CHEMICAL ENGINEERING TRANSACTIONS  
 

VOL. 51, 2016 

A publication of 

 
The Italian Association 

of Chemical Engineering 
Online at www.aidic.it/cet 

Guest Editors: Tichun Wang, Hongyang Zhang, Lei Tian 
Copyright © 2016, AIDIC Servizi S.r.l., 

ISBN 978-88-95608-43-3; ISSN 2283-9216 

Research on Power Load Forecasting Based on the Improved 
Elman Neural Network 

Jiarui Zhang 

College of Electrical Engineering & New Energy,China Three Gorges University, Yichang Hubei province China 
zhangjiarui2055@126.com                                 

The forecast of the electric power load is related to the development of economy. It is also related to the 
national security and the daily operation of the society. The result of the power load forecasting is not only 
directly related to the economic benefits of the power enterprise, but also is very important to the users. From 
improving the accuracy of the power load forecasting, this paper proposes an improved Elman neural network 
algorithm to predict the power load. Then, we analyze and compare the experimental results by the numerical 
experiments. We find that the experimental results are better than the traditional prediction algorithm. The 
experimental results show that the algorithm is reliable and effective.  

1. Introduction                   

The power load changes with the change of the climate and the industrial structure adjustment (Wang and 
Chui, 2015). In addition, with the development of the economy and the improvement of people's living 
standard, the electric power load is also increasing. These factors make it difficult to manage the power 
system (Koprinska, 2015). It can improve the safety and economy operation of the power grid to study the 
power load. It also has the profound theoretical guidance and practical application value of studying the power 
system. In addition, it has the great significance for the stability and the economic operation of the power 
system (Yang, 2015).  
Power load characteristic index is the number of load characteristics, that is, the characteristic value of the 
load change. 
The load characteristic index in common use of china is shown as follows. 

Table 1: Load characteristic index in common use of china 

Description 
class (absolute) 

Maximum load, minimum load, average load, peak valley 
difference, maximum load utilization hours 

Comparative 
class (relative) 

Loading rate, average daily load rate, minimum load rate, peak 
valley ratio, month rate of balanced production, annual rate of 
balanced production, at the same time rate, the rate, peak load 

Curve class load curve 

 

Table 2: Classification of the power load forecasting (Time) 

Prediction type Time Main use 
Ultra short term power load forecasting 10min~1hour Power grid on-line control 
short term power load forecasting 1day~1year Generation, power supply and 

distribution plan 
Medium term power load forecasting 1year~5year Grid operation plan and 

development plan 
Long term power load forecasting More than 5year Power grid development planning 

                               
 
 

 

 
   

                                                  
DOI: 10.3303/CET1651099

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Please cite this article as: Zhang J.R., 2016, Research on power load forecasting based on the improved elman neural network, Chemical 
Engineering Transactions, 51, 589-594  DOI:10.3303/CET1651099   

589



Power load forecasting is used to predict the time distribution and spatial distribution of future power grid load. 
The power load forecasting is classified by the time as follows. 
And the power load forecasting is classified by the different industries as follows. 

Table 3: Classification of the power load forecasting (industries) 

Serial number Name 
1 Urban civil load 
2 Commercial load 
3 Rural load 
4 Industrial load 

 
Considering the influence on the power load by the economic, social, climate and other uncertain factors, if we 
only consider a change trend or a single factor, it is difficult to accurately describe the actual complex variation 
law of the power load forecasting. Now the methods of the power load forecasting are mainly the following. 
(1) Grey forecasting method. The grey forecasting method has the advantages of not considering the load 
distribution and the changed trend of the load. However, the value of grey prediction in the later period is 
larger (Bahrami, 2014). 
(2) Artificial neural network. This method has strong robustness and strong learning ability. The disadvantage 
is that the learning convergence speed is slow (Wang, 2012).  
(3) Combination forecasting method. The method is to obtain the final results by the weighted average of the 
predicted values obtained by the multiple prediction methods. (Lee and Hong, 2015). 
(4) Fuzzy theory. In recent years, the system modeling, the selection of prediction algorithm and the improved 
algorithm of the short term load forecasting of power system based on Fuzzy theory are in the exploration and 
development stage. Fuzzy theory is often combined with other methods to achieve good prediction results. 
The research of influencing factors is the precondition of using fuzzy theory to predict. Therefore, the 
application of fuzzy theory in power load forecasting has some limitations (Thair et al., 2015). 
The characteristics of power load forecasting are shown in the following figure. 
 

Characteristics of power load 
forecasting

Knowability principle

Uncertainty

Conditionity

Timeliness

Multi-scheme

 
Figure 1: The characteristics of power load forecasting 

2. Elman structure 

2.1 Network structure 

In addition to the input layer, the hidden layer and the output layer, neural network also has a special 
undertaking layer. Its structure is shown in figure 1. The undertaking layer is also called the context layer or 
the state layer. It is used to memory the output value of the previous unit time for the hidden layer. It can be 
considered as one step delay operator and it makes the Internet have the function of the dynamic 
memory(Muhammad and Saeed, 2010). 

590



2.2 Learning algorithm 

In the figure 2, we assume that the number of the neurons of the input layer, the hidden layer and the output 
layer are M, N, L. W1ij(t) is the connected weight matrix from the input layer to the hidden layer. W2jq(t)  is the 
connected weight matrix from the hidden layer to the output layer. W3rt(t) is the connected weight matrix from 
the undertaking layer to the hidden layer. f() is the nonlinear vector function which is constituted by the 
excitation function of the hidden layer unit. g() is the nonlinear vector function which is constituted by the 
excitation function of the output layer unit (Sanjay and Sanjay, 2012). 

( )
L

y tOutput layer

Hidden layer

Input layer

Undertake 
layer

( )
M

U t

1
( )X t ( )NX t 1 ( )cX t

( )
cN

X t

1
( )W t

2
( )W t

3
( )W t

1
( )y t

1
( )U t  

Figure 2: Structure of Elman neural network 

According to the network structure, the nonlinear state space expression is as follows. 
The output of the hidden layer is, 

1 3

1 1

( ) [ ( ) ( ) ( ) ( )]
M N

L ij i rj Cr

i r

X t f W t U t W t X t
 

        (1) 

Where 

( ) ( 1)
Cr j

X t X t       (2) 

The output of the output layer is, 

2

1

( ) [ ( ) ( )]
N

q jq j

j

y t g W t X t


       (3) 

The learning algorithm of Elamn  neural network can adopt the LM learning algorithm. Compared with the 
conventional gradient descent method of BP and its improved algorithm, the LM algorithm has fast 
convergence and good robustness (Zhao et al., 2013). 
The weight value W1ij(t) of Elamn  neural network and the correction of W2jq(t) are similar to BP neural 
network. The main difference is W3rj(t). We can use the chain derivative rule to obtain (Liu et al., 2015).  

3 0 2

1

( ) [( ( ) ( )) ( )] ( ( )) ( 1)
T

rj q jq L L

t

W t y t y t W t f X t X t


        (4) 

3. Improved ELAMN neural network  

3.1 The selection of the network parameter 

Before the adjustment of the connection weight, it needs to give a random initial weight to each connection 
weight. Because the system is nonlinear, the initial value has the great influence on whether the learning is 
convergence and is be trapped in local minimum or not (Wang et al., 2014). In general, we hope that the initial 
weight value can make the state value of each neuron is close to zero. At the same time, they are not zero or 

591



equal to a constant. Otherwise, the system cannot be trained. The initial weight value is a random number in (-
0.3,+0.3). It can guarantee the normal training of the network and it can make the network maintain in a good 
state. During the training process, we can consider the adjusted learning rate automatically. The formula of the 
adjusting the learning rate is as follows.  

1.1 ( ), ( ) ( 1) 1.05

( 1) 0.8 ( ), ( ) ( 1)

( ),

k SSE k SSE k

k k SSE k SSE k

k otherwise



 



  


   



     (5) 

Where, SSE is the number of the network output errors. The selection of the initial learning rate (0) has big 
randomness. In general, we take 0.1. In addition, in order to avoid that the network connection weight 
coefficient matrix correction is in minimum energy predicament, we add the momentum item when correcting 
the correction weight coefficient matrix. In the training of the additional momentum, we can use the following 
conditions to adjust the momentum value. 

0, ( ) ( 1) 1.05

0.9, ( ) ( 1)

,

SSE k SSE k

mc SSE k SSE k

mc otherwise

  


  



     (6) 

When  

( ) ( 1)SSE k SSE k        (7) 

This shows that the number of the error in this moment is smaller than the number of the error in the last one. 
Therefore, in general, the initial value of the momentum factor mc is 0.95. 

3.2 Improvement of the excitation function  

In neural network, in a certain sense, the excitation function can determine the nature of the error function E. 
In the general Elamn neural network, the hidden function f(x) adopts sigmoid function. That is,  

( ) 1 (1 )
x

f x e


       (8) 

The output layer f(x) function adopts the linear function. However, sigmoid function may makes the 
convergence rate of the network slow and makes the network fall into the local minimum. Therefore, it needs 
to be improved. 
Aiming at sigmoid function curve, the improved method is to add the independent variable factor k, the 
adjustable bias parameter b, the constant a and the extended function gain c. The improved f(x) function can 
be expressed as follows. 

( )
( , , , , ) (1 )

k x b
f x a b c k a c e

 
        (9) 

Derivative function is, 

2
( (2 ) 2) 4f k c f a c kc         (10) 

In the learning algorithm of the neural network, The common  learning rule (Error correction learning) is 
established based on the idea of minimizing the variance of the error output. The learning rate of the neural 
network is related to f’. The bigger f’ is, the quicker the learning rate is. Through the adjustment of the 
parameters, we can realize the translation and expansion of the image of the excitation function. By the 
excitation function and its derivative, when the function value f is close to (2a+c)/2, the derivative value is 
bigger and the convergence speed of the function is faster. At the same time, the maximum value of f’ is kc/4. 
With the increase of the k and c, the value of f’ is bigger and the convergence speed is faster. In the above 
formula, the coefficients k and c are mainly used to change the amplitude of the excitation function and its 
derivative. The parameters a and b are mainly used to translate in the horizontal direction and the vertical 
direction. Through the adjustment of the parameters, it can make the convergence rate and the prediction 
accuracy of the function f achieve an optimal value. 

3.3 Data pre-processing 

In order to avoid the saturation of the neuron, we normalize the input data in the input layer. We transform the 
numerical value to the interval of [0,1]. In the output layer, we adopt the formula (10) to transform the actual 
value of the output value.  

592



min max min
( ) ( )

i i
y x x x x      (11) 

max min min
( )

i i
x x x y x       (12) 

Where, xmax and xmin are the maximum value and the minimum value of the input data. yi is the normalized 
value of the sample. 

4. Experiment 

In order to validate the reliability and validity of the improved Elamn neural network algorithm which is 
proposed by this paper, we use this algorithm to forecast the power load for one province. Among them, the 
monthly load historical data of the first 5 years are the training set and the monthly load data of the sixth year 
is the test set. The predicted results are shown as follows. 

 
Figure 3: Comparison of prediction effects of different methods 

The specific values are shown in Table 4. 

Table 4: The power load value of the seventh year and the eighth year 

Month Actual value Improved Elman BP Gray Prediction 
1 40.28 40.31 42.31 41.07 
2 35.76 36.78 38.54 37.66 
3 40.13 39.66 36.79 38.03 
4 40.52 40.12 41.42 42.38 
5 43.33 43.56 45.64 44.21 
6 47.63 47.41 49.17 46.15 
7 47.41 47.65 50.30 48.54 
8 48.12 48.53 51.21 52.11 
9 46.25 47.21 50.11 52.45 
10 45.58 45.34 48.56 50.34 
11 44.11 44.80 47.12 49.13 
12 45.12 44.91 46.03 45.31 

 
From Figure 3 and table 4, we can see that the curve of the actual value of the improved neural network is the 
most similar to the curve of the forecasting value compared with other methods. The predicted results are 
closer to the actual value. It shows that the proposed method is most accurate. The experimental results show 
that the method is effective and reliable. 

593



5. Conclusion 

Power system load forecasting is an important and routine work in the power sector. The result of the forecast 
is not only directly related to the economic benefits of the power enterprise, but also related to the livelihood of 
the people. Therefore, it is very necessary to study the power load forecasting. In this paper, we propose an 
improved neural network algorithm and use this algorithm to study the power load forecasting. In this paper, 
we mainly do the following work. Firstly, we introduce the research background of the power load forecasting. 
Secondly, we introduce the neural network algorithm. Thirdly, we improve the neural network algorithm and 
propose the improved neural network algorithm. Then, we use this algorithm to carry on the research to the 
electric power load forecast. The experimental results show that the algorithm has good validity and reliability. 

References 

Ardalani-Farsa M., Zolfaghari S., 2010, Chaotic time series prediction with residual analysis method using 
hybrid Elman–NARX neural networks, Neurocomputing, 73: 2540-2553, DOI: 
10.1016/j.neucom.2010.06.004 

Bahrami S., Hooshmand R.A., Parastegari M., 2014, Short term electric load forecasting by wavelet transform 
and grey model improved by PSO (particle swarm optimization) algorithm, Energy 72:434-442, DOI: 
10.1016/j.energy.2014.05.065 

Kelo S., Dudul S., 2012, A wavelet Elman neural network for short-term electrical load prediction under the 
influence of temperature, International Journal of Electrical Power & Energy Systems, 43: 1063-1071, DOI: 
10.1016/j.ijepes.2012.06.009 

Koprinska I., Rana M., Agelidis V.G., 2015, Correlation and instance based feature selection for electricity load 
forecasting, Knowledge-Based Systems, 82:29-40, DOI: 10.1016/j.knosys.2015.02.017 

Lee W., Hong J.Y., 2015, A hybrid dynamic and fuzzy time series model for mid-term power load forecasting, 
International Journal of Electrical Power & Energy Systems, 64:1057-1062, DOI: 
10.1016/j.ijepes.2014.08.006 

Liu H., Tian H.Q., Liang X.F., Li Y.F., 2015, Wind speed forecasting approach using secondary decomposition 
algorithm and Elman neural networks, Applied Energy, 157: 183-194, DOI: 
10.1016/j.apenergy.2015.08.014 

Li Y., Bao Y.Q., Yang B., Chen C., Ruan W.J., 2015, Modification method to deal with the accumulation 
effects for summer daily electric load forecasting, International Journal of Electrical Power & Energy 
Systems, 73: 913-918, DOI: 10.1016/j.ijepes.2015.06.027 

Lou C.W., Dong M.C., 2015, A novel random fuzzy neural networks for tackling uncertainties of electric load 
forecasting, International Journal of Electrical Power & Energy Systems, 73:34-44, DOI: 
10.1016/j.ijepes.2015.03.003 

Mahmoud T.S., Habibi D., Hassan M.Y., Bass O., 2015, Modelling self-optimised short term load forecasting 
for medium voltage loads using tunning fuzzy systems and Artificial Neural Networks, Energy Conversion 
and Management, 106: 1396-1408, DOI: 10.1016/j.enconman.2015.10.066. 

Wang J.J., Zhang W.Y., Li Y.N., Wang J.Z., Dang Z.L., 2014, Forecasting wind speed using empirical mode 
decomposition and Elman neural network, Applied Soft Computing, 23: 452-459, DOI: 
10.1016/j.asoc.2014.06.027 

Wang Y.L., Niu D.X., Ji L., 2012, Short-term power load forecasting based on IVL-BP neural network 
technology, Systems Engineering Procedia, 4:168-174, DOI: 10.1016/j.sepro.2011.11.062 

Zhao J., Zhu X.L., Wang W., Liu Y., 2013, Extended Kalman filter-based Elman networks for industrial time 
series prediction with GPU acceleration, Neurocomputing, 118: 215-224, DOI: 
10.1016/j.ijepes.2012.06.009 

 
 
 
 
 
 
 
 
 

 

594