An adaptive interval forecasting method for short-term residential load

Abstract

The present invention discloses an adaptive interval prediction method for short-term residential load, the prediction method comprising the following steps: collecting and processing data, establishing upper and lower limit prediction models for load intervals; reducing the number of hyperparameters of the biased convex loss function by parameter transformation, and using it as the loss function for optimizing the parameters of the upper and lower limit prediction models, and realizing automatic optimization of the hyperparameters of the loss function under the iterative adjustment of the proposed adaptive update strategy, and solving the minimized loss function; constructing the optimal prediction interval that achieves the expected coverage and has the narrowest average prediction interval width according to the minimized loss function; and further improving the prediction performance and stability of the model by integrating the unilateral coverage index into the proposed adaptive update strategy. The prediction method of the present invention constructs upper and lower limit prediction models, adjusts the hyperparameters of the loss function based on the unilateral coverage, simplifies the number of hyperparameters through parameter transformation, and significantly reduces the difficulty of hyperparameter adjustment.

Description

Technical Field

[0001] The invention relates to the technical field of power load forecasting, in particular to an adaptive interval forecasting method for short-term resident load. Background Art

[0002] Short-term residential load forecasting is an important part of power load forecasting, which has high requirements on computational efficiency, iteration frequency and prediction accuracy. Accurate short-term residential load forecasting is of great significance for the safe and stable dispatch of power grids. Most existing studies focus on load point forecasting, which can only provide a certain point prediction result and lack the assessment of load data uncertainty, making decision-making work risky. Therefore, a prediction interval based on a certain confidence level that reflects the load fluctuation range and uncertainty can reasonably describe the future change trend of the load.

[0003] At present, with the rapid growth of data volume, deep learning methods are widely used in the field of load forecasting, which can better extract useful information from massive data. To construct high-quality prediction intervals, a large number of hyperparameters limit its computational efficiency.

[0004] In view of the above existing problems, an adaptive interval prediction method for short-term residential load is proposed. Summary of the invention

[0005] The purpose of the present invention is to provide an adaptive interval prediction method for short-term residential load, so as to solve the problems in the above-mentioned background technology, such as lack of evaluation of load data instability, unreasonable evaluation, and a large number of hyperparameters affecting calculation efficiency.

[0006] The purpose of the present invention can be achieved by the following technical solutions:

[0007] An adaptive interval prediction method for short-term residential load, the prediction method comprising the following steps:

[0008] Step 1: Collect and process data to establish upper and lower limit prediction models for the load range.

[0009] Step 2: Reduce the number of hyperparameters of the biased convex loss function through parameter transformation, and use it as the loss function to optimize the parameters of the upper and lower prediction models. Under the iterative adjustment of the proposed adaptive update strategy, the automatic optimization of the hyperparameters of the loss function is achieved to solve the minimized loss function.

[0010] Step 3: Construct the optimal prediction interval that achieves the expected coverage and has the narrowest average prediction interval width based on the minimization loss function.

[0011] Step 4: By incorporating the unilateral coverage ratio indicator into the proposed adaptive update strategy, the prediction performance and stability of the model are further improved.

[0012] Furthermore, the upper limit prediction model in step 1 is The lower bound prediction model is E(·) is the improved biased convex loss function, P u and P l are the network parameters of the upper and lower prediction models, Ω u and Ω l are the hyper parameters of the loss functions of the upper and lower prediction models, respectively, u = {W u ,c u} and Ω l = {W l ,c l},W u 、c u are the weight and translation coefficient of the penalty term of the upper limit prediction model with improved convex loss function, respectively. l 、c l They are the weight and translation coefficient of the penalty term of the convex loss function for improving the lower limit prediction model, is the forecast deviation of the upper limit of the interval, is the forecast deviation of the lower limit of the interval, y t is the true value corresponding to the t-th prediction point, u t , l t are the upper and lower limits of the prediction interval for the tth prediction point.

[0013] Furthermore, the step 2 includes predicting the interval coverage rate PICP as N is the number of samples in the data set, and the function Measure the actual value y of the t-th prediction point t Is it in the prediction interval [l t ,u t ],

[0014] The average prediction interval width PINAW is R is the span of the true value,

[0015] The overall evaluation index CWC of the prediction interval is γ is used to determine whether to introduce exponential terms.

[0016] The normalized root mean square width of the prediction interval PINRW is η1 linearly expands the value of PINRW, η2 is the penalty coefficient of PICP, and PINC is the expected coverage of the prediction interval preset when testing the model.

[0017] Furthermore, the method of reducing the number of hyperparameters of the loss function by using parameter transformation in step 2 is: making an equivalent transformation on the biased convex loss function, eliminating the scaling coefficient in the scenario of minimizing the loss function, and removing the regularization coefficient, thereby reducing the number of hyperparameters from eight to four.

[0018] Furthermore, the steps for obtaining the optimal prediction interval in step three are: S1. When the prediction interval coverage reaches the startup coverage, the hyperparameters are adjusted using the adaptive update strategy to construct an improved biased loss function, otherwise the hyperparameters remain unchanged; S2. The updated parameters of the upper and lower limit prediction models are obtained by solving the minimization loss function problem according to the Adam algorithm; S3. The prediction interval is constructed using the outputs of the upper and lower limit prediction models. This process is iterated in sequence until convergence to obtain the optimal prediction interval.

[0019] Furthermore, the unilateral coverage index in step four divides the prediction interval into upper and lower sub-prediction intervals, and through an adaptive update strategy, the coverage of the upper and lower sub-prediction intervals reaches the expected coverage, so as to ensure that the true value is more evenly distributed in the prediction interval, making the control of the prediction interval coverage more precise and the average width further reduced.

[0020] Furthermore, the adaptive update strategy proposed in the step 4 directly utilizes the relationship between the improved biased convex loss function hyperparameters and the prediction interval coverage to construct a hyperparameter adaptive update strategy. In the process of minimizing the improved biased loss function to obtain the optimal parameters of the upper and lower limit prediction models, the loss function hyperparameters are optimized to simultaneously achieve optimal hyperparameter adjustment and optimal prediction interval construction.

[0021] Furthermore, the iterative update formula of the adaptive update strategy is:

[0022]

[0023]

[0024]

[0025]

[0026] In the above formula: k1 and k2 control the iteration update rate, PICP * The expected coverage of the prediction interval preset for the training model, i represents the current iteration number.

[0027] Furthermore, the data collection and processing in step 1 includes preprocessing, feature extraction and normalization of the input data including temperature forecast data and load history data at the same time of the previous week, and then inputting them into the interval prediction model.

[0028] Furthermore, the upper limit prediction model and the lower limit prediction model are implemented by a gate recurrent network and a fully connected neural network, initialization parameters are obtained by Xavier and He initialization methods respectively, and the network structure is determined by cross-validation of the model point prediction results.

[0029] Beneficial effects of the present invention:

[0030] 1. The prediction method of the present invention converts the short-term residential load interval prediction problem into two independent prediction sub-problems of upper and lower limits, uses two independent networks to respectively construct the upper and lower limits of the prediction interval, supervises the parameter learning of the upper and lower limit prediction models through two independent loss functions, and adaptively adjusts the hyperparameters of the two loss functions based on two independent unilateral coverage rates, which significantly improves the independence and degree of freedom of model training;

[0031] 2. The prediction method of the present invention reduces the number of hyperparameters to four through parameter transformation and reasonable simplification, significantly reducing the difficulty of hyperparameter adjustment and simplifying calculations. An adaptive update method is constructed based on the intrinsic connection between hyperparameters and prediction interval coverage, which automatically optimizes the hyperparameters of the loss function during training, thereby solving the problem of difficulty in pre-selecting the optimal hyperparameters of the biased loss function and improving the stability of the training effect.

[0032] 3. The prediction method of the present invention divides the prediction interval into two sub-intervals. Its combination with the adaptive update strategy is conducive to obtaining a prediction interval with a more uniform distribution of true values, achieving a more detailed construction of the prediction interval, further improving the quality of the prediction interval, and the evaluation result is reasonable. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] The present invention will be further described below in conjunction with the accompanying drawings.

[0034] Figure 1 is a flow chart of predicting short-term residential load intervals according to the present invention;

[0035] Figure 2 It is a comparison chart of the predicted interval of the present application and the actual value under the single-step ahead 95% predicted interval coverage of the present invention;

[0036] Figure 3 The present invention Figure 2 A partial enlarged view of the

[0037] Figure 4 It is a comparison chart of the predicted interval of the present application and the actual value under the four-step ahead 95% predicted interval coverage of the present invention;

[0038] Figure 5 The present invention Figure 4 A partial enlarged view of the

[0039] Figure 6It is a schematic diagram of the convergence curve of the loss function hyperparameters of the present invention under the single-step ahead 85% prediction interval coverage;

[0040] Figure 7 It is a schematic diagram of the convergence curve of the loss function hyperparameters under the single-step ahead 85% prediction interval coverage of the present invention. DETAILED DESCRIPTION

[0041] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0042] An adaptive interval prediction method for short-term residential load, the present invention is an adaptive iterative optimization framework, such as Figure 1 As shown, the prediction method includes the following steps:

[0043] S1. Data preprocessing, feature extraction, and generation of tensors required for training

[0044] The input data including temperature forecast data and load history data at the same time in the previous week are integrated into a data sample form containing input and output vectors. The data is preprocessed and feature extracted, and the data variables are normalized to the range of [0,1]. Based on the time window size obtained by correlation analysis, the tensors required for training suitable for the deep learning model are generated.

[0045] S2. Propose load forecast interval evaluation indicators and initialize the overall parameters of the model

[0046] The evaluation indexes of load forecast interval include average forecast interval width PINAW, forecast interval coverage PICP and interval overall evaluation index CWC. Given a training data set of {(x1,y1),…,(x N ,y N )}, the prediction interval evaluation indicators are shown in formulas (1) to (7):

[0047]

[0048]

[0049]

[0050]

[0051]

[0052]

[0053]

[0054] In the above equations (1) to (7), N is the number of statistical data samples in the training data set, y1 is the actual value of the first prediction point x1, and y N is the Nth predicted point x N The actual value of the function Measure the actual value y of the t-th prediction point t Is it in the prediction interval [l t ,u t ],u t , l t are the upper and lower limits of the prediction interval of the t-th prediction point, R is the span of the true value, γ is used to determine whether to introduce an exponential term, η1 linearly expands the value of PINRW, η2 is the penalty coefficient of PICP, and PINC is the preset expected coverage.

[0055] The Xavier and He initialization methods are used to obtain the initialization network parameters of the GRU network and the fully connected neural network respectively. The model point prediction results are cross-validated to determine the network structure. The cross-validation method is used to obtain the update rates k1, k2 and the expected interval coverage rate PICP set by the training. * , randomly generate loss function hyperparameters, where the weight W of the loss function penalty term is randomly generated in [10,15], and the translation coefficient c is randomly generated in [2,4].

[0056] S3. Construct an interval prediction model with the optimization goal of improving the biased convex loss function

[0057] The prediction model adopts a GRU network and a single-output fully connected neural network. GRU is used to extract features from time series data, and the extracted information is sent to the fully connected neural network to generate prediction interval boundary values. Two independent networks are used as the upper and lower limit prediction models of the interval respectively, and the optimal parameters of the prediction model are obtained by solving the improved biased convex loss function minimization problem.

[0058] The steps to construct an improved biased convex loss function are as follows:

[0059] (a) For the training data set {(x t ,y t )|t=1,…N} target y t The corresponding upper and lower limits of the prediction interval are represented by u t and l t The prediction deviation of the upper and lower limits of the interval is defined as follows:

[0060] θ u,t=y t -u t ,θ l,t = l t -y t (8)

[0061] The upper and lower limit deviations corresponding to the true value falling within the prediction interval must satisfy formula (9):

[0062] θ u,t ≤0,θ l,t ≤0 (9)

[0063] With q t Instead of q u,t and q l,t , then the initial biased convex loss function is as follows:

[0064]

[0065]

[0066] W is the weight of the penalty term S(·) of the biased convex loss function, r and c are the scaling coefficient and translation coefficient of the function S(·).

[0067] (b) Reducing the number of hyperparameters in the loss function through parameter transformation: An equivalent transformation is performed on the biased convex loss function, the scaling coefficient is eliminated in the scenario of minimizing the loss function, and the regularization coefficient is removed, reducing the number of hyperparameters from eight to four.

[0068] Transform the parameters of the above formula (10) Then the hyperparameter r in S(·) can be eliminated, and the transformed loss function is as follows:

[0069]

[0070]

[0071] In the scenario of minimizing the loss function, and The effect is the same, so use replace The improved biased convex loss function is obtained, as shown in equations (14) and (13):

[0072]

[0073] Therefore, the improved loss function has only two hyperparameters, namely W and c.

[0074] (c) Based on the improved biased convex loss function, the optimization objective function of the upper and lower limit prediction model parameters is constructed, and the optimal parameters of the prediction model are obtained by solving its minimization problem, as shown in equations (15) and (16):

[0075]

[0076]

[0077] Where P u and P l are the network parameters of the upper and lower prediction models, Ω u and Ω l are the hyper parameters of the loss function of the upper and lower prediction models, respectively, u = {W u ,c u} and Ω l = {W l , c l},N b Represents the number of samples in the training batch, W u 、c u are the weight and translation coefficient of the penalty term of the upper limit prediction model with improved convex loss function, respectively. l 、c l They are the weight and translation coefficient of the penalty term of the convex loss function for improving the lower limit prediction model, is the forecast deviation of the upper limit of the interval, is the forecast deviation of the lower limit of the interval, y t is the true value corresponding to the t-th prediction point, u t , l t are the upper and lower limits of the prediction interval of the tth prediction point, and its calculation formula is the same as formula (8).

[0078] S4. Use the unilateral adaptive update strategy to optimize and adjust the loss function hyperparameters

[0079] According to the intrinsic relationship between the hyperparameters of the improved biased convex loss function and the coverage of the prediction interval, an adaptive update strategy is designed to automatically find the optimal hyperparameters during the iterative training process. The hyperparameter W controls the proportion of the penalty term in the loss function. Increasing its value imposes a greater penalty on points outside the prediction boundary, so that the prediction boundary is quickly adjusted to include the point, and the corresponding coverage is improved. Conversely, reducing the value of W can reduce the prediction interval coverage. Therefore, the adaptive update formula for W is shown in formula (17):

[0080] W←W-k1·(PICP-PICP * ) (17)

[0081] PICP* Represents the expected coverage set when training the model.

[0082] Since the prediction interval coverage is not required to reach 100%, the role of the hyperparameter c is to mitigate the effect of the penalty term on the target true value. Reducing the value of c improves the prediction interval coverage, while increasing the value of c reduces the coverage. The adaptive update formula for c is shown in formula (18):

[0083] c←c+k2·(PICP-PICP * ) (18)

[0084] In order to improve the precision of the adaptive update strategy for controlling prediction performance and further improve the prediction quality, a prediction interval evaluation index of unilateral coverage is proposed, which divides the prediction interval into two sub-intervals and calculates the coverage respectively. The calculation formula is shown in equations (19) to (21):

[0085]

[0086]

[0087]

[0088] Ideally, the interval coverage satisfies PICP u =PICP l =PICP=PICP * , at this time, the true value is more evenly distributed in the prediction interval, thereby optimizing the average width of the prediction interval. Based on the unilateral coverage index, the adaptive update formula of the loss function hyperparameter is obtained, as shown in formula (22):

[0089]

[0090] Where i represents the number of iterations.

[0091] The above formula is called a unilateral adaptive update strategy. When the prediction interval coverage reaches the startup coverage, the above formula is used to iteratively adjust the value of the hyperparameter, and then pass it into the loss function to solve the parameters of the prediction model. This iteration is repeated until convergence to obtain the optimal prediction interval.

[0092] The average value of load power of more than 200 households in a certain area in the first quarter of a certain year was selected as the data source for the implementation case, and the time resolution of the data was 15 minutes / point. The original data was preprocessed into data samples, and the first 2 / 3 of the data was used as training data, and the last 1 / 3 of the data was used as test data. For the rated coverage of 85%, 90% and 95%, the prediction models with prediction steps of 15 minutes and 1 hour were trained respectively, namely the single-step and four-step advance prediction models.

[0093] Based on the prediction results of the test set, the average coverage deviation index is used to evaluate the reliability and stability of the prediction model. The calculation formula is shown in formula (23), and the evaluation index CWC is used to make an overall evaluation of the prediction interval.

[0094] ACD=PICP-PINC (23)

[0095] The evaluation results of the prediction interval obtained by the method disclosed in this application are shown in Table 1.

[0096] Table 1 Evaluation results of the prediction interval of this application under various look-ahead steps and expected coverage

[0097]

[0098] It can be seen from the evaluation results that the present application can carefully control the coverage rate near the preset expected coverage rate PINC and meet the coverage requirements, while ensuring excellent average interval width and overall interval quality. Figure 2 and Figure 3 , showing some prediction intervals for one-step-ahead forecasts with an expected coverage of 95%, Figure 4 and Figure 5 Shows some prediction intervals for a four-step-ahead forecast with 95% expected coverage. Figure 2-5 It can be seen that the method of the present invention can achieve better interval sharpness while ensuring good reliability.

[0099] Figure 6 and Figure 7 The convergence performance curve of the method disclosed in this application is demonstrated, and convergence can be achieved in 40 iterations, meeting the calculation time requirement of short-term load forecasting.

[0100] Table 2 demonstrates the role of the unilateral coverage index in the method described in this application through specific experiments. The unilateral coverage deviation index is used to measure the uniformity of the distribution of the true value in the prediction interval. Its calculation formula is shown in formula (24). The smaller the value, the more uniform the distribution of the true value in the prediction interval.

[0101] ΔPICP=|PICP u -PINC|+|PICP l -PINC| (24)

[0102] The adaptive update method using the overall coverage of the prediction interval is called a bilateral adaptive update strategy, while the method of the present application using a unilateral coverage is called a unilateral adaptive update strategy.

[0103] Table 2 Comparison results of bilateral and unilateral adaptive update strategies under 90% expected coverage in a single step

[0104]

[0105] According to the comparison results, the unilateral coverage index makes the adaptive update strategy more precise in controlling the coverage, the distribution of the true value in the prediction interval is more uniform, and the average width of the prediction interval is effectively reduced.

[0106] In the description of this specification, the description with reference to the terms "one embodiment", "example", "specific example", etc. means that the specific features, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

[0107] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, and these changes and improvements all fall within the scope of the present invention to be protected.

Claims

1. An adaptive interval prediction method for short-term residential load, characterized in that: The prediction method comprises the following steps: Step 1: Collect and process data to establish upper and lower limit prediction models for the load range; Step 2: Reduce the number of hyperparameters of the biased convex loss function through parameter transformation, and use it as the loss function to optimize the parameters of the upper and lower prediction models. Under the iterative adjustment of the proposed adaptive update strategy, the hyperparameters of the loss function are automatically optimized to minimize the loss function. Step 3: Construct the optimal prediction interval that achieves the expected coverage and has the narrowest average prediction interval width based on the minimized loss function; Step 4: Further improve the prediction performance and stability of the model by incorporating the unilateral coverage index into the proposed adaptive update strategy; The second step includes predicting the interval coverage rate PICP as follows: N is the number of samples in the data set, and the function Measure the actual value y of the t-th prediction point t Is it in the prediction interval [l t ,u t ], The average prediction interval width PINAW is R is the span of the true value, The overall evaluation index CWC of the prediction interval is γ is used to determine whether to introduce exponential terms. The normalized root mean square width of the prediction interval PINRW is η1 linearly expands the value of PINRW, η2 is the penalty coefficient of PICP, and PINC is the expected coverage of the prediction interval preset when testing the model.

2. The adaptive interval prediction method for short-term residential load according to claim 1, characterized in that: The upper limit prediction model in step 1 is: The lower bound prediction model is E(·) is the improved biased convex loss function, P u and P l are the network parameters of the upper and lower prediction models, Ω u and Ω l are the hyper parameters of the loss function of the upper and lower prediction models, respectively, u = {W u ,c u } and Ω l = {W l ,c l },W u 、c u are the weight and translation coefficient of the penalty term of the upper limit prediction model with improved convex loss function, respectively. l 、c l They are the weight and translation coefficient of the penalty term of the convex loss function for improving the lower limit prediction model, is the forecast deviation of the upper limit of the interval, is the forecast deviation of the lower limit of the interval, y t is the true value corresponding to the t-th prediction point, u t , l t are the upper and lower limits of the prediction interval for the tth prediction point.

3. The adaptive interval prediction method for short-term residential load according to claim 1, characterized in that: The method of using parameter transformation in step 2 to reduce the number of hyperparameters of the loss function is: make an equivalent transformation on the biased convex loss function, eliminate the scaling coefficient in the scenario of minimizing the loss function, and remove the regularization coefficient, so as to reduce the number of hyperparameters from eight to four.

4. The adaptive interval prediction method for short-term residential load according to claim 1, characterized in that: The steps of obtaining the optimal prediction interval in step three are as follows: S1. When the prediction interval coverage reaches the startup coverage, the hyperparameters are adjusted using the adaptive update strategy to construct an improved biased loss function, otherwise the hyperparameters remain unchanged; S2. The updated parameters of the upper and lower limit prediction models are obtained by solving the minimization loss function problem according to the Adam algorithm; S3. The prediction interval is constructed using the output of the upper and lower limit prediction models. This process is iterated in sequence until convergence to obtain the optimal prediction interval.

5. The adaptive interval prediction method for short-term residential load according to claim 1, characterized in that: The unilateral coverage index in step four divides the prediction interval into upper and lower sub-prediction intervals. Through the adaptive update strategy, the coverage of the upper and lower sub-prediction intervals reaches the expected coverage to ensure that the true value is more evenly distributed in the prediction interval, making the control of the prediction interval coverage more precise and the average width further reduced.

6. The adaptive interval prediction method for short-term residential load according to claim 5, characterized in that: The adaptive update strategy proposed in the step 4 directly utilizes the relationship between the improved biased convex loss function hyperparameters and the prediction interval coverage to construct a hyperparameter adaptive update strategy. In the process of minimizing the improved biased loss function to obtain the optimal parameters of the upper and lower limit prediction models, the loss function hyperparameters are optimized to simultaneously achieve optimal hyperparameter adjustment and optimal prediction interval construction.

7. The adaptive interval prediction method for short-term residential load according to claim 6, characterized in that: The iterative update formula of the adaptive update strategy is: In the above formula: k1 and k2 control the iteration update rate, PICP * The expected coverage of the prediction interval preset for the training model, i represents the current iteration number.

8. The adaptive interval prediction method for short-term residential load according to claim 1, characterized in that: The data collection and processing in step 1 includes preprocessing, feature extraction and normalization of the input data including temperature forecast data and load history data at the same time of the previous week, and then inputting them into the interval prediction model.

9. The adaptive interval prediction method for short-term residential load according to any one of claims 2 to 8, characterized in that: The upper limit prediction model and the lower limit prediction model are implemented by a gate recurrent network and a fully connected neural network, initialization parameters are obtained by Xavier and He initialization methods respectively, and the network structure is determined by cross-validation of the model point prediction results.

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