A Method, System, Medium, and Device for Modeling Wind Power Uncertainty Sets

Abstract

The present invention discloses a method, system, medium, and device for modeling a wind power uncertainty set, which relates to the technical field of electrical engineering. The method includes: obtaining historical measured wind power output data of different wind farms and historical predicted wind power output data predicted based on the historical measured wind power output data; grouping the wind farms based on the spatial correlation intensity of the historical measured wind power output data, taking the historical measured wind power output data corresponding to each wind farm group as a fractal body, and modeling the spatial correlation of the wind power uncertainty set based on each fractal body; based on the historical predicted wind power output data, using the e-index method and the probability distribution method to model the time correlation of the wind power uncertainty set; and using Gibbs sampling to associate the time and spatial correlations of the wind power uncertainty set to obtain a wind power uncertainty set with spatio-temporal correlations. The present invention has self-adaptability to the distribution shape of historical data.

Description

Technical Field

[0001] The present invention relates to the technical field of electrical engineering, and particularly to a method, system, medium, and device for modeling a wind power uncertainty set. Background Art

[0002] Power generation through new energy is a key means to achieve the "dual carbon" goal, and wind power generation is an important part of it. However, due to the significant uncertainty of wind power and the difficulty in accurately characterizing it, the flexibility requirements of the system are affected. Under the condition of inaccurate description of wind power characteristics, the decisions made in dispatching operation will deviate from the optimal operation point, resulting in a reduction in decision-making economy.

[0003] Robust optimization is one of the mainstream methods for dealing with wind power uncertainty, which has the advantage of ensuring the reliability of the dispatching plan and is in line with the requirement of putting safety first in energy dispatching. However, it has great conservatism in decision-making economy. Robust optimization mainly uses a box-type set to describe wind power uncertainty and focuses on considering the safety of dispatching. However, it fails to enclose historical data with the smallest area or space, resulting in the flexible reserve capacity reserved for real-time operation by robust optimization exceeding the actual requirement, reducing the decision-making economy, and thus being very conservative in decision-making economy. To improve the economy of robust optimization decisions, some studies use a polyhedral uncertainty set considering a budget set to describe wind power uncertainty. However, when the polyhedral set considering the budget set reduces conservatism, it does not consider the distribution shape of wind power historical data, so it cannot fully ensure the safety of the dispatching plan. To improve decision-making economy, some studies consider establishing a more refined uncertainty set, that is, an uncertainty set that can fully approximate the distribution shape of historical data. The distribution shape of historical data is an embodiment of the spatial and temporal correlation of the uncertainty set. Such as using a non-linear ellipsoid equation to establish a spatio-temporal correlation model, a minimum elliptical convex hull to establish a spatial correlation model, a rhombic convex hull to establish a spatial correlation model, etc. Most of them describe the historical data distribution based on a specific geometric shape, and the method is only applicable when the historical data distribution is similar to the selected geometric shape. However, the wind power output of different wind farms and the wind power output of the same system in different seasons may present different data distribution characteristics, and most of them are irregular shapes. Describing the correlation of the uncertainty set with only a specific shape is not self-adaptive. Summary of the Invention

[0004] The purpose of the present invention is to propose a method for modeling a wind power uncertainty set to solve the problem that describing the correlation of the uncertainty set with only a specific shape is not self-adaptive. The method includes the following steps:

[0005] S1. Obtain historical output data of different wind farms, including historical measured wind power output data and historical predicted wind power output data predicted based on the historical measured wind power output data;

[0006] S2. Group the wind farms based on the spatial correlation intensity of the historical measured wind power output data, take the historical measured wind power output data corresponding to each grouped wind farm as a fractal body, and model the spatial correlation of the wind power uncertainty set based on each fractal body;

[0007] S3. Based on the historical measured wind power output data and the historical predicted wind power output data, use the e-index method and the probability distribution method to model the temporal correlation of the wind power uncertainty set;

[0008] S4. Use Gibbs sampling to correlate the temporal correlation and the spatial correlation of the wind power uncertainty set to obtain a wind power uncertainty set with spatio-temporal correlation.

[0009] Further, divide each fractal body to obtain a set of subsets, cut off the boundary subsets that do not contain historical measured wind power output data, obtain a polyhedron with an irregular shape, and use the scene set composed of the boundary points of the polyhedron with an irregular shape to characterize the spatial correlation of the wind power uncertainty set.

[0010] Further, divide the historical measured wind power output data of the polyhedron with an irregular shape into two types of subsets, one containing boundary points and the other not containing boundary points, and use only the vertices belonging to the subset containing boundary points as the elements describing the boundary of the uncertainty set.

[0011] Further, S3 is specifically as follows:

[0012] S31. For the th wind farm, construct the time covariance matrix of the historical measured wind power output data in different time periods :

[0013] (1),

[0014] The elements in the covariance matrix are calculated according to the following formula:

[0015] (2),

[0016] where , are any two time periods, , , is the covariance of the jth wind farm between , time periods, is used to control the temporal correlation intensity of the jth wind farm;

[0017] S32. Each wind farm generates samples that follow the joint distribution of a Gaussian random sequence, is the number of scenarios in the wind power uncertainty set, is an n-dimensional zero vector; is the covariance matrix;

[0018] S33. Calculate the cumulative distribution function values of the respective random variables of the Gaussian random sequence in step S32 , is the Gaussian cumulative distribution function, represents the value of the Gaussian random sequence at the t-th time period for each time period of the j-th wind farm under the s-th scenario in the wind power uncertainty set, is a random data uniformly distributed on [0, 1] for the j-th wind farm at the t-th time period under the s-th scenario in the wind power uncertainty set;

[0019] S34. Using the method of piecewise mapping, transform the that follows a uniform distribution into the given range of each time period of the wind power uncertainty set based on the historical predicted wind power output data scenarios , and complete the time correlation modeling of the wind power uncertainty set, where represents the historical predicted wind power output data at the t-th time period, represents the wind farm capacity, represents the width of the selected range, represents the time correlation of the wind power uncertainty set at the t-th time period under the s-th scenario.

[0020] Furthermore, step S4 is specifically as follows:

[0021] S41. Based on the boundary points of the polyhedron with an irregular shape, calculate the conditional cumulative distribution function of the actual wind power output of the wind farm, expressed as:

[0022] (3),

[0023] (4),

[0024] where represents the -th wind farm at the -th scenario in the wind power uncertainty set at the -th time period of the conditional joint probability density function, represents the -th wind farm at the -th scenario in the wind power uncertainty set at the -th time period of the actual output value, The lower boundary point representing the boundary points of the polyhedron with an irregular shape in the first time period The lower boundary point representing the boundary points of the polyhedron with an irregular shape in the 24th time period The upper boundary point representing the boundary points of the polyhedron with an irregular shape in the first time period The upper boundary point representing the boundary points of the polyhedron with an irregular shape in the 24th time period, P Denote the conditional probability;

[0025] Let (5)

[0026] Wherein, Denote the sequence of actual output values of n wind farms in the first scenario of the wind power uncertainty set at the th time period, Denote the sequence of historical measured wind power output data of n wind farms at the th time period;

[0027] S42. Combining the time correlation of the wind power uncertainty set, discretize and sample the conditional cumulative distribution function to obtain the cumulative probability of the th wind farm in the th time period under the th scenario of the wind power uncertainty set;

[0028] S43. Use the inverse transformation to update ;

[0029] S44. Implement steps S41 - S43 for each time period and each scenario, discard the scenarios during the running - in period, and finally obtain the spatio - temporal correlation wind power uncertainty set.

[0030] Furthermore, combining the time correlation of the wind power uncertainty set, the discretized sampling of the conditional cumulative distribution function is expressed as:

[0031] (6)

[0032] Wherein, Denote the length of the vector, Denote rounding up to the nearest integer, Denote sampling and taking values of the index within the brackets for .

[0033] The present invention also proposes a wind power uncertainty set modeling system, including:

[0034] A data acquisition module, configured to acquire historical output data of different wind farms, including historical measured wind power output data and historical predicted wind power output data predicted based on the historical measured wind power output data;

[0035] A spatial correlation modeling module for wind power uncertainty sets, configured to group wind farms based on the spatial correlation intensity of historical measured wind power output data, use the historical measured wind power output data corresponding to each wind farm group as a fractal body, and model the spatial correlation of the wind power uncertainty sets based on each fractal body;

[0036] A temporal correlation modeling module for wind power uncertainty sets, configured to model the temporal correlation of the wind power uncertainty sets based on the historical measured wind power output data and the historical predicted wind power output data by using the e-index method and the probability distribution method;

[0037] A spatio-temporal correlation wind power uncertainty set acquisition module, configured to use Gibbs sampling to associate the temporal correlation and the spatial correlation of the wind power uncertainty sets to obtain a wind power uncertainty set with spatio-temporal correlation.

[0038] The present invention also provides a computer-readable storage medium storing a computer program, and when the computer program is executed by a processor, the above-mentioned wind power uncertainty set modeling method is implemented.

[0039] The present invention also provides an electronic device, including a processor and a memory, where the processor is connected to the memory. The memory is configured to store a computer program, and the computer program includes computer-readable instructions. The processor is configured to call the computer-readable instructions to execute the above-mentioned wind power uncertainty set modeling method.

[0040] The beneficial effects brought by the technical solution provided by the present invention are:

[0041] The present invention proposes a method for constructing a wind power uncertainty set based on the fractal method. First, the spatial correlation of the wind power uncertainty set is modeled based on the fractal body, and the temporal correlation of the wind power uncertainty set is modeled. Then, the temporal correlation and the spatial correlation of the two models are associated to obtain a spatio-temporal correlation wind power uncertainty modeling. The present invention has self-adaptability to the distribution shape of historical data. By integrating the probability distribution technology in the modeling process, the decoupled modeling of the spatio-temporal correlation of the uncertainty set is realized, avoiding the curse of dimensionality problem in the joint modeling of spatio-temporal correlation. It can not only retain the advantages of the fractal method and improve the decision-making economy, but also take into account the computational tractability of the optimization method. Description of the Drawings

[0042] Figure 1 is a flowchart of the wind power uncertainty set modeling method according to an embodiment of the present invention;

[0043] Figure 2 It is an example diagram of a polyhedron with an irregular shape according to an embodiment of the present invention;

[0044] Figure 3 It is a block diagram of an electronic device in an exemplary embodiment of Embodiment 1 of the present invention. Detailed implementation manners

[0045] To make the objectives, technical solutions and advantages of the present invention clearer, the embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0046] Embodiment 1: The flowchart of the wind power uncertainty set modeling method according to the embodiment of the present invention is as Figure 1 , and specifically includes the following steps:

[0047] S1. Obtain historical output data of different wind farms, including historical measured wind power output data and historical predicted wind power output data predicted based on the historical measured wind power output data.

[0048] In a preferred embodiment of the present invention, the wind power output data is measured once every hour. For example, the historical measured wind power output data includes the dth day, with a total of n days of historical measured data of 24 hours per day. The 24-hour historical measurement on the dth day is expressed as: . The historical predicted wind power output data includes the 24-hour historical prediction on the dth day: , and the predicted data is predicted based on the data of the previous n - 1 days before the dth day.

[0049] S2. Group the wind farms based on the spatial correlation intensity of the historical measured wind power output data, use the historical measured wind power output data corresponding to each wind farm group as a fractal body, and model the spatial correlation of the wind power uncertainty set based on each fractal body.

[0050] In a preferred embodiment of the present invention, first, according to the historical output data of different wind farms, the spatial correlation intensity of the output of different wind farms is statistically analyzed, and the wind farms are grouped in the order of the magnitude of the correlation intensity. For example: Wind farm group 1, Wind farm group 2, Wind farm group 3, etc. Use the historical output data corresponding to the wind farm group as a fractal body. For example: Fractal body 1 is the historical output data of wind farm group 1, and fractal body 1 constitutes hypercube 1. Fractal body 2 is the historical output data of wind farm group 2, and fractal body 2 constitutes hypercube 2.

[0051] Each fractal body is segmented to obtain a set of subsets, and the boundary subsets that do not contain historical output data are cut off to obtain a polyhedron with an irregular shape. For an example diagram of the polyhedron with an irregular shape according to the embodiment of the present invention, refer to Figure 2, according to the principle that the worst-case scenario in robust optimization lies at the vertices of the convex hull, a scenario set composed of the boundary points of a polyhedron with an irregular shape and its spatial distribution are used to characterize the spatial correlation of the uncertainty set. This scenario-based description form transforms the subsequent robust optimization problem into an equivalent deterministic optimization problem, thus facilitating the application of distributed optimization methods. The historical measured wind power output data of the polyhedron with an irregular shape is divided into two subsets, one containing boundary points and the other not containing boundary points. For Figure 2 the two subsets containing and not containing boundary points are compared to obtain the characteristic differences between them. Based on the above method, the boundary subset is identified, and the vertices that only belong to the subset containing boundary points are selected as the elements describing the boundary of the uncertainty set.

[0052] S3. Based on the historical measured wind power output data and historical predicted wind power output data, the e-index method and probability distribution method are used to model the temporal correlation of the wind power uncertainty set.

[0053] In the preferred embodiment of the present invention, specifically:

[0054] S31. For the th wind farm, construct the temporal covariance matrix of the historical measured wind power output data in different time periods :

[0055] (1),

[0056] The elements in the covariance matrix are calculated according to the following formula:

[0057] (2),

[0058] where , are any two time periods, , , is the covariance of the jth wind farm between , time periods, and is used to control the temporal correlation intensity of the jth wind farm.

[0059] S32. Each wind farm generates Gaussian random sequences that follow the joint distribution , is the number of scenarios in the wind power uncertainty set, is the -dimensional zero vector; is the covariance matrix.

[0060] S33. Calculate the cumulative distribution function (CDF) values of each random variable in the Gaussian random sequence in step S32. , represents the value of the Gaussian random sequence at the t-th time period for each time period in the s-th scenario of the wind power uncertainty set of the j-th wind farm. The Gaussian random sequences of different time periods in the s-th scenario of the wind power uncertainty set of the j-th wind farm are expressed as: ( ), ; is the Gaussian cumulative distribution function, is the random data that follows a uniform distribution on [0, 1] at the t-th time period in the s-th scenario of the wind power uncertainty set of the j-th wind farm.

[0061] S34. Using the method of piecewise mapping, transform the that follows a uniform distribution into the given range of the wind power uncertainty set of different time periods based on the historical predicted wind power output data scenarios , and complete the time correlation modeling of the wind power uncertainty set. Among them, represents the historical predicted wind power output data at the t-th time period, represents the wind farm capacity, represents the width of the selected range, represents the time correlation of the wind power uncertainty set at the t-th time period in the s-th scenario.

[0062] S4. Use Gibbs sampling to correlate the time correlation and space correlation of the wind power uncertainty set to obtain a wind power uncertainty set with spatio-temporal correlation.

[0063] In the preferred embodiment of the present invention, specifically:

[0064] S41. Based on the boundary points of the polyhedron with an irregular shape, such as Figure 2 the boundary points of the uncertainty set in, take the points above the polyhedron with an irregular shape as the upper boundary points and the points below the polyhedron with an irregular shape as the lower boundary points. Calculate the conditional cumulative distribution function of the actual wind power output of the wind farm, expressed as:

[0065] (3),

[0066] (4),

[0067] Among them, represents the -th wind farm in the The conditional joint probability density function of the time period under a certain scenario, denotes the actual output value of the nth wind farm in the mth scenario of the wind power uncertainty set at the kth time period, denotes the conditional probability.

[0068] Determine the initial value of Gibbs sampling, and let:

[0069] (5)

[0070] where, denotes the sequence of actual output values of the nth wind farm in the kth

[0071] S42. Combine the time correlation of the wind power uncertainty set, and discretize and sample the conditional cumulative distribution function to obtain the cumulative probability of the nth wind farm in the mth

[0072] scenario of the wind power uncertainty set at the

[0073] (6)

[0074] where, denotes the length of the vector, denotes rounding up to the nearest integer, denotes sampling and taking values of the index value within the parentheses for .

[0075] S43. Use the inverse transformation to update .

[0076] S44. Implement steps S41 - S43 for each time period and each scenario, discard the scenarios during the running - in period, and finally obtain the spatio - temporal correlation wind power uncertainty set.

[0077] Embodiment 2: The present invention also proposes a wind power uncertainty set modeling system, including:

[0078] A data acquisition module, configured to acquire historical output data of different wind farms, including historical measured wind power output data and historical predicted wind power output data predicted based on the historical measured wind power output data;

[0079] A spatial correlation modeling module of the wind power uncertainty set, configured to group wind farms based on the spatial correlation intensity of historical measured wind power output data, use the historical measured wind power output data corresponding to each wind farm group as a fractal body, and model the spatial correlation of the wind power uncertainty set based on each fractal body;

[0080] A time correlation modeling module of the wind power uncertainty set, configured to model the time correlation of the wind power uncertainty set based on the historical measured wind power output data and the historical predicted wind power output data by using the e - index method and the probability distribution method;

[0081] A spatio - temporal correlation wind power uncertainty set obtaining module, configured to use Gibbs sampling to associate the time correlation and the spatial correlation of the wind power uncertainty set to obtain a wind power uncertainty set with spatio - temporal correlation.

[0082] Embodiment 3: In an exemplary embodiment, there is provided a computer - readable storage medium storing a computer program, and when the computer program is executed by a processor, the above - mentioned wind power uncertainty set modeling method is implemented.

[0083] Embodiment 4: Please refer to Figure 3 , in an exemplary embodiment, there is also provided an electronic device, including at least one processor, at least one memory, and at least one communication bus.

[0084] Wherein, a computer program is stored on the memory, the computer program includes computer - readable instructions, and the processor calls the computer - readable instructions stored in the memory through the communication bus to execute the above - mentioned wind power uncertainty set modeling method.

[0085] The foregoing description of the disclosed embodiments enables those skilled in the art to practice or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A modeling method for wind power uncertainty sets, characterized in that, It includes the following steps: S1. Obtain the historical output data of different wind farms, including historical measured wind power output data and historical predicted wind power output data predicted based on the historical measured wind power output data; S2. Group the wind farms based on the spatial correlation intensity of the historical measured wind power output data. Take the historical measured wind power output data corresponding to each wind farm group as a fractal body, and model the spatial correlation of the wind power uncertainty set based on each fractal body; S3. Based on the historical measured wind power output data and the historical predicted wind power output data, use the e-index method and the probability distribution method to model the temporal correlation of the wind power uncertainty set; S4. Use Gibbs sampling to correlate the temporal correlation and the spatial correlation of the wind power uncertainty set to obtain a wind power uncertainty set with spatio-temporal correlation.

2. A method for modeling a wind power uncertainty set according to claim 1, wherein Each fractal body is segmented to obtain a set of subsets, and the boundary subsets that do not contain historical measured wind power output data are cut off to obtain a polyhedron with an irregular shape. Use the scene set composed of the boundary points of the polyhedron with an irregular shape to characterize the spatial correlation of the wind power uncertainty set.

3. A method for modeling a wind power uncertainty set according to claim 2, wherein The historical measured wind power output data of the polyhedron with an irregular shape is divided into two types of subsets, one containing boundary points and the other not containing boundary points. Take only the vertices belonging to the subset containing boundary points as the elements describing the boundary of the uncertainty set.

4. A method for modeling a wind power uncertainty set according to claim 3, wherein S3 specifically is: S31. For the th wind farm, construct the time covariance matrix of the historical measured wind power output data for different time periods : （1）， Covariance matrix The elements in are calculated according to the following formula: （2）， Among them, and are any two time periods, , , is the covariance of the j-th wind farm between and time periods, which is used to control the time correlation intensity of the j-th wind farm; S32. Each wind farm generates Gaussian random sequences that follow a joint distribution of number of Gaussian random sequences, where is the number of scenarios in the wind power uncertainty set, and is the covariance matrix; S33. Calculate the cumulative distribution function values of each random variable in the Gaussian random sequence in step S32 , is the Gaussian cumulative distribution function, represents the value of the Gaussian random sequence at the t-th time period in different time periods of the s-th scenario in the wind power uncertainty set of the j-th wind farm, represents the random data uniformly distributed on [0,1] at the t-th time period in the s-th scenario in the wind power uncertainty set of the j-th wind farm; S34. Using the method of piecewise mapping, transform the into the wind power uncertainty sets for each time period based on historical predicted wind power output data within a given range to complete the time-correlation modeling of the wind power uncertainty sets. Among them, represents the number of scenarios , where represents the historical predicted wind power output data for the t-th time period, represents the wind farm capacity, represents the width of the selected range, represents the time correlation of the wind power uncertainty set at the t-th time period in the s-th scenario.

5. A wind power uncertainty set modeling method according to claim 4, characterized in that Step S4 specifically is: S41. Based on the boundary points of the polyhedron with an irregular shape, calculate the conditional cumulative distribution function of the actual wind power output of the wind farm, expressed as: （3）， （4）， Among them, represents the th conditional joint probability density function of the th wind farm at the th time period under the th scenario of the wind power uncertainty set, represents the actual output value of the th wind farm at the th time period under the th scenario of the wind power uncertainty set, represents the lower boundary point of the boundary points of the irregular polyhedron at the nd time period, represents the lower boundary point of the boundary points of the irregular polyhedron at the th time period, P represents the conditional probability; Let (5), Among them, represents the sequence of actual output values of n wind farms at the th time period in the first scenario of the wind power uncertainty set, represents the sequence of historical measured wind power output data of n wind farms at the th time period; S42. Combining the time correlation of the wind power uncertainty set, discretely sample the conditional cumulative distribution function to obtain the cumulative probability at the -th scenario of the -th time period in the wind power uncertainty set for the -th wind farm; S43. Perform the inverse transformation on for updating; S44. Implement steps S41 - S43 for each time period and each scene, and discard the scenes during the running-in period. Finally, obtain a wind power uncertainty set with spatio-temporal correlation.

6. A method for modeling a wind power uncertainty set according to claim 5, characterized in that, Combined with the time correlation of the wind power uncertainty set, the conditional cumulative distribution function is discretized and sampled and expressed as: （6）， Among them, represents the length of the vector, represents rounding up to the nearest integer, represents taking a sampled value of the index within the parentheses for 7. A wind power uncertainty set modeling system, characterized in that It includes: A data acquisition module, used to obtain the historical output data of different wind farms, including historical measured wind power output data and historical predicted wind power output data predicted based on the historical measured wind power output data; A spatial correlation modeling module for wind power uncertainty set, used to group the wind farms based on the spatial correlation intensity of the historical measured wind power output data. Take the historical measured wind power output data corresponding to each wind farm group as a fractal body, and model the spatial correlation of the wind power uncertainty set based on each fractal body; A temporal correlation modeling module for wind power uncertainty set, used to model the temporal correlation of the wind power uncertainty set based on the historical measured wind power output data and the historical predicted wind power output data, using the e-index method and the probability distribution method; A module for obtaining a wind power uncertainty set with spatio-temporal correlation, used to use Gibbs sampling to correlate the temporal correlation and the spatial correlation of the wind power uncertainty set to obtain a wind power uncertainty set with spatio-temporal correlation.

8. A computer-readable storage medium storing a computer program, characterized in that: The computer program, when executed by a processor, implements the method according to any one of claims 1 - 6.

9. An electronic device, characterized in that, It includes a processor and a memory, the processor is interconnected with the memory, wherein the memory is used to store a computer program, the computer program includes computer-readable instructions, and the processor is configured to call the computer-readable instructions to execute the method according to any one of claims 1-6.

Images