameter search process, solving the problems of slow convergence speed and insufficient generalization ability of existing technologies, and improving the generation efficiency and prediction accuracy of wind and solar power prediction models.

[0015] The following details a method for generating a wind and solar power prediction model based on elliptic curves, as described in this invention. Please refer to [link / reference]. Figure 1 and Figure 2 The method 100 includes steps 101 to 104: Step 101: Perform spatiotemporal matching and fusion on the acquired multi-source meteorological data to obtain spatiotemporal multi-source meteorological data. Construct a wind and solar power prediction feature matrix based on the spatiotemporal multi-source meteorological data, including: Step 1011: Acquire multi-source meteorological data : ; In the formula, temp is the ambient temperature, humidity is the relative humidity, pressure is the atmospheric pressure, wind speed is the wind speed, wind direction is the wind direction, irradiance is the solar irradiance, cloud cover is the cloud cover, precipitation is the precipitation, visibility is the visibility index, and stability index is the atmospheric stability index.

[0016] Specifically, taking a wind farm (installed capacity of 50MW) as an example, the operation data of the wind farm from January 1, 2025 to December 31, 2025 is collected to construct a training set. ,in The total number of samples (2 years × 365 days × 96 15-minute intervals).

[0017] Single sample The specific components are as follows: , Single sample feature vector In this context, `temp` represents the ambient temperature, ranging from -20 to 40°C, with an initial value set to 15.5°C as output by the current numerical weather forecast; `humidity` represents the relative humidity, ranging from 0 to 100% with an initial value set to 65%; `pressure` represents the atmospheric pressure, ranging from 980 to 1030 hPa with an initial value set to 1013.25 hPa; `wind_speed` represents the wind speed, ranging from 0 to 25 m / s with an initial value set to 8.5 m / s; and `wind_direction` represents the wind direction, ranging from 0 to 360° with an initial value set to 225°. ° (Southwest wind); irradiance is solar irradiance, ranging from [0, 1200] W / m², with an initial value set at 450 W / m²; cloud_cover is cloud cover, ranging from [0, 100]%, with an initial value set at 35%; precipitation is precipitation, ranging from [0, 50] mm, with an initial value set at 0 mm; visibility is visibility, ranging from [0, 30] km, with an initial value set at 12 km; stability_index is atmospheric stability index, ranging from [-5, 5], with an initial value set at 0.8. Multi-source meteorological data were constructed based on the data from the above single sample. .

[0018] In this way, by acquiring meteorological elements in 10 dimensions, including temperature, humidity, wind speed, wind direction, and irradiance, and combining them with multi-source data fusion technology, the data bias problem caused by the limitations of a single numerical weather prediction model is effectively solved, providing a more comprehensive and reliable data foundation for subsequent wind and solar power prediction, thereby improving the input quality of the prediction model.

[0019] Step 1012, process the multi-source meteorological data Spatiotemporal matching and fusion are performed to obtain multi-source meteorological data in spatiotemporal regions. : ; In the formula, t represents the time of data collection, loc represents the geographic location identifier, and N represents the total number of data sources. For the i-th data source at time t and location loc, Let the weight of the i-th data source satisfy the following condition: .

[0020] Specifically, in this embodiment, the total number of data sources N=3, corresponding to meteorological stations, satellites, and the ECMWF numerical weather prediction model, respectively. The weights for meteorological stations are w1=0.4, satellites w2=0.3, and ECMWF w3=0.3. The geographic location loc includes longitude 118.5°, latitude 25.2°, and altitude 850m. The meteorological data from the three data sources at the same time t and the same location loc are weighted and fused to obtain the fused spatiotemporal multi-source meteorological data. .

[0021] In this way, by weighted fusion of three data sources—meteorological stations, satellites, and ECMWF—the advantages of each data source are fully utilized, and the shortcomings of insufficient resolution or low accuracy of a single data source are made up for. This results in a significant improvement in the spatiotemporal continuity of the fused meteorological data, providing more accurate meteorological input for power prediction.

[0022] Step 1013, according to the above The wind and solar power prediction feature matrix F is constructed based on geographical features, historical power generation data, and temporal characteristics. ; In the formula, It is multi-source meteorological data in time and space. Geographical features Historical power generation data, It is a time-related feature.

[0023] Specifically, Geographical features include longitude (lon) 118.5°, latitude (lat) 25.2°, altitude (alt) 850m, and slope (slope) 15°; Historical power generation data is to That is, the historical power values ​​of the previous 24 time steps (time resolution 15 minutes, i.e., the previous 6 hours), and the initial value. =25.3MW, =24.8MW, ..., =18.2MW; The time features include hour (14), weekday (Wednesday), month (June), and season (unique hot code) [0,1,0,0] (summer). The total feature dimensions are 10+5+24+7=46.

[0024] In this way, the constructed 46-dimensional feature matrix integrates four types of features: meteorological, geographical, historical, and temporal. Among them, the historical power data covers the temporal information of the first 6 hours, and the temporal features depict the variation patterns of day and night, week, month, and season. This allows the feature matrix to comprehensively reflect the multi-dimensional factors affecting wind and solar power output, providing the LightGBM model with information-rich and highly discriminative input features, which helps to improve the model's prediction accuracy and generalization ability.

[0025] Step 102: Map the hyperparameter vectors of the LightGBM algorithm to the parameter space of the elliptic curve, and construct an optimization objective function based on the geometric constraint regularization term of the elliptic curve, the prediction loss, the LightGBM native regularization term, and the wind and solar power prediction feature matrix, including: Step 1021, the standard equation of elliptic curve E is: ; In the formula, y is the ordinate of a point on the elliptic curve, x is the abscissa of a point on the elliptic curve, and a and b are the coefficients of the elliptic curve, satisfying the discriminant: ; Hyperparameter vector of the LightGBM algorithm for: ; In the formula, learning_rate is the learning rate, num_leaves is the number of leaf nodes, max_depth is the maximum depth of the tree, min_gain_to_split is the minimum split gain, feature_fraction is the feature sampling ratio, bagging_fraction is the data sampling ratio, lambda_l1 is the L1 regularization coefficient, and lambda_l2 is the L2 regularization coefficient. Parameter mapping function for: ; In the formula, Let E(R) be an n-dimensional real space, where n corresponds to the dimension of the hyperparameter vector, and E(R) be the set of real points on the elliptic curve E. The hyperparameter vector of the LightGBM algorithm Points P(x,y) ∈ E(R) mapped onto the elliptic curve E: ; In the formula, hyperparameter vector The Middle One hyperparameter, , For the first The empirical lower and upper bounds of the range of values ​​for each hyperparameter. For the first The mapping weight coefficients of each parameter, Scaling factor for the domain of the elliptic curve. This is the offset of the elliptic curve center. It is a linear combination function; ; in, For symbolic functions, Let be the median value of the empirical range of the i-th hyperparameter, where i ranges from 1 to 8, and a and b be the elliptic curve coefficients. To find the solution to the standard equation of the elliptic curve E; Based on P(x,y), the set of parameter points S in the parameter space of the elliptic curve is obtained: ; In the formula, for Mapped elliptic curve points, .

[0026] Specifically, in this embodiment, we first try to select an elliptic curve E: y²=x³-3x+2 (i.e., a=-3, b=2), calculate the discriminant Δ=0, which does not satisfy the non-singular condition. Therefore, we adjust it to an elliptic curve E: y²=x³-3x+3 (i.e., a=-3, b=3). At this time, Δ≠0, which satisfies the non-singular condition.

[0027] The 8-dimensional hyperparameter vector at the kth iteration initial value The ranges of each hyperparameter are as follows: θ1=learning_rate∈[0.01,0.3], θ2=num_leaves∈[10,150], θ3=max_depth∈[3,12], θ4=min_gain_to_split∈[0.0,1.0], θ5=feature_fraction∈[0.1,1.0], θ6=bagging_fraction∈[0.1,1.0], θ7=lambda_l1∈[0.0,1.0], θ8=lambda_l2∈[0.0,1.0]. Mapping weight coefficients. The values ​​are: α1=0.20, α2=0.20, α3=0.15, α4=0.10, α5=0.15, α6=0.10, α7=0.05, and α8=0.05, which satisfy... Scaling factor =10, center offset =0, =0.155. The initial parameter point P0(3.966, -7.313) is calculated and verified to satisfy the elliptic curve equation.

[0028] In this way, the discrete 8-dimensional LightGBM hyperparameter space is mapped to a continuous elliptic curve parameter space, transforming the originally geometrically unstructured hyperparameter search problem into a mathematical problem of finding optimal points on elliptic curves with rich algebraic structure. This is achieved by introducing trainable mapping weight coefficients. It can adaptively adjust the mapping relationship according to the actual contribution of each hyperparameter to the prediction error, so that hyperparameters that have a great impact on prediction accuracy (such as learning rate and number of leaf nodes) occupy a larger range of coordinate changes on the elliptic curve, thereby obtaining a finer search granularity.

[0029] Step 1022: Calculate the prediction loss based on the wind and solar power prediction feature matrix F and the prediction loss function: ; Regularization terms based on the geometric constraints of the elliptic curve E The predicted loss and LightGBM native regularization terms Construct an optimization objective function with geometric constraints. :

[0030] In the formula, For the first The actual power value of each sample, with the superscript "power" indicating the power value. For the first The feature vector in the landscape feature prediction matrix of each sample This is the LightGBM hyperparameter vector. For the LightGBM prediction function, hyperparameter vector Mapped to the corresponding point on elliptic curve E As a reference point, The constraint strength coefficient, For the current parameter point To the reference point The distance of the elliptic geodesic.

[0031] Specifically, in this embodiment, for the selected elliptic curve E: y²=x³-3x+3, the order of its Hasse-Weil L function L(E,s) at s=1 is calculated.

[0032] When constructing the objective function J(θ), the first prediction loss uses the mean absolute error (MAE), based on the 46-dimensional wind and solar power prediction feature matrix F constructed in step 1013 and the LightGBM prediction function f( ;θ) Calculate the deviation between the predicted power and the actual power; the second term The first term is the L1 / L2 regularization term built into LightGBM, used to control the complexity of the tree model; the third term is the elliptic curve geometry constraint regularization term, where the reference point... Choose the initial parameter point P0(3.966, -7.313), and the constraint strength coefficient. Take 0.05, geodesic distance Discrete approximation calculations are performed by taking 15 sampling points on the arc segment of the elliptic curve.

[0033] In this way, the objective function is optimized. Introducing elliptic curve geometric constraint regularization terms Using geodesic distance Constrain the hyperparameter vector θ to move along the parameter space so that the update of the hyperparameter vector θ is performed along the shortest path of the elliptic curve E, thereby avoiding random walks of parameters and improving the directionality and convergence speed of parameter search.

[0034] The elliptic curve geodesic distance in the elliptic curve geometric constraint regularization term The calculation method is as follows: Based on the current parameter point and reference points , confirm connection and Elliptic curve segments as integration paths ; Calculate the geodesic distance based on the elliptic curve coefficient 'a' and the coordinates x and y on the arc segment of the elliptic curve. : ; Discrete approximation calculation of approximate geodesic distance : ; In the formula, j is, For sampling points on the arc segment of the elliptic curve, The number of samples.

[0035] Specifically, in this embodiment, when calculating the geodesic distance of an elliptic curve, the current parameter point... and reference points Both points lie on the elliptic curve E: y² = x³ - 3x + 3 (i.e., a = -3). First, determine the elliptic curve segment connecting these two points as the integration path γ, and then proceed along this path... Integrating is performed. To facilitate numerical calculation, a discrete approximation method is adopted, and m=15 sampling points are uniformly selected along the integration path. , ), calculate the Euclidean distance between adjacent sampling points and sum them up to obtain The approximate value. As the number of iterations increases, the parameter points... Gradually approaching the optimal solution, As the value gradually decreases, the penalty effect of geometric constraints weakens, allowing the model to be guided by strong geometric constraints to search along the elliptic curve path in the initial stage. As it approaches the optimal solution, the constraints are weakened to achieve fine-tuning.

[0036] In this way, by using the geodesic distance of the elliptic curve as a regularization term, the search path of the LightGBM hyperparameters is constrained to the geometric manifold of the elliptic curve. This effectively utilizes the algebraic geometry of the elliptic curve to guide the parameter optimization process and avoids the blind search in Euclidean space by traditional methods.

[0037] Step 103: Based on the optimization objective function, the L-function of the parameter space of the elliptic curve, the rational point group structure, the tangent space projection, and group operations, iteratively update the hyperparameter vector to determine the target hyperparameter vector corresponding to the multi-source meteorological data, including: Step 1031: Determine the rank r of the elliptic curve E based on the order of the Hasse-Weil L function L(E,s) at s=1: ; In the formula, Let be the rank of the rational point group E(Q) of the elliptic curve E. Let L be the order of the function at s=1; The size of the candidate point space for parameter search is determined based on the rational point group structure: ; In the formula, For scratching groups, To group integers, Let r be a free abelian group; Calculate the optimization objective function For the hyperparameter vector gradient : ; In the formula, To predict the loss gradient (calculated via LightGBM's gradient boosting mechanism). The gradient of the native regularization term (calculated by LightGBM). The gradient of the geometric constraint term needs to be calculated using the chain rule of elliptic curve parameter mapping: The gradient of the geometric constraint term The calculation formula is: , ; In the formula, From the mapping function φ:R n →The Jacobian matrix of E(R) is determined; Calculate the elliptic curve E at point gradient vector at : ; In the formula, These are the coefficients of the standard equation of the elliptic curve; gradient vector Projecting onto the tangent space yields the tangential gradient. : ; In the formula, This is an inner product operation; Calculate the Hasse-Weil L function value for the k-th iteration based on the elliptic curve E. : ; In the formula, The Euler product symbol represents the product of all prime numbers. an infinite product; Elliptic curve The derivative of the discriminant is determined by the discriminant. Prime factorization and Tate algorithm determination are used to characterize the decomposition behavior of elliptic curves. Elliptic curve In prime numbers Frobenius trace at the location , for mold After reduction in a finite field The number of rational points (including the point at infinity) on the x-axis satisfies Hasse's inequality. ; For the decompression type indicator: when When multiplication is reduced (Split type) Non-splitting type ),when When addition is reduced to a non-existent state ; Representing prime numbers Divisible guide (Deduction case) Representing prime numbers Non-divisible guide (The case of reduction); This is an index variable for iterating through all prime numbers; For the first The evaluation point of the L function in the nth iteration Take in the early stage of iteration make Moderate step size to control the step size; According to the above rank of elliptic curve E Calculate adaptive step size : ; In the formula, The initial step size, For the Hasse-Weil L function in the th The value at the next iteration The attenuation coefficient is... For the natural constant An exponential function with base 0; The elementary point G is determined based on the elliptic curve E, and the elementary point G and the tangential gradient are used as the basis for the determination. and the adaptive step size Calculate scalar multipliers : ; In the formula, This is the learning rate scaling factor. To round to the nearest integer, The norm symbol, Let be the Euclidean norm of the tangential gradient vector. To generate the origin point The magnitude of the coordinate vector; According to the scalar multiplier And the generator point G, calculate the elliptic curve scalar multiplication. ; According to the scalar multiplication Update parameter points using elliptic curve group addition. : ; In the formula, For the addition of elliptic curve groups, For the updated parameter points; Verify the updated parameter points Does it satisfy the standard equation of an elliptic curve? If not, then according to... Calculate the coordinates of the projection point : ; In the formula, For symbolic functions, .

[0038] Specifically, in this embodiment, during the 0th iteration, the current parameter point is P0(3.966, -7.313), and the gradient of the current optimization objective function is... The predicted loss gradient Calculate the normal vector at point P0. =(0.949,0.314), the gradient is projected onto the tangent space through inner product operation to obtain the tangent gradient. According to the elliptic curve E: y² = x³ - 3x + 3, its discriminant Δ = 432 = 2. 4 ×3³, the prime factors of the derivative N are 2 and 3. The rank r=1 of the elliptic curve is estimated based on the order of the L function at s=1.

[0039] In the first iteration, s1 = 1.1 is chosen, and L(E,s1) ≈ 0.5 is calculated using the Euler product formula. This is then substituted into the adaptive step size formula α1 = 0.141. The generator G = (1,1) is chosen, with a modulus of... The scalar multiplier n1≈2 is calculated by the tangential gradient magnitude and the learning rate scaling factor η=1.0. After calculating the scalar multiplication [2]G=(-2,-1) using the double addition algorithm, the new parameter point is obtained by the elliptic curve group addition P1=P0⊕[2]G. It is verified whether P1 satisfies the elliptic curve equation. If it does not, the projection is corrected by the sign function.

[0040] In this way, the tangent space projection of the elliptic curve ensures that the parameter update direction always follows the tangent direction of the curve, so that the parameter points in each iteration are strictly kept on the elliptic curve, maintaining the geometric consistency of the parameter search. The gradient of the optimization objective function is calculated in this step. It includes three items: predicting the loss gradient. gradient of the original regularization term gradient of geometric constraint terms The gradient of the geometric constraint term is obtained through the chain rule. The constraint on the geodesic distance of the elliptic curve is backpropagated to the hyperparameter update. Simultaneously, based on the rational point group structure... A defined rank r is used as the exponential decay factor exp(-λ·r) in the adaptive step size calculation. The step size automatically decreases when the rank r is high to accommodate a more complex candidate point space; Torsion group Provides candidate points of finite order. Rational point group structure. It theoretically describes the algebraic structure of the parameter search space: rank The degree of freedom (number of generators in a free Abelian group) determines the direction of continuous search, and the order of the scratch group. This determines the number of discrete candidate points. Together, they determine the "size" of the candidate point space—that is, the algebraic complexity of the search space, which is expressed through the rank... This indirectly affects the step size control strategy. The step size is adaptively adjusted using the L-function. When the L-function value is large, the square root reciprocal automatically decreases the step size for finer searching; when the L-function value is small, the step size increases accordingly to accelerate convergence. Combined with the exponential decay factor of the rank, more refined step size control is achieved in the high-dimensional search space, avoiding skipping potential optimal solutions. This two-factor adaptive step size mechanism allows the parameter update process to dynamically adjust the search granularity based on the curve position of the current parameter point, ensuring both rapid convergence in the initial stage and stability and accuracy when approaching the optimal solution.

[0041] Step 1032, based on the number of validation set samples The true power value of the i-th sample and the predicted power value output by the wind and solar power prediction model Calculate the mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE): , , ; The evaluation results are calculated based on MAE, RMSE, and MAPE, and the decay coefficient during iterative updates is adjusted accordingly. and adaptive step size .

[0042] Specifically, in this embodiment, the validation set uses the wind farm's operational data from November 2024, and the number of validation set samples is... =2880 (30 days × 96 15-minute intervals). Using initial parameters. The trained model evaluation results are: MAE=2.45MW, RMSE=3.80MW, MAPE=9.8%. When the validation set MAE decreases compared to the previous iteration, the search continues along the current direction, keeping the current generator G=(1,1) unchanged; when overfitting occurs (training error decreases but validation error increases), the decay coefficient λ is increased from 0.01 to 0.02 to reduce the search step size, and the generator point G is considered to be replaced.

[0043] In this way, the decay coefficient and adaptive step size are dynamically adjusted through validation set error feedback. When the validation set error continues to decrease, the current search direction is maintained, and the closure property of elliptic curve group operations is used to efficiently traverse candidate parameter points in the rational point group. When overfitting signs appear, the decay coefficient is automatically increased to compress the step size, and the generator point G is considered for replacement to switch the search direction. This adaptive adjustment mechanism based on validation set feedback achieves a dynamic balance between convergence speed and generalization ability in the parameter search process, effectively avoiding the overfitting or slow convergence problems caused by fixed step sizes in traditional methods.

[0044] Step 1033, based on the updated elliptic curve points Calculate normalized coordinate increments : ; In the formula, This is the center offset of the elliptic curve's x-coordinate, used to shift the normalized combination of hyperparameters to the elliptic curve. The center of the real domain ensures the mapping point satisfy , here The initial value is 0; For the first The adjustment coefficients for the reverse mapping of each hyperparameter are used to compensate for the nonlinear coupling effect of the weighted combination of multiple parameters in the forward mapping, satisfying... initial value The algorithm adaptively adjusts based on the validation set error during iteration. The scaling factor for the domain of the x-coordinate of the elliptic curve; For the first Hyperparameters Weighting coefficients when mapping to the x-coordinate of an elliptic curve; According to the normalized coordinate increment The lower bound of the empirical range of hyperparameters and the Upper Realm Update hyperparameters : ; For integer hyperparameters, based on the normalized coordinate increments The lower and upper bounds of the empirical range of hyperparameter values ​​are rounded down. ; According to hyperparameters Obtain the target hyperparameter vector.

[0045] Specifically, in this embodiment, after the first iteration, a new parameter point P1 (5.2, -11.4) is obtained. Assuming that only θ1 (learning rate) and θ2 (number of leaf nodes) are adjusted, while keeping other parameters unchanged (θ3=6, θ4=0.1, θ5=0.8, θ6=0.8, θ7=0.0, θ8=1.0), the new learning rate is calculated using the back-mapping formula. =0.184, number of new leaf nodes =75. Updated parameters Repeat the above iterative process for a total of K=50 iterations, until finally converging to the optimal parameter point. Corresponding to the optimal hyperparameter .

[0046] In this way, the update points on the elliptic curve are accurately restored to LightGBM hyperparameter values ​​through the inverse mapping formula, achieving a complete closed-loop optimization from geometric space to parameter space. This represents the center offset of the elliptic curve's x-axis. This is the adjustment coefficient for the inverse mapping of the i-th hyperparameter. The scaling factor for the domain of the x-coordinate of the elliptic curve. For the i-th hyperparameter Weighting coefficients when mapping to the x-coordinate of an elliptic curve. Adjustment coefficients. To compensate for discretization errors, rounding ensures the validity of integer parameters (such as the number of leaf nodes and tree depth), while boundary truncation ensures that all parameters remain within their valid range. After 50 iterations, the algorithm finally converges to the optimal parameter point, completing an efficient optimization process from initial parameters to optimal parameters.

[0047] Step 104: Generate a wind and solar power prediction model based on the target hyperparameter vector.

[0048] Specifically, in this embodiment, the target hyperparameter vector obtained in step 1033 is used. Configure the LightGBM model with the following settings: learning rate = 0.15, number of leaf nodes = 55, maximum tree depth = 8, minimum split gain = 0.05, feature sampling ratio = 0.7, data sampling ratio = 0.75, L1 regularization coefficient = 0.01, and L2 regularization coefficient = 0.5. Perform model training using an early stopping mechanism, with a maximum of 500 training iterations and an early stopping patience value of 50 iterations (stopping if the MAE on the validation set does not decrease for 50 consecutive iterations). Calculate the prediction accuracy metrics on the validation set (November 2024 data): MAE = 2.15MW, RMSE = 3.42MW, MAPE = 6.2%. (Compare with the initial parameters.) Compared to the results (MAE=2.45MW, RMSE=3.80MW, MAPE=9.8%), the prediction error was significantly reduced. Based on the prediction error feedback, the elliptic curve search strategy was adjusted: due to the decrease in MAE, the search continued along the current direction, and the reference point was updated. =P1. The final generated wind and solar power prediction model has higher prediction accuracy and better generalization ability.

[0049] In this way, the LightGBM model configured with the target hyperparameter vector employs an early stopping mechanism to automatically control the number of training epochs during training, avoiding overfitting caused by excessive iterations. After training, the model performance is objectively evaluated using an independent validation set. Compared with the initial parameter model, the optimized model shows a significant reduction in prediction error, verifying the effectiveness of the elliptic curve parameter space optimization method. The final generated wind and solar power prediction model has higher prediction accuracy and stronger generalization ability, better meeting the grid dispatching requirements for refined wind and solar power prediction.

[0050] As described above, this embodiment maps the LightGBM hyperparameter optimization problem to the elliptic curve parameter space and utilizes the group operation rules, L-function, and rank properties of elliptic curves to guide the hyperparameter search path and update step size, fundamentally overcoming the predicament of traditional parameter tuning lacking mathematical theoretical guidance. This embodiment uses the elliptic curve geodesic distance as a geometric constraint regularization term, effectively preventing model overfitting and enhancing the model's generalization ability. The entire parameter optimization process has fast convergence speed and high search efficiency, resulting in a significantly improved prediction accuracy for the final wind and solar power prediction model, better meeting the grid dispatch's refined requirements for wind and solar power prediction.

[0051] Please refer to Figure 3 An embodiment of the present invention provides a wind and solar power prediction model generation system 200 based on elliptic curves, including a memory 201, a processor 202, and a computer program stored in the memory and executable on the processor. When the processor 202 executes the computer program, it implements the various steps of the wind and solar power prediction model generation method based on elliptic curves as described above.

[0052] The above description is merely an embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent modifications made based on the content of the present invention specification and drawings, or direct or indirect applications in related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A method for generating a wind and solar power prediction model based on elliptic curves, characterized in that, include: Spatiotemporal matching and fusion of the acquired multi-source meteorological data are performed to obtain spatiotemporal multi-source meteorological data, and a wind and solar power prediction feature matrix is ​​constructed based on the spatiotemporal multi-source meteorological data. The hyperparameter vectors of the LightGBM algorithm are mapped to the parameter space of the elliptic curve, and an optimization objective function is constructed based on the geometric constraint regularization term of the elliptic curve, the prediction loss, the LightGBM native regularization term, and the wind and solar power prediction feature matrix. Based on the optimization objective function and the L-function, rational point group structure, tangent space projection, and group operation of the parameter space of the elliptic curve, the hyperparameter vector is iteratively updated to determine the target hyperparameter vector corresponding to the multi-source meteorological data. A wind and solar power prediction model is generated based on the target hyperparameter vector.

2. The method for generating a wind and solar power prediction model based on elliptic curves according to claim 1, characterized in that, The acquired multi-source meteorological data are spatiotemporally matched and fused to obtain spatiotemporally multi-source meteorological data, including: Acquiring multi-source meteorological data : ； In the formula, temp is the ambient temperature, humidity is the relative humidity, pressure is the atmospheric pressure, wind speed is the wind speed, wind direction is the wind direction, irradiance is the solar irradiance, cloud cover is the cloud cover, precipitation is the precipitation, visibility is the visibility index, and stability index is the atmospheric stability index. For the multi-source meteorological data Spatiotemporal matching and fusion are performed to obtain multi-source meteorological data in spatiotemporal regions. : ； In the formula, t represents the time of data collection, loc represents the geographic location identifier, and N represents the total number of data sources. For the i-th data source at time t and location loc, Let the weight of the i-th data source satisfy the following condition: .

3. The method for generating a wind and solar power prediction model based on elliptic curves according to claim 2, characterized in that, Based on the aforementioned spatiotemporal multi-source meteorological data, a wind and solar power prediction feature matrix is ​​constructed, including: According to the above The wind and solar power prediction feature matrix F is constructed based on geographical features, historical power generation data, and temporal characteristics. ； In the formula, It is multi-source meteorological data in time and space. Geographical features Historical power generation data, It is a time-related feature.

4. The method for generating a wind and solar power prediction model based on elliptic curves according to claim 1, characterized in that, Mapping the hyperparameter vectors of the LightGBM algorithm to the parameter space of elliptic curves includes: The standard equation of elliptic curve E is: ； In the formula, y is the ordinate of a point on the elliptic curve, x is the abscissa of a point on the elliptic curve, and a and b are the coefficients of the elliptic curve, satisfying the discriminant: ; Hyperparameter vector of the LightGBM algorithm for: ； In the formula, learning_rate is the learning rate, num_leaves is the number of leaf nodes, max_depth is the maximum depth of the tree, min_gain_to_split is the minimum split gain, feature_fraction is the feature sampling ratio, bagging_fraction is the data sampling ratio, lambda_l1 is the L1 regularization coefficient, and lambda_l2 is the L2 regularization coefficient. Parameter mapping function for: ； In the formula, Let E(R) be an n-dimensional real space, where n corresponds to the dimension of the hyperparameter vector, and E(R) be the set of real points on the elliptic curve E. The hyperparameter vector of the LightGBM algorithm Points P(x,y) ∈ E(R) mapped onto the elliptic curve E: ； In the formula, hyperparameter vector The Middle One hyperparameter, , For the first The empirical lower and upper bounds of the range of values ​​for each hyperparameter. For the first The mapping weight coefficients of each hyperparameter. The scaling factor for the domain of the elliptic curve. This is the offset of the elliptic curve center. It is a linear combination function; ； in, For symbolic functions, Let a and b be the median of the empirical range of values ​​for the i-th hyperparameter, and a and b be the elliptic curve coefficients. To find the solution to the standard equation of the elliptic curve E; Based on P(x,y), the set of parameter points S in the parameter space of the elliptic curve is obtained: ； In the formula, for Mapped elliptic curve points, , k represents...

5. The method for generating a wind and solar power prediction model based on elliptic curves according to claim 3, characterized in that, An optimization objective function is constructed based on the elliptic curve geometric constraint regularization term, prediction loss, LightGBM native regularization term, and wind and solar power prediction feature matrix, including: The prediction loss is calculated based on the wind and solar power prediction feature matrix F and the prediction loss function: ； Regularization terms based on the geometric constraints of the elliptic curve E The predicted loss and LightGBM native regularization terms Construct an optimization objective function with geometric constraints. : In the formula, For the first The actual power value of each sample, with the superscript "power" indicating the power number; For the first The feature vector in the landscape feature prediction matrix of each sample This is the LightGBM hyperparameter vector. For the LightGBM prediction function, hyperparameter vector Mapped to the corresponding point on elliptic curve E As a reference point, The constraint strength coefficient, For the current parameter point To the reference point The distance of the elliptic geodesic.

6. The method for generating a wind and solar power prediction model based on elliptic curves according to claim 5, characterized in that, The hyperparameter vector is iteratively updated based on the optimization objective function, the L-function of the parameter space of the elliptic curve, the rational point group structure, the tangent space projection, and group operations, including: The rank r of the elliptic curve E is determined by the order of the Hasse-Weil L function L(E,s) at s=1: ； In the formula, Let be the rank of the rational point group E(Q) of the elliptic curve E. Let L be the order of the function at s=1; The size of the candidate point space for parameter search is determined based on the rational point group structure: ； In the formula, For scratching group, To group integers, Let r be a free abelian group; Calculate the optimization objective function For the hyperparameter vector gradient : ； In the formula, To predict the loss gradient, The gradient of the original regularization term. Gradient of the geometric constraint term; The gradient of the geometric constraint term The calculation formula is: ， ； In the formula, From the mapping function φ:R n →The Jacobian matrix of E(R) is determined; Calculate the elliptic curve E at point gradient vector at point : ； In the formula, These are the coefficients of the standard equation of the elliptic curve; gradient vector Projecting onto the tangent space yields the tangential gradient. : ； In the formula, This is an inner product operation; Calculate the Hasse-Weil L function value for the k-th iteration based on the elliptic curve E. : ； In the formula, The symbol for Euler product is used. Elliptic curve The guide; Elliptic curve In prime numbers Frobenius trace at the location, , for mold After reduction in a finite field The number of rational points on the x-axis that satisfy Hasse's inequality ; This is a decompression type indicator; Representing prime numbers Divisible guide , Representing prime numbers Non-divisible guide ; This is an index variable for iterating through all prime numbers; For the first The evaluation point of the L function in the nth iteration ; Based on the Hase-Weil L function value rank of elliptic curve E Calculate adaptive step size : ； In the formula, The initial step size, For the Hasse-WeilL function in the th The value at the next iteration The attenuation coefficient is... For the natural constant An exponential function with base 0; The elementary point G is determined based on the elliptic curve E, and the elementary point G and the tangential gradient are used as the basis for the determination. and the adaptive step size Calculate scalar multipliers : ； In the formula, This is the learning rate scaling factor. To round to the nearest integer, The norm symbol, Let be the Euclidean norm of the tangential gradient vector. To generate the origin point The magnitude of the coordinate vector; According to the scalar multiplier And the generator point G, calculate the elliptic curve scalar multiplication. ; According to the scalar multiplication Update parameter points using elliptic curve group addition. : ； In the formula, For the addition of elliptic curve groups, For the updated parameter points; Verify the updated parameter points Does it satisfy the standard equation of an elliptic curve? If not, then according to... Calculate the coordinates of the projection point : ； In the formula, It is a symbolic function; According to the projection point Obtain the updated elliptic curve points and according to Update the hyperparameter vector.

7. The method for generating a wind and solar power prediction model based on elliptic curves according to claim 6, characterized in that, The hyperparameter vector is iteratively updated based on the optimization objective function, the L-function of the parameter space of the elliptic curve, the rational point group structure, the tangent space projection, and group operations, and the update also includes: Based on the number of validation set samples The true power value of the i-th sample and the predicted power value output by the wind and solar power prediction model Calculate the mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE): ， ， ； The evaluation results are calculated based on MAE, RMSE, and MAPE, and the decay coefficient during iterative updates is adjusted accordingly. and adaptive step size .

8. The method for generating a wind and solar power prediction model based on elliptic curves according to claim 6, characterized in that, Determining the target hyperparameter vector corresponding to the multi-source meteorological data includes: Based on the updated elliptic curve points Calculate normalized coordinate increments : ； In the formula, This represents the center offset of the elliptic curve's x-axis. For the first Adjustment coefficients for inverse mapping of hyperparameters The scaling factor for the domain of the x-coordinate of the elliptic curve. For the first Hyperparameters Weighting coefficients when mapping to the x-coordinate of an elliptic curve; According to the normalized coordinate increment The lower bound of the empirical range of hyperparameters and the Upper Realm Update hyperparameters : ； For integer hyperparameters, based on the normalized coordinate increments The lower and upper bounds of the empirical range of hyperparameter values ​​are rounded down. ； According to hyperparameters Obtain the target hyperparameter vector.

9. The method for generating a wind and solar power prediction model based on elliptic curves according to claim 5, characterized in that, The elliptic curve geodesic distance in the geometric constraint regularization term of the elliptic curve The calculation method is as follows: Based on the current parameter point and reference points , confirm connection and Elliptic curve segments as integration paths ; Calculate the geodesic distance based on the elliptic curve coefficient 'a' and the coordinates x and y on the arc segment of the elliptic curve. : ； Discrete approximation calculation of approximate geodesic distance : ； In the formula, j is, For sampling points on the arc segment of the elliptic curve, The number of samples.

10. A wind and solar power prediction model generation system based on elliptic curves, characterized in that, The method includes a memory, a processor, and a computer program stored in the memory and running on the processor. When the processor executes the computer program, it implements each step of the method for generating a wind and solar power prediction model based on an elliptic curve as described in any one of claims 1 to 9.

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