Long-term wind power generation capacity prediction method
By introducing rate-damped conformal fractional-order accumulation operator and gray wolf optimization algorithm in the gray Bernoulli model, the RDCFBM (1,1,tβ) model was constructed, and the accuracy problem of long-term wind power prediction under the influence of uncertainty was solved. , achieving higher prediction accuracy and adaptability.
Patent Information
- Application Number
- CN202411518046.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-10-29
- Publication Date
- 2025-02-21
AI Technical Summary
It is difficult for the prior art to make accurate and effective long-term wind power forecasts under uncertain influence, especially when climate and economic differences in different regions are large.
The rate-damped conformal fractional order accumulation operator and the gray Bernoulli model are used, combined with the gray wolf optimization algorithm, and the nonlinear parameters of the model are optimized to construct the rate-damped conformal fractional order gray Bernoulli model RDCFBM(1,1, tβ).
The prediction accuracy of annual wind power generation in regions under the influence of uncertain growth rates is improved, the adaptability and robustness of the model are enhanced, and the application and prediction performance are better.
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Figure CN119496112A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of wind power generation prediction, and in particular to a long-term wind power generation prediction method. Background Art
[0002] Traditional wind power generation prediction methods include physical models, time series models, and machine learning models. However, physical models rely heavily on the accuracy of weather and climate data, are sensitive to terrain information, and are prone to prediction errors; time series models require a large amount of historical data to build models to ensure prediction accuracy; machine learning models not only require a large amount of training data, but also have complex prediction algorithms and large amounts of calculation. At the same time, annual wind power generation data has the characteristics of small samples, nonlinearity, non-smoothness, and uncertain growth rates. Therefore, it is difficult to use traditional prediction methods to establish accurate, efficient, and applicable prediction models to accurately predict long-term wind power generation in different countries and regions.
[0003] The grey prediction model has the advantages of simple structure, few samples and high computational efficiency. It has significant advantages in simulating and predicting systems with small samples and poor information. At present, there are many short-term and ultra-short-term wind power forecasting schemes, and the sampling interval is generally hours or minutes, while there are few studies on long-term annual wind power forecasting. In recent years, the fractional-order grey Bernoulli model and the adaptive grey discrete model have been successively applied to long-term wind power forecasting and obtained good forecasting accuracy. Some grey models have also been used for renewable energy power forecasting. From the existing research results, it can be seen that when the wind power data has nonlinear smooth characteristics, a higher forecasting accuracy is achieved. When faced with uncertain influences other than natural conditions, the uncertain growth rate will significantly reduce the simulation and forecasting accuracy of wind power. At the same time, the climate and economy of different regions are quite different, which further increases the uncertainty and diversity of wind power forecasting. Therefore, it is difficult to use existing models to make accurate and effective long-term wind power forecasts for different regions under uncertain influences. Summary of the invention
[0004] Purpose of the invention: The purpose of the invention is to provide a long-term wind power generation prediction method with high accuracy and strong applicability.
[0005] Technical solution: A long-term wind power generation prediction method includes the following steps:
[0006] (1) Collect annual wind power generation data in the target area and establish the original sequence X (0) ;
[0007] (2) constructing a rate-damped conformal fractional-order accumulation operator, and introducing a conformal fractional-order matrix, a damping matrix, and a rate matrix into the rate-damped fractional-order accumulation operator;
[0008] (3) Using the original sequence X (0) The rate damping conformal fractional order accumulation operator is used to calculate the rate damping conformal fractional order sequence;
[0009] (4) The rate damping conformal fractional sequence is introduced into the grey Bernoulli model NGBM(1,1) to construct the rate damping conformal fractional grey Bernoulli model RDCFBM(1,1,t β ), and establish the rate damping conformal fractional-order grey Bernoulli model RDCFBM(1,1,t β ) differential equation;
[0010] (5) The rate damping conformal fractional-order grey Bernoulli model RDCFBM(1,1,t β ) is optimized to obtain the optimal nonlinear parameter value, and then the parameters of the differential equation in step (4) are solved by the least square method to obtain the optimal rate damping conformal fractional-order grey Bernoulli model RDCFBM(1,1,t β );
[0011] (6) Using the optimal rate damping conformal fractional-order grey Bernoulli model RDCFBM (1,1,t β ) to predict annual wind power generation.
[0012] Specifically, the rate damping conformal fractional-order accumulation operator formula is:
[0013]
[0014] Where: is the rate-damped conformal fractional-order accumulator, A α is a conformal fractional matrix, D ζ is the damping matrix, A r is the rate matrix, x r (0) is the original sequence X (0) The growth rate, [α] is an integer not less than α, α is the conformal fractional order, ζ is the damping coefficient, r is the model order, and n is the original sequence X (0) Length.
[0015] Specifically, the rate damping conformal fractional order sequence formula is:
[0016]
[0017] Where: is a rate-damped conformal fractional order sequence, is the rate-damped conformal fractional-order accumulator, α is the conformal fractional order, and n is the original sequence X (0) Length.
[0018] Specifically, the rate-damped conformal fractional-order grey Bernoulli model RDCFBM(1,1,t β ) is:
[0019]
[0020] Where: t is time, α is the conformal fractional order, r is the model order, β is the structural index, a, b, c are model parameters, is a rate-damped conformal fractional order sequence.
[0021] Specifically, the parameters of the differential equation in step (4) are solved by the least squares method, and the formula is:
[0022] (a,b,c) T =(B T B) -1 B T Y
[0023]
[0024] Where: a, b, c are model parameters, is the rate-damped conformal fractional sequence, α is the conformal fractional order, r is the model order, β is the structural index, and n is the length of the original sequence X(0).
[0025] Specifically, the Grey Wolf Optimization (GWO) algorithm takes the minimization of the mean relative error (MAPE) as the fitness function, and the rate damping conformal fractional-order Grey Bernoulli model (RDCFBM(1,1,t β ) is the nonlinear parameter to be determined, and the parameter is solved. The fitness function is:
[0026]
[0027] Where: x(0)(k) is the original sequence, is the rate damped conformal fractional-order grey Bernoulli model RDCFBM(1,1,t β ), and m is the number of modeling data.
[0028] Specifically, the steps of solving the parameters of the Grey Wolf Optimization GWO algorithm include:
[0029] (51) The nonlinear parameter to be optimized is set as the individual position of the gray wolf, and the initial population is randomly generated;
[0030] (52) The fitness function is minimized by taking the mean relative error MAPE, and the fitness value of the individual gray wolf is calculated. According to the fitness value, the δ1 wolf, δ2 wolf, and δ3 wolf of the initial population are selected. The δ1 wolf has the best fitness value, the δ2 wolf has the second-best fitness value, and the δ3 wolf has the second-best fitness value.
[0031] (53) Update the location of the gray wolf population and generate a new population;
[0032] (54) According to the fitness function, update the positions of wolf δ1, wolf δ2 and wolf δ3;
[0033] (55) If the maximum number of iterations is reached, the globally optimal gray wolf position and the corresponding minimum MAPE value are output; otherwise, the process returns to step (53), and the nonlinear parameter value corresponding to the globally optimal gray wolf position is the optimal nonlinear parameter value.
[0034] Specifically, the simulation value of the rate-damped conformal fractional sequence is:
[0035] When 0<β≤1,
[0036]
[0037] When β = 0,
[0038]
[0039] Where: is the simulated value of the rate damping conformal fractional sequence, a, b, c are model parameters, α is the conformal fractional order, r is the model order, β is the structural index, is a rate-damped conformal fractional sequence, k = 1, 2, ..., n, where n is the original sequence X (0) Length.
[0040] Specifically, the rate-damped conformal fractional-order grey Bernoulli model RDCFBM(1,1,t β ) is:
[0041] When 0<α≤1,
[0042]
[0043] When a>1,
[0044]
[0045] Where: is the rate damped conformal fractional-order grey Bernoulli model RDCFBM(1,1,t β ), is the simulated value of the rate-damped conformal fractional sequence, x r (0) is the original sequence X (0) The growth rate of k is α, α is the conformal fractional order, α∈(l,l+1], l is an integer greater than zero, k [α]-α Δ lrepresents the conformal fractional inverse operation, [α] is an integer not less than α, ζ is the damping coefficient, and n is the original sequence X (0) Length.
[0046] Specifically, the nonlinear parameters include conformal fractional order, damping coefficient, model order, and structural index.
[0047] Beneficial effects: Compared with the prior art, the present invention has the following significant effects: the present invention designs a rate-damped conformal fractional-order accumulator to reduce the uncertainty of wind power data and improve the effectiveness and efficiency of wind power data mining. The proposed RDCFBM (1,1,t β ) model, introducing conformal fractional order, damping coefficient and structural index into the traditional NGBM (1,1) model, improves the prediction accuracy of regional annual wind power under the influence of uncertain growth rate. The nonlinear parameters of the model are optimized by using the gray wolf optimization algorithm to enhance the adaptability of the model. Compared with the traditional gray prediction model, RDCFBM (1,1,t β ) model improves the simulation accuracy and prediction accuracy of annual wind power generation in multiple regions, and has better robustness and applicability. BRIEF DESCRIPTION OF THE DRAWINGS
[0048] Figure 1 It is a step flow chart of Example 1 of the present invention.
[0049] Figure 2 This is a graph showing the change in the uncertain wind power generation growth rate in three different regions according to Example 2 of the present invention.
[0050] Figure 3 is the RDCFBM(1,1,t β ) model and the existing grey model to simulate and predict the wind power generation in the first region.
[0051] Figure 4 is the RDCFBM(1,1,t β ) model and the existing grey model to simulate and predict the wind power generation in the second region.
[0052] Figure 5 is the RDCFBM(1,1,t β ) model and the existing grey model to simulate and predict the wind power generation in the third region. DETAILED DESCRIPTION
[0053] The present invention is further described below in conjunction with the accompanying drawings.
[0054] Example 1
[0055] See also Figure 1As shown, this embodiment provides a long-term wind power generation prediction method, comprising the following steps:
[0056] (1) Collect annual wind power generation data in the target area and establish the original sequence X (0) ={x 0 (k), k = 1, 2, ..., n}, n is the length of the original sequence, and k represents the kth data.
[0057] (2) Constructing a rate-damped conformal fractional-order accumulator In the rate-damped fractional-order accumulator The conformal fractional-order matrix, damping matrix and rate matrix are introduced.
[0058]
[0059] Where: is the rate-damped conformal fractional-order accumulator, A α is a conformal fractional matrix, D ζ is the damping matrix, A r is the rate matrix, x r (0) is the original sequence X (0) The growth rate, [α] is an integer not less than α, α is the conformal fractional order, ζ is the damping coefficient, r is the model order, and n is the original sequence X (0) Length.
[0060] (3) Using the original sequence X (0) Sum rate damped conformal fractional order accumulator Computing rate-damped conformal fractional sequences
[0061]
[0062] Where: is a rate-damped conformal fractional order sequence, is the rate-damped conformal fractional-order accumulator, α is the conformal fractional order, and n is the original sequence X (0) Length.
[0063] (4) The rate damping conformal fractional sequence is introduced into the grey Bernoulli model NGBM(1,1) to construct the rate damping conformal fractional grey Bernoulli model RDCFBM(1,1,t β ), and establish the rate damping conformal fractional-order grey Bernoulli model RDCFBM(1,1,t β ) is the differential equation:
[0064]
[0065] Where: t is time, α is the conformal fractional order, r is the model order, β is the structural index, a, b, c are model parameters, is a rate-damped conformal fractional order sequence.
[0066] The parameters a, b, and c of the differential equation are solved by the least squares method. The formula is:
[0067] (a,b,c) T =(B T B) -1 B T Y
[0068]
[0069] Where: a, b, c are model parameters, is the rate-damped conformal fractional sequence, α is the conformal fractional order, r is the model order, β is the structural index, and n is the length of the original sequence X(0).
[0070] Computes the simulated values of a rate-damped conformal fractional sequence
[0071] When 0<β≤1,
[0072]
[0073] When β=0,
[0074]
[0075] Where: is the simulated value of the rate damping conformal fractional sequence, a, b, c are model parameters, α is the conformal fractional order, r is the model order, β is the structural index, is a rate-damped conformal fractional sequence, k=1,2,…,n, where n is the length of the original sequence X(0).
[0076] Calculation of rate damping conformal fractional order grey Bernoulli model RDCFBM(1,1,t β )
[0077] When 0<α≤1,
[0078]
[0079] When α>1,
[0080]
[0081] Where: is the rate damped conformal fractional-order grey Bernoulli model RDCFBM(1,1,tβ ), is the simulated value of the rate-damped conformal fractional sequence, x r (0) is the original sequence X (0) The growth rate of k is α, α is the conformal fractional order, α∈(l,l+1], l is an integer greater than zero, k [α]-α Δ l represents the conformal fractional inverse operation, [α] is an integer not less than α, ζ is the damping coefficient, and n is the original sequence X (0) Length.
[0082] (5) The rate damping conformal fractional-order grey Bernoulli model RDCFBM(1,1,t β ) is optimized to obtain the optimal nonlinear parameter values, and then the parameters a, b, c of the differential equation in step (4) are solved by the least squares method provided in step (4) to obtain the optimal rate damping conformal fractional-order grey Bernoulli model RDCFBM(1,1,t β ).
[0083] In this embodiment, the Grey Wolf Optimization (GWO) algorithm takes the minimization of the mean relative error (MAPE) as the fitness function, the relationship between parameters as the constraint condition, and the rate damping conformal fractional order Grey Bernoulli model (RDCFBM(1,1,t β )'s nonlinear parameters α, ζ, r, β are the variables to be determined, and the parameters are solved. The fitness function is:
[0084]
[0085] Where: x (0) (k) is the original sequence, is the rate damped conformal fractional-order grey Bernoulli model RDCFBM(1,1,t β ), and m is the number of modeling data.
[0086] The specific steps of the Gray Wolf Optimization GWO algorithm for parameter solution include:
[0087] (51) Set the nonlinear parameters to be optimized α, ζ, r, β as the individual positions of gray wolves, and randomly generate the initial population, including the gray wolf position vector Population size S and number of iterations G.
[0088] (52) The fitness function is minimized by taking the mean relative error (MAPE) as the fitness function, and the fitness value of individual gray wolves is calculated. The wolf pack is divided into four categories of different levels. The initial population of δ1 wolves, δ2 wolves and δ3 wolves are selected according to the fitness value. The δ1 wolf has the best fitness value, the δ2 wolf has the second best fitness value, and the δ3 wolf has the second second best fitness value. These three levels of wolves together lead the hunting behavior of the wolf pack.
[0089] (53) Update the position of the gray wolf population and generate a new population. Specifically, the gray wolf population adopts the prey encirclement strategy to update the population position.
[0090]
[0091] In the formula, is the wolf position vector of δ1, is the wolf position vector of δ2, is the wolf position vector of δ3, D j is the distance vector between the wolf pack and the prey, A and C are coefficient vectors, a1 is the convergence factor, rand is a random number between 0 and 1, P G+1 The new population location.
[0092] (54) According to the fitness function, the positions of wolf δ1, wolf δ2 and wolf δ3 are updated as follows: and
[0093] (55) If the maximum number of iterations is reached, the globally optimal gray wolf position and the corresponding minimum MAPE value are output; otherwise, the process returns to step (53), and the nonlinear parameter value corresponding to the globally optimal gray wolf position is the optimal nonlinear parameter value.
[0094] (56) After obtaining the optimal nonlinear parameter value, the least squares method provided in step (4) is used to solve the parameters a, b, and c of the differential equation in step (4) to obtain the optimal rate damping conformal fractional-order grey Bernoulli model RDCFBM (1,1,t β ).
[0095] (6) Using the optimal rate damping conformal fractional-order grey Bernoulli model RDCFBM (1,1,t β ) to predict annual wind power generation.
[0096] Example 2
[0097] This embodiment provides a specific application scenario of the long-term wind power generation prediction method described in Embodiment 1.
[0098] This embodiment collects three sets of annual wind power generation data from 2012 to 2022 in three different regions, selects appropriate modeling ranges, and establishes the optimal RDCFBM (1,1,tβ ) prediction model, and carried out modeling error and prediction error tests.
[0099] See also Figure 2 As shown, Figure 2 Neutron image (a) is the first region, Figure 2 Neutron map (b) second region, Figure 2 Neutron graph (c) is the third region. Analysis of the annual wind power growth rates in the three regions shows that, although the overall wind power generation in the three regions is on an upward trend, the annual growth rate of wind power has a strong uncertainty. At the same time, due to differences in economic volume, policies and geographical environment, the uncertainty growth rates in different regions have great differences and different characteristics.
[0100] In this embodiment, for these three regions, 2012-2019 is selected as the modeling data for the first region, 2012-2021 is selected as the modeling data for the second region, and 2012-2020 is selected as the modeling data for the third region. The parameters of the GWO algorithm are set to a population size of 50 and a maximum number of iterations of 100. The long-term wind power generation prediction method provided in Example 1 is used to establish RDCFBM (1,1,t β ) model, and optimize the parameters using the GWO algorithm according to the fitness function. The optimal RDCFBM (1,1,t β ) model and solved it for the simulation and prediction of long-term wind power generation in three regions. The optimal parameters of the model in the three regions are shown in Table 1.
[0101] Table 1
[0102]
[0103]
[0104] (2) Please refer to Figures 3 to 5 As shown in the figure, the traditional grey Bernoulli model NGBM(1,1), the existing fractional grey Bernoulli model FANGBM(1,1) and the adaptive grey discrete model SDGOM(1,1,t α ), and the RDCFBM(1,1,t β ) model for the simulation and prediction results of long-term wind power generation in the three regions. Table 2 below shows the calculation results of simulation errors and prediction errors in the three regions. The NGBM (1,1) model has large simulation errors and prediction errors for the second and first regions, both greater than 6%; the FANGBM (1,1) model has a prediction error greater than 10% for the second region; the SDGOM (1,1,t α) model has a simulation error of more than 9% and a prediction error of more than 25% for the second region case, while the RDCFBM(1,1,t β ) model for the three regions has a simulation error of less than 4.2% and a prediction error of less than 6%, which has the best annual wind power generation simulation and prediction performance. β ) model is designed for multiple application cases with uncertainty in wind power growth and differences in wind power generation. Compared with the traditional grey model and the existing improved grey model, both have the advantages of high prediction accuracy, strong applicability and strong ability to overcome uncertainty.
[0105] Table 2
[0106]
Claims
1. A long-term wind power generation prediction method, characterized in that: The following steps are involved: (1) Collect annual wind power generation data in the target area and establish the original sequence X(0); (2) constructing a rate-damped conformal fractional-order accumulation operator, and introducing the conformal fractional-order matrix, the damping matrix, and the rate matrix into the rate-damped fractional-order accumulation operator; (3) Calculate the rate-damped conformal fractional order sequence using the original sequence X(0) and the rate-damped conformal fractional order accumulation operator; (4) The rate damping conformal fractional order sequence is introduced into the grey Bernoulli model NGBM(1,1) to construct the rate damping conformal fractional order grey Bernoulli model RDCFBM(1,1,t β ), and establish the rate damping conformal fractional-order grey Bernoulli model RDCFBM(1,1,t β ) differential equation; (5) The rate damping conformal fractional-order grey Bernoulli model RDCFBM (1, 1, t β ) is optimized to obtain the optimal nonlinear parameter value, and then the parameters of the differential equation in step (4) are solved by the least squares method to obtain the optimal rate damping conformal fractional-order grey Bernoulli model RDCFBM (1, 1, t β ); (6) Using the optimal rate damping conformal fractional-order grey Bernoulli model RDCFBM (1, 1, t β ) to predict annual wind power generation.
2. The long-term wind power generation prediction method according to claim 1, characterized in that: The rate damping conformal fractional order accumulation operator formula is: Where: is the rate-damped conformal fractional-order accumulator, A α is a conformal fractional matrix, D ζ is the damping matrix, A r is the rate matrix, x r (0) is the original sequence X (0) The growth rate, [α] is an integer not less than α, α is the conformal fractional order, ζ is the damping coefficient, r is the model order, and n is the original sequence X (0) Length.
3. The long-term wind power generation prediction method according to claim 2, characterized in that: The rate damping conformal fractional order sequence formula is: Where: is a rate-damped conformal fractional order sequence, is the rate-damped conformal fractional-order accumulator operator, α is the conformal fractional order, and n is the length of the original sequence X(0).
4. The long-term wind power generation prediction method according to claim 3, characterized in that: In step (4), the rate damping conformal fractional-order grey Bernoulli model RDCFBM (1, 1, t β ) is: Where: t is time, α is the conformal fractional order, r is the model order, β is the structural index, a, b, c are model parameters, is a rate-damped conformal fractional order sequence.
5. The long-term wind power generation prediction method according to claim 4, characterized in that: In the step (5), the parameters of the differential equation in step (4) are solved by the least square method, and the formula is: (a,b,c) T =(B T B) -1 B T Y Where: a, b, c are model parameters, is the rate-damped conformal fractional sequence, α is the conformal fractional order, r is the model order, β is the structural index, and n is the length of the original sequence X(0).
6. The long-term wind power generation prediction method according to claim 1, characterized in that: In the step (5), the Grey Wolf Optimization (GWO) algorithm takes the minimization of the mean relative error (MAPE) as the fitness function, and the rate damping conformal fractional-order Grey Bernoulli model (RDCFBM) (1, 1, t β ) is the nonlinear parameter to be determined, and the parameter is solved. The fitness function is: Where: x(0)(k) is the original sequence, is the rate damped conformal fractional-order grey Bernoulli model RDCFBM(1, 1, t β ), and m is the number of modeling data.
7. The long-term wind power generation prediction method according to claim 6, characterized in that: The steps of performing parameter solving by the Grey Wolf Optimization GWO algorithm include: (51) The nonlinear parameter to be optimized is set as the individual position of the gray wolf, and the initial population is randomly generated; (52) The fitness function is minimized by taking the mean relative error MAPE, and the fitness value of the individual gray wolf is calculated. According to the fitness value, the δ1 wolf, δ2 wolf, and δ3 wolf of the initial population are selected. The δ1 wolf has the best fitness value, the δ2 wolf has the second-best fitness value, and the δ3 wolf has the second-best fitness value. (53) Update the location of the gray wolf population and generate a new population; (54) Update the positions of wolf δ1, wolf δ2 and wolf δ3 according to the fitness function; (55) If the maximum number of iterations is reached, the globally optimal gray wolf position and the corresponding minimum MAPE value are output; otherwise, the process returns to step (53), and the nonlinear parameter value corresponding to the globally optimal gray wolf position is the optimal nonlinear parameter value.
8. The long-term wind power generation prediction method according to claim 1, characterized in that: The simulated value of the rate-damped conformal fractional sequence is: When 0<β≤1, When β = 0, Where: is the simulated value of the rate damping conformal fractional sequence, a, b, c are model parameters, α is the conformal fractional order, r is the model order, β is the structural index, is a rate-damped conformal fractional sequence, k = 1, 2, …, n, where n is the length of the original sequence X(0).
9. The long-term wind power generation prediction method according to claim 8, characterized in that: The rate damping conformal fractional-order grey Bernoulli model RDCFBM(1,1,t β ) is: When 0<α≤1, When α>1, Where: is the rate damped conformal fractional-order grey Bernoulli model RDCFBM(1, 1, t β ), is the simulated value of the rate-damped conformal fractional sequence, x r (0) is the original sequence X (0) The growth rate of k is α, α is the conformal fractional order, α∈(l, l+1], l is an integer greater than zero, k [α]-α Δ l represents the conformal fractional inverse operation, [α] is an integer not less than α, ζ is the damping coefficient, and n is the original sequence X (0) Length.
10. The long-term wind power generation prediction method according to claim 1, characterized in that: The nonlinear parameters include conformal fractional order, damping coefficient, model order, and structural index.