1 Introduction

With the steady develop of economy and society, building the global energy Internet become more and more important [1, 2]. The research of electrical power big data is one of the important sub-topics of smart grid technology. With the mining for the data from Supervisory Control and Data Acquisition (SCADA) system and Energy Management System (EMS), ones can obtain the efficient decision-making and the dispatching control of power system. As one of the most important concerns of the power industry staff, power load forecasting focus on how to extract the data related to load forecasting from the huge business flow, information flow and data flow of the smart grid and analyze these data in the environment of power big data [3, 4].

Existing studies have reported common prediction methods, such as grey theory [5], fuzzy theory [6, 7], time-series theory [8], artificial neutral network(ANN) [9, 10], wavelet theory [11], decision tree [12], support vector machine(SVM) [11, 13], etc., these methods provide a variety of effective ways for power load forecasting. However, most of these methods are based on single-alone machine load forecasting model, which only adapt good historical data and small dataset. As the amount of data and dimensions increasing, methods based on single-alone machine have many shortcomings, such as over-fitting, local optimization, insufficient memory to process the large-scale dataset. Therefore, the new data processing architecture with big data and distributed computing platform is becoming more and more urgent.

With new research methods based on Apache Spark emerging [14, 15], more sophisticated methods have been developed. By studying the allocation of memory in distributed cluster, an automatic algorithm with memory usage decision is proposed, which has a good application effect [16]. Both typical clustering algorithm (k-means) and association analysis algorithm (Apriori) are deployed and tested on the distributed cluster and verified more efficient than single-alone machine on large-scale data sets [17,18,19], improved support vector machine algorithm, Spark support vector machine (SP-SVM), suitable for distributed environment [20], and the parameters in SVM of distributed cluster is optimized [21]. In addition, the Boosting method is used to strengthen the weak learning process component-wise linear least squares(CWLLS), and the L2-Boosting algorithm in the distributed cluster is proposed. It is used for load forecasting, results verified the validity of L2-Boosting model [22]. Short term load forecasting is usually used to arrange the start and stop of the generator, adjust the power generation ratio of the hydropower unit and thermal power unit, make the load distribution more economical, and arrange the maintenance plan of the equipment; mid-long term load forecasting is generally used for the planning and design of regional power grids [23, 24], as well as the reconstruction and capacity increase of power plants, such as increasing the generating sets of power plants.

This paper is motivated by short term load forecasting problem and makes another attempt to tackle the following challenge: short term load forecasting with power big data. We present a solution to this problem by “clustering–regression” model in distributed cluster and implemented by Apache Spark machine learning library (MLlib). The proposed scheme can predict reasonably the short-term power load and has excellent robustness, so, it is significantly superior to existing single-alone machine load forecasting model and or directly regression load forecasting model. The main contributions of this paper are as follows:

  • This paper tackles short term load forecasting problem by “clustering–regression” model with distributed cluster. We emphasized that proposed scheme is rather different from existing work due to the application of “load characteristic curves of each cluster”.

  • Motivated by the “load characteristic curves of each cluster”, we design “clustering–regression” short term load forecasting model. Since the “load characteristic curves of each cluster” represents the electrical features of various types of power users and is considered as the properties of a regional total load, the users’ electrical features are fully reflected and the proposed short term load forecasting model’s performance has greatly improved.

  • The “clustering–regression” load forecasting model is realized by using Apache Spark machine learning library [25, 26]. We perform comprehensive performance test with “clustering–regression” model. The experimental results demonstrate that our proposed model shows a significant advantage over the directly regression model and single-alone model.

The rest of this paper is organized as follows. Section 2 describes the core technologies of Apache Spark and brief introduction of power load forecasting. In Sect. 3, we provide the detailed procedures of constructing “clustering–regression” model. The corresponding experimental results and discussions are presented in Sect. 4. Finally, Sect. 5 concludes this paper.

2 Related works

2.1 Apache Spark and MLlib

Apache Spark is a distributed cluster computing framework, which is developed in the AMPLab at UC Berkeley [27] and focuses on simplifying the design of parallel programs on cluster. In a cluster, a task scheduling server with a high memory is termed as a Driver, while a number of high-disk-stored task computing machines are denoted as Workers. In the calculation, the Driver accepts user’s commands and divides the tasks into each Worker to execute; the Worker can extract data from the Hadoop Distributed File System (HDFS) or other distributed file system. The data processed by Worker is stored in memory and then returned to the Driver to get the final result. Spark inherited MapReduce linear scalability and fault tolerance, while data processing has improved [28]. The MapReduce must be enforced to perform steps Map and Reduce sequently; Spark can send intermediate results directly to the next step of the job through a directed acyclic graph (DAG) operator, rather than being stored in HDFS as MapReduce.

Resilient distributed datasets (RDD) is the core of Spark, has the following characteristics:

  • RDD represents the data set that has been partitioned and can be operated in parallel. The organization, operation, scheduling and error recovery of the calculation task in Spark are carried out by RDD as the unit.

  • RDD can be a collection of dataset that consists of data distributed on the Worker nodes.

  • RDD has a fault tolerance mechanism. The dependencies between the parent RDD and the child RDD are stored in the lineage. When the data is lost or damaged during the RDD processing, the recovery can be recalculated according to the lineage.

MLlib is Apache Spark’s scalable machine learning library. Its goal is to make practical machine learning scalable and easy. It provides tools including: common machine learning algorithms, such as classification, regression, clustering, collaborative filtering, feature extraction, transformation and dimensionality reduction. In this paper, the clustering and regression correlation algorithm in MLlib is used to establish the “clustering–regression” short-term load forecasting model.

2.2 Power load forecasting

Electrical load data has a clear periodicity, for two weeks in a region of the working load curve as shown in Fig. 1.

Fig. 1
figure 1

Weekly load characteristic curve

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Figure 1 shows that the load curves of two adjacent working days in the same week are very similar. The load curves for two adjacent weeks of the same workday type (for example, Tuesday of 30thweek and Tuesday of 31stweek) are highly similar.

Let Load(m) denotes the real load of the day m, Load\(^{*}(m)\) denotes the forecasting load of the day m, Data(m) denotes the relating data of corresponding day’s power load. There are five types of m: “ Mon., Tue., Wed., Thu., Fri.”. The purpose of load forecasting is using the existing data to train model and construct mapping \(\mathfrak {R}\) while aiming the Load\(^{*}(m)\), which depended on Eq. (1), as close as possible to the actual Load(m) [29].

$$\begin{aligned} Load^{*}\left( m \right) =\left\{ {\begin{array}{l} \mathfrak {R}\left( {\begin{array}{l} Data\left( {m-6} \right) ,Data\left( {m-7} \right) , \\ Data\left( {m-14} \right) \\ \end{array}} \right) ,\quad m\in Mon. \\ \mathfrak {R}\left( {\begin{array}{l} Data\left( {m-7} \right) ,Data\left( {m-8} \right) , \\ Data\left( {m-14} \right) \\ \end{array}} \right) ,\quad m\in Fri. \\ \mathfrak {R}\left( {\begin{array}{l} Data\left( {m-6} \right) ,Data\left( {m-7} \right) , \\ Data\left( {m-8} \right) ,Data\left( {m-14} \right) \\ \end{array}} \right) ,\quad else \\ \end{array}} \right. \end{aligned}$$
(1)

3 Short-term load forecasting based on “clustering–regression” model

The proposed “clustering–regression” model comprises of two parts: clustering stage and regression stage. In clustering stage, according to users’ electrical features, we clustering the users and get the “load characteristic curves of each cluster”. These curves are used as a factor of the regional total load. In regression stage, combining with the corresponding day’s load, we gather relating days’ “load characteristic curve of each cluster” to train the model. The detail of proposed model is shown in Algorithm 1.

figure e

3.1 “Clustering” stage

3.1.1 Data preprocessing

The “user grouping raw data” and “electrical power load data” are provided by a power company in western China from March to August of 2016. The original user grouping data contains 11 attributes in total, which is the electric characters of users. The line number of “original user grouping data” is more than forty thousand, some of them are shown in Table 1. Since the existing classification is not accurate enough and meticulous, the original attributes is transformed to get fivve physical quantities to characterize the user’s electrical features, which includes maximum power, load ratio, peak to total ratio, flat to total ratio and valley to total ratio [30], where

$$\begin{aligned} load\,ratio= & {} \frac{total\,load}{24^{*}1000^{*}maximum\,power} \end{aligned}$$
(2)
$$\begin{aligned} peak\,to\,total\, ratio= & {} \frac{peak\,load}{total\,load} \end{aligned}$$
(3)
$$\begin{aligned} flat\,to\,total\,ratio= & {} \frac{flat\,load}{total\,load} \end{aligned}$$
(4)
$$\begin{aligned} valley\,to\,total\,ratio= & {} \frac{valley\,load}{total\,load} \end{aligned}$$
(5)

The raw data is normalized by above mentioned ratio method and the ratio is basically kept between 0 and 1. Preprocessing procedure makes the electrical features is more obvious and facilitate for the program processing.

Table 1 User grouping raw data
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3.1.2 Data clustering

Clustering the processed data with the electrical features above, the users with similar electrical features will in the same cluster. In our proposed model, the Spark k-means clustering algorithm is used in clustering stage, to build “clustering–regression” model. The classical K-means algorithm is shown in Algorithm 2 [31]. Here, “C” presents the number of clusters.

Algorithm 2 k-means

Algorithm K-means

1

Select C points as the initial centroids(center point)

2

Repeat

3

Form C clusters by assigning all points to the closest centroid

4

Recomputed the centroid of each cluster.

5

Until the centroids don’t change

In MLlib, the core step of implementing the k-means algorithm as follows [32]:

  • Generating the centroid of clustering; there are two ways to generate clustering centroid:“Random selection of sample points as initial clustering centroid” and “using k-means++ method to select the optimal clustering centroid”. The latter option is adopted in the proposed model. We realized this part of function by the methods initRandomand initKmeansParallel of runAlgorithmin the class of KMeans.

  • Iteratively calculates the centroid of the samples. Firstly, determine the centroid class of samples. Secondly, use the aggregate function to count the sum of the values that samples belonging to each centroid and the number of samples belonging to each centroid. Thirdly, select the latest centroid through judging whether the centroid has changed.

Notably, the clustering model k-means in the MLlib defines a method which quickly determinant the distance. The method is called “quick judgment” due to the distance formula lowerBoundOfSqDist.

For example, the centroid is \((a_{1}, b_{1})\), the sample point is \((a_{2}, b_{2})\), lowerBoundOfSqDist is calculated as follows:

$$\begin{aligned} lowerBoundOfSqDist= & {} \left( {\sqrt{a_1^2 +b_1^2 }-\sqrt{a_2^2 +b_2^2 }} \right) ^{2} \nonumber \\= & {} a_1^2 +b_1^2 +a_2^2 +b_2^2 \nonumber \\&-2\sqrt{\left( {a_1^2 +b_1^2 } \right) \left( {a_2^2 +b_2^2 } \right) }\nonumber \\ \end{aligned}$$
(6)

And the Eculidean distance is calculated as:

$$\begin{aligned} EuclideanDist= & {} \left( {a_{1}^{2} +b_{1}^{2}} \right) ^{2}+\left( {a_{2}^{2} +b_{2}^{2}} \right) ^{2}\nonumber \\= & {} a_{1}^{2} +b_{1}^{2} +a_{2}^{2} +b_{2}^{2} -2\left( {a_{1}a_{2}+b_{1}b_{2}} \right) \nonumber \\ \end{aligned}$$
(7)

Obviously, lowerBoundOfSqDist\(\le \)EculideanDist. Therefore, when iterative computing the centroid, the lowerBoundOfSqDist is calculated firstly, that is the \(\hbox {L}_{2}\) norm of centroid and sample point. We can analysis two cases:

  1. (1)

    If the lowerBoundOfSqDist is not less than the minimum distance bestDistance, then to save the operation time, EuclideanDistwill be not calculated.

  2. (2)

    If the lowerBoundOfSqDist is less than the minimum distance bestDistance, then fastSquaredDistancewill be used to quickly calculate the distance.

Notably, the calculate precision of fastSquaredDistance method is compared with the pre-set value “precisionBound”. The approximate formula is used to calculate theEuclidean distance if the precision is satisfied, otherwise, the original formula is used.

3.1.3 Building the load characteristic curve of each cluster

In this paper, we perform several experiments and comparison and train the parameter \(``C''\) as 20. The definition of “load characteristic curve of each cluster” is given as Eq. (8). For the \(``n_{i}''\) users in the cluster \(``i''\), the mean load of each metering point (total of 96 points) is calculated. An example is given in Fig. 2.

$$\begin{aligned} \mathbf{Load}\left( \mathbf{i} \right)= & {} \left[ {l_1^{\left( i \right) } ,l_2^{\left( i \right) } ,\cdots ,l_j^{\left( i \right) } ,\cdots ,l_{96}^{\left( i \right) } } \right] ^{T} \nonumber \\ l_j^{\left( i \right) }= & {} \frac{1}{n_i }\sum _{k^{\left( i \right) }=1}^{n_i } {load\left( {k^{\left( i \right) },j} \right) }\nonumber \\&\quad i\in \left[ {1,C} \right] , j\in \left[ {1,96} \right] \end{aligned}$$
(8)

Here, \(\mathbf{Load}\left( \mathbf{i} \right) \)is the load characteristic curve of cluster “i”;\(l_j^{\left( i \right) } \)is the mean load of cluster “i” at the time of “j”; \(load\left( {k^{\left( i \right) },j} \right) \)is the \(k^{th}\) user’s load of cluster “i” at time “j”.

Fig. 2
figure 2

Accumulate the load of each measuring point (96 points)

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Plot load(i), \(\hbox {i}\in [1,\hbox {C}]\) in a figure, load characteristic curve of different cluster marked with different colors. Figure 3 shows the load characteristic curve of each cluster by clustering the data of one day.

Fig. 3
figure 3

Load characteristic curve of each cluster (by Apache Spark k-means algorithms)

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3.2 “Regression” stage

3.2.1 Constructing training datasets

In this section, we integrate the load characteristic curve of each cluster of (m-6)th, (m-7)th, (m-8)th, (m-14)th as the “attributes” and the real-time load as a “tag” of the predictable day’s load. Notably, “regression” comes from “classification”, and the data label of “regression” is continuous, while the data label of “classification” is discrete. In order to test the validity and robustness of the “clustering–regression” model, we select the Spark decision tree and the Spark random forest as the comparison in the regression stage.

3.2.2 Regression prediction

The random forest algorithm is an ensemble algorithm, which is comprised of multiple single decision tree whose details are shown in Algorithm 3. Due to the diversity and unstable of results from individual decision tree, ensemble scheme is not easy to cause over-fitting and has the better prediction and classification performance.

In the Apache spark MLlib, the decision tree is wrapped in a Random Forest [32]. The regression procedures are explained as the follows:

  • First establish a Random Forest containing one decision tree, and then grow the decision tree in the Random Forest. The methodtrain is defined in object DecisionTree to set the parameters of the training model. The class DecisionTree is used for training classification and regression model, in the process of establishing the tree call the run method in class RandomForest,set the parameter seed=0, that only generate one decision tree.

  • The method buildMetadata of object DecisionTreeMetadata calculate the number of possible splits and the number of leaf nodes that are generated. The method findSplitsBins of object DecisionTree search for each possible splitting attribute and the number of leaf nodes generated. Furthermore, the method findBestSplitof object DecisionTreefinds the best splitting attribute, mainly through the method binsToBestSplit to determine the best splitting attribute.

  • In the process of establishing a random forest, all of the trees need to be training by the method run. The decision tree training process is actually the decision tree construction process. The top-down recursive structure is used until meeting certain stop conditions.

Note that class DecisionTreeModel defined the method predict, but need to call the method predict of class Node to achieve the forecast.

figure f

4 Experimental results

4.1 Distributed cluster construction based on Apache Spark platform

We use a distributed platform constructed in the laboratory to give the comprehensive simulation experiments. The distributed cluster use a DELL server, with 12 core CPU, clocked at 2.6 GHZ, 32 G memory, 10 T hard disk, Linux Ubuntu12.04 desktop operating system, as a management node driver. 4 Lenovo ordinary desktop, with 2 core CPU, clocked at 2.94 GHz, 2 G memory, 1T hard disk, Linux Ubuntu12.04 desktop operating system, is used as a computing node worker. The open source software versions of the cluster include Hadoop version 2.7.3, Spark version 2.0.1, jdk version 1.8, Scala version 2.11.8 and python version 2.7. The complete experimental framework is shown in Fig. 4.

Fig. 4
figure 4

Topology of distributed cluster

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4.2 Experimental design and analysis

The “user grouping raw data” has been introduced in Sect. 3.1. The “electrical power load data” is automatically collected the load values of the users in the region at intervals of 15 min by the metering automation system, producing 96 records one day.

According to Algorithm 1, the process of the “cluster-regression” model is performed. The details of the steps have been shown in Sect. 3.The error evaluation of model regression prediction can be calculated by the mean absolute percentage error (MAPE) and root-mean-square error (RMSE).

$$\begin{aligned}&{} \textit{MAPE}=\frac{1}{n}\sum _{i=1}^n {\left| {\frac{x_i -\hat{x}_i}{x_i}} \right| } \times 100\% \end{aligned}$$
(9)
$$\begin{aligned}&{} \textit{RMSE}=\sqrt{\frac{1}{n}\sum _{i=1}^n {\left( {\frac{x_i -\hat{{x}}_i }{x_i }} \right) ^{2}} }\times 100\% \end{aligned}$$
(10)

where\(x_i \) is the actual value of the time i-th load, and \(\hat{x}_{i}\) is the corresponding predicted value.

In order to test the validity and robustness of the “clustering–regression” model, the comprehensive experiments include the following four cases.

Experiment 1: Examining the validity of the “clustering–regression” model.

In our experiments, we compare proposed scheme with the scheme that use random forest regression directly. The data from a certain substation 2016-03-01 to 2016-08-25 are used as the training set to predict the load of a line of 2016-08-26, and the results are shown in Fig. 5.

With Eqs. (9) and (10), the error of two load forecasting methods is calculated and the corresponding MAPE and RMSE on the test set are shown in Table 2. Moreover, the predicted percentage error curve for each algorithm at each metering point are also shown in Fig. 6.

Fig. 5
figure 5

Comparison of load forecasting results between “clustering–regression” (k-means-RF) model and RF model

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Table 2 Comparison of load forecasting accuracy “clustering–regression” (k-means-RF) model and RF model
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Fig. 6
figure 6

Comparison of load forecasting error percent between “clustering–regression” (k-means-RF) model and RF model

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As can be seen from Table 2, Figs. 5 and 6, the load forecasting method using the “cluster-regression” model is superior to the general regression prediction model in the test set. Two reasons can explain this phenomenon: (1) Proposed scheme uses the “clustering–regression” model of k-means-RandomForest (k-means-RF). Although the RF-based load forecasting method shows excellent learning ability and adaptability [33,34,35], and has a relatively simple structure and lower spatial structure complexity, proposed scheme clustering the users by electrical features and got the “load characteristic curve of each cluster” and considered as factors in “regression” stage. As can be seen from Figs. 6 and 7, the prediction accuracy of “clustering–regression” model is higher than general regression prediction model. (2) The “clustering–regression” model proposed in this paper does not directly uses the historical load data, but analyzes the composition of the load. Since different types of users have different electrical power characteristics, the contribution for the total load is also different. This fine-grained analysis leads to an improvement of prediction.

Experiment 2: Robustness Analysis of “clustering–regression” Model.

The “clustering” stage uses k-means algorithm, while the “regression” stage use two algorithms: (1) classification and regression tree (CART) and (2) the FR, so the “clustering–regression” model produces two predictive datasets. The data from a certain substation 2016-03-01 to 2016-08-25 are used as the training set to predict one line’s load of 2016-08-26, and the results are shown in Fig. 7. Also, the error statistics are shown in Table 3.

Fig. 7
figure 7

Comparison of load forecasting results that with different combination of “clustering–regression” model

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Table 3 Experiment’s result of “clustering–regression” model
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Fig. 8
figure 8

Comparison of running time between algorithms based on distributed cluster and based on single machine

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Table 4 Data sets with different volume
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Table 5 Load forecasting MAPE in different data sets
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With the analysis of the results in Table 3 and Fig. 7, we can obtain two conclusions: (1) It can be seen that the forecasting result of “clustering–regression” model is reasonable, according to the two predictive datasets. The model is rather robust. (2) k-means-RF model based on RF has higher prediction accuracy than that of k-means-CART in the “regression” stage. This is because the RF combines the “Bagging” method to make decision tree together, the establishment of the model not only retain the statistical characteristics of the original data set, and in the establishment of the model as much as possible to reflect the randomness of attributes set. RF is more robust to errors and outliers. With the increasing the number of trees in the forest, the generalization error of random forest is converged, and the risk of over-fitting is reduced. From Fig. 8, the load curve predicted by the k-means-RF model is closest to the actual load.

Experiment 3: Testing and verifying the “clustering–regression” model with a larger data set. The size of experimental data set is shown in Table 4. Since the experimental data is limited and original data will be artificially expanded, different sizes of data files are used into our experiments.

The five data sets are incremented in succession, k-means-RF is run on each data set, and MAPE is calculated according to Eq. (5). Table 5 shows the results. We can see that with the increasing of the data volume, the prediction error increases slightly. Furthermore, the maximum MAPE is 1.81% and the minimum MAPE is 1.65%. This demonstrates that the fluctuation of forecasting error is smoothly and irregularly. As results, experiments show that proposed model can be applied in big data platform on load forecasting.

Experiment 4: Constructing the distributed cluster to solve the problem that the stand-alone model cannot be processed in the face of massive data.

In order to test this feature of the distributed computing platform, a set of stress tests was designed. Compared with the single-alone model, the proposed model in the distributed cluster is tested. The model in the distributed cluster uses the “clustering–regression” model (k-means-RF) and the spark classification and regression tree (SP-CART), while the single-alone model uses the CART. The establishment time of model in the three algorithms on the same data set is examined. The worker nodes running the three algorithms shave the same CPU clock and the same operating system (Ubuntu12.04). The worker node running the single-alone CART, has 4 G memory. The two worker nodes running the k-means-RF and the SP-CART have 2 G memory. So the distributed cluster memory is totally 4 G either. Three algorithms use the same training data sets, whose size is 100 MB, 200 MB \(\ldots \) up to 800 MB.The testing results are shown in Table 6 and Fig. 8. Single-alone CART model has an inefficient memory error when analyzing 800MB datasets. This demonstrates that single-alone CART model is not suitable for analyzing bigger data sets (Table 6).

Table 6 Running time of algorithms based on distributed cluster and based on single machine
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From Table 6 and Fig. 8, we can also see that the load forecasting method based on distributed cluster has no speed advantage when the data set is small (less than 650 M). The stand-alone CART load forecasting method has a shorter run time than that of distributed cluster k-means-RF and SP-CART methods when the data set is less than 650 M. This is because the distributed cluster task allocation and scheduling needs a certain time. The single-alone model is restricted by machine memory, and it is grandly saturation up to 700 M. When data is up to 650 M, both the single-alone model and the distributed cluster model have the approximate running time. When data is more than 700 M, the single-alone model memory is insufficient and cannot be used. Moreover, with the increasing of data set, the computational time of distributed clustering based on distributed cluster basically increases linearly. As long as the distributed cluster size is expanding, the processing capacity of the cluster can ignore the affected by the size of the data set.

In addition, comparing the time curves of k-means-RF model with SP-CART model in Fig. 8, it can be found that the time curves of k-means-RF is slightly higher than SP-CART, but the height difference is substantially stable. This phenomenon can be explained as follows. On one hand, the “clustering–regression” model needs to “clustering” before “regression”, while the SP-CART model only needs “regression”. On the other hand, at the “regression” stage, the RF algorithm needs to “bagging”, while the SP-CART algorithm does not need. Compared to the algorithm running time, this part of the time consuming can be ignored. As the amount of computation nodes increases, the algorithm running time will be reduced. In summary, the current distributed clusters still have a great performance improvement.

5 Conclusion and future work

Based on the analysis of users’ electrical power characteristics, a clustering–regression model of short-term load forecasting is proposed. By clustering users’ electrical power characteristics, we obtain the load characteristic curve of each cluster. Relating to the forecast day, the load characteristic curve of each cluster is collected and the regression is made. The Apache Spark MLlib is used to realize proposed “clustering–regression” model.

With the actual load data of a power company in China, the comprehensive experiments are designed. The accuracy of load forecasting of proposed model is significantly improved. For the model, the combinations of different algorithms are used in the “clustering” and “regression” stages, the validity is verified. Since the model is to be used in distributed cluster, it can be tested with a large-capacity dataset, and is demonstrated to be robust. Compared with single-alone model for stress testing, the proposed model has obvious advantage in the background of big data and provides significant engineering practice. Although the proposed model has some advantages, the structure of the “clustering–regression” model can be further optimized. Further optimization will be considered to improve the data processing capacity of the “clustering–regression” model and make it suitable for medium or long term power load forecasting.