Short-term Electric Load Forecasting Using TensorFlow and Deep Auto-Encoders

TL;DR

This paper proposes a novel short-term electric load forecasting model using Deep Auto-Encoder Networks and TensorFlow, improving accuracy, stability, and scalability over traditional neural network methods in big data scenarios.

Contribution

It introduces a new distributed forecasting approach combining DAENs with TensorFlow, addressing over-fitting and convergence issues of traditional neural networks.

Findings

Enhanced prediction accuracy compared to traditional methods

Improved model stability and scalability

Effective handling of big data for load forecasting

Abstract

This paper conducts research on the short-term electric load forecast method under the background of big data. It builds a new electric load forecast model based on Deep Auto-Encoder Networks (DAENs), which takes into account multidimensional load-related data sets including historical load value, temperature, day type, etc. A new distributed short-term load forecast method based on TensorFlow and DAENs is therefore proposed, with an algorithm flowchart designed. This method overcomes the shortcomings of traditional neural network methods, such as over-fitting, slow convergence and local optimum, etc. Case study results show that the proposed method has obvious advantages in prediction accuracy, stability, and expansibility compared with those based on traditional neural networks. Thus, this model can better meet the demands of short-term electric load forecasting under big data scenario.

Figures

Tables

Table 1. TABLE I: Day Type Encoding.

Date	Encoded Value
Monday	$(0,0,0,0,0,0,0.5)$
Tuesday	$(0,0,0,0,0,0.5,0)$
Wednesday	$(0,0,0,0,0.5,0,0)$
Thursday	$(0,0,0,0.5,0,0,0)$
Friday	$(0,0,0.5,0,0,0,0)$
Saturday	$(0,0.5,0,0,0,0,0)$
Sunday	$(0.5,0,0,0,0,0,0)$

Table 2. TABLE II: Data Samples.

Samples	Month	Day	00:30	01:00	…	23:30	24:00	Temperature	Day Type	Holiday
Pretraining Set
	1	1	797	794	…	692	686	-7.6	Wednesday	yes
	.	.	.	.	…	.	.	.	.	.
X=Y	.	.	.	.	…	.	.	.	.	.
	.	.	.	.	…	.	.	.	.	.
	11	30	665	640	…	617	623	7.2	Sunday	no
Fine-tuning Set
	12	1	637	626	…	613	644	6.7	Monday	no
	.	.	.	.	…	.	.	.	.	.
X	.	.	.	.	…	.	.	.	.	.
	.	.	.	.	…	.	.	.	.	.
	12	23	674	664	…	640	646	2.4	Tuesday	no
	12	8	—	677	…	—	710	—	—	—
	.	.	.	.	…	.	.	.	.	.
Y	.	.	.	.	…	.	.	.	.	.
	.	.	.	.	…	.	.	.	.	.
	12	30	—	673	…	—	663	—	—	—
Testing Set
	12	24	650	652	…	621	645	1.1	Wednesday	yes
	.	.	.	.	…	.	.	.	.	.
X	.	.	.	.	…	.	.	.	.	.
	.	.	.	.	…	.	.	.	.	.
	12	30	678	673	…	663	663	-0.2	Tuesday	no
Y	12	31	—	668	…	—	692	—	—	—

Table 3. TABLE III: Comparison of Load Forecast Value and Actual Value.

Moments	AV/MW	FV/MW	Re/$\%$
1:00	668	673.3406	0.7995
2:00	642	650.3174	1.2955
3:00	623	625.4593	0.3948
4:00	602	620.9128	3.1417
5:00	618	621.4146	0.5525
6:00	619	611.1831	1.2628
7:00	599	601.7022	0.4511
8:00	602	604.8622	0.4754
9:00	643	640.9628	0.3168
10:00	669	655.8308	1.9685
11:00	700	679.4819	2.9312
12:00	688	689.8511	0.2691
13:00	710	700.154	1.3868
14:00	717	713.8212	0.4433
15:00	700	706.6741	0.9534
16:00	681	687.7114	0.9855
17:00	704	691.7314	1.7427
18:00	691	684.2487	0.9770
19:00	692	688.7641	0.4676
20:00	700	705.1727	0.7390
21:00	648	675.6137	4.2614
22:00	635	656.4427	3.3768
23:00	681	689.8683	1.3022
24:00	692	690.3376	0.2402

Table 4. TABLE IV: The Indicator Comparison of Different Load Forecast Methods.

Indicators	DAENs/$\%$	BPNNs/$\%$	ELM/$\%$
$MaxRe$	4.26	8.78	4.57
$MinRe$	0.24	0.31	0.36
$Mae$	1.28	2.97	2.06

Equations

$$\begin{array}{r}h=f(x)=S_f(\text{W}x+\text{p})\end{array},$$

$$\begin{array}{r}y=g(h)=S_g(\hat{\text{W}}h+\text{q})\end{array},$$

$$\begin{array}{r}L(\text{x},\text{y})=-\sum _{i=1}^n\left[{\text{x}}_i\log ({\text{y}}_i)+(1-{\text{x}}_i)\log (1-{\text{y}}_i)\right]\end{array}.$$

$$\begin{array}{r}{J}_{AE}(\theta )=\frac{1}{N}\sum _{\text{x}\in \mathbf{S}}L(\text{x},g(f(\text{x})))\end{array}.$$

$$\begin{array}{r}{\hat{\rho }}_j=\frac{1}{N}\sum _{i=1}^N{h}_j({\text{x}}^{(i)})\end{array}.$$

$$\begin{array}{r}{\hat{\rho }}_j=\rho \end{array},$$

$$\begin{array}{r}{J}_{AE+sp}(\theta )=\sum _{\text{x}\in \mathbf{S}}L(\text{x},g(f(\text{x})))+\beta \sum _{j=1}^{m}KL(\rho ||{\hat{\rho }}_j)\end{array},$$

$$\begin{array}{r}KL(\rho ||{\hat{\rho }}_j)=\rho \ast \log \frac{\rho }{{\hat{\rho }}_j}+(1-\rho )\ast \log \frac{1-\rho }{1-{\hat{\rho }}_j}\end{array}.$$

$$\begin{array}{r}L=\frac{L_t-L_{\min }}{L_{\max }-L_{\min }}\end{array},$$

$$\begin{aligned} {p_{1}}=\left\{\begin{array}[]{l}0\;\;\;\;\;\;\;\;\;t\geq 10\\ \frac{{10{\rm{-}}t}}{{15}}\;\;\;-5\leq t\leq 10\\ 1\;\;\;\;\;\;\;\;\;t\leq-5\end{array}\right.\end{aligned},$$

$$\begin{aligned} {p_{2}}=\left\{\begin{array}[]{l}0\;\;\;\;\;\;\;\;\;t\leq 0,t\geq 20\\ \frac{t}{{10}}\;\;\;\;\;\;\;0\leq t\leq 10\\ \frac{{20{\rm{-}}t}}{{10}}\;\;\;\;10\leq\;t\leq 20\end{array}\right.\end{aligned},$$

$$\begin{aligned} {p_{3}}=\left\{\begin{array}[]{l}0\;\;\;\;\;\;\;\;\;t\leq 15\\ \frac{{t{\rm{-}}10}}{{20}}\;\;\;\;15\leq t\leq 30\\ 1\;\;\;\;\;\;\;\;\;t\geq 30\end{array}\right.\end{aligned}.$$

$$\begin{array}{r}MaxRe=\max (\left|\frac{F_i-{\hat{F}}_i}{F_i}\right|.100\%)\end{array},$$

$$\begin{array}{r}MinRe=\min (\left|\frac{F_i-{\hat{F}}_i}{F_i}\right|.100\%)\end{array},$$

$$\begin{array}{r}Mae=\frac{1}{n}\sum _{i=1}^n(\left|\frac{F_i-{\hat{F}}_i}{F_i}\right|.100\%)\end{array},$$

$$\begin{array}{r}F=\sum _{k=1}^n{e}^{-\alpha k}{F}_k\end{array},$$

Full text

I Introduction

Serving as the basis of the planning and dispatching of power systems, short-term electric load forecasting is the premise of achieving automatic generation control and economic dispatching. Its accuracy has an impact on the safety, stability, and economy of the normal operation of the power systems. An accurate load forecast method can reduce operating costs, keep power markets efficient, and provide a better understanding of the dynamics of the monitored systems[1][2]. Therefore, it is of great importance to study short-term load forecast methods.

For a long time, electric load forecast methods have been researched by scholars at home and abroad, which in general fall into two categories, traditional methods and artificial intelligence methods. The former mainly include time series [3][4], regression [5] and grey system theory [6][7], etc. They have simple models and fast calculation speed, but cannot simulate electric load under complicated situations, leading to an unsatisfying prediction accuracy. The latter mainly refer to some machine learning methods, including back propagation neural networks (BPNNs) [8][9], support vector machine (SVM) [10][11], extreme learning machine (ELM) [12][13], etc. The prediction accuracy has been improved to some extent by using those intelligent methods. However, those intelligent methods have limited learning ability and are not capable of transforming and processing large data samples, which can easily lead to over-fitting, slow convergence, local optimum, and many other problems. As a result, the prediction accuracy has certain limitations, which cannot meet the demands and challenges of big data analysis.

With the emergence of big data in the power sector, load-related data dimensions continue to increase, which brings new challenges to the electric load forecast work. We must find a new method to effectively achieve the goal of electric load forecasting and analysis under this scenario. In 2006, Geoffrey Hinton from Canada proposed the method of deep learning[14][15], which opened a new era of deep learning in academic and industrial fields. Deep Auto-Encoder Networks (DAENs), a deep learning method, conducts feature transformation on training samples, layer by layer, to build a machine learning model with multiple hidden layers, projecting the feature representation in the original scenario into a new one, which makes it easier to predict, and ultimately improves prediction accuracy. Compared to methods that construct features by artificial rules, the DAENs method is better at depicting the rich inner information of data, effectively meeting the demands of big data analysis. It has been the hot spot of international machine learning research field[16][17][18], but few attempts have been made to introduce it in the application of electric load forecasting.

I-A Contributions

In this paper, based on multidimensional load-related data such as historical load values, temperature, day types etc., a new distributed short-term load forecast method using TensorFlow and DAENs is proposed. In Sect. II we give the mathematical background and theoretical foundation. The training processes of DAENs include pre-training and fine-tuning, which are introduced and analyzed in detail. In Sect. III, we first introduce TensorFlow. Then we construct load forecast model based on DAENs. Considering the complex structure of DAENs and high real-time demand of load forecasting, we designed a parallel algorithm flowchart using the multi-GPU mode analysis framework of TensorFlow, which greatly enhances the calculation speed. Load-related data is processed using the normalization formula, fuzzy membership function, and weighted one-hot encoding method. The evaluation index of load forecasting is defined at the end. In Sect. IV, with load-related data provided by European Smart Technology Network(EUNITE), the forecast method proposed in this paper is validated and its advantages are highlighted. Furthermore, comparison of this method with the method based on BPNNs and ELM is made. In Sect. V, we report our conclusions.

I-B Related Works

Auto-Encoder networks have been widely explored in the past years. Reference [19] introduces a new method to analyze the human immunodeficiency virus using a combination of Auto-Encoder networks and genetic algorithms, which outperforms the conventional feedforward neural network models and is a much better classifier. Reference [20] extracts and composes robust features by using denoising Auto-Encoders, which shows surprising results. In reference [21], an algorithm that aids the curation of gene annotations and predicts previously-unidentified gene functions is designed by using deep Auto-Encoder neural networks. Experiments show that deep Auto-Encoder neural networks achieve better performance than other standard machine learning methods, including the popular truncated singular value decomposition. Reference [22] proposes a novel method for modeling the excitation through an Auto-Encoder, which produces speech of higher perceptual quality compared to conventional pulse-excited speech signals. Reference [23] uses Auto-Encoder neural networks for water demand predictive modeling. In the research done above, Auto-Encoder networks have been successfully used for solving classification or predication problems.

II Mathematical Background and Theoretical Foundation

II-A Deep Auto-Encoder Networks

DAENs are one kind of neural networks composed of multi-layer Auto-Encoders(AE), which are similar to traditional multi-layer neural networks in structure. For example, take one layer of an AE, the network structure is shown in Figure 1.

One basic AE can be viewed as a three-layer traditional neural network, including one input layer, one hidden layer and one output layer. The input layer and output layer are of the same size. Transition from the input layer to the hidden layer is called the encoding process. The transition from the hidden layer to the output layer is called the decoding process. Assume $f$ and $g$ respectively represent the encoding and decoding function. Then the two processes above can be defined as

[TABLE]

[TABLE]

where ${S}_{f}$ and ${S}_{g}$ are the sigmoid functions, W is the weight matrix between the input layer and the hidden layer, and ${\bf{\hat{\emph{W}}}}$ is the weight matrix between the hidden layer and the output layer, whose initial value is ${{\bf{\emph{W}}}^{\mathop{\rm T}\nolimits}}$. p and q are the bias vectors of the hidden layers and output layers separately. For simplicity, we use ${\bf{\theta}}$ to represent those parameters, namely ${\bf{\theta=}}\left\{{{\bf{\emph{W},\emph{p},\emph{q}}}}\right\}$.

Assuming training sample sets as ${\rm{\bf{S}}}=\left\{{{{\bf{\emph{x}}}^{(1)}},{{\bf{\emph{x}}}^{(2)}},\cdots,{{\bf{\emph{x}}}^{(N)}}}\right\}$, we can optimize ${\bf{\theta}}$ through training the AE network on it. The target of training the AE network is to make its output y and input x be as equal as possible. The approximation can be described by the reconstruction error function ${{L}({\bf{\emph{x},\emph{y}}})}$, which is defined as

[TABLE]

Combining ${{L}({\bf{\emph{x},\emph{y}}})}$ and ${\bf{S}}$, we can obtain the loss function as

[TABLE]

Then we can get ${\bf{\theta}}$ by optimizing ${J_{AE}}\left({\bf{\theta}}\right)$ through gradient descent methods, such as SGD [24], ADAM [25], RMSPROP [26], etc. However, it is likely to obtain an identity function in practical application if we optimize the loss function directly. To solve this problem, we can add sparse limits into the loss function. Assuming the input is ${{\rm{\emph{x}}}^{(i)}}$ and ${h_{j}}({{\bf{\emph{x}}}^{(i)}})$ indicates the activation degree of the $j$th neuron in the hidden layer, the average activation on training sets ${\bf{S}}$ is

[TABLE]

In order to guarantee the sparse limits, neurons in the hidden layers are suppressed to zero most of the time, that is

[TABLE]

where ${\rho}$ is the sparse parameter and usually gets a small value. ${\hat{\rho}_{j}}$ that is obviously different from ${\rho}$ should be “punished” using KL divergence method [27]. We can add $\sum\limits_{j=1}^{m}{KL(\rho||{{\hat{\rho}}_{j}})}$ into the loss function. Then the loss function is

[TABLE]

where ${\beta}$ is the weight coefficient of sparse penalty term, and

[TABLE]

Equation (8) shows that $\sum\limits_{j=1}^{m}{KL(\rho||{{\hat{\rho}}_{j}})}$ gradually decreases as ${\hat{\rho}_{j}}$ approaches ${\rho}$, and reaches zero when ${\hat{\rho}_{j}}$ equals ${\rho}$. Therefore, we can minimize the difference between ${\hat{\rho}_{j}}$ and ${\rho}$ by optimizing the loss function in equation (7).

II-B Training

DAENs is trained layer by layer. The outputs of the previous layer serve as the inputs of next level, which effectively solves the problem of gradient diffusion in traditional neural networks. The entire network training process is divided into two stages: pre-training and fine-tuning .

Pre-training is essentially the process of initializing network parameters layer by layer through unsupervised feature optimization algorithms. In this process, we set the target value equal to the input value, and adopt stochastic gradient descent or similar methods as the training algorithms, which means the output vector of the hidden layer is taken as the input of the next layer for training after one layer of AE training is completed. The steps above are repeated until the training of all AE layers is finished. After pre-training, the labelled data set is used to calibrate the parameters of the whole DAENs to achieve the global optimum by training with stochastic gradient descent or similar methods, which is called fine-tuning. The method combining pre-training with fine-tuning usually outperforms those based on traditional neural networks, because it can effectively avoid slow convergence, over-fitting, local optimum, and instability problems.

III Load Forecasting Based on DAENs and TensorFlow

III-A Introduction to TensorFlow

TensorFlow is an open source artificial intelligence programming system released by Google in November, 2015 [28]. It can transmit data of complex structure to artificial neural networks for process and analysis. It has been widely used in deep machine learning areas, such as speech recognition [29][30], image processing [31][32], natural language processing [33][34], etc. It runs on devices ranging from a small smartphone to thousands of data center servers. TensorFlow conducts calculation in the form of data flow graphs and this flexible architecture allows it to support single or multiple CPU or GPU computing, which greatly improves the ability of data computation and analysis in big data case. Based on TensorFlow, this paper combines the DAENs model and TensorFlow distributed data analysis framework to realize the distributed short-term load forecasting of power system.

TensorFlow provides the following key concepts for data flow graph calculation.

• •

Graph: It is used to represent the calculation task and describe the calculation process.

• •

Op: The acronym for operation, which represents the nodes in the graph and is responsible for performing the computation.

• •

Session: It is responsible for the implementation of the graph, namely distributing the ops to CPU or GPU devices and providing op implementation methods.

• •

Tensor: It is used to indicate data.

• •

Variable: It is used to maintain the states.

• •

Feed/Fetch: It is used to input or output data for any operation.

III-B Load Forecast Model Based on DAENs and TensorFlow

The load forecast model based on DAENs constructed in this paper is shown in Fig.2. The DAENs consist of all layers except for the last one. The number of layers is determined by the dimension and volume of input data. High dimension and large volume of data will lead to the increasing of AE layers, and vice versa. We add an output layer at the end of the model to serve as the forecast layer, where a linear regression model is used. The input of the model is multidimensional load-related data including historical load value, temperature, day types, etc., and the output is the load value at certain time on the forecast day. What is important about the model is that it is scalable, which means we can achieve good performance of the model through adding the number of network layers and neurons when dimension and volume of sample data increase, because its training method overcomes gradient diffusion while traditional machine learning methods do not.

A parallel algorithm flow chart is designed, shown in Fig. 3, that combines the DAENs-based load forecast model with multi-GPU mode analysis framework of TensorFlow.

As displayed in Fig. 3, the load-related data is processed and loaded into TensorFlow’s tensors to form data samples. Then data samples are distributed into GPUs by the computer CPU and further divided into pre-training sets, fine-tuning sets, and testing sets for pre-training, fine-tuning, and testing the forecast model respectively. Load forecast value at different moments of the forecast day are accomplished by parallel model training of multiple GPUs. The load-related data is defined and processed as follows.

1. Electric load forecasting is related to multiple factors, including historical load value, daily temperature, day types, etc. Here we define the load-related dataset as ${\rm{\bf{S}}}=\left\{{\bf{L}},{\bf{T}},{\bf{D}},{\bf{H}}\right\}$. L is the source load data set,T is the daily average temperature data set, D is the day type data set, and H is the holiday data set.

2. Source load data are normalized according to equation (9).

[TABLE]

where ${L_{\max}}$ and ${L_{\min}}$ respectively represent the maximum and minimum load value in the training sample sets, ${L_{t}}$ represents the current load value, and $L$ represents the normalized load value.

3. Fuzzy membership functions of low, medium, and high temperature are defined to blur temperature data to be 0, 0.25, and 0.5 separately, which are shown as equation (10), (11) and (12).

[TABLE]

[TABLE]

[TABLE]

In the equations above, ${t}$ is the daily average temperature value and ${P_{i}}$ is the probability value.

4. Day type here is used to distinguish weekday attributes by using a weighted one-hot encoding method [35]. The weight value is 0.5. The encoded data is shown in Table I.

5. Holiday falls into either the “yes” or “no” category here, which is encoded as 0.5 or 0 respectively.

III-C *Evaluation Index *

Prediction error is an important index to evaluate the performance of one forecast method. In this paper, maximum relative error ($MaxRe$), minimum relative error ($MinRe$), and mean absolute error ($Mae$) are used to evaluate the prediction performance of the method proposed, which are separately defined as

[TABLE]

[TABLE]

[TABLE]

where ${F_{i}}$ is the actual load value and ${\hat{F}_{i}}$ is the forecast load value at time $i$. We can conclude from the formulas above that, $MaxRe$ and $MinRe$ can reflect the stability and reliability of the prediction model, while $Mae$ reflects the prediction accuracy of it.

IV Case Studies

IV-A Data Samples of the Case

Based on the load-related data provided by EUNITE, the short-term electric load forecast method proposed in this paper is employed to predict the load data at moments 1:00, 2:00,…, 24:00 on December 31st. We set up 24 load forecast models in total. There are 57 items for each of the model inputs: 1 to 48 for electric loads at moments 0:30, 1:00, 1:30,…,24:00 on a historical day; 49 for the fuzzy value of the historical daily average temperature; 50 to 56 for the day type encoded value of the historical day; 57 for the encoded value of the holiday. The output of each model is the forecast load value at one certain moment, such as 1:00, 2:00, 3:00, etc. The data set is divided as follows for the training process: sample data from January 1st to November 30th is used for pre-training while from November 1st to 23th is used for fine-tuning, with a total of 20169 items. For the testing set, we choose sample data from December 24th to 31st. The data sample format is shown in Table II.

IV-B Experimental Design and Implementation

The experiment was conducted on a DELL T430 server, which provides multiple PCIE3.0x16 interfaces for expansion, effectively supporting parallel computing of multi-GPU mode. We mainly used “Ubuntu14.04” and “TensorFlow-0.9.0” softwares. The experimental parameters are set as follows.

• •

AE layers: 2.

• •

Number of neurons for each layer: 57, 24, 12, 1.

• •

Initial learning rate: 0.01.

• •

Maximum pre-training iteration: 2000.

• •

Maximum fine-tuning iteration: 250.

Tensorboard, a visualization tool of TensorFlow, can display the data flow graph of the model, which is shown in Fig. 4.

In Fig. 4, the solid line represents data dependency, while the dashed line represents control dependency. “${\mathop{\rm Loss}\nolimits}\_{\rm pretrain}$” and “${\mathop{\rm RMSprop}\nolimits}\_{\rm pretrain}$” modules represent the network pre-training process, “${\mathop{\rm Loss}\nolimits}\_{\rm finetuning}$” and “${\mathop{\rm RMSprop}\nolimits}\_{\rm finetuning}$” modules represent the network fine-tuning process, and “$\rm Model$” module represents the network structure. Each module in the figure can be expanded by clicking on the “$\rm+$” button in the upper right corner. The expansion form of “$\rm Model$”, for example, shows the data flow and operation process, which is displayed in Fig. 5.

Function $tf.scalar\_summary()$ in TensorFlow can be used to trace the error function of pre-training and fine-tuning. Taking GPU 1 for example, the tracing results are separately shown in Fig. 6 and Fig. 7. As can be seen from the figures, errors of pre-training and fine-tuning are continuously decreasing with the increase of iteration times, nearing 0 in the end. The performance of the pre-trained network quickly converges to global optimum with only a few training iterations, which shows that the proposed forecast method has good convergence.

IV-C Comparison and Analytics of Experimental Results

In the experiment, we conduct load forecasting on the forecast day by using the load-related data of its previous $1$ to $n$ day. Assuming the forecast results are ${F_{1}}$, ${F_{2}}$, … , ${F_{n}}$, we calculate the final load forecast value $F$ according to equation (16).

[TABLE]

where $n$ is 7 and $\alpha$ is 0.69 through empirical data in the fine-tuning process. The equation indicates that for each historical day, the closer it is to the forecast day, the more it will contribute to the forecast result.

Comparison of the load forecast value (FV) and the actual value (AV) is shown in Table III, and we calculate the relative error (Re) at each moment, which is also included in Table III.

As can be seen from Table III, the relative error can be maintained at about $1{\rm{\%}}$ at most moments, the maximum is $4.26{\rm{\%}}$, and the minimum is $0.24{\rm{\%}}$. Besides, the forecast error fluctuation is relatively small. All of these indicate that the overall forecast effect is ideal.

In contrast, we have conducted experiments using load forecasting method based on BPNNs and ELM. 24 models are set up for each method to forecast the load value at 1:00, 2:00, . . . , 24:00. Because pre-training is not required for them, we just choose the fine-tuning set and testing set separately as training set and testing set in the experiment. Experimental parameters of BPNNs are set as follows.

• •

Number of neurons for each layer: 57, 24, 1.

• •

Initial learning rate: 0.01.

• •

Maximum pre-training iteration: 2000.

For ELM, number of neurons for network input layer, hidden layer, and output layer are separately set as 57, 30, and 1.

Comparison of the forecast value and the actual one is shown in Fig. 8.

It can be seen from Fig. 8 that compared with the actual load value, the load forecast result of the DAENs-based method is more accurate and stable than that of the BPNNs-based and ELM-based method. The comparison also shows that the DAENs-based method can effectively avoid the situation where the BPNNs-based method can easily fall into local optimum. As shown at 17:00 and 18:00 in the figure, compared with the actual load value, there occurs a large deviation in BPNNs-based prediction result, which is likely to result from falling into the local optimal results.

Cumulative distribution function (CDF) of the forecast relative error based on DAENs, BPNNs, and ELM is shown in Fig. 9.

We can see that the CDF of the DAENs-based forecast relative error lower than 1%, 2% and 3% is about 0.6, 0.85 and 0.9 respectively. The CDF of the BPNNs-based forecast relative error lower than 1%, 2% and 3% is separately only about 0.2, 0.3 and 0.4, and that of the ELM-based forecast relative error lower than 1%, 2% and 3% is separately about 0.15, 0.6 and 0.75. Obviously, the CDF of the DAENs-based forecast relative error is the highest among them in any error range, which shows that the DAENs-based forecast method is more reliable than the other two methods. Further comparison of the DAENs-based method , the BPNNs-based method, and the ELM-based method is made in terms of $MaxRe$, $MinRe$ and $Mae$. The results are shown in Table IV.

It can be seen from Table IV that the $MaxRe$ of the DAENs-based method is almost 2 times lower than that of the BPNNs-based method, and the $MinRe$ of the former is also lower than that of the the BPNNs-based and the ELM-based method. The $Mae$ of the DAENs-based method is $1.28{\rm{\%}}$, which is nearly 2 times lower than that of the other two methods. It shows that the DAENs-based load forecast method outperforms the BPNNs-based method and the ELM-based method in predicting accuracy and reliability.

V Conclusion

With the emergence of big data in the power sector, traditional load forecast methods present some limitations, such as over-fitting, slow convergence, local optimum, etc., resulting in inadequate forecast accuracy. To enhance load forecast accuracy in a big data scenario, a new distributed short-term load forecast method based on TensorFlow and DAENs by taking advantage of multidimensional load-related data is proposed, and its performance is tested and analyzed. The work of this paper is summarized as follows.

1. The pre-training and fine-tuning process of the DAENs-based load forecast method are separately unsupervised learning and supervised learning. A combination of the two processes makes it possible to overcome the shortcomings of traditional methods, such as slow convergence, over-fitting, local optimum, and instability, which contributes to a more accurate, stable, and reliable forecast result.

2. The DAENs-based load forecast method can easily tackle high-dimension and large-scale data by expanding its network structure, e.g. increasing the number of network layers and neurons. It has good expansibility and can thus meet the requirements for load forecast accuracy under the background of big data.

3. When applied in a big data scenario, the network structure of the DAENs-based model is complex, usually involving a huge amount of computation. By combining the TensorFlow multi-GPU framework, we realize distributed parallel computing to speed up the process of data calculation and analysis and improve work efficiency.