A hierarchical coordination prediction method for photovoltaic power under a probabilistic framework

Abstract

A hierarchical harmonic prediction method for photovoltaic power under a probabilistic framework belongs to the field of photovoltaic power generation technology. To solve the problem that current probabilistic hierarchical forecasting methods are difficult to ensure probability aggregation consistency and have slow calculations, the present invention includes collecting photovoltaic power and base forecasts of nodes at each level of the power system corresponding to the same time resolution and forecast range, calculating the base forecast error of each node, and constructing a base forecast error matrix; using a sample rearrangement bottom-up aggregation technique, aggregating from the bottom-level nodes upward layer by layer based on the base forecast error matrix to obtain initial aggregated probabilistic forecasts for all nodes; constructing a base forecast vector based on the initial aggregated probabilistic forecast and the probabilistic base forecast, and using a harmonic matrix to convert the base forecast vector into a revised probabilistic forecast for the bottom-level nodes; and again using a sample rearrangement bottom-up aggregation technique on the revised probabilistic forecast for the bottom-level nodes, aggregating layer by layer from bottom to top into a probabilistic forecast that meets aggregation consistency for all nodes.

Description

Technical Field

[0001] The present invention belongs to the technical field of photovoltaic power generation, and in particular relates to a hierarchical coordination prediction method applied to photovoltaic power under a probabilistic framework. Background Art

[0002] Photovoltaic power is highly random and intermittent, and its grid integration poses a significant threat to the stable operation of power systems. Therefore, accurate forecasts of future photovoltaic power are necessary to develop reliable power generation plans and maintain grid load balance. The power system can be viewed as a hierarchical structure, with nodes representing the transmission network, distribution network, and photovoltaic sites, from top to bottom. To characterize forecast uncertainty and support risk assessment, each node at each level often generates a set of probabilistic power forecasts using its own data and forecasting methods. Although the actual photovoltaic power injected by any parent node in the hierarchical structure is equal to the sum of the photovoltaic powers of its subordinate child nodes (aggregate consistency), due to the inherent uncertainty of the forecast and the asymmetry of available information among different power system participants, the probabilistic forecasts of nodes at each level are often not aggregately consistent. That is, the probability distribution of the parent node's predicted variables is not equal to the probability distribution of the sum of the predicted variables of its subordinate child nodes. This seriously hinders the development of joint decision-making solutions.

[0003] The probabilistic hierarchical harmonic forecasting method is an effective means to achieve probabilistic forecast aggregation consistency. The method can be divided into two steps: the first step is to use an applicable forecasting method to independently generate a probabilistic base forecast of photovoltaic power (abbreviated as base forecast) for each node at each level; the second step is to use the harmonization technique to correct the base forecast to achieve probabilistic aggregate consistency. The main difference between the proposed probabilistic hierarchical harmonic forecasting methods lies in the different harmonization techniques. Some methods use harmonization techniques to make the prediction distribution of each parent node equal to the convolution of the prediction distributions of its subordinate child nodes; some methods aim to correct the mean of the base forecasts of all nodes so that they meet deterministic aggregate consistency; and some methods assume that the probabilistic hierarchical forecast is composed of several deterministic hierarchical forecasts (ensemble forecast), and when the forecasts of each group member meet deterministic aggregate consistency, the group forecast also meets probabilistic aggregate consistency. Comparing the three methods, it is not difficult to see that the first method has the most stringent requirements on the consistency of probability aggregation, but the corresponding harmonic technology is also the most complex. It is necessary to obtain the distribution of the sum of random variables through the Copula function, which is slow to calculate for high-dimensional hierarchical structures.

[0004] Therefore, it is of great significance to propose a hierarchical harmonic prediction method that can achieve probabilistic forecasts of nodes at different levels with probability aggregation consistency and computational efficiency. Summary of the Invention

[0005] The problem to be solved by the present invention is that the current probabilistic hierarchical forecasting method is difficult to ensure the consistency of probability aggregation and the calculation is slow. A hierarchical harmonic prediction method applied to photovoltaic power under a probabilistic framework is proposed.

[0006] To achieve the above object, the present invention is implemented through the following technical solutions:

[0007] A hierarchical coordinated prediction method for photovoltaic power in a probabilistic framework includes the following steps:

[0008] S1. Collect the photovoltaic power and base forecasts of nodes at each level of the power system corresponding to the same time resolution and prediction range, calculate the base forecast error of each node, and construct the base forecast error matrix;

[0009] S2. Using the sample rearrangement and bottom-up aggregation technique, the base prediction error matrix obtained in step S1 is aggregated from the bottom nodes upward layer by layer, and the initial aggregated probabilistic forecasts for all nodes are finally obtained;

[0010] S3. Constructing a base forecast vector based on the initial aggregated probabilistic forecast and the probabilistic base forecast obtained in step S2, and then converting the base forecast vector into a probabilistic forecast of the underlying node using a harmonic matrix;

[0011] S4. The probabilistic forecasts of the bottom nodes obtained in step S3 are again aggregated layer by layer from bottom to top using the sample rearrangement and bottom-up aggregation technology to obtain probabilistic forecasts that meet the aggregation consistency for all nodes.

[0012] Furthermore, the specific implementation method of step S1 includes the following steps:

[0013] S1.1. For each underlying node, use the ensemble numerical weather forecast as the ensemble forecast for the PV station, and then calculate the quantiles at different quantile levels to obtain the underlying node base forecast.

[0014] S1.2. For upper-level nodes, use statistical extrapolation to calculate the quantiles at different quantile levels to obtain the upper-level node base forecast;

[0015] S1.3. Based on the methods of steps S1.1 and S1.2, collect the base forecasts of the bottom-level nodes, the base forecasts of the upper-level nodes, and the corresponding measured PV power. Divide the total time into a training set, a validation set, and a test set according to a 60:20:20 ratio. Each sample includes the base forecast and the measured value of each node at each level at the same time.

[0016] S1.4. Assume that the number of bottom nodes is m and the total number of nodes is n, then the probabilistic base prediction mean of node i in the training set is recorded as The measured value of node i in the training set is recorded as y i =(y i,1+h ,yi,2+h ,...,y i,N+h ) T , where N is the total time of the training set, is the mean of the predicted distribution generated by node i at time t for time t+h, y i,t is the measured value of node i at time t, and h is the interval time;

[0017] Then calculate the basic prediction error e of node i i (h), calculated as:

[0018]

[0019] Then combine the base prediction errors of all nodes into the base prediction error matrix E(h), and the expression is:

[0020] E(h)=(e1(h),e2(h),...,e n (h))∈R N×n .

[0021] Furthermore, the bottom-level nodes in step S1 are bottom-level photovoltaic stations, and the upper-level nodes include middle-level distribution networks and upper-level transmission networks.

[0022] Furthermore, the specific implementation method of step S2 includes the following steps:

[0023] S2.1. For node i, set the time t to generate a forecast for time t+h, l is the length of the historical measured vector, then collect the historical measured vector x of node i i,t =(y i,t-l+1 ,...,y i,t ) T , the quantile level of node i is {τ1,τ2,...,τ Q}, where Q is the number of quantile levels, and the probabilistic base prediction b of node i i,t (h) is:

[0024]

[0025] Set the child nodes of node i to {j,j+1,...,j+n i -1}, where n i is the number of child nodes of node i, then the probabilistic basis predictions of the child nodes of node i are merged into the probabilistic basis prediction matrix B of the child nodes of node i i,t (h), we get:

[0026]

[0027] The initial aggregated probabilistic forecasts of the child nodes of node i are combined into the initial aggregated probabilistic forecast matrix C of the child nodes of node i i,t (h), we get:

[0028]

[0029] Among them, c j,t (h) is the initial aggregated probabilistic forecast of node i’s child node j;

[0030] S2.2. Concatenate the historical measured vectors of all nodes in the same sample and use the nearest neighbor algorithm to match the concatenated vectors at each training moment in the training set to obtain the Q closest training moments.

[0031] The measured vectors of each node at time t are spliced together to obtain the spliced measured vector (x 1,t T ,x 2,t T ,...,x n,t T ) T , use the k-nearest neighbor algorithm to obtain the Q closest training moments closest to the spliced measured vector from the training set, and merge the base prediction deviations of the subordinate nodes of node i at the Q closest training moments into the base prediction error matrix E at time t i,t (h), the expression is:

[0032]

[0033] Among them, e′ j (h) is the base prediction error of child node j at the Q closest training moments;

[0034] S2.3. E i,t Each column vector of (h) calculates the ranking of each element, and the calculation formula is:

[0035]

[0036] Among them, rank(·) is a sorting operation, which calculates the size order of each element among all elements in the vector; is the ranked matrix, describing the multivariate dependency structure between child nodes;

[0037] S2.4. Basis The initial aggregated probabilistic forecast matrix is rearranged and a multivariate dependency structure is introduced. The calculation formula is:

[0038]

[0039] in, is the rearranged matrix, perm(c,r) is the rearrangement operation, which rearranges the elements in vector c so that the order of the rearranged elements is the same as that of vector r;

[0040] Z i,t Each row of (h) is considered as a sample of the multivariate variable consisting of the predictor variables of the child nodes under node i. By summing each row, we can get Q samples of the parent node predictor variable. Finally, we calculate the initial aggregate probability distribution of the parent node at the quantile level {τ1,τ2,...,τ Q} and used as the initial aggregated probability forecast c for the node i,t (h);

[0041] S2.5. Based on steps S2.1 to S2.4, aggregate from the bottom nodes upward layer by layer to finally obtain the initial aggregated probabilistic forecasts of all nodes.

[0042] Furthermore, the specific implementation method of step S3 includes the following steps:

[0043] S3.1. Calculate the difference vector between the initial aggregated probabilistic forecast of node i and the probabilistic base forecast using the following formula:

[0044] d i,t (h) = c i,t (h)-b i,t (h)

[0045] Among them, d i,t (h)∈R Q is the difference vector of node i;

[0046] S3.2. Combine the difference vector calculated in step S3.1 with the probabilistic basis prediction of the underlying node to form the basis prediction vector D t (h), we get:

[0047] D t (h)=(d 1,t (h),...,d n-m,t (h),b n-m+1,t (h),...,b n,t (h))∈R Q×n ;

[0048] S3.3. Use the harmonic matrix to transform D t (h) is converted into the probabilistic forecast of the bottom node correction, and the expression is:

[0049] L t =PD t (h) T

[0050] Among them, L tT =(q n-m+1,t (h),...,q n,t (h))∈R Q×m is the modified probabilistic forecast of the bottom node, Represents the bottom node k at the quantile level {τ1,τ2,…,τ Q}; P∈R m×n is the reconciliation matrix to be optimized, which is used to convert the aggregated inconsistency information of a certain quantile level into the modified quantile forecast of all underlying nodes at that quantile level.

[0051] Furthermore, the optimization method of the harmonic matrix in step S3.3 is to use matrix decomposition to construct a small-scale matrix to approximate P, which is expressed as:

[0052] P=[P1 P2]≈[WVW T P2]

[0053] Where P1∈R m×m It is the matrix composed of the elements on the left side of P, P2∈R m×(n-m) It is the matrix composed of the right part of P;

[0054] Since the number of bottom-level nodes is much larger than the number of upper-level nodes, that is, m>>nm, the number of weight parameters of P1 is much larger than that of P2, and W∈R m×v With V∈R v×v The product of WVW T Approximate P1, where v < < m, and optimize P by minimizing the quantile loss function, which is expressed as:

[0055]

[0056] Among them, Loss is the value of the quantile loss function, f(·) is the Huber quantile loss, The level of the score generated by node i at time s for time s+h is τ k quantile of ;

[0057] The Huber quantile loss is expressed as:

[0058]

[0059]

[0060] in, is a function with u as the independent variable, and λ is a value of 2 -8 The constant, τ k is the quantile level.

[0061] An electronic device includes a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the steps of a hierarchical coordination prediction method applied to photovoltaic power under a probabilistic framework are implemented.

[0062] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements a hierarchical coordination prediction method for photovoltaic power under a probabilistic framework.

[0063] Beneficial effects of the present invention:

[0064] The present invention describes a hierarchical harmonic prediction method for photovoltaic power under a probabilistic framework, and the harmonic prediction method involved mainly includes a base prediction vector based on distribution difference, a harmonic matrix based on matrix decomposition technology, and a sample-reordering bottom-up aggregation (SRBU) technology. The base prediction vector based on distribution difference can fully contain the aggregated inconsistency information of the probabilistic base prediction to generate a higher quality corrected probabilistic forecast. The harmonic matrix based on matrix decomposition technology is used to map the base prediction vector into a corrected probabilistic forecast of the bottom node, which uses matrix decomposition technology to approximate a large-scale weight matrix, effectively reducing the number of weight parameters. The SRBU technology can utilize the dependency relationship between nodes at different levels to aggregate the probabilistic forecast of the bottom node into the probabilistic forecast of the upper node.

[0065] The present invention describes a hierarchical harmonic prediction method for photovoltaic power under a probabilistic framework. The base forecast vector based on distribution differences involved can fully contain the aggregated inconsistency information of the probabilistic base forecast to generate a higher-quality corrected probabilistic forecast; the harmonic moment based on matrix decomposition technology uses matrix decomposition technology to approximate large-scale weight matrices, effectively reducing the number of weight parameters; SRBU combines with the nearest neighbor algorithm to accurately characterize the dependency relationship between nodes at different levels, thereby generating a higher-quality probabilistic forecast. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 This is a flowchart of a hierarchical harmonic prediction method for photovoltaic power under a probabilistic framework according to the present invention. DETAILED DESCRIPTION

[0067] In order to make the objectives, technical solutions, and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only intended to explain the present invention and are not intended to limit the present invention. That is, the specific embodiments described herein are only some embodiments of the present invention, not all embodiments. Generally, the components of the specific embodiments of the present invention described and illustrated in the drawings herein can be arranged and designed in various different configurations, and the present invention can also have other embodiments.

[0068] Therefore, the following detailed description of the specific embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention as claimed, but is merely representative of selected specific embodiments of the present invention. All other specific embodiments obtained by those skilled in the art based on the specific embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0069] In order to further understand the content, features and effects of the present invention, the following specific embodiments are given as examples, and the attached Figure 1 The detailed instructions are as follows:

[0070] Example 1:

[0071] A hierarchical coordinated prediction method for photovoltaic power in a probabilistic framework includes the following steps:

[0072] S1. Collect the photovoltaic power and base forecasts of nodes at each level of the power system corresponding to the same time resolution and prediction range, calculate the base forecast error of each node, and construct the base forecast error matrix;

[0073] Furthermore, the specific implementation method of step S1 includes the following steps:

[0074] S1.1. For each underlying node, use the ensemble numerical weather forecast as the ensemble forecast for the PV station, and then calculate the quantiles at different quantile levels to obtain the underlying node base forecast.

[0075] S1.2. For upper-level nodes, use statistical extrapolation to calculate the quantiles at different quantile levels to obtain the upper-level node base forecast;

[0076] S1.3. Based on the methods of steps S1.1 and S1.2, collect the base forecasts of the bottom-level nodes, the base forecasts of the upper-level nodes, and the corresponding measured PV power. Divide the total time into a training set, a validation set, and a test set according to a 60:20:20 ratio. Each sample includes the base forecast and the measured value of each node at each level at the same time.

[0077] S1.4. Assume that the number of bottom nodes is m and the total number of nodes is n, then the probabilistic base prediction mean of node i in the training set is recorded as The measured value of node i in the training set is recorded as y i =(y i,1+h ,y i,2+h ,...,y i,N+h ) T , where N is the total time of the training set, is the mean of the predicted distribution generated by node i at time t for time t+h, y i,t is the measured value of node i at time t, and h is the interval time;

[0078] Then calculate the basic prediction error e of node i i (h), calculated as:

[0079]

[0080] Then combine the base prediction errors of all nodes into the base prediction error matrix E(h), and the expression is:

[0081] E(h)=(e1(h),e2(h),...,e n (h))∈R N×n .

[0082] Furthermore, the bottom layer node in step S1 is the bottom layer photovoltaic station, and the upper layer node includes the middle layer distribution network and the upper layer transmission network;

[0083] S2. Using the sample rearrangement and bottom-up aggregation technique, the base prediction error matrix obtained in step S1 is aggregated from the bottom nodes upward layer by layer, and the initial aggregated probabilistic forecasts for all nodes are finally obtained;

[0084] Furthermore, the specific implementation method of step S2 includes the following steps:

[0085] S2.1. For node i, set the time t to generate a forecast for time t+h, l is the length of the historical measured vector, then collect the historical measured vector x of node i i,t =(y i,t-l+1 ,...,y i,t ) T , the quantile level of node i is {τ1,τ2,...,τ Q}, where Q is the total number of quantile levels, and the probabilistic base prediction b of node i is i,t (h) is:

[0086]

[0087] Set the child nodes of node i to {j,j+1,...,j+n i -1}, where n iis the number of child nodes of node i, then the probabilistic basis predictions of the child nodes of node i are merged into the probabilistic basis prediction matrix B of the child nodes of node i i,t (h), we get:

[0088]

[0089] The initial aggregated probabilistic forecasts of the child nodes of node i are combined into the initial aggregated probabilistic forecast matrix C of the child nodes of node i i，t (h), we get:

[0090]

[0091] Among them, c j,t (h) is the initial aggregated probabilistic forecast of node i’s child node j;

[0092] Further, is the initial aggregation probability distribution of node j at the quantile level {τ1,τ2,...,τ Q}, and the initial aggregated probabilistic forecast of the bottom node is equal to its probabilistic base forecast.

[0093] S2.2. Concatenate the historical measured vectors of all nodes in the same sample and use the nearest neighbor algorithm to match the concatenated vectors at each training moment in the training set to obtain the Q closest training moments.

[0094] The measured vectors of each node at time t are spliced together to obtain the spliced measured vector (x 1,t T ,x 2,t T ,...,x n,t T ) T , use the k-nearest neighbor algorithm to obtain the Q closest training moments closest to the spliced measured vector from the training set, and merge the base prediction deviations of the subordinate nodes of node i at the Q closest training moments into the base prediction error matrix E at time t i,t (h), the expression is:

[0095]

[0096] Among them, e′ j (h) is the base prediction error of child node j at the Q closest training moments;

[0097] S2.3. E i,t Each column vector of (h) calculates the ranking of each element, and the calculation formula is:

[0098]

[0099] Among them, rank(·) is a sorting operation, which calculates the size order of each element among all elements in the vector; is the ranked matrix, describing the multivariate dependency structure between child nodes;

[0100] Further, for example, rank((3.4,5.1,2.6,7.3) T )=(2,3,1,4) T , is the ranked matrix, describing the multivariate dependency structure between child nodes. i,t (h) only reflects the marginal distribution of the initial aggregate probability forecast of each child node, and does not include the forecast size dependence between nodes, so it is necessary to Rearrange it;

[0101] S2.4. Basis The initial aggregated probabilistic forecast matrix is rearranged and a multivariate dependency structure is introduced. The calculation formula is:

[0102]

[0103] in, is the rearranged matrix, perm(c,r) is the rearrangement operation, which rearranges the elements in vector c so that the order of the rearranged elements is the same as that of vector r;

[0104] Z i,t Each row of (h) is considered as a sample of the multivariate variable consisting of the predictor variables of the child nodes under node i. By summing each row, we can get Q samples of the parent node predictor variable. Finally, we calculate the initial aggregate probability distribution of the parent node at the quantile level {τ1,τ2,...,τ Q} and used as the initial aggregated probability forecast c for the node i,t (h);

[0105] Further, for example, perm((2.6,3.4,5.1,7.3) T ,(2,3,1,4) T )=(3.4,5.1,2.6,7.3) T ;

[0106] S2.5. Based on steps S2.1 to S2.4, aggregate the data from the bottom nodes upwards layer by layer to obtain the initial aggregated probabilistic forecasts for all nodes.

[0107] S3. Constructing a base forecast vector based on the initial aggregated probabilistic forecast and the probabilistic base forecast obtained in step S2, and then converting the base forecast vector into a probabilistic forecast of the underlying node using a harmonic matrix;

[0108] Furthermore, the specific implementation method of step S3 includes the following steps:

[0109] S3.1. Calculate the difference vector between the initial aggregated probabilistic forecast of node i and the probabilistic base forecast using the following formula:

[0110] d i,t (h) = c i,t (h)-b i,t (h)

[0111] Among them, d i,t (h)∈R Q is the difference vector of node i;

[0112] Furthermore, at this time, node i represents the upper node;

[0113] S3.2. Combine the difference vector calculated in step S3.1 with the probabilistic basis prediction of the underlying node to form the basis prediction vector D t (h), we get:

[0114] D t (h)=(d 1,t (h),...,d n-m,t (h),b n-m+1,t (h),...,b n,t (h))∈R Q×n ;

[0115] Furthermore, D t Each row of (h) not only contains the information of the probabilistic basis forecast of all nodes at a certain quantile level, but also reflects the aggregation inconsistency of the upper-level nodes;

[0116] S3.3. Use the harmonic matrix to transform D t (h) is converted into the probabilistic forecast of the bottom node correction, and the expression is:

[0117] L t =PD t (h) T

[0118] Among them, L t T =(q n-m+1,t (h),...,q n,t (h))∈R Q×m is the modified probabilistic forecast of the bottom node, Represents the bottom node k at the quantile level {τ1,τ2,…,τ Q}; P∈R m×nis the reconciliation matrix to be optimized, which is used to convert the aggregated inconsistency information of a certain quantile level into the modified quantile forecast of all underlying nodes at that quantile level.

[0119] Furthermore, the optimization method of the harmonic matrix in step S3.3 is to use matrix decomposition to construct a small-scale matrix to approximate P, which is expressed as:

[0120] P=[P1 P2]≈[WVW T P2]

[0121] Where P1∈R m×m It is the matrix composed of the elements on the left side of P, P2∈R m×(n-m) It is the matrix composed of the right part of P;

[0122] Since the number of bottom-level nodes is much larger than the number of upper-level nodes, that is, m>>nm, the number of weight parameters of P1 is much larger than that of P2, and W∈R m×v With V∈R v×v The product of WVW T Approximate P1, where v < < m, and optimize P by minimizing the quantile loss function, which is expressed as:

[0123]

[0124] Among them, Loss is the value of the quantile loss function, f(·) is the Huber quantile loss, The level of the score generated by node i at time s for time s+h is τ k quantile of ;

[0125] The Huber quantile loss is expressed as:

[0126]

[0127]

[0128] in, is a function with u as the independent variable, and λ is a value of 2 -8 The constant, τ k is the quantile level.

[0129] S4. The probabilistic forecasts of the bottom nodes obtained in step S3 are again aggregated layer by layer from bottom to top using the sample rearrangement and bottom-up aggregation technology to obtain probabilistic forecasts that meet the aggregation consistency for all nodes.

[0130] The data used in this embodiment comes from the Solar Power Data for Integration studies (SPDIS) dataset developed by the National Renewable Energy Laboratory (NREL). The dataset contains simulated solar power generation power for one year at thousands of different locations in the United States with a time resolution of 5 minutes. According to previous studies, the 5-minute simulated photovoltaic power of 318 regions in California is first averaged into hourly data as the bottom layer (L2) sequence. Subsequently, the k-nearest neighbor algorithm is used to divide these locations into five regions, and the corresponding bottom layer sequences are aggregated to form the first layer (L1) sequence. Finally, the five sequences of the first layer are aggregated to obtain a top layer (L0) sequence representing the overall photovoltaic power generation in California, thereby obtaining a hierarchical structure. Among them, the L1 layer sequence is connected to 27, 73, 101, 86 and 31 L2 sequences respectively. For each hierarchical node, a quantile random forest model is used, with the hourly photovoltaic power data of the past 7 days as the input of the model to generate a probabilistic base forecast of photovoltaic power per hour for the next day. The first 80% of the dataset in the first half of the year was used to optimize the weight parameters of the quantile random forest and the harmonic matrix, and the second 20% was used to determine the hyperparameters of the quantile random forest and the dimensions of the member matrix in the approximate harmonic matrix. The second half of the dataset was used as a test set to verify the effectiveness of the proposed forecasting method. The forecast performance was evaluated using the widely used continuous ranked probability score skill score (CRPS skill score):

[0131]

[0132]

[0133] Among them, CRPS ref CRPS for the reference model complete-historypersistence ensemble; is the predicted distribution of the i-th sample; z i is the corresponding observation value; the value of 1(·) is 1 when the condition in the brackets is met, and 0 otherwise.

[0134] The proposed method is denoted as NMDHPF. Furthermore, several comparative models are set up to verify the effectiveness of NMDHPF. BF-BU, BF-OLS, BF-WLS, BF-HLS, and BF-MinT respectively employ bottom-up, ordinary least squares, weighted least squares, hierarchical least squares, and minimum trace to deterministically harmonize the means of the probabilistic base forecasts. The probabilistic base forecasts at each node are then shifted so that their means are equal to the deterministic harmonization results. SRBU-BU, SRBU-OLS, SRBU-WLS, SRBU-HLS, and SRBU-MinT respectively employ bottom-up, ordinary least squares, weighted least squares, hierarchical least squares, and minimum trace to deterministically harmonize the means of the initial aggregated probabilistic forecasts. The initial aggregated probabilistic forecasts at each node are then shifted so that their means are equal to the deterministic harmonization results. BF represents the probabilistic base forecast, and SRBU represents the initial aggregated probabilistic forecast. The proposed harmonic matrix is not subjected to matrix decomposition approximation to obtain the comparison model NHPF. The effectiveness of the constructed harmonic matrix can be verified by comparing NMDHPF and NHPF. The basis prediction vector of the proposed prediction method is replaced with the basis prediction of all nodes at a certain quantile level, and the harmonic matrix is not subjected to matrix decomposition approximation to obtain the comparison model BF-NHPF. The effectiveness of the constructed basis prediction vector can be verified by comparing NHPF and BF-NHPF. The prediction performance of each model at different levels is shown in Table 1:

[0135] Table 1 CRPS skillscore of the model proposed in this embodiment and various hierarchical coordination prediction techniques on the test set

[0136]

[0137]

[0138] As can be seen from Table 1, first, through analysis, it can be found that the predictability of the proposed method is better than the comparative model based on deterministic harmony. Second, compared with the probabilistic base forecast BF, the probability prediction performance of the proposed method is significantly improved, which proves the effectiveness of the harmony. Third, compared with the initial aggregated probabilistic forecast SRBU, the forecast quality of the proposed method is higher, which proves the rationality of using distribution difference information to correct the base forecast. Fourth, the CRPS skill score of NHPF is higher than that of BF-NHPF, indicating that the constructed base forecast vector helps to improve the performance of the forecast; finally, compared with NHPF, the performance of the proposed model is higher, proving that the approximate harmonic matrix based on matrix decomposition does not reduce the quality of the forecast while reducing the number of weight parameters. This fully demonstrates the beneficial effects of the invention of this application.

[0139] It should be noted that relational terms such as "first" and "second" are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or apparatus. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of additional identical elements in the process, method, article, or apparatus comprising the element.

[0140] Although the present application has been described above with reference to specific embodiments, various modifications may be made thereto and components may be substituted with equivalents without departing from the scope of the present application. In particular, as long as there are no structural conflicts, the various features of the embodiments disclosed herein may be combined with each other in any manner, and the omission of an exhaustive description of these combinations in this specification is solely for the sake of space and resource conservation. Therefore, the present application is not limited to the specific embodiments disclosed herein, but includes all technical solutions within the scope of the claims.

Claims

1. A hierarchical harmonic prediction method for photovoltaic power in a probabilistic framework, characterized by: The steps include: S1. Collect the photovoltaic power and base forecasts of nodes at each level of the power system corresponding to the same time resolution and prediction range, calculate the base forecast error of each node, and construct the base forecast error matrix; S2. Using the sample rearrangement and bottom-up aggregation technique, the base prediction error matrix obtained in step S1 is aggregated from the bottom nodes upward layer by layer, and the initial aggregated probabilistic forecasts for all nodes are finally obtained; S3. Constructing a base forecast vector based on the initial aggregated probabilistic forecast and the probabilistic base forecast obtained in step S2, and then converting the base forecast vector into a probabilistic forecast of the underlying node using a harmonic matrix; The specific implementation method of step S3 includes the following steps: S3.

1. Calculate the difference vector between the initial aggregated probabilistic forecast of node i and the probabilistic base forecast using the following formula: d i,t (h)=c i,t (h)-b i,t (h) Among them, d i,t (h)∈R Q is the difference vector of node i; S3.

2. Combine the difference vector calculated in step S3.1 with the probabilistic basis prediction of the underlying node to form the basis prediction vector D t (h), we get: D t (h)=(d 1,t (h),...,d n-m,t (h),b n-m+1,t (h),...,b n,t (h))∈R Q×n ; S3.

3. Use the harmonic matrix to transform D t (h) is converted into the probabilistic forecast of the bottom node correction, and the expression is: L t =PD t (h) T Among them, L t T =(q n-m+1,t (h),...,q n,t (h))∈R Q×m is the modified probabilistic forecast of the bottom node, Represents the bottom node k at the quantile level {τ1,τ2,…,τ Q }; P∈R m×n is the reconciliation matrix to be optimized, which is used to convert the aggregated inconsistency information of a certain quantile level into the modified quantile forecast of all underlying nodes at that quantile level; The optimization method of the harmonic matrix in step S3.3 is to use matrix decomposition to construct a small-scale matrix to approximate P, which is expressed as: P=[P1 P2]≈[WVW T P2] Where P1∈R m×m It is the matrix composed of the elements on the left side of P, P2∈R m×(n-m) It is the matrix composed of the right part of P; Since the number of bottom-level nodes is much larger than the number of upper-level nodes, Therefore, the number of weight parameters of P1 is much larger than that of P2, and W∈R m×v With V∈R v×v The product of WVW T Approximate P1, where And optimize P by minimizing the quantile loss function, which is expressed as: Among them, Loss is the value of the quantile loss function, f(·) is the Huber quantile loss, The level of the score generated by node i at time s for time s+h is τ k Quantile, y i,s+h is the true value of node i at time s+h; The Huber quantile loss is expressed as: in, is a function with u as the independent variable, and λ is a value of 2 -8 The constant, τ k is the quantile level; S4. The probabilistic forecasts of the bottom nodes obtained in step S3 are again aggregated layer by layer from bottom to top using the sample rearrangement and bottom-up aggregation technology to obtain probabilistic forecasts that meet the aggregation consistency for all nodes.

2. The hierarchical harmonic prediction method for photovoltaic power in a probabilistic framework according to claim 1, characterized in that: The specific implementation method of step S1 includes the following steps: S1.

1. For each underlying node, use the ensemble numerical weather forecast as the ensemble forecast for the PV station, and then calculate the quantiles at different quantile levels to obtain the underlying node base forecast. S1.

2. For upper-level nodes, use statistical extrapolation to calculate the quantiles at different quantile levels to obtain the upper-level node base forecast; S1.

3. Based on the methods of steps S1.1 and S1.2, collect the base forecasts of the bottom-level nodes, the base forecasts of the upper-level nodes, and the corresponding measured PV power. Divide the total time into a training set, a validation set, and a test set according to a 60:20:20 ratio. Each sample includes the base forecast and the measured value of each node at each level at the same time. S1.

4. Assume that the number of bottom nodes is m and the total number of nodes is n, then the probabilistic base prediction mean of node i in the training set is recorded as The measured value of node i in the training set is recorded as y i =(y i,1+h ,y i,2+h ,...,y i,N+h ) T , where N is the total time of the training set, is the mean of the predicted distribution generated by node i at time t for time t+h, y i,t is the measured value of node i at time t, and h is the interval time; Then calculate the basic prediction error e of node i i (h), calculated as: Then combine the base prediction errors of all nodes into the base prediction error matrix E(h), and the expression is: E(h)=(e1(h),e2(h),...,e n (h))∈R N×n 。 3. The hierarchical harmonic prediction method for photovoltaic power under a probabilistic framework according to claim 2, characterized in that: The bottom-level nodes in step S1 are bottom-level photovoltaic stations, and the upper-level nodes include middle-level distribution networks and upper-level transmission networks.

4. The hierarchical harmonic prediction method for photovoltaic power under a probabilistic framework according to claim 3, characterized in that: The specific implementation method of step S2 includes the following steps: S2.

1. For node i, set the time t to generate a forecast for time t+h, l is the length of the historical measured vector, then collect the historical measured vector x of node i i,t =(y i,t-l+1 ,...,y i,t ) T , the quantile level of node i is {τ1,τ2,...,τ Q }, where Q is the number of quantile levels, and the probabilistic base prediction b of node i i,t (h) is: Set the child nodes of node i to {j,j+1,...,j+n i -1}, where n i is the number of child nodes of node i, then the probabilistic basis predictions of the child nodes of node i are merged into the probabilistic basis prediction matrix B of the child nodes of node i i,t (h), we get: The initial aggregated probabilistic forecasts of the child nodes of node i are combined into the initial aggregated probabilistic forecast matrix C of the child nodes of node i i,t (h), we get: Among them, c j,t (h) is the initial aggregated probabilistic forecast of node i’s child node j; S2.

2. Concatenate the historical measured vectors of all nodes in the same sample and use the nearest neighbor algorithm to match the concatenated vectors at each training moment in the training set to obtain the Q closest training moments. The measured vectors of each node at time t are spliced together to obtain the spliced measured vector (x 1,t T ,x 2,t T ,...,x n,t T ) T , use the k-nearest neighbor algorithm to obtain the Q closest training moments closest to the spliced measured vector from the training set, and merge the base prediction deviations of the subordinate nodes of node i at the Q closest training moments into the base prediction error matrix E at time t i,t (h), the expression is: Among them, e′ j (h) is the base prediction error of child node j at the Q closest training moments; S2.

3. E i,t Each column vector of (h) calculates the ranking of each element, and the calculation formula is: Among them, rank(·) is a sorting operation, which calculates the size order of each element among all elements in the vector; is the ranked matrix, describing the multivariate dependency structure between child nodes; S2.

4. Basis The initial aggregated probabilistic forecast matrix is rearranged and a multivariate dependency structure is introduced. The calculation formula is: in, is the rearranged matrix, perm(c,r) is the rearrangement operation, which rearranges the elements in vector c so that the order of the rearranged elements is the same as that of vector r; Z i,t Each row of (h) is considered as a sample of the multivariate variable consisting of the predictor variables of the child nodes under node i. By summing each row, we can get Q samples of the parent node predictor variable. Finally, we calculate the initial aggregate probability distribution of the parent node at the quantile level {τ1,τ2,...,τ Q } and used as the initial aggregated probability forecast c for the node i,t (h); S2.

5. Based on steps S2.1 to S2.4, aggregate from the bottom nodes upward layer by layer to finally obtain the initial aggregated probabilistic forecasts of all nodes.

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