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 

Study on Medium and Long Term Power Load Forecasting 
Based on Combination Forecasting Model 

Yue Feng 

School of Automation, Harbin University of Science and Technology, Harbin Heilongjiang 150080, China      
fengyue307@sina.com                      

Load forecasting is an important work in the electric power department, and the medium and long term load 
forecasting is mainly aimed at the electric power generation planning and development planning. Accurate 
forecasting is the basis of rational planning, and the planning will greatly affect the investment. Therefore, it 
has a great significance to improve the accuracy of load forecasting. Accuracy of the medium and long term 
load forecasting is affected by various stochastic factors, such as economy, policy, and climate. So, the 
accurate forecast is a very complex work. In order to improve the accuracy of load forecasting, this paper 
introduces a combined forecasting model, which can obtain more accurate results by combining the 
advantages of each model. In this paper, we use the gray prediction model, neural network prediction model, 
and regression analysis model for the whole society annual electricity consumption in long-term load 
combination forecast. The method of this paper can make full use of the advantages of the grey prediction 
which requires less data, simple operation, and easy to test. It can make full use of the advantages of the 
neural network method which has the function of self adaptation, and has a strong ability of learning and 
mapping. It can also make full use of the advantages of the regression analysis method that does not need to 
take into account the distribution of the data and the trend of change. Finally, we conduct an example 
verification. We choose the proposed method, the traditional GM (1,1) model, regression analysis prediction 
model and BP neural network prediction model for comparison. The results show that the proposed method is 
feasible and effective. 

1. Introduction 

Load forecasting is an important work in the electric power department, and the medium and long term load 
forecasting is mainly aimed at the electric power generation planning and development planning. Accurate 
forecasting is the basis of rational planning, and planning will greatly affect the investment. Accuracy of the 
medium and long term load forecasting is affected by various stochastic factors, such as economy, policy, and 
climate. So, the accurate forecast is a very complex work. The commonly used forecasting methods include 
artificial intelligence prediction method, regression analysis method and gray prediction method. Next, we will 
introduce the research status of these three methods in power load forecasting. 
Artificial neural network method. Artificial neural network has adaptive function for a large number of data with 
non structural and non-accurate rules, and it has strong learning and mapping ability, which can be easily 
fitted to any complex nonlinear relation, so it is suitable for power load forecasting. Therefore, it has been 
widely used in power load forecasting in recent years. However, the learning process of neural networks is 
usually slow, and the adaptability to unexpected events is poor. The commonly used method is the feed 
forward network method (Miao and Xing, 2000; Zheng et al., 2002; Jiang and Lu, 2001) and radial basis 
function method (Zhang et al., 2001; Zhao and Zhang, 2003). 
Grey forecasting method. The grey system theory, which is widely used in network, uses all random variation 
as the grey quantity which is changed in a certain range. The commonly used accumulated generation method 
is to collate the raw data into a regular data columns. After that, the differential equation of the grey model is 
used to forecast the power load. After verifying the accuracy and reliability of the model, the model can be 
applied to predict the future load (Zhang et al., 2001; Xing et al., 2005; Bao et al., 2004). In addition, this 
method is suitable for short, medium and long period of load forecasting. 

                               
 
 

 

 
   

                                                  
DOI: 10.3303/CET1651144

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Please cite this article as: Feng Y., 2016, Study on medium and long term power load forecasting based on combination forecasting model, 
Chemical Engineering Transactions, 51, 859-864  DOI:10.3303/CET1651144   

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Regression analysis method, the change of long-term load in power system is restricted by many factors, 
which is difficult to describe qualitatively. In view of the complexity and uncertainty of load influencing factors, 
the multiple linear regression analysis is applied to the medium and long term load forecasting. In the 
regression analysis, the random variable is the independent variable, and the non random variable is the 
dependent variable. Of course, we can also define the dependent variable is the power system load, the 
independent variable is the various factors that affect the power system load, such as economy, population, 
climate and so on. In the end, the relationship between the independent variables and dependent variables is 
studied by the given data, so as to form the regression equation(Wang, 2009; Hu, et al., 2008). 

2. Combination forecasting model with the square sum of minimum prediction errors 

Suppose there are m  kinds of unbiased single prediction methods to predict a certain index sequence 
{ , 1, 2, , }

t
x t N of the same object. Then, we use 

it
x , 1, 2, ,i m , 1, 2, ,t n  as the predictive value of 

the i th single prediction method on the t  time, use 
it t it

e x x  as the prediction error of the i th single 

prediction method on t  time, and set 
1 2
, , ,

m
l l l  as the weighted coefficient of m  single prediction methods. 

In order to keep the unbiasedness of combination forecasting, the weighted coefficient should be satisfied as: 

1

1
m

i

i

l


 , 0il  , 1, 2, ,i m                                                                                                                              (1) 

Let 
1 1 2 2

ˆ
t t t m mt

x l x l x l x    be the combination forecast value of ˆ
t

x , and let 
t

e  be the prediction error on 
the t  time. Then, we have: 

1

ˆ
m

t t t i it

i

e x x l e


                                                                                                                                               (2) 

We use 
1

Q  to represent the sum of squared error of the combination forecast, and we have: 

2

1

1 1 1 1

n n m m

t i it j jt

t t i j

Q e l e l e
   

                                                                                                                                (3) 

Therefore, the combination forecasting model which uses the square sum of prediction error as the criterion is 
the following optimization problem. 

1

1 1 1

1

min

1

n m m

i it j jt

t i j

m

i

i

Q l e l e

l

  








 






                                                                                                                                (4) 

Let 
1 2

( , , , )
m

L l l l , (1,1, ,1)R  ,
1 2

( , , , )
i i i iN

e e e e , then L  represents the column vector of the 

weighted coefficient of the combination forecast, R  indicates that all the elements of column vector are 1, and 

i
e  represents the column vector of prediction error of the i th single prediction method. 

1

N
T

ij i j it jt

i

E e e e e


   , , 1, 2, ,i j m , *( )ij m nE E                                                                                            (5) 

For the combined forecasting model, the weighted coefficient of combination forecasting is given by the follow 
formula: 

1

1T

E R
L

R E R




                                                                                                                                                       (6) 

1 1

1
T

Q
R E R


                                                                                                                                                     (7) 

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3. Combination forecasting model 

In this paper, three different prediction models are used to build a long-term combined forecasting model of 
power load. Next, we introduce the basic concepts and the calculation methods of the neural network 
prediction model, the grey forecasting model and the regression analysis prediction model. 

3.1 BPNN model 
Next, we will introduce the basic knowledge of BPNN model. BPNN (Back Propagation neural network) is a 
Multilayer Feed-forward Neural Networks based on the error back propagation algorithm. The input layer is 
provided with M input signals, wherein any input signal is expressed by m. The hidden layer has I neurons, 
wherein any neuron is represented by i, and the output layer has p neurons, wherein any neuron is 
represented by p. The weight of the input layer and the hidden layer is expressed by 

mi
w , and the weight of 

the hidden layer and the output layer is expressed by 
ip

w . The input of the neuron is expressed by u, and the 

output of the excitation is expressed by v. Then, we use 
1 2

[ , , , , , ]
k N

X X X X X  as the training sample 

set that corresponding to any training sample 
1 2

[ , , , ]
T

k k k kM
X x x x , (1, 2, , )k M . The input training 

sample of neural network is 
k

X . Through the forward propagation, we can get: 

1

M
I

i mi km

m

u w x


  ,
1

( ) ( )
M

I I

i i mi km

m

v f u f w x


   , ( 1, 2, , )i I                                                                              (8) 

1

I
P I

p ip i

i

u w v


  ,
1

( ) ( )
I

P P I

p p ip i

i

v u w v 


   , ( 1, 2, , )p P                                                                               (9) 

P

kp p
y v                                                                                                                                                            (10) 

The error signal of the p th neuron in the output layer is:  

( ) ( ) ( )
kp kp kp

e n d n y n                                                                                                                                     (11) 

The error energy of the neuron is defined as 2
1

( )
2

kp
e n , and the total error energy of all the neurons in the 

output layer is 2
1

1
( )

2

P

kp

p

E n e


  . 

Through the output of the network, the learning error can be calculated, and the forward propagation is 
finished. In the back propagation process, the error signal is transmitted from back to front, and the connection 
weights are modified by each layer. 

3.2 Grey model 

The grey prediction model uses accumulated generating operator to generate the accumulated generating 
sequence of the target state, which is used to reduce the randomness of the state. Then, the parameters of 
the grey differential equation are estimated by using the accumulated value, and the future accumulated value 
is predicted by the grey differential equation. In the end, the predictive value of the target state is obtained by 
using the inverse accumulation generating operator. GM (1,1) is the most commonly used grey forecasting 
model, its modeling and forecasting process can be described as:  
(1) the length of the grey prediction sequence is m , and the target history sequence is: 

(0)

1 1
ˆ ˆ ˆ( , , , )

k m k m k
X x x x

   
                                                                                                                          (12) 

(2) the accumulated generating sequence is: 
(1) (1) (1) (1)

1 1
ˆ ˆ ˆ( , , , )

k m k m k
X x x x

   
                                                                                                                           (13) 

Where, (1)ˆ ˆ
n

k n k i

i m

x x
 



  , 1, 2, ,n m . 

(3) the mean generating sequence is: 
(1) (1) (1) (1)

1 2 1
ˆ ˆ ˆ( , , , )

k m k m k
Z z z z

    
                                                                                                                         (14) 

861



Where,
(1) (1)

(1) 1
ˆ ˆ

ˆ
2

k n k n

k n

x x
z   




 , 1, 2, , 1n m  . 

(4) according to the minimum variance criterion, the GM (1,1) grey differential equation is: 

(0) (1)
X aZ b                                                                                                                                                 (15) 

Where, a  and b  are the parameters of the grey differential equation. 

1
[ , ] ( )

T T T
a b B B B Y


                                                                                                                                      (16) 

(1) (1) (1)

1 2 1
ˆ ˆ ˆ[ , , , ]

k m k m k
Y x x x

    
                                                                                                                              (17) 

(1)

1

(1)

2

(1)

1

1

1

1

k m

k m

k

z

z
B

z

 

 



 
 
 
 
 
  

                                                                                                                                               (18) 

(5) put the a  and b  into the follow formula, then we can predict the state on the k  time: 

ˆ ˆ[ ] (1 )
ak a

k k m

b
g x e e

a




                                                                                                                                 (19) 

3.3 Regression analysis model 
The univariate regression prediction method is based on the correlation between the independent variables x  
and the dependent variable y , so as to establish the linear regression equation of x  and y . 
(1) The prediction model of univariate regression analysis. 

i i
Y a bx                                                                                                                                                        (20) 

Where, 
i

x  represents the value of the independent variable at i  time, 
i

Y  represents the value of the 
dependent variable at i time. The x  and y  represent the parameters of a linear regression equation, which 
can be calculated by the following formula: 

1 1

1 1 1

2 2

1 1

( )

n n

i i

i i

n n n

i i i i

i i i

n n

i i

i i

Y x

a b
n n

n x Y x Y

b

n x x

 

  

 



  








 


 

  

 

                                                                                                                             (21) 

(2) Using the sample data ( , )
i i

x y , 1, 2, ,i n  to establish the model. 

y a bx    , 2~ (0, )N                                                                                                                             (22) 

(3) The parameters of â  and b̂  are estimated, and the linear regression equation ˆˆ ˆy a bx   is obtained. 
(4) Hypothesis testing of the model to determine its use value. 
(5) Calculate the predicted value. 

4. Simulation experiment and result analysis 

From Figure 1 shows that the power industry has maintained a rapid and healthy development, the total 
electricity consumption in the society is in a rapid growth phase. However, the total electricity consumption has 
slowed the growth twice times during this period. The first time is in 1997 and 1998, the reason is mainly that 
the Southeast Asian financial crisis has had a impact on the domestic economy, which makes the whole 
society electricity consumption growth slowed. The second time is in 2007 and 2008,due to the emergence of 
a global financial crisis, electricity production and consumption has been greatly affected. If the above factors 

862



are ignored, and the direct use a single model for modeling, it is not consistent with the reality, and the 
accuracy of the model is not reliable. 

 

Figure 1: Annual electricity consumption of the whole society 

Next, the data of 1980~2008 is used as modeling data, three methods are used to fit the historical data, and 
the fitting results are shown in Table 1. 

Table 1: The fitting results of Annual electricity consumption of the whole society 

Years Annual electricity consumption 
(100 million kilowatt hours) 

BPNN model GM model Regression analysis model 

1980 3006.3 3090.339 3169.122 3173.154 
1981 3095.7 3138.801 3238.675 3329.072 
1982 3280.1 3285.276 3316.109 3336.051 
1983 3518.7 3601.456 3698.205 3793.21 
1984 3777.6 3790.609 3860.442 3867.818 
1985 4117.6 4192.01 4248.273 4326.397 
1986 4429.04 4432.138 4482.403 4524.606 
1987 4902.69 4926.553 4977.349 4982.938 
1988 5358.65 5380.727 5388.888 5448.535 
1989 5761.98 5844.521 5911.357 5977.235 
1990 6125.96 6219.479 6219.961 6269.884 
1991 6696.79 6724.243 6793.891 6860.738 
1992 7455.39 7474.573 7562.45 7574.135 
1993 8201.08 8298.236 8359.507 8365.843 
1994 9046.49 9127.851 9134.284 9219.725 
1995 9886.36 9908.031 9952.677 9959.821 
1996 10570.29 10620.77 10677.54 10743.05 
1997 11039.11 11109.93 11156.24 11197.45 
1998 11347.3 11428.13 11520.02 11575.2 
1999 12092.28 12162.25 12165.64 12172.26 
2000 13466.22 13487.77 13513.63 13559.73 
2001 14682.51 14742.91 14756.14 14809.92 
2002 16386.28 16418.63 16449.6 16457.61 
2003 18891.21 18988.31 19028.35 19103.18 
2004 21761.3 21821.61 21849.94 21882.41 
2005 24688.54 24769.4 24850.72 24936.16 
2006 29368 29388.86 29399.29 29425.08 
2007 32458 32477.22 32486.53 32543.92 
2008 34268 34355.91 34417.14 34516.42 

 
Finally, we use the above three methods to synthesize the combination forecasting method. Then, we use it 
and the other 3 models to predict the whole society electricity consumption between 2009 to 2012. Next, we 
compare it with the actual value to obtain the table of prediction error comparison. 
Choose the following two kinds of error indicators to evaluate the effectiveness of the method in this paper: 

863



(1) Mean absolute percentage error 

2

1

1
ˆ[( ) ]

N

t t t

i

MSPE x x x
N 

                                                                                                                       (23) 

(2) Mean Square Percent Error 

2

1

1
ˆ[( ) ]

N

t t t

i

MSPE x x x
N 

                                                                                                                       (24) 

Where, tx  is the actual value at t  time, ˆtx  is the predicted value of some kind of prediction method at t  time. 
According to the above 2 indexes, the prediction error of each prediction method is showed on Table 2, and 
the numerical value is expressed as a percentage. 

Table 2. Comparison of prediction results 

Evaluation index of prediction effect MAPE MSPE 
Combination forecasting method 2.46 1.37 
GM model 6.88 5.11 
Regression analysis model 10.22 6.93 
BPNN model 8.23 5.01 

5. Conclusion 

In order to improve the accuracy of load forecasting, this paper introduces a combined forecasting model, 
which can obtain more accurate results by combining the advantages of each model. In this paper, we use the 
gray prediction model, neural network prediction model, and regression analysis model for the whole society 
annual electricity consumption in long-term load combination forecast. Finally, we conduct an example 
verification. The results show that the proposed method is feasible and effective.. 

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