A data-driven approach to modeling new energy uncertainty sets

Abstract

The present invention relates to the field of electrical engineering technology, and its purpose is to provide a data-driven new energy uncertainty set modeling method, which specifically includes the following steps: first collect the actual and predicted output error data of the new energy field group processing; then use the principal component analysis method to project the error data onto each principal component; then estimate the probability distribution of the data on each principal component; finally determine the closed polyhedron that can surround the distribution data under the specified confidence probability. Its beneficial effect is that the present invention constructs a new type of more compact and dense uncertainty set that describes the fluctuation of new energy prediction errors through the collected historical prediction error data of new energy stations. The set is surrounded by multiple arc convex hulls and is a generalized polyhedron structure. It has good adaptability to robust optimization and two-stage robust optimization, and the algorithm complexity only grows linearly with the dimension, and the calculation speed is fast.

Description

Technical Field

[0001] The present invention relates to the field of electrical engineering technology, and in particular to a data-driven new energy uncertainty set modeling method. Background Art

[0002] With the increasing social and environmental demands, the proportion of renewable energy power generation in the power grid is getting higher and higher. In recent years, both the international and domestic governments have been committed to the development of renewable energy. The development of renewable energy is the key to realizing the energy revolution. However, the four characteristics of renewable energy (volatility, uncertainty, weak support for the power grid, and low anti-interference) have always been a problem, which has brought great challenges to the stable operation of the power grid. Focusing on the power grid dispatching level, the traditional dispatching method treats the solution of multi-objective decision-making, day-ahead dispatching and other problems as deterministic optimization problems, and even directly arranges a certain proportion of spare capacity to adjust the power grid stability problems caused by renewable energy fluctuations. Now many literatures use probability constraints and two-stage robust optimization methods to establish uncertain sets, but the disadvantage of probability constraints is that it cannot guarantee that the dispatching strategy can fully meet the safety and reliability requirements of the power grid. In the two-stage robust optimization, box uncertain sets are often used, which cannot guarantee the compactness of uncertain sets, resulting in the arrangement of more abundant spare capacity in most cases. This inevitably leads to over-conservatism in the decision-making process, resulting in waste of resources and reduced economic efficiency. Summary of the invention

[0003] The purpose of the present invention is to overcome the above-mentioned technical deficiencies and provide a data-driven new energy uncertainty set modeling method. Through the collected historical prediction error data of new energy stations, a new, more compact and denser uncertainty set describing the fluctuations of new energy prediction errors is constructed. The set is surrounded by multiple arc convex hulls and is a generalized polyhedral structure. It has good adaptability to robust optimization and two-stage robust optimization, and the algorithm complexity only grows linearly with the dimension, and the calculation speed is fast.

[0004] In order to achieve the above object, the specific scheme adopted by the present invention is as follows:

[0005] A data-driven new energy uncertainty set modeling method includes the following steps:

[0006] 1) Collect the historical actual and predicted output of the new energy field group, and use the error between the two as input data;

[0007] 2) Projecting the data onto the divided principal components to achieve data decomposition on each principal component;

[0008] 3) Estimate the probability distribution of the data on each principal component, and determine the data interval points on each principal component according to the set confidence probability;

[0009] 4) Determine the closed polyhedron that can enclose the specified confidence level as the uncertain set.

[0010] Furthermore, in step 1), the historical actual and predicted outputs of the new energy field group are collected, and the error between the historical actual and predicted outputs is used as input data and represented by a matrix P:

[0011]

[0012] Where N is the number of new energy field groups, T1 is the number of error data periods collected, and one column of the above matrix is ​​written in matrix form as follows:

[0013] P i =[P 1,i …P N,i ] T ∈R N×1 ,

[0014] Furthermore, the method of projecting the data onto the divided principal components in step 2) is:

[0015] P0=P-eP μ (2)

[0016]

[0017] t j =h j [P i -P μ ](5)

[0018] Where P0 is the regularized new energy output error matrix, P μ is the sample mean, Λ∈R N×N The covariance matrix S∈R N×N The diagonal matrix composed of the eigenvalues ​​arranged from large to small, H = [h1,…,h j ,…h N ]∈R N×N is the corresponding feature matrix, h j ∈R N×1 is the eigenvector corresponding to the jth eigenvalue, It is the projection of the uncertain data on the jth principal component.

[0019] Furthermore, the probability distribution calculation method for estimating the data on each principal component in step 3) is as follows:

[0020]

[0021] In the formula, f j is the error distribution probability matrix on the jth principal component, and h is the bandwidth parameter.

[0022] Furthermore, in step 3), the calculation method for determining the data interval points on each principal component according to the set confidence probability is as follows:

[0023] g j (α)=min{t j |F j (t j )≥1-α} (7)

[0024] In the formula, g j (α) represents the matrix F formed after the uncertain data on the jth principal component is screened under the requirement of confidence probability α j (t j ) is the cumulative density matrix of uncertain data on the jth principal component, which can be calculated by the probability distribution function.

[0025] Furthermore, in step 4), the closed polyhedron equation that can enclose the specified confidence level is determined as:

[0026]

[0027] In the formula, is the projection of the i-th error data of the new energy source after the specified confidence probability screening on the j-th principal component, and then the tolerance coefficient σ>0 is set. If |r i+1 -r i |≤σ then r i+1 =r i , on the contrary r i+1 =r i+1 The setting of the tolerance coefficient reflects the sensitivity of the multi-cambered surface set to the data. The smaller the tolerance coefficient, the higher the data sensitivity, which is reflected in the multi-cambered surface set as more arcs. In fact, in the limit case, the number of arcs does not exceed the matrix g. j (α), the tolerance coefficient is the minimum value 0.

[0028] Compared with the prior art, the present invention constructs a new, more compact and denser uncertainty set that describes the fluctuations in new energy prediction errors through the collected historical prediction error data of new energy stations. The set is surrounded by multiple arc convex hulls and is a generalized polyhedral structure. It has good adaptability to robust optimization and two-stage robust optimization, and the algorithm complexity only grows linearly with the dimension, with fast calculation speed, and can be easily applied to existing new energy optimization scheduling methods based on uncertainty sets. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 A flow chart of a data-driven new energy uncertainty set modeling method provided by the present invention.

[0030] Figure 2 A schematic diagram of the distribution of new energy uncertainty data provided by the present invention.

[0031] Figure 3 Schematic diagram of data projection probability distribution on the principal component t1 of the present invention.

[0032] Figure 4 Schematic diagram of data projection probability distribution on the principal component t2 of the present invention.

[0033] Figure 5 It is a schematic diagram of a multi-arc surface assembly of the present invention. DETAILED DESCRIPTION

[0034] The structure and beneficial effects of the present invention are further described below in conjunction with the accompanying drawings.

[0035] It should be emphasized that the following description is only for exemplary purposes and is not intended to limit the scope and application of the present invention.

[0036] Example 1

[0037] like Figure 1 The present invention discloses a data-driven new energy uncertainty set modeling method, which includes the following steps:

[0038] 1) Collect the historical actual and predicted output of the new energy field group, and use the error between the two as input data;

[0039] 2) Projecting the data onto the divided principal components to achieve data decomposition on each principal component;

[0040] 3) Estimate the probability distribution of the data on each principal component, and determine the data interval points on each principal component according to the set confidence probability;

[0041] 4) Determine the closed polyhedron that can enclose the specified confidence level as the uncertain set.

[0042] In step 1), the historical data and predicted data processed by each new energy field group are collected, and the error between the historical data and the predicted data is used as input data and represented by a matrix P:

[0043]

[0044] Where N is the number of new energy field groups, T1 is the number of error data periods collected, and one column of the above matrix is ​​written in matrix form as follows:

[0045] P i =[P 1,i … P N,i ] T ∈RN×1 ,

[0046] The decomposition method of the data on the principal components in step 2) is:

[0047] P0=P-eP μ (10)

[0048]

[0049] t j =h j [P i -P μ ](13)

[0050] Where P0 is the regularized new energy output error matrix, P μ is the sample mean, Λ∈R N×N The covariance matrix S∈R N×N The diagonal matrix composed of the eigenvalues ​​arranged from large to small, H = [h1,…,h j ,…h N ]∈R N×N is the corresponding feature matrix, h j ∈R N×1 is the eigenvector corresponding to the jth eigenvalue, It is the projection of the uncertain data on the jth principal component.

[0051] The method for calculating the probability distribution of the data on each principal component in step 3) is as follows:

[0052]

[0053] In the formula, f j is the error distribution probability matrix on the jth principal component, and h is the bandwidth parameter.

[0054] In step 3), the cumulative density is used to calculate the screening of data on the principal component under the specified confidence probability as follows:

[0055] g j (α)=min{t j |F j (t j )≥1-α} (15)

[0056] In the formula, g j (α) represents the matrix F formed after the uncertain data on the jth principal component is screened under the requirement of confidence probability α j (t j ) is the cumulative density matrix of uncertain data on the jth principal component, which can be calculated by the probability distribution function.

[0057] In step 4), the arc surface equation of the polyhedron is determined as:

[0058]

[0059] In the formula, is the projection of the i-th error data of the new energy source after the specified confidence probability screening on the j-th principal component, and then the tolerance coefficient σ>0 is set. If |r i+1 -r i |≤σ then r i+1 =r i , on the contrary r i+1 =r i+1 The setting of the tolerance coefficient reflects the sensitivity of the multi-cambered surface set to the data. The smaller the tolerance coefficient, the higher the data sensitivity, which is reflected in the multi-cambered surface set as more arcs. In fact, in the limit case, the number of arcs does not exceed the matrix g. j (α), the tolerance coefficient is the minimum value 0.

[0060] Experimental description:

[0061] First, relevant historical data are collected, and the error between the measured output and the predicted output processed by each new energy station is expressed by matrix P:

[0062]

[0063] In order to simplify the calculation, in the specific calculation process, the data of two wind farms in Guazhou in the west are used for illustration. The number of historical time periods collected is T1=1300, and the sampling time is once every 15 minutes. At this time, the matrix P is a 2×1300 matrix.

[0064] Then according to the formula Calculate the average value

[0065]

[0066] According to the formula P0 = P-eP μ Calculate the regularized new energy output error matrix;

[0067] Then by the formula Calculate the characteristic matrix and diagonal matrix, sort them and get the characteristic matrix H. In this example, we get:

[0068]

[0069] Furthermore, according to the formula t j =h j [P i -P μ] Calculate the projection on the uncertain principal component. In this example, the number of new energy stations is 2, and the number of principal components is also 2. Taking the principal component t1 as the x-axis and t2 as the y-axis, we can draw Figure 2 Distribution of new energy uncertainty data shown.

[0070] The probability distribution calculation method of the data on each principal component is as follows. In this example, h is 14:

[0071]

[0072] In this example, the data projection probability distributions on the principal components t1 and t2 are as follows: Figure 3 and Figure 4 shown.

[0073] The cumulative density in the calculation realizes the screening of data on the principal component under the specified confidence probability, as follows:

[0074] g j (0.95) = min{t j |F j (t j )≥0.05}(23)

[0075] In order to determine the generalized polyhedron that encloses the historical scene under the specified confidence probability, the confidence probability α is set to 95%, the tolerance coefficient σ is set to 5 to take into account the compactness and complexity of the uncertain set, and the angle of the single arc surface is set to be no less than 5% rounded (18°). The obtained multi-arc surface set is as follows: Figure 5 shown.

[0076] In summary, the data-based new energy uncertain set modeling method provided by the present invention has an algorithm complexity that only grows linearly with the dimension, has fast calculation speed and high efficiency, and can be easily applied to existing new energy optimization scheduling methods based on uncertain sets, which helps to improve economic benefits.

[0077] Compared with the prior art, the present invention has the following technical features and effect advantages:

[0078] 1) The data-based multi-arc surface uncertainty set constructed in the method of the present invention is composed of multiple arc surface convex hulls surrounding uncertain data, which can be easily applied to the existing new energy optimization scheduling method based on uncertainty sets;

[0079] 2) The present invention can adjust the tolerance coefficient according to the needs of decision makers to balance the compactness and computational complexity of the uncertainty set, thereby affecting the economic efficiency of the decision;

[0080] 3) The data-based multi-arc surface uncertainty set constructed by the present invention can ensure the robustness of the decision by shrinking the arc surface radius.

[0081] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A data-driven new energy uncertainty set modeling method, characterized in that: The following steps are involved: 1) Collect the historical actual and predicted output of the new energy field group, and use the error between the two as input data; 2) Projecting the data onto the divided principal components to achieve data decomposition on each principal component; 3) Estimate the probability distribution of the data on each principal component, and determine the data interval points on each principal component according to the set confidence probability; 4) Determine the closed polyhedron that can enclose the specified confidence level as the uncertain set.

2. A data-driven new energy uncertainty set modeling method according to claim 1, characterized in that: In step 1), the historical actual and predicted outputs of the new energy field group are collected, and the error between the historical actual and predicted outputs is used as input data and represented by a matrix P: Where N is the number of new energy field groups, T1 is the number of error data periods collected, and one column of the above matrix is ​​written in matrix form as follows: P i =[P 1,i … P N,i ] T ∈R N×1 , i=1,...,T1, j=1,...,N.

3. The data-driven new energy uncertainty set modeling method according to claim 1, characterized in that: The method of projecting the data onto the divided principal components in step 2) is: P0=P-eP μ (2) t j =h j [P i -P μ ] (5) Where P0 is the regularized new energy output error matrix, P μ is the sample mean, Λ∈R N×N The covariance matrix S∈R N×N The diagonal matrix composed of the eigenvalues ​​arranged from large to small, H = [h1,…,h j ,…h N ]∈R N×N is the corresponding feature matrix, h j ∈R N×1 is the eigenvector corresponding to the jth eigenvalue, It is the projection of the uncertain data on the jth principal component.

4. The data-driven new energy uncertainty set modeling method according to claim 1, characterized in that: The method for calculating the probability distribution of the data on each principal component in step 3) is as follows: In the formula, f j is the error distribution probability matrix on the jth principal component, and h is the bandwidth parameter.

5. The data-driven new energy uncertainty set modeling method according to claim 1, characterized in that: In step 3), the calculation method for determining the data interval points on each principal component according to the set confidence probability is as follows: g j (a)=min{t j |F j (t j )≥1-α} (7) In the formula, g j (α) represents the matrix F formed after the uncertain data on the jth principal component is screened under the requirement of confidence probability α j (t j ) is the cumulative density matrix of uncertain data on the jth principal component, which can be calculated by the probability distribution function.

6. The data-driven new energy uncertainty set modeling method according to claim 1, characterized in that: In the step 4), the closed polyhedron equation that can enclose the specified confidence level is determined as: In the formula, is the projection of the i-th error data of the new energy source after the specified confidence probability screening on the j-th principal component, and then the tolerance coefficient σ is set to 0. If |r i+1 -r i |≤σ then r i+1 =r i , on the contrary r i+1 =r i+1 The setting of the tolerance coefficient reflects the sensitivity of the multi-cambered surface set to the data. The smaller the tolerance coefficient, the higher the data sensitivity, which is reflected in the multi-cambered surface set as more arcs. In fact, in the limit case, the number of arcs does not exceed the matrix g. j (α), the tolerance coefficient is the minimum value 0.

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