Multi-distance clustering and information aggregation based load interval prediction method, system and medium

Abstract

The application discloses a load interval prediction method and system based on multi-distance clustering and information aggregation, and a medium. The method comprises the following steps: clustering normalized load curve data by a K-means algorithm based on multi-distance to obtain a k-class curve set result; for the i-th result, the i-th result and corresponding meteorological data are divided into a training set and a test set; the training set and the test set are input into an intraday local fluctuation probability prediction model and an intraday overall trend probability prediction model respectively for training, and the characteristic values of the test sets of the two models are input respectively to obtain the upper and lower limits of the two model intervals under t quantiles; and the upper limit and the lower limit of the prediction intervals of the two models are respectively subjected to information aggregation, and the aggregated prediction interval is calculated by a Choquet integral aggregation function.

Description

Technical Field

[0001] This invention belongs to the technical field of power load forecasting, specifically relating to a load interval forecasting method, system, and medium based on multi-distance clustering and information aggregation. Background Technology

[0002] Load forecasting can be categorized into deterministic forecasting and probabilistic forecasting based on the different forecasting methods. Deterministic forecasting yields the expected value of the predicted object at a single point in the future, while probabilistic forecasting presents the predicted result for future times in the form of a probability distribution or confidence interval, effectively enabling the quantitative analysis of forecast uncertainty. Compared to deterministic forecasting, probabilistic forecasting can provide the power system with richer and more accurate uncertainty information.

[0003] Luo Fengzhang, Zhang Xu, Yang Xin, et al. Load analysis and prediction of integrated energy distribution system based on deep learning [J]. High Voltage Engineering, 2021, 47(01): 23-32. A load prediction model based on convolutional neural network and support vector regression was constructed. The convolutional neural network was used to extract the implicit features of the data, and relatively accurate prediction results were obtained. Li Dan, Zhang Yuanhang, Yang Baohua, et al. Short-term power load probability prediction method based on constrained parallel LSTM quantile regression [J]. Power System Technology, 2021, 45(04): 1356-1364. A quantile regression prediction method based on constrained parallel long short-term memory (LSTM) neural network was proposed. It combines LSTM with quantiles and considers the constraint relationship between quantile prediction values, and obtains better probability prediction results. Zhang Shuqing, Li Jun, Jiang Anqi, et al. A novel two-stage short-term power load forecasting method based on FPA-VMD and BiLSTM neural network [J]. Power System Technology, 2022, 46(08): 3269-3279. A two-stage load forecasting method is proposed by combining optimized variational mode decomposition and bidirectional long short-term memory neural network (BiLSTM). This method utilizes the advantage of BiLSTM network in mining the temporal features of data, and its effectiveness is verified by numerical examples. Huang Nantian, Liu Debao, Cai Guowei, et al. Electric vehicle charging load interval forecasting based on multi-correlation daily scene generation [J]. Proceedings of the CSEE, 2021, 41(23): 7980-7990. A scene generation method is introduced before forecasting to enrich the scene feature expression, thereby further improving the accuracy of the forecasting model. Xiao Bai, Nie Peng, Mu Gang, et al. Spatial load forecasting method based on multi-level clustering analysis and support vector machine [J]. Automation of Electric Power Systems, 2015, 39(12): 56-61.] proposed a load forecasting method based on multi-level clustering and support vector machine, which performs multi-level clustering of cell load according to each attribute, and obtains more accurate forecasting results.

[0004] However, since the variation patterns of daily load curves are not uniform, the above-mentioned literature will lead to problems such as unsatisfactory model training and low accuracy of prediction results if the model is only used to learn the variation patterns of all load curves. Summary of the Invention

[0005] The main objective of this invention is to overcome the shortcomings and deficiencies of the prior art and to provide a method, system and medium for predicting load intervals using multi-distance clustering and information aggregation.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] One aspect of the present invention provides a load interval prediction method based on multi-distance clustering and information aggregation, comprising the following steps:

[0008] The normalized load curve data is clustered using the K-means algorithm based on multiple distances to obtain a set of k types of curves.

[0009] For the i-th type of result, it is divided into a training set and a test set along with the corresponding meteorological data;

[0010] The training set and the test set are respectively input into the intraday local fluctuation probability prediction model and the intraday overall trend probability prediction model for training, and the parameters are updated to obtain the intraday local fluctuation probability prediction model and the intraday overall trend probability prediction model.

[0011] Input the feature values ​​of the test set of the two models respectively to obtain the upper and lower limits of the interval of the two models under the t quantile;

[0012] The upper and lower limits of the prediction intervals of the two models are aggregated separately, and the aggregated prediction interval is calculated using the Choquet integral aggregation function.

[0013] As a preferred technical solution, the K-means algorithm based on multiple distances specifically includes:

[0014] (1) Input the dataset S of iso-length curve samples to be clustered, S = {s1, s2, ..., s3} i s h}, where s i This is the sample of the i-th curve;

[0015] (2) Randomly select k different samples in S as the initial cluster centers of K-means;

[0016] (3) Traverse all samples and calculate the distance D between the i-th sample and all cluster centers using the following formula. total (X, Y), and classify it into the class with the smallest distance to the sample;

[0017] Dtotal (X, Y)=r1D1(X,Y)+r2 D2(X,Y)+r3 D3(X,Y)

[0018] Where D1(X,Y) is the distance between corresponding sampling points of two samples calculated using Euclidean distance, D2(X,Y) is the distance between corresponding sampling points of two samples calculated using DTW distance, and D3(X,Y) is the distance between corresponding sampling points of two samples calculated by first using the antecedent difference method and then calculating the DTW distance.

[0019] r1, r2 and r3 are the weights corresponding to the three distances, and their weights are determined by the entropy weight method.

[0020] (4) Traverse all categories and recalculate the cluster center of the category. If the current cluster center has changed compared to the previous clustering, repeat steps (3) and (4) until the cluster center no longer changes, and output the clustering result.

[0021] As a preferred technical solution, the K-means algorithm based on multiple distances uses the DBI index to measure the clustering effect and gives the number of clusters with the best index as the K value; the DBI index I DBI Specifically:

[0022]

[0023] In the formula, A i For the i-th cluster center, Let be the average distance from the i-th sample within the cluster to the cluster center. Let be the average distance from the j-th sample within the cluster to the cluster center, representing the dispersion of the curves within the cluster. The calculation formula is:

[0024]

[0025] In the formula, T i The number of samples in the i-th class, X i,l This is the l-th sample of the i-th class.

[0026] As a preferred technical solution, the intraday local fluctuation probability prediction model is BiLSTM, which includes a forward LSTM network and a backward LSTM network, and a quantile regression layer is added at the end of the network.

[0027] The regression model for the quantile regression layer is as follows:

[0028]

[0029] In the formula, Q M (τ|V) is the τth conditional quantile of the response variable M; c is the number of explanatory variables V; β0 is the intercept, βi (τ) is the regression coefficient vector at the τ quantile, where i ranges from 1 to c, obtained by solving the optimization problem of the following equation:

[0030]

[0031] Where, V′=[1V′ i [] represents the column vector of explanatory variables.

[0032] The response variable under the τ quantile of the quantile regression layer is:

[0033]

[0034] In the formula: H is the number of units in the hidden layer; f is the activation function of the output layer; h j (τ) represents the output of the LSTM hidden layer; W j (τ and b(τ) represent the weights and biases of the output layer.)

[0035] As a preferred technical solution, the intraday overall trend probability prediction model is a Gaussian regression process model. By learning the mapping relationship between the input daily meteorological data and the output actual load values ​​of each sampling point within the day, it obtains an interval prediction result that reflects the overall intraday load trend under this scenario and matches the predicted daily meteorological data. Specifically:

[0036] For a training set containing n samples, the input feature matrix is ​​X = [x1, x2, ..., xn]. n ] T x n Let be the input vector of the nth sample, with length d, and the corresponding output response be y = [y1, y2, ..., y]. n ] T y n This is the nth output response value;

[0037] Define f(X) as x n The corresponding functions are f(x1), f(x2), ..., f(x) n A set of random variables consisting of , , and following a joint Gaussian distribution, can be represented by the following Gaussian process:

[0038] f(x): GP(m(x), k(x, x′))

[0039] In the formula, x and x′ are both random variables, m(x) is the mean function, and k(x, x′) is the covariance function, calculated as follows:

[0040] m(x)=E(f(x))

[0041] k(x,x′)=E((f(x)-m(x))·(f(x′)-m(x′)))

[0042] Let m(x) = 0, that is, the expected value of the function is 0 when there are no observations;

[0043] The regression model is expressed as:

[0044] y = f(x″) + ε i

[0045] In the formula, That is, it follows a mean of 0 and a variance of . Gaussian white noise, x″ is a d-dimensional random vector, and y is the observed value;

[0046] The prior distribution of the output observation y is: y:

[0047] In the formula, K(X, X) is an n-order covariance matrix, and the corresponding element k ij =k(x i x j ), I n It is an n-order identity matrix;

[0048] Given the test set input X * =[x n+1 , ..., x n+m ], where the i-th corresponding vector is denoted as The predicted value output by the test set is y * Then the observed value y in the training set and the predicted value y * The joint prior distribution is:

[0049]

[0050] Predicted value y * The posterior distribution is:

[0051]

[0052] In the formula, These represent the mean and variance of the predicted values ​​output by the test set, respectively. The mean corresponds to the deterministic prediction result, and the variance can be used to construct a confidence interval.

[0053] As a preferred technical solution, the prediction intervals of two models are aggregated into one interval using an aggregation function. The aggregation function uses a Choquet integral based on a fuzzy measure, where the fuzzy measure represents the degree of relationship between the elements to be aggregated, specifically:

[0054] For n elements A = {a1, a2, ..., a...} to be aggregated n The aggregated value y is:

[0055] y = g(a1, a2, ..., a n )

[0056] In the formula, g() represents the aggregate function, i.e., g: [0, 1] 2 →[0, 1], holds if and only if the following condition is met:

[0057] (1) Boundary conditions: g(01, 02, ..., 0) n ) = 0 and g(11, 12, ..., 1) n ) = 1;

[0058] (2) Monotonicity: If x i ≤y i , There is: g(x1, K, x) n )≤g(y1, K, y n );

[0059] Define fuzzy measure: for a reference set Q = {1, ..., n}, 2 Q Let Q be the power set, and if the function μ: 2 Q →If [0, 1] satisfies the following properties, it is called a fuzzy measure:

[0060] (a) Boundary conditions: μ(X) = 1;

[0061] (b) Monotonicity: If μ(A) ≤ μ(B);

[0062] The power-mean of the cardinality of the aggregated value set is used as the fuzzy measure, with a q value of 2. Specifically:

[0063]

[0064] In the formula, {a′1, a′2, K, a′ n The i-th element in} is a′ i It is through A = {a1, a2, ..., a} n The new set obtained by rearranging the elements according to an increasing order is Pi = {x'} i , K, x′ n} represents the largest n-i+1 element in A.

[0065] Another aspect of the present invention provides a load interval prediction system based on multi-distance clustering and information aggregation, applied to the above-mentioned load interval prediction method based on multi-distance clustering and information aggregation, including a clustering module, a local-global model training module, a local-global model prediction module, and an information aggregation module;

[0066] The clustering module is used to cluster the normalized load curve data using the K-means algorithm based on multiple distances to obtain a set of k curves; for the i-th result, it is divided into a training set and a test set with the corresponding meteorological data.

[0067] The local-global model training module is used to train the intraday local fluctuation probability prediction model and the intraday overall trend probability prediction model by inputting the training set and the test set into the intraday local fluctuation probability prediction model and the intraday overall trend probability prediction model respectively, so as to obtain the intraday local fluctuation probability prediction model and the intraday overall trend probability prediction model with updated parameters.

[0068] The local-global model prediction module is used to input the test set feature values ​​of the two models respectively to obtain the upper and lower limits of the two model intervals under the t quantile;

[0069] The information aggregation module is used to aggregate the upper and lower limits of the prediction intervals of the two models respectively, and calculate the aggregated prediction interval using the Choquet integral aggregation function.

[0070] In another aspect, the present invention provides a storage medium storing a program that, when executed by a processor, implements the above-described load interval prediction method based on multi-distance clustering and information aggregation.

[0071] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0072] (1) The present invention uses dynamic bending distance (DTW) to more effectively measure the similarity between two samples, thereby describing various features of the curve.

[0073] (2) This invention fully considers various characteristics of curves, adopts a similarity distance that takes into account the numerical distribution characteristics, morphological trend characteristics, and local fluctuation characteristics of curves, and uses the entropy weight method to determine its weight. (Formula 1 in Implementation Scheme 1)

[0074] (3) The K-means algorithm of the present invention requires a set of vectors and the number of clusters K as input. Since the value of K given by humans is highly subjective, the DBI index is used to measure the clustering effect, and the number of clusters with the best index is given as the value of K.

[0075] (4) This invention uses a BiLSTM deep learning probabilistic prediction model based on quantile regression to predict the local fluctuation pattern of the load.

[0076] (5) The present invention adopts a kernel-based GPR nonlinear nonparametric regression method.

[0077] (6) The present invention adopts a post-processing method based on QR-BiLSTM and GPR model information aggregation to effectively reduce prediction error, thereby improving prediction performance.

[0078] (7) The aggregation function of the present invention uses Choquet integral based on fuzzy measure, with fuzzy measure representing the degree of relationship between the elements to be aggregated. Attached Figure Description

[0079] Figure 1 This is a flowchart of the ultra-short-term load interval prediction method based on multi-distance curve feature clustering and information aggregation according to an embodiment of the present invention;

[0080] Figure 2 This is a schematic diagram of the structure of the BiLSTM neural network according to an embodiment of the present invention;

[0081] Figure 3 This is a schematic diagram of the load interval prediction results of QR-BiLSTM on a certain day in the test set according to an embodiment of the present invention;

[0082] Figure 4 This is a schematic diagram of the interval prediction results of the GPR model under different confidence levels on the same day according to an embodiment of the present invention;

[0083] Figure 5 This is a schematic diagram comparing the prediction bias of the three models in this embodiment of the invention;

[0084] Figure 6 This is a schematic diagram of the structure of the ultra-short-term load interval prediction system based on curve feature clustering and information aggregation according to an embodiment of the present invention;

[0085] Figure 7 This is a schematic diagram of the structure of the storage medium according to an embodiment of the present invention. Detailed Implementation

[0086] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are merely some embodiments of the present application, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present application without creative effort are within the scope of protection of the present application.

[0087] Example 1

[0088] like Figure 1 As shown, this embodiment provides a method for predicting ultra-short-term load intervals based on multi-distance curve feature clustering and information aggregation, including the following steps:

[0089] S1. The normalized load curve data is clustered using the K-means algorithm based on multiple distances to obtain a set of k types of curves.

[0090] S2. For the i-th type of result, divide it and the corresponding meteorological data into a training set and a test set;

[0091] S3. Input the training set and the test set into the intraday local fluctuation probability prediction model and the intraday overall trend probability prediction model respectively for training, and obtain the intraday local fluctuation probability prediction model and the intraday overall trend probability prediction model with updated parameters.

[0092] S4. Input the test set feature values ​​of the two models respectively to obtain the upper and lower limits of the intervals for the two models under the t-quantile. The upper and lower limits of the intraday local fluctuation model prediction interval are denoted as follows: The upper and lower limits of the intraday overall trend model prediction range are denoted as follows: t represents the sampling time point of the predicted day.

[0093] S5. Aggregate the upper and lower bounds of the prediction intervals of the two models respectively, and calculate the aggregated prediction interval using the Choquet integral aggregation function.

[0094] I. Daily Load Curve Clustering Considering Multiple Features

[0095] Electricity load is influenced by many factors, such as user behavior and weather conditions. Therefore, the daily load curve exhibits strong regularity while also experiencing random fluctuations. Its curve characteristics mainly include overall trend characteristics and local fluctuation characteristics. Euclidean distance is used to measure the distance between corresponding sampling points of two samples, denoted as D1(X,Y). The overall trend characteristic matches the regularity of the load curve and reflects the overall trend of the curve's change over time. DTW distance is used as its similarity distance, denoted as D2(X,Y). Local fluctuation characteristics reflect the degree of fluctuation of the curve at each sampling point. The sequences X and Y are obtained by using the antecedent difference method to obtain two sequences X′,′ that can map the fluctuation situation. Then, their DTW distance is calculated to describe the local fluctuation characteristics, denoted as D3(X,Y).

[0096] To effectively distinguish load curves and fully consider various curve characteristics, a similarity distance method is adopted that takes into account the curve's numerical distribution characteristics, morphological trend characteristics, and local fluctuation characteristics. The calculation formula is as follows:

[0097] D total (X, Y)=r1D1(X, Y)+r2D2(X, Y)+r3D3(X, Y)......(1)

[0098] In the formula, r1, r2 and r3 are the weights corresponding to the three distances, and their weights are determined by the entropy weight method.

[0099] The K-means algorithm for curve clustering requires a set of vectors and the number of clusters K as input. Since the manually assigned value of K is highly subjective, this paper uses the DBI metric to measure clustering performance and provides the optimal number of clusters for K. The formula for calculating the DBI metric is:

[0100]

[0101] In the formula, A i S is the i-th cluster center. i Let be the average distance from the i-th sample within a cluster to the cluster center, representing the dispersion of the curves within the cluster. The calculation formula is:

[0102]

[0103] In the formula, T i The number of samples in the i-th class, X i，l This is the l-th sample of the i-th class.

[0104] Based on D total The steps of the K-means algorithm for distance are as follows:

[0105] S1.1 Input the dataset S of isochronous curve samples to be clustered, S = {s1, s2, ..., s3} i s h}, where s i This is the sample of the i-th curve;

[0106] S1.2. Randomly select k different samples from S as the initial cluster centers for K-means;

[0107] S1.3. Traverse all samples, calculate the distance between the i-th sample and all cluster centers using equation (1), and assign it to the class with the smallest distance to the i-th sample.

[0108] S1.4. Traverse all categories and recalculate the cluster center of each category. If the current cluster center has changed compared to the previous clustering, repeat steps S1.3 and S1.4 until the cluster center no longer changes, and output the clustering result.

[0109] II. Intraday Local Fluctuation Probability Prediction Model

[0110] BiLSTM is a bidirectional recurrent network built on the LSTM principle. The forward and backward LSTM networks work together, enabling BiLSTM to simultaneously learn the changes in the sequence, further improving its performance. Its structure is as follows: Figure 2 As shown.

[0111] The intraday local volatility probability prediction model is finally supplemented with a quantile regression layer.

[0112] Quantile regression can determine the relationship between the explanatory variable V and the conditional quantiles of the response variable M. Its regression model is as follows:

[0113]

[0114] In the formula, c represents the number of explanatory variables V; Q M (τ|V) is the τth conditional quantile of the response variable M; β0 is the intercept, β i (τ) is the regression coefficient vector under the τ quantile, where i ranges from 1 to c. The calculation method for β(τ) can be obtained by solving the optimization problem of equation (5):

[0115]

[0116] Where, V′=[1V i '] is the column vector of explanatory variables.

[0117] Training a BiLSTM network essentially involves solving and updating its network parameters W and b. Since the probability predictions need to be derived through the BiLSTM network, a quantile regression layer is added at the end of the network. The response variable at the τ quantile is:

[0118]

[0119] In the formula: H is the number of units in the hidden layer; f is the activation function of the output layer; h j (τ) represents the output of the LSTM hidden layer; W j b(τ) and b(τ) are the weights and biases of the output layer.

[0120] III. Intraday Overall Trend Probability Prediction Model

[0121] After calculating the k-class load curves using the aforementioned clustering method, the overall intraday trend of the load curves can reflect the overall load pattern under this clustering scenario. Therefore, a Gaussian regression process model is used to learn the mapping relationship between the input (daily meteorological data) and the output (the actual load value of each sampling point within the day), obtaining an interval prediction result that reflects the overall intraday load trend under this scenario and matches the predicted daily meteorological data. GPR is a kernel-based nonlinear nonparametric regression method that can obtain a mapping function describing the relationship between input feature data and output data through training. It has advantages such as ease of implementation, parameter adaptation, and probabilistic output when dealing with high-dimensional nonlinear problems. Using GPR, the mean and variance of the output prediction values ​​of the test set are obtained. The mean corresponds to its deterministic prediction result, and confidence intervals can be constructed by combining the variance.

[0122] Specifically:

[0123] For a training set containing n samples, the input feature matrix is ​​X = [x1, x2, ..., xn]. n ] T x n Let be the input vector of the nth sample, with length d, and the corresponding output response be y = [y1, y2, ..., y]. n ] T y n This is the nth output response value;

[0124] Define f(X) as x n The corresponding functions are f(x1), f(x2), ..., f(x) n A set of random variables consisting of , , and following a joint Gaussian distribution, can be represented by the following Gaussian process:

[0125] f(x): GP(m(x), k(x, x′))

[0126] In the formula, x and x′ are both random variables, m(x) is the mean function, and k(x, x′) is the covariance function, calculated as follows:

[0127] m(x)=E(f(x))

[0128] k(x,x′)=E((f(x)-m(x))·(f(x′)-m(x′)))

[0129] Let m(x) = 0, that is, the expected value of the function is 0 when there are no observations;

[0130] The regression model is expressed as:

[0131] y = f(x″) + ε i

[0132] In the formula, That is, it follows a mean of 0 and a variance of . Gaussian white noise, x″ is a d-dimensional random vector, and y is the observed value;

[0133] The prior distribution of the output observation y is:

[0134] y:

[0135] In the formula, K(X, X) is an n-order covariance matrix, and the corresponding element k ij =k(x i x j ), I n It is an n-order identity matrix;

[0136] Given the test set input X * =[x n+1 , ..., xn+m ], where the i-th corresponding vector is denoted as The predicted value output by the test set is y * Then the observed value y in the training set and the predicted value y * The joint prior distribution is:

[0137]

[0138] Predicted value y * The posterior distribution is:

[0139]

[0140] In the formula, These represent the mean and variance of the predicted values ​​output by the test set, respectively. The mean corresponds to the deterministic prediction result, and the variance can be used to construct a confidence interval.

[0141] IV. Choquet Integral Aggregate Functions

[0142] Information aggregation is the process of combining different pieces of information from multiple sources to obtain a unified decision. In the prediction process, an aggregation function is used to merge the prediction intervals of two models into a single interval. The aggregation function uses Choquet integrals based on fuzzy measures, where the fuzzy measure represents the degree of relationship between the elements to be aggregated.

[0143] For n elements A = {a1, a2, ..., a...} to be aggregated n The aggregated value y is:

[0144] y = g(a1, a2, ..., a n )

[0145] In the formula, g() represents the aggregate function, i.e., g: [0, 1] 2 →[0, 1], holds if and only if the following condition is met:

[0146] (1) Boundary conditions: g(01, 02, ..., 0) n ) = 0 and g(11, 12, ..., 1) n ) = 1;

[0147] (2) Monotonicity: If x i ≤y i , There is: g(x1, K, x) n )≤g(y1, K, y n );

[0148] Definition (fuzzy measure) [DEEPLSTM]: For a reference set Q = {1, ..., n}, 2 Q Let Q be the power set, and if the function μ: 2Q →If [0, 1] satisfies the following properties, it is called a fuzzy measure:

[0149] (a) Boundary conditions: μ(X) = 1;

[0150] (b) Monotonicity: If μ(A) ≤ μ(B);

[0151] The power-mean of the cardinality of the aggregated value set is used as the fuzzy measure, with a q value of 2. Specifically:

[0152]

[0153] In the formula, {a′1,a′2,K,a′ n The i-th element in} is a′ i It is through A = {a1, a2, ..., a} n The new set P obtained by rearranging the elements according to an increasing order is called P. i ={x′ i ,K,x′ n} represents the largest n-i+1 element in A.

[0154] Example 2

[0155] This embodiment further illustrates the ultra-short-term load interval prediction method based on multi-distance curve feature clustering and information aggregation described in Embodiment 1 by using the electricity load data of a certain region in a certain province for the entire year of 2012.

[0156] 1. Electricity load data for a specific region in a province throughout 2012 was used, with a resolution of 15 minutes, meaning 96 sampling points per day. In addition to load data, available meteorological data included daily maximum temperature (°C), daily minimum temperature (°C), daily average temperature (°C), daily relative humidity, and daily rainfall (mm). All of these data had a 24-hour resolution, meaning only one data point per day. The following three indicators were used to quantitatively evaluate the model's predictive performance: Empirical Coverage Probability (ECP). Winker score Average width

[0157] 2. Set the K-means algorithm to K=3, and the weights r1, r2, and r3 for the three distances are 0.4538, 0.3248, and 0.2214, respectively. Cluster all normalized daily load curve data, and use the first 80% of the load curves in each class as the training set to train the model, and the last 20% as the test set to evaluate the model performance.

[0158] The advantage of the QR-BiLSTM model lies in its ability to remember the time sequence before and after the load sequence. Therefore, this paper uses it as a load interval prediction model that focuses on local fluctuation patterns, and makes its training input features the load values ​​of the 1st, 2nd and 3rd sampling points before the prediction time, so as to better capture its local dynamic features. Figure 3 The load range prediction results of QR-BiLSTM on a certain day in the test set are shown in Table 1. The corresponding evaluation indicators under different confidence levels are shown in Table 1. As can be seen from the figure, the overall range width of the model is relatively small, and it is more sensitive to load fluctuations. The prediction range can match the load fluctuation pattern, but the ECP index, which represents reliability, is not high enough, making it difficult to achieve more accurate predictions.

[0159] The advantage of the GPR model lies in its ability to extract the overall distribution pattern of load data. Therefore, this paper uses it as an interval prediction model that focuses on the overall trend of load data. Its training input features are the normalized meteorological data for the prediction date. Figure 4 The GPR model provides interval forecast results at different confidence levels on the same day. Compared to the QR-BiLSTM model, the GPR model generally has a higher ECP (Earning Capacity Scale) and better reliability. This is because the GPR model builds its forecast by fitting the load data distribution under this scenario and determines the mapping relationship based on meteorological data input. However, except for the 95% confidence level where it is similar to the QR-BiLSTM model, the GPR model's forecast interval width significantly exceeds that of the QR-BiLSTM model at all other confidence levels. This results in poor sharpness performance when used as a single model's forecast output, making it less reliable for reference.

[0160] 3. As shown in Table 1, to verify the effect of curve clustering on this method, the prediction performance of the three models on prediction day 1 will be compared below. Among them, Model 1 is the prediction method of this method, Model 2 does not include the curve clustering step in this method, and Model 3 does not introduce DTW distance in this method.

[0161] Predictive Model ECP <![CDATA[Winker(×10 3 )]]> Model 1 0.9167 0.6936 Model 2 0.7188 1.9469 Model 3 0.8750 0.7280

[0162] Table 1. Comparison of evaluation indicators for the three models in predicting day 1

[0163] Prediction bias is a common method for measuring the accuracy of model predictions. In interval-based predictions, the deviation is used when the true value exceeds the limit of the prediction interval. When the true value is within the interval, the deviation is 0. Figure 5The prediction biases of the three models were compared. Model 1 had the fewest number and magnitude of load exceedances, while Model 2 had the highest number of exceedances. Based on the evaluation metrics in Table 1, the comparison between Model 1 and Model 2 shows that the introduction of curve clustering significantly improved prediction accuracy. Furthermore, the comparison between Model 1 and Model 3 indicates that the introduction of DTW distance makes the clustering patterns of the load curves more suitable for the prediction model's learning, thereby further improving prediction accuracy.

[0164] 4. Overall, a method for ultra-short-term interval forecasting of power load based on multi-distance curve feature clustering and information aggregation is more practical and has greater scalability.

[0165] like Figure 6 As shown, in another embodiment of this application, an ultra-short-term load interval prediction system based on curve feature clustering and information aggregation is provided. The system includes a clustering module, a local-global model training module, a local-global model prediction module, and an information aggregation module.

[0166] The clustering module is used to cluster the normalized load curve data using the K-means algorithm based on multiple distances to obtain a set of k curves; for the i-th result, it is divided into a training set and a test set with the corresponding meteorological data.

[0167] The local-global model training module is used to train the intraday local fluctuation probability prediction model and the intraday overall trend probability prediction model by inputting the training set and the test set into the intraday local fluctuation probability prediction model and the intraday overall trend probability prediction model respectively, so as to obtain the intraday local fluctuation probability prediction model and the intraday overall trend probability prediction model with updated parameters.

[0168] The local-global model prediction module is used to input the test set feature values ​​of the two models respectively to obtain the upper and lower limits of the two model intervals under the t-quantile. The upper and lower limits of the intraday local fluctuation model prediction interval are denoted as follows: The upper and lower limits of the intraday overall trend model prediction range are denoted as follows: t represents the sampling time point of the predicted day.

[0169] The information aggregation module is used to aggregate the upper and lower limits of the prediction intervals of the two models, and calculate the aggregated prediction interval using the Choquet integral aggregation function.

[0170] It should be noted that the system provided in the above embodiments is only an example of the division of the above functional modules. In practical applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure can be divided into different functional modules to complete all or part of the functions described above. The system is applied to the ultra-short-term load interval prediction method based on multi-distance curve feature clustering and information aggregation in the above embodiments.

[0171] like Figure 7 As shown, in another embodiment of this application, a storage medium is also provided, storing a program. When the program is executed by a processor, it implements the ultra-short-term load interval prediction method based on multi-distance curve feature clustering and information aggregation of the above embodiments, specifically:

[0172] The normalized load curve data is clustered using the K-means algorithm based on multiple distances to obtain a set of k types of curves.

[0173] For the i-th type of result, it is divided into a training set and a test set along with the corresponding meteorological data;

[0174] The training set and the test set are respectively input into the intraday local fluctuation probability prediction model and the intraday overall trend probability prediction model for training, and the parameters are updated to obtain the intraday local fluctuation probability prediction model and the intraday overall trend probability prediction model.

[0175] Input the test set feature values ​​of the two models respectively to obtain the upper and lower limits of the intervals for the two models under the t-quantile. The upper and lower limits of the intraday local fluctuation model prediction interval are denoted as follows: The upper and lower limits of the intraday overall trend model prediction range are denoted as follows: t represents the sampling time point of the predicted day.

[0176] It should be understood that various parts of this application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented using software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0177] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A load interval prediction method based on multi-distance clustering and information aggregation, characterized in that, Includes the following steps: The normalized load curve data were clustered using a K-means algorithm based on multiple distances to obtain... Results of the curve set; For the The results are then divided into training and testing sets, along with the corresponding meteorological data. The training set and the test set are respectively input into the intraday local fluctuation probability prediction model and the intraday overall trend probability prediction model for training, and the intraday local fluctuation probability prediction model and the intraday overall trend probability prediction model with updated parameters are obtained. The intraday local volatility probability prediction model is a BiLSTM, which includes a forward LSTM network and a backward LSTM network, with a quantile regression layer added at the end of the network. The regression model for the quantile regression layer is as follows: ； In the formula, For response variables The Conditional quantiles; For explanatory variables The number of; The intercept is... for Regression coefficient vector under quantiles The value range is 1 to The following optimization problem is solved to obtain: ； in, For the column vector of explanatory variables; The quantile regression layer The response variable at the quantile is: ； In the formula: The number of units in the hidden layer; The activation function for the output layer; The output of the LSTM hidden layer; , The weights and biases of the output layer; The intraday overall trend probability prediction model is a Gaussian regression process model. By learning the mapping relationship between the input daily meteorological data and the output actual load values ​​of each sampling point within the day, it obtains interval prediction results that reflect the overall intraday load trend and match the predicted daily meteorological data. Specifically: For including The training set of samples, with the input feature matrix as follows: , For the first The input vector of *n* samples has a length of *i*. The corresponding output response is , For the first Each output response value; definition for corresponding function The set of random variables constituted by the given condition, which follows a joint Gaussian distribution, can be represented by the following Gaussian process: ； In the formula, All are random variables. It is a mean function. Let covariance be the function, and the calculation formula is: ； ； set up That is, the expected value of the function is 0 when there are no observations. The regression model is expressed as: ； In the formula, That is, it follows a mean of 0 and a variance of . Gaussian white noise, for 3D random vector, These are the observed values; Obtain output observations The prior distribution is: ; In the formula, for The covariance matrix of order, corresponding elements , for An identity matrix of order 1; Given the test set input , of which The corresponding vectors are denoted as The predicted value output by the test set is Then the training set observations Compared with the predicted value The joint prior distribution is: ； Predicted value The posterior distribution is: ； In the formula, , These represent the mean and variance of the predicted values ​​output by the test set, respectively. The mean corresponds to the deterministic prediction result, and the confidence interval can be constructed by combining the variance. Input the test set feature values ​​of the two models respectively, and obtain Upper and lower limits of the two model intervals under quantiles; The upper and lower limits of the prediction intervals of the two models are aggregated separately, and the aggregated prediction interval is calculated using the Choquet integral aggregation function.

2. The load interval prediction method based on multi-distance clustering and information aggregation according to claim 1, characterized in that, The K-means algorithm based on multiple distances is specifically as follows: (1) Input the dataset of equal-length curve samples to be clustered , ,in For the first Curve samples; (2) In Random selection Use 10 distinct samples as the initial cluster centers for K-means; (3) Traverse all samples and calculate the first sample using the following formula. Distance between each sample and all cluster centers And classify it into the class with the smallest distance from that sample; ； in, This refers to the distance between corresponding sampling points of two samples, calculated using Euclidean distance. This refers to the distance between corresponding sampling points of two samples calculated using DTW distance. The distance between corresponding sampling points of two samples is obtained by first using the antecedent difference method and then calculating the DTW distance; , and The weights are determined using the entropy weighting method, corresponding to the three distances. (4) Traverse all categories and recalculate the cluster center of the category. If the current cluster center has changed compared to the previous clustering, repeat steps (3) and (4) until the cluster center no longer changes, and output the clustering result.

3. The load interval prediction method based on multi-distance clustering and information aggregation according to claim 1, characterized in that, The K-means algorithm based on multiple distances uses the DBI metric to measure clustering performance and assigns the optimal number of clusters (K) as the K value. Specifically: ； In the formula, For the first Cluster centers, For the first The average distance from each sample within a class to the cluster center. For the first The average distance from each sample within a cluster to the cluster center represents the dispersion of the curves within each cluster. The calculation formula is as follows: ； In the formula, No. Number of samples in each class For the first Class 1 One sample.

4. The load interval prediction method based on multi-distance clustering and information aggregation according to claim 1, characterized in that, The prediction intervals of two models are aggregated into a single interval using an aggregation function. This aggregation function employs a Choquet integral based on a fuzzy measure, where the fuzzy measure represents the degree of relationship between the elements to be aggregated. Specifically: For the aggregation element The aggregated values for: ； In the formula, Represents aggregate functions, i.e. It holds true if and only if the following conditions are met: (1) Boundary conditions: and ; (2) Monotonicity: If , have: ; Define fuzzy measure: for a reference set , for The power set of the function, if the function A fuzzy measure is called a fuzzy measure if it satisfies the following properties: (a) Boundary conditions: ; (b) Monotonicity: If have ; The power-mean of the cardinality of the aggregated value set is used as a fuzzy measure. The value is set to 2, specifically: ； In the formula, The Middle The elements are It is through The new set is obtained by rearranging the elements according to an increasing order. express The largest Each element.

5. A load interval prediction system based on multi-distance clustering and information aggregation, characterized in that, The load interval prediction method applied to multi-distance clustering and information aggregation as described in any one of claims 1-4 includes a clustering module, a local-global model training module, a local-global model prediction module, and an information aggregation module; The clustering module is used to cluster the normalized load curve data using a K-means algorithm based on multiple distances, to obtain... Results of the curve set; for the first The results are then divided into training and testing sets, along with the corresponding meteorological data. The local-global model training module is used to train the intraday local fluctuation probability prediction model and the intraday overall trend probability prediction model by inputting the training set and the test set into the intraday local fluctuation probability prediction model and the intraday overall trend probability prediction model respectively, so as to obtain the intraday local fluctuation probability prediction model and the intraday overall trend probability prediction model with updated parameters. The local-global model prediction module is used to input the test set feature values ​​of the two models respectively, and obtain... Upper and lower limits of the two model intervals under quantiles; The information aggregation module is used to aggregate the upper and lower limits of the prediction intervals of the two models respectively, and calculate the aggregated prediction interval using the Choquet integral aggregation function.

6. A storage medium storing a program, characterized in that: When the program is executed by the processor, it implements the load interval prediction method of multi-distance clustering and information aggregation as described in any one of claims 1-4.

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