Hierarchical Coordination Prediction Method for Photovoltaic Power under Probabilistic Framework

Abstract

Hierarchical Coordination Prediction Method for Photovoltaic Power under Probabilistic Framework, which solves the problem of how to generate a high-quality and aggregated consistent photovoltaic power prediction distribution in the multi-level structure of the power system, belongs to the field of photovoltaic power generation technology. The present invention includes: S1. Generating a basic photovoltaic prediction power matrix χ for each level of the power system and including a prediction range h; S2. According to χ, calculating the basic photovoltaic prediction power error for one step forward and forming a basic photovoltaic prediction power error matrix, and using the block bootstrap method to draw J error block matrices ε<supgt;(j)< / supgt; from the basic photovoltaic prediction power error matrix with replacement, and superimposing them into χ to obtain a matrix χ<supgt;(j)< / supgt>; S3. Extracting the h-th column vector in each matrix χ<supgt;(j)< / supgt>, and arranging all the extracted column vectors into H new basic photovoltaic prediction power matrices of m×J order, and obtaining the harmonic photovoltaic prediction power sequences for each level of the power system according to the new basic photovoltaic prediction power matrices

Description

Technical Field

[0001] The present invention relates to a hierarchical coordinated prediction method for photovoltaic power under a probabilistic framework, belonging to the technical field of photovoltaic power generation. Background Art

[0002] Photovoltaic power prediction can be either deterministic or probabilistic. The former provides a single-point estimate of the photovoltaic power at a future time, while the latter provides the prediction distribution of most or even all of the photovoltaic power through prediction intervals or quantiles. Obviously, probabilistic prediction can carry more information than deterministic prediction. In fact, once the probability distribution is estimated, the predictor can also summarize it according to the statistical function corresponding to the scoring function to obtain a single-point photovoltaic power prediction value that is better than using only deterministic prediction. However, the benefits of probabilistic prediction have not been recognized by all scholars in the field of photovoltaic prediction, that is, probabilistic photovoltaic prediction has not been widely practiced in this field. When looking at its application in the power system, it is not difficult to find that probabilistic photovoltaic prediction can also inform the system operator of the probability of the event that the photovoltaic grid-connected power is within a certain interval. Based on this, the system operator can balance risks and costs and avoid adopting a scheduling scheme that is too conservative and thus incurs unaffordable costs. From these two aspects, probabilistic photovoltaic prediction is undoubtedly a technology worthy of promotion and even becomes the standard or specification of this industry.

[0003] The injection of photovoltaic power into the power grid can be modeled as a multi-level structure. At this time, the total photovoltaic power injection at the higher level of the power system can be obtained by summing up the photovoltaic power injections at the lower levels divided by different characteristics such as regions or nodes. However, this property does not apply to the predicted photovoltaic power. Specifically, assume that the predicted value of photovoltaic power for a certain region in the next hour is required. At this time, there are two strategies to choose from. First, this value can be directly predicted based on the historical photovoltaic output time series of this region. On the other hand, it can also be simply obtained by directly summing up the predicted photovoltaic powers submitted by all photovoltaic power plants in this region. Considering that the available information sets and prediction models are not the same, these two predictions are not equal in most cases. This phenomenon is called "aggregation inconsistency" in hierarchical forecasting. To solve this problem, some scholars have used the hierarchical reconciliation forecast method to achieve the aggregation consistency of different time series and have applied it to photovoltaic power. Generally speaking, the predicted values before and after using the hierarchical reconciliation forecast method are commonly known as the base PV forecast power and the reconciled PV forecast power, respectively. At this time, the hierarchical reconciliation forecast method can also be regarded as a post-processing technology that combines and modifies the base PV forecast powers at different levels, so that the final prediction, that is, the reconciled PV forecast power, is aggregation-consistent. It is worth pointing out that the aggregation-consistent photovoltaic predictions at different levels can help the collaborative decision-making of power system operation management, and can fully capture the spatio-temporal relationships of different time series, thereby improving the individual and overall prediction performance. From this point of view, when the base PV forecast powers at different levels of the power system are obtained, it is necessary to apply the hierarchical reconciliation forecast method to generate the aggregation-consistent reconciled PV forecast power to improve the overall efficiency of the system.

[0004] As can be seen from the above, probabilistic forecasting and hierarchical reconciliation forecast methods are new research directions pursued by relevant scholars in the solar energy field in recent years, let alone the combination of the two, that is, the probabilistic forecast reconciliation method. According to whether the type of the predicted distribution is assumed in advance, the probabilistic forecast reconciliation method can be divided into parametric and non-parametric types. Generally, the actual probability distribution does not strictly conform to a certain type of classical probability distribution. At this time, the non-parametric probabilistic forecast reconciliation that is not restricted by these assumptions should be the first choice of forecasters. However, it should be noted that the aggregation consistency in the probabilistic framework means that the predicted distribution of each aggregated time series is equal to the convolution of the predicted distributions of the corresponding disaggregated time series.

[0005] In this context, there is a need for a probabilistic prediction coordination method in a non-parametric framework that can describe the uncertainty of photovoltaic power prediction and achieve the aggregation and consistency of photovoltaic power predictions for different time series of power systems, thereby improving the performance of photovoltaic power prediction. Summary of the Invention

[0006] Aiming at the problem of how to generate a high-quality and aggregated and consistent photovoltaic power prediction distribution in the multi-level structure of a power system, the present invention provides a hierarchical coordinated prediction method for photovoltaic power under a probabilistic framework.

[0007] A hierarchical coordinated prediction method for photovoltaic power under a probabilistic framework of the present invention includes:

[0008] S1. Generate a basic photovoltaic power prediction matrix for each level of the power system and including a prediction range h The prediction range h ∈ {1,..., H}, where H represents the maximum prediction range, m represents the number of all basic photovoltaic power prediction time series in the matrix;

[0009] S2. According to the basic photovoltaic power prediction matrix Calculate the basic photovoltaic power prediction error for one step forward and form a basic photovoltaic power prediction error matrix. Use the block bootstrap method to draw J error block matrices ε (j) , j ∈ {1,…, J}, with replacement from the basic photovoltaic power prediction error matrix, and superimpose the J error block matrices ε (j) onto the basic photovoltaic power prediction matrix to obtain a matrix

[0010] S3. Extract the h-th column vector in each matrix , and rearrange all the extracted column vectors into a new basic photovoltaic power prediction matrix of order m×J A total of new basic photovoltaic power prediction matrices are obtained: Obtain the harmonic photovoltaic power prediction for each level of the power system according to the new basic photovoltaic power prediction matrix

[0011] Preferably, the harmonic photovoltaic power prediction for each level of the power system is:

[0012]

[0013] where S is a summation matrix of order m×m b , m b is the number of the lowest-level photovoltaic measurement power time series, m = 1 + m 1 +···+m b , 1, m1 …m b are the numbers of the photovoltaic measurement power time series contained in the l-th level, l-th level, …, and the bottommost l-th level of the B-level hierarchy of the power system from top to bottom with decreasing aggregation degree; in the summation matrix, a certain row of the summation matrix corresponding to a certain photovoltaic measurement power time series contains the i-th photovoltaic measurement power time series at the bottommost level, and the i-th value in this row is 1, otherwise it is 0, where i = 1, …, m 0 -th level, l 1 -th level ··· and the bottommost l b -th level; and P is the optimal coordination matrix. b ,P is the optimal coordination matrix.

[0014] Preferably, the method for obtaining the optimal coordination matrix includes:

[0015] Obtain the photovoltaic measurement power time series Y corresponding to the same time resolution and prediction range for the participants at each level of the power system t+h and the basic photovoltaic prediction power time series

[0016] According to the obtained photovoltaic measurement power time series Y t+h and the basic photovoltaic prediction power time series calculate the optimal coordination matrix P, and the optimal coordination matrix P minimizes the sum of variances of the harmonic photovoltaic prediction power errors for all power time series h steps forward.

[0017] And five methods for calculating the optimal coordination matrix P are given. The first method, the optimal coordination matrix P is:

[0018] P = P OLS =(S T S) -1 S T .

[0019] The second method, the optimal coordination matrix P is:

[0020]

[0021] where is a diagonal matrix composed of the in-sample variance estimates of the basic photovoltaic prediction power errors for all power time series one step forward at each level.

[0022] The third method, the optimal coordination matrix P is:

[0023] P = P HLS =(S T Λ -1 S) -1 S T Λ -1 ,

[0024] where wherein is a column vector with a length of m b and all elements being 1.

[0025] For the fourth method, the optimal coordination matrix P is:

[0026]

[0027] wherein,

[0028] is the estimated value of the in - sample covariance matrix of the one - step - ahead basic PV prediction power errors of all power time series at each level, and λ D is the shrinkage intensity parameter; R 1 is the in - sample correlation matrix of the one - step - ahead basic PV prediction power of all power time series, is R 1 's element in the j - th row and k - th column.

[0029] For the fifth method, the optimal coordination matrix P is:

[0030]

[0031] In the formula, W h is the covariance matrix of the h - step - ahead basic PV prediction power errors of all power time series .

[0032] Preferably, the method of the present invention further includes:

[0033] S4. Calculate the standardized continuous ranked probability score nCRPS:

[0034]

[0035] wherein, x t is the harmonic PV prediction power value when using the S3 verification dataset t, y t is the PV measurement power value at the verification dataset t, n is the number of data of the harmonic PV prediction power value or the PV measurement power value in the verification dataset, is the mean value of the PV measurement power values in the verification dataset, represents the prediction distribution of x t , and 1(z - y t ) is the Heaviside step function translated to y t .

[0036] Preferably, S4 further includes: calculating the standardized root mean square error nRMSE:

[0037]

[0038] The beneficial effects of the present invention are as follows. After considering the uncertainty of photovoltaic power prediction, the present invention uses the predictive probability distribution in the non-parametric framework to describe this uncertainty, and can generate high-quality and aggregation-consistent photovoltaic power prediction distributions in the multi-level structure of the power system. In addition, this method can further summarize the prediction distribution with a statistical function consistent with the scoring function to obtain a more accurate deterministic photovoltaic prediction than only using the hierarchical prediction coordination method. The present invention has significant practical significance for improving the accuracy of photovoltaic prediction and facilitating the collaborative decision-making of the power system, and thus promoting the large-scale penetration of photovoltaic power in the power system. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 is a schematic flow chart of the method of the present invention;

[0040] Figure 2 is a simple schematic diagram of a power system including two substations and four photovoltaic power plants. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0041] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0042] It should be noted that, without conflict, the embodiments in the present invention and the features in the embodiments can be combined with each other.

[0043] Next, the present invention will be further described in conjunction with the accompanying drawings and specific embodiments, but it is not a limitation of the present invention.

[0044] The hierarchical coordinated prediction method of photovoltaic power under the probabilistic framework of this embodiment includes:

[0045] Step 1: Generate a basic photovoltaic prediction power matrix for each level of the power system and including the prediction range h

[0046] Specifically, first use different prediction models and training sample data including t hours ago and t hours to generate deterministic basic photovoltaic prediction powers for each time series in the multi-level structure for h steps forward (different h values correspond to different prediction ranges). For each prediction range h ∈ {1,..., H}, where H represents the maximum prediction range of interest, all photovoltaic prediction power time series arranged in a certain order can be combined into a column vector x with a length of m t+h, where m is the number of all basic photovoltaic predicted power time series in the matrix.

[0047] Next, combine H x t+h to form a matrix of dimension m×H as follows:

[0048]

[0049] Step 2: Calculate the basic photovoltaic predicted power error for 1 step forward based on the basic photovoltaic predicted power matrix and form a basic photovoltaic predicted power error matrix. Use the block bootstrap method to draw J error block matrices ε (j) , j ∈ {1, …, J}, with replacement from the basic photovoltaic predicted power error matrix, and stack the J error block matrices ε (j) onto the basic photovoltaic predicted power matrix to obtain the matrix

[0050] Specifically, based on the basic photovoltaic predicted power matrix first calculate the basic photovoltaic predicted power error for 1 step forward and form an m×t order matrix ε, that is:

[0051]

[0052] where e i = y i - x i , i ∈ {1, …, t} is an error column vector of length m calculated from the i-th historical photovoltaic measurement power column vector y i and the basic photovoltaic predicted power column vector x i .

[0053] Next, use the block bootstrap method to randomly select J sub-matrices of order m×H with continuous data in each row from ε with replacement, that is, this process needs to be repeated J times in total. The m×H order sub-matrix for the j-th time is denoted as ε (j) , j ∈ {1, …, J}. It should be noted that when obtaining the hourly day-ahead photovoltaic predicted power, the bootstrap method should only consider data blocks containing a complete time period within a day. That is, the time corresponding to each ε (j) should start from 00:00 and end at 23:00. For intraday prediction, data at night is often removed during the data preprocessing stage, and the start time of each ε (j) is not important.

[0054] Finally, stack each error block matrix ε (j) onto the basic photovoltaic predicted power matrix to obtain:

[0055]

[0056] At this time, each row of represents H bootstrapped predictions of the time series corresponding to that row. For example, the first row of represents H bootstrapped predictions of the l 0 -level time series.

[0057] Step 3. Extract the h-th column vector from each matrix and rearrange all the extracted column vectors into a new basic photovoltaic predicted power matrix of order m×J Because has H columns, the following new basic photovoltaic predicted power matrix is obtained: Obtain the harmonic photovoltaic predicted power of each level of the power system according to the new basic photovoltaic predicted power matrix Furthermore, the distribution of the harmonic photovoltaic predicted power can be summarized according to a statistical function consistent with the evaluation function to obtain a deterministic harmonic photovoltaic predicted power column vector.

[0058] The present invention is applied to samples extracted from an aggregated inconsistent basic photovoltaic predicted power distribution, so as to ensure that the generated new samples have an aggregated consistent prediction distribution. In addition, the method can obtain a definite point prediction by using a suitable statistical function based on an aggregated consistent prediction distribution.

[0059] In the preferred embodiment, obtain the harmonic photovoltaic predicted power of each level of the power system according to the new basic photovoltaic predicted power matrix

[0060]

[0061] where P is the optimal coordination matrix and S is an m×m b order summing matrix;

[0062] In hierarchical coordinated prediction, a summing matrix (S) with elements of 0 or 1 can be used to characterize the hierarchical structure of the system. Generally, the levels of the hierarchical structure are numbered from 0 from top to bottom until the bottom layer, which means that the l 0 -level has the highest degree of aggregation, and the bottom layer l b -level has the highest degree of dispersion, where b is the total number of levels of the hierarchical structure. S is an m×m b order summing matrix, m b is the number of photovoltaic measurement power time series at the bottom layer, m = 1 + m 1 + ··· + m b , 1, m 1 …m bThey are the numbers of the photovoltaic measurement power time series contained in level l, level l, ···, and the bottommost level l of the B-level hierarchical structure of the power system from top to bottom with decreasing aggregation degree; in the summation matrix, a certain photovoltaic measurement power time series corresponds to a certain row of the summation matrix. When the bottommost i-th photovoltaic measurement power time series is included, the i-th value in this row is 1, otherwise it is 0, where i = 1, ···, m 0 level, level 1 ··· and the number of photovoltaic measurement power time series contained in the bottommost level b level; in the summation matrix, a certain photovoltaic measurement power time series corresponds to a certain row of the summation matrix. When the bottommost i-th photovoltaic measurement power time series is included, the i-th value in this row is 1, otherwise it is 0, where i = 1, ···, m b . As Figure 2 shown, the summation matrix of this simplified power system

[0063] It should be noted that each column of is a sample of the joint prediction distribution of all power time series in the hierarchical structure, and each row contains J bootstrap predictions that can characterize the marginal prediction distribution of the time series corresponding to that row

[0064] The optimal coordination matrix P of the calculation hierarchical coordination prediction method in this embodiment is obtained by appropriately simplifying the ordinary least squares (OLS) method, weighted least squares (WLS) method, hierarchical least squares (HLS) method, and minimum trace–shrinkage (MinT–shrink) method based on the minimum trace (MinT) method. For the four corresponding coordination techniques, the optimal coordination matrices can be denoted as P OLS , P WLS , P HLS and P MinT-shrink .

[0065] The objective function of the MinT method is to minimize the sum of the variances of the harmonic photovoltaic prediction power errors of all power time series h steps forward, as follows:

[0066]

[0067] In the formula, is the harmonic photovoltaic prediction power error of all power time series h steps forward at time t, Y t+h is the photovoltaic measurement power of all power time series at time t + h, is the harmonic photovoltaic prediction power of all power time series at time t, is the covariance matrix operator

[0068] The optimal coordination matrix P that satisfies Equation (2) is given by the following formula:

[0069]

[0070] where W h is the covariance matrix of the base PV prediction power errors for all power time series h steps ahead, and the base PV prediction power error is defined as where where is the base PV prediction power for all power time series h steps ahead at time t.

[0071] Due to the complexity of error propagation, it is also very challenging to obtain the base PV prediction power error h steps ahead. Therefore, this invention patent considers four simplified optimal coordination matrices.

[0072] 1. The ordinary least squares (OLS) method assumes that W h = I m where I m is an m×m identity matrix, and the optimal coordination matrix P is:

[0073] P = P OLS = (S T S) -1 S T .

[0074] A major drawback of the OLS method is that when the bottom - level objects have incomparable scales, such as different installed capacities of PV power plants, the hierarchical coordinated prediction based on OLS usually produces very poor PV prediction power.

[0075] 2. The weighted least squares (WLS) method considers where is a diagonal matrix composed of the in - sample variance estimates of the base PV prediction power errors for all power time series 1 step ahead at each level, and the optimal coordination matrix P is:

[0076]

[0077] Compared with the OLS method, the WLS method can, to a certain extent, reduce the impact of incomparable scales of the bottom - level objects.

[0078] 3. The hierarchical least squares (HLS) method only uses the weights based on the hierarchical structure, that is, it assumes where is a column vector of length m b with all elements equal to 1. At this time, the optimal coordination matrix P is:

[0079] P = P HLS = (S T Λ -1 S) -1 S T Λ -1 。

[0080] Mathematically, the product of S and gives an integer vector, and the elements of this vector characterize the number of the bottom-layer photovoltaic measurement power time series aggregated to a specific node, that is, a certain row of the corresponding summation matrix. Compared with the OLS method, the advantage of the HLS method is that it only assumes that the base photovoltaic prediction power errors at the same level are consistent, rather than unrealistically assuming that the base photovoltaic prediction power errors at different levels are all consistent. Of course, it has the same shortcoming as the OLS method, that is, it performs poorly on the bottom-layer time series with different scales.

[0081] 4. The minimum trace–shrinkage (MinT–shrink) method requires where is the in-sample covariance matrix estimate of the one-step-ahead base photovoltaic prediction power errors of all power time series at each level, and λ D is the shrinkage intensity parameter. At this time, the optimal coordination matrix P is:

[0082]

[0083] In the preferred embodiment, according to experience, λ D can be obtained from the in-sample correlation matrix R 1 of the one-step-ahead base photovoltaic prediction power of all power time series, as follows:

[0084]

[0085] where is the element in the j-th row and k-th column of R 1 . Compared with the previous three simplified forms, the MinT–shrink method is the closest approximation to the MinT method.

[0086] In the preferred implementation manner, evaluation indexes are defined to evaluate the distribution performance of the harmonized photovoltaic prediction power.

[0087] Specifically, to evaluate the effects of different probabilistic prediction coordination techniques, this embodiment considers the accuracy metric of the normalized continuous ranked probability score (nCRPS). The nCRPS can give a comprehensive score of the calibration and sharpness of the prediction distribution to be evaluated, and its averaged version is defined as follows:

[0088]

[0089] In the formula, x t is the harmonic photovoltaic prediction power value when verifying the dataset t using step 3, y t is the photovoltaic measured power value at the verification dataset t, n is the number of data of the harmonic photovoltaic prediction power value or the photovoltaic measured power value in the verification dataset, is the mean value of the photovoltaic measured power values in the verification dataset, represents the prediction distribution of x t , and 1(z - y t ) is the Heaviside step function translated to y t .

[0090] Next, summarize the distribution of the harmonic photovoltaic prediction power according to a statistical function consistent with the evaluation function, that is, map each row of data that can characterize the prediction distribution to a specific number according to a statistical function, such as the mean value function, to obtain a deterministic photovoltaic prediction column vector of dimension m.

[0091] Finally, to measure the accuracy of the deterministic photovoltaic prediction, the normalized root mean square error (nRMSE) is defined as follows:

[0092]

[0093] It should be noted that the smaller the values of the two metrics, namely nCRPS and nRMSE, the better the photovoltaic prediction performance.

[0094] The data used in this embodiment comes from a part of the Solar Power Data for Integration studies (SPDIS) simulated by the National Renewable Energy Laboratory (NREL) in the United States to study the impact of large-scale wind and solar power grid connection on the power system. Specifically, the data in this embodiment only includes the 5-minute measurement power and hourly prediction power of 405 photovoltaic power plants with different installed capacities in California in 2006. Considering that there are a total of 36 high-voltage substations with an AC voltage of 345 kV or 500 kV in California, connecting the 405 photovoltaic power plants to the nearest substation respectively can obtain a two-level hierarchy. Among them, l 1 The number of time series at level 1 is 34 - there are no photovoltaic power plants near two substations, l 2 The number of time series at level 2 is 405. According to the aforementioned variable definitions, the number of rows of the summation matrix is m = 440, and the number of columns is m b = 405.

[0095] Furthermore, the 5-minute measurement power of the 405 photovoltaic power plants is aggregated into an hourly time series to match the photovoltaic prediction power in terms of time resolution. Then, the bottom-up (BU) method is used to accumulate the underlying photovoltaic measurement power time series in sequence according to the hierarchy to obtain 1 l 0 -level and 34 l 1 -level photovoltaic measurement power time series. As for the l 0 -level and l 1 -level basic photovoltaic prediction power, the autoregressive integrated moving average with Fourier terms (AFT) can be used to obtain it in the form of rolling prediction, because this model can effectively capture the periodicity of photovoltaic power. In addition, when applying the hierarchical coordinated prediction method to calculate the optimal coordination matrix in different simplified forms, the first half of the annual dataset (except for the 1st - 7th of January) is used to train the model, and the second half is used as the test dataset.

[0096] To respond to the day-ahead setting of this embodiment, steps 2 and 3 are repeated for each day of the test dataset, and the maximum prediction range (H) is taken as 24. For the 179 days (from January 8th to July 5th) of the training dataset, the number of columns of the in-sample basic photovoltaic prediction power error matrix (ε) is 4296. When using the block bootstrap method to extract the error block matrix (ε (j)) When it was repeated a total of 99 times, that is, J = 99. Finally, it should be pointed out that in addition to the OLS method, WLS method, HLS method, and MinT–shrink method, this implementation also considered the AFT model and the BU method and used them as benchmarks.

[0097] To test whether using the probabilistic prediction coordination method can obtain better deterministic predictions, this embodiment summarizes the corresponding harmonic probabilistic predictions according to the mean function consistent with the evaluation function nRMSE, l 1 The results at level l are shown in Table 1 (because the number of time series at level l is too large, it is not given here). In addition, Table 1 also lists the evaluation results of only using the hierarchical prediction coordination method. It can be seen from Table 1 that compared with the harmonic deterministic prediction extracted from the prediction distribution and the harmonic deterministic prediction of only using the hierarchical coordination prediction method, the value of nRMSE is slightly different, but the former usually has better performance. Especially for the BU coordination method, the improvement in prediction accuracy is quite remarkable, that is, the average value of nRMSE is reduced from 30.5% to 28.0%. This must be attributed to the fact that the probabilistic prediction coordination method generates l 2 the ensemble forecast at level l and can carry more information. Comparing various coordination techniques, the MinT–shrink method comes out on top; its average value of nRMSE is also reduced from the original 22.8% to the current 22.3%. After evaluating the performance of the harmonic deterministic prediction, the harmonic probabilistic prediction verification will be carried out for l 2 level (similarly, due to space reasons, the results at level l are not given here). Table 2 lists the nCRPS values of the harmonic probabilistic predictions at level l after adopting five different hierarchical coordination prediction techniques and the AFT model. As in the previous conclusion, Table 2 once again confirms that the MinT–shrink method can achieve the best overall performance, while the WLS method and the HLS method also show satisfactory results. At the same time, it can be found that the average value of nCRPS of the AFT model is much higher than the average value of nCRPS of other hierarchical coordination prediction techniques, because the AFT model makes an inappropriate assumption of the Gaussian prediction distribution when generating the ensemble forecast. Based on the above discussion, the prediction coordination under the probabilistic framework is more significant in performance than the prediction coordination under the deterministic framework, which fully demonstrates the beneficial effects of the invention of this application. 1 level (similarly, due to space reasons, the results at level l are not given here). Table 2 lists the nCRPS values of the harmonic probabilistic predictions at level l after adopting five different hierarchical coordination prediction techniques and the AFT model. As in the previous conclusion, Table 2 once again confirms that the MinT–shrink method can achieve the best overall performance, while the WLS method and the HLS method also show satisfactory results. At the same time, it can be found that the average value of nCRPS of the AFT model is much higher than the average value of nCRPS of other hierarchical coordination prediction techniques, because the AFT model makes an inappropriate assumption of the Gaussian prediction distribution when generating the ensemble forecast. Based on the above discussion, the prediction coordination under the probabilistic framework is more significant in performance than the prediction coordination under the deterministic framework, which fully demonstrates the beneficial effects of the invention of this application. 2 level. The results at level l are not given here). Table 2 lists the nCRPS values of the harmonic probabilistic predictions at level l after adopting five different hierarchical coordination prediction techniques and the AFT model. As in the previous conclusion, Table 2 once again confirms that the MinT–shrink method can achieve the best overall performance, while the WLS method and the HLS method also show satisfactory results. At the same time, it can be found that the average value of nCRPS of the AFT model is much higher than the average value of nCRPS of other hierarchical coordination prediction techniques, because the AFT model makes an inappropriate assumption of the Gaussian prediction distribution when generating the ensemble forecast. Based on the above discussion, the prediction coordination under the probabilistic framework is more significant in performance than the prediction coordination under the deterministic framework, which fully demonstrates the beneficial effects of the invention of this application. 1 level. The results at level l are not given here). Table 2 lists the nCRPS values of the harmonic probabilistic predictions at level l after adopting five different hierarchical coordination prediction techniques and the AFT model. As in the previous conclusion, Table 2 once again confirms that the MinT–shrink method can achieve the best overall performance, while the WLS method and the HLS method also show satisfactory results. At the same time, it can be found that the average value of nCRPS of the AFT model is much higher than the average value of nCRPS of other hierarchical coordination prediction techniques, because the AFT model makes an inappropriate assumption of the Gaussian prediction distribution when generating the ensemble forecast. Based on the above discussion, the prediction coordination under the probabilistic framework is more significant in performance than the prediction coordination under the deterministic framework, which fully demonstrates the beneficial effects of the invention of this application.

[0098] Table 1 The nRMSE values of the harmonic deterministic predictions at level l summarized from five groups of harmonic probability predictions in this embodiment and the nRMSE values of only using the hierarchical prediction coordination method (the latter values are in parentheses). 1 level. The results at level l are not given here). Table 2 lists the nCRPS values of the harmonic probabilistic predictions at level l after adopting five different hierarchical coordination prediction techniques and the AFT model. As in the previous conclusion, Table 2 once again confirms that the MinT–shrink method can achieve the best overall performance, while the WLS method and the HLS method also show satisfactory results. At the same time, it can be found that the average value of nCRPS of the AFT model is much higher than the average value of nCRPS of other hierarchical coordination prediction techniques, because the AFT model makes an inappropriate assumption of the Gaussian prediction distribution when generating the ensemble forecast. Based on the above discussion, the prediction coordination under the probabilistic framework is more significant in performance than the prediction coordination under the deterministic framework, which fully demonstrates the beneficial effects of the invention of this application.

[0099]

[0100]

[0101] Table 2 of this Example 1 1 nCRPS value of hierarchical harmonic probabilistic prediction

[0102]

[0103]

[0104]

[0105] Although the present invention has been described herein with reference to particular embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the invention. Accordingly, it should be understood that numerous modifications may be made to the exemplary embodiments, and other arrangements may be devised, without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that the different dependent claims and the features described herein may be combined in a manner different from that described in the original claims. It should also be understood that the features described in connection with separate embodiments may be used in other described embodiments.

Claims

1. Hierarchical Coordination Prediction Method for Photovoltaic Power under Probabilistic Framework Characterized in that The method includes S1. Generate a basic photovoltaic prediction power matrix for each level of the power system and including the prediction range h The prediction range h ∈ {1,..., H}, where H represents the maximum prediction range m represents the number of all basic photovoltaic prediction power time series in the matrix S2. According to the basic PV predicted power matrix Calculate the basic PV predicted power error for one-step ahead prediction, and form a basic PV predicted power error matrix. Use the block bootstrap method to draw J error block matrices ε (j) with replacement from the basic PV predicted power error matrix, where j ∈ {1, …, J}, and stack the J error block matrices ε (j) onto the basic PV predicted power matrix to obtain a matrix S3. Extract the h-th column vector from each matrix and rearrange all the extracted column vectors into a new basic PV predicted power matrix of order m×J A total of new basic PV predicted power matrices are obtained as follows: Obtain the harmonic PV predicted power of each level of the power system based on the new basic PV predicted power matrix The harmonic PV predicted power of each level of the power system is as follows: Among them, S is an m×m b order summation matrix, and m b is the number of photovoltaic measurement power time series at the bottom layer, and m = 1 + m 1 +…+m b , 1, m 1 …m b are respectively the number of photovoltaic measurement power time series at the l 0 th level, l 1 th level… and the bottom l b th level of the b-level hierarchical structure of the power system from high to low aggregation degree; in the summation matrix, a certain photovoltaic measurement power time series corresponds to a certain row of the summation matrix. When the row contains the i-th photovoltaic measurement power time series at the bottom layer, the i-th value of this row is 1, otherwise it is 0, where i = 1,…,m b , and P is the optimal coordination matrix; The method also includes S4. Calculate the standardized continuous ranked probability score nCRPS where x t is the harmonic PV predicted power value when using the S3 validation dataset t, y t is the PV measured power value at the validation dataset t, and n is the number of data of the harmonic PV predicted power value or the PV measured power value in the validation dataset, is the mean value of the PV measured power value in the validation dataset, represents the predictive distribution of x t , and 1(z - y t ) is the Heaviside step function translated to yt; The S4 also includes: Calculate the standardized root mean square error nRMSE 2. The hierarchical coordination prediction method for photovoltaic power under the probabilistic framework according to claim 1 Characterized in that The method for obtaining the optimal coordination matrix includes Obtain the photovoltaic measurement power time series Y of the participants at each level of the power system corresponding to the same time resolution and prediction range t+h and the basic photovoltaic prediction power time series According to the obtained photovoltaic measurement power time series Y t+h and the basic photovoltaic predicted power time series calculate the optimal coordination matrix P, and the optimal coordination matrix P minimizes the sum of variances of the power time series forward h steps and the photovoltaic prediction power error.

3. The hierarchical coordination prediction method for photovoltaic power under the probabilistic framework according to claim 2 Characterized in that The optimal coordination matrix P is P = P OLS = (S T S) -1 S T 。 4. The hierarchical coordination prediction method for photovoltaic power under the probabilistic framework according to claim 2 Characterized in that The optimal coordination matrix P is Among them, is a diagonal matrix composed of the in-sample variance estimates of the one-step-ahead basic PV prediction power errors of all power time series at each level.

5. The hierarchical coordination prediction method for photovoltaic power under the probabilistic framework according to claim 2 Characterized in that The optimal coordination matrix P is P = P HLS = (S T Λ -1 S) -1 S T Λ -1 , Among them, wherein is a column vector with a length of m b and all elements are 1.

6. The hierarchical coordination prediction method for photovoltaic power under the probabilistic framework according to claim 2 Characterized in that The optimal coordination matrix P is Among them, is the estimated value of the in-sample covariance matrix of the base PV forecast power errors for all power time series at each level, one step ahead, and λ D is the shrinkage intensity parameter; R 1 is the in-sample correlation matrix of the base PV forecast power for all power time series, one step ahead, is the 1 element in the j-th row and k-th column of R.

7. The hierarchical coordination prediction method for photovoltaic power under the probabilistic framework according to claim 2 Characterized in that The optimal coordination matrix P is Where, W h is the covariance matrix of the forward h-step base photovoltaic prediction power errors of all power time series ,

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