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Renewable Energy 32 (2007) 1165–1174

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Predictive analysis on electric-power supply anddemand in China

Min Huang, Yong He�, Haiyan Cen

College of Biosystems Engineering and Food Science, Zhejiang University, Hangzhou 310029, PR China

Received 18 November 2005; accepted 6 April 2006

Available online 2 June 2006

Abstract

In order to analyze the electric-power demand and supply in China efficiently, this paper presents a

Grey–Markov forecasting model to forecast the electric-power demand in China. This method takes

into account the general trend series and random fluctuations about original time-series data. It has

the merits of both simplicity of application and high forecasting precision. This paper was based on

historical data of the electric-power requirement from 1985 to 2001 in China, and forecasted and

analyzed the electric-power supply and demand in China by the Grey–Markov forecasting model. The

forecasting precision of Grey-Markov forecasting model from 2002 to 2004 is 99.42%, 98.05% and

97.56% respectively, and in GM(1,1) Grey forecasting model, it is 98.53%, 94.02% and 88.48%,

respectively. It shows that the Grey–Markov forecasting models has higher precision than GM(1,1)

Grey forecasting model. The forecast values from 2002 to 2013 were as follows: 16106.7, 18541.3,

20575.7, 23940.5, 24498.0, 26785.1, 27977.2, 29032.2, 31247.5, 33428.8, 35865.4, and 38399.3TWh.

The results provide scientific basis for the planned development of the electric-power supply in China.

r 2006 Elsevier Ltd. All rights reserved.

Keywords: GM(1,1); Markov chain; Grey–Markov; Forecast; Electric-power demand

1. Introduction

Along with economic growth of nearly 10% per year over the last two decades, electric-power use has been rapidly increasing in China. During the 1980s, because the developingspeed of the economy was quicker than that of the electric-power industry, China had a

see front matter r 2006 Elsevier Ltd. All rights reserved.

.renene.2006.04.005

nding author. Tel.: +8657186971143; fax: +86 571 86971143.

dress: yhe@zju.edu.cn (Y. He).

ARTICLE IN PRESSM. Huang et al. / Renewable Energy 32 (2007) 1165–11741166

scarcity of electric-power. To deal with the situation, China first innovated the investmentsystem. In 1981, the Longkou power plant was constructed with joint venture by thecentral government and local units in Shandong province. In 1987, State Departmentadvanced a ‘‘twenty-words policy’’ about power system innovation, which translated toEnglish was ‘‘government and corporation should be separated, a province is an entity,unite the electric-power network, attemp the system united, raise funds to build powerplants’’. In 1984, a Japanese company constructed a new hydropower station in theYunnan province, which was called as Lubuge hydropower station. Because it was the firstpower plant constructed by foreign capital, it was also called as ‘‘Lubuge shock wave’’which influenced the investment system of electric-utility industry very much. From 1985,State Department set up Huaneng Power International Corporation and other powercorporations to raise foreign capital.With the new policies, Chinese electric-utility industry developed very quickly. After the

total electric-power equipped capacity exceeded 1TW in 1987, the total electric-powerequipped capacity exceeded 2TW in 1995 and exceeded 3TW in 2000. In 2004, theadditional electric-power equipped capacity was 0.51TW, which was at the first place of theworld. The total electric-power equipped capacity was 4.47TW. Chinese electric-powerdemand and supply began to keep a balance from 1996 [1]. The electric generationproduction of 1985 was 4117.6TWh, and that of 2004 was 20418.08TWh. It means thatthere was 4.98 times increase from 1985. The electric generation production had grown at8.82% per year between 1985 and 2004. The total electric-power equipped capacity and thegeneration production of China were at the second place of the world, from 1996 untill now.While great development was accessed in Chinese electric-utility industry, there were

many problems which influenced the development of the society badly. Electric-power wasa resource that could not be stored. The supply quantity had to equal the consumption. Soneither the shortage of supply nor the short of consumption would influence the electric-utility industry seriously. Perhaps, the whole occupation would be deficient due to lackwork, and maybe insufficient supply would affect the function of different fields in society.In late 1980s, consumption of electricity in our country kept increasing between 9% and10%. It reached 16% and became the top in history in 1991, while in 1992 and 1993, it keptabove 11%. This period was called as over-economic. The lack of electricity appeared in thewhole society. The power cut appeared even in Beijing. The government started to adjustthe quo-status in 1993, which made the economy in China come into ‘‘soft-land’’. Theconsumption of the whole country was decreasing, and reached the bottom of 2.8%. It ledto the free of electric equipments and the whole coal industry fell into deficit. Thegovernment made a stipulation on prohibiting building new electric factory during threeyears. However, the increase of consumption in 1999 recovered 6.2% and 9% in 2000. Since2000, the lack of electricity pervaded from the delta in Changjiang River to Zhujiang Rivereven the whole country. There were 12 provinces to cut power and limit the electric use. Thelack of electric equipment was 20.35GW. In 2003, the power of 22 provinces cut, the lack ofelectric equipment was 44.85GW, which doubling compared to last year. The power of 24provinces cut till 2004, and the largest lack of electricity reached 30GW. It diffused in thewhole country, including the undeveloped areas such as Guangxi, Yunnan, Guizhou,Shanxi, Neimenggu, Gansu, Qinghai, Ningxia et al. The summer of 2004, was considered tohave experienced as the most serious lack of power since more than twenty years. Theconsumption of electricity was 19,458.4 TWh from January to November in this year. Itincreased 15.13% more than that in last year at the same time approaching to the top value.

ARTICLE IN PRESSM. Huang et al. / Renewable Energy 32 (2007) 1165–1174 1167

There are many factors that cause lack of electricity, such as insufficient investment inelectricity, the distinction in the speed of new electrical product and the demand increase,the rapid increase of the industry and electrical industry with high energy consumption, thelow ability of electrical transport and the accidents, the quick increase in the load of air-conditioning, the overwrought supply caused by the controversy in the price of electricityand coal, the shortage of water, etc. Because of many undermining factors, includingeconomical development, the structure of industry, the incoming lever of citizen, climateand the national policy, etc., fluctuation in the consumption of electricity and the increaseof load appeared obvious. Efficient methods to predict the electrical demand in middle andlong term are scarce. We attempt to study a reasonable approach for development ofelectricity using scientific methods.

Thus, according to the data of the total consumption of electricity, this paper proposed aGrey–Markov forecasting model to forecast and analyze the electric-power supply anddemand in China.

Deng initially presented the Grey system theory in 1982 [2]. The Grey forecasting modeladopts the essential part of the Grey system theory. The GM(1,1) Grey forecasting modelcan be used in circumstances with relatively little data and it can use a first-orderdifferential equation to characterize an unknown system. So the GM(1,1) Grey forecastingmodel is suitable for forecasting the competitive environment where decision makers canrefer only to a limited historical data [3]. But the forecasting precision for data sequenceswith large random fluctuation is low.

The Markov-chain forecasting model can be used to forecast a system with randomlyvarying time series. It is a dynamic system which forecasts the development of the systemaccording to transition probabilities between states which reflect the influence of allrandom factors. So the Markov-chain forecasting model is applicable to problems withrandom variation, which could improve the GM(1,1) model [4]. The disadvantage of themodel is that it demands that the process be a stationary one, that is, the trend curve is ahorizontal line. If the trend curve is nonhorizontal, the forecast is less accurate because thestates of the ordinary Markov probability matrix forecast are stationary. To improve theMarkov-chain forecasting model, this paper builds a GM(1,1) Grey forecasting model todescribe the historical data of the electric-power demand in China to calculate thefluctuating trend curve first [5].

The rationale of Grey–Markov forecasting model is as follows: first a GM(1,1) Greyforecasting model is built to calculate the fluctuating trend curve of the historical dataseries, then specify some states around the trend curve, a Markov transition matrix can bebuilt to find out the transition probability, finally these two models should be combined toforecast accurately by the historical time-series data. This forecasting method can makefull use of the information given by historical data, and increase greatly the forecastingprecision of random fluctuating sequences.

2. Research methodology

2.1. GM(1,1) Grey forecasting model

Step 1: Assume the original series to be X(0),

X ð0Þ ¼ fX ð0Þð1Þ; X ð0Þð2Þ; . . . ; X ð0ÞðnÞg. (1)

ARTICLE IN PRESSM. Huang et al. / Renewable Energy 32 (2007) 1165–11741168

Step 2: A new sequence X(1) is generated by the accumulated generating operation(AGO).

X ð1Þ ¼ fX ð1Þð1Þ; X ð1Þð2Þ; . . . ; X ð1ÞðnÞg, (2)

where X ð1ÞðkÞ ¼Pki¼1

xð0ÞðiÞ; k ¼ 1; 2; . . . n:

Step 3: Establish a first-order differential equation.

dxð1Þ=dt� �

þ az ¼ u, (3)

where zð1ÞðkÞ ¼ axð1ÞðkÞ þ ð1� aÞxð1Þðk þ 1Þ; k ¼ 1; 2; . . . n� 1: a denotes a horizontaladjustment coefficient, and 0oao1. The selecting criterion of a value is to yield thesmallest forecasting-error rate [6].

Step 4: From step 3, we can have xð1Þðk þ 1Þ and Y kð Þ.

xð1Þðk þ 1Þ ¼ ðxð0Þð1Þ �u

aÞe�ak þ

u

a, (4)

where

y ¼a

u

� �¼ ðBTBÞ�1BTY ; B ¼

�zð1Þð2Þ 1

�zð1Þð3Þ 1

� � � � � �

�zð1ÞðnÞ 1

266664

377775; Y ðkÞ ¼ xð0Þð2Þ; xð0Þð3Þ; . . . ; xð0ÞðnÞ

� �T.

(5)

Step 5: Inverse accumulated-generation operation (IAGO). Because the Grey forecast-ing model is formulated using the data of AGO rather than original data, IAGO can beused to reverse the forecasting value. Namely

xð0Þ0 ðkÞ ¼ xð1ÞðkÞ � xð1Þðk � 1Þ; k ¼ 2; 3; . . . ; n. (6)

Step 6: From Step 5, a trend curve equation can be built:

Y ðkÞ ¼ xð0Þðk þ 1Þge�ak, (7)

where g ¼ ðxð0Þð1Þ � m=aÞð1� eaÞ; k ¼ 0; 1; . . . ; n� 1:Y ðkÞ denotes the forecasting data [7].

2.2. Partition of states by Markov-chain forecasting model

The values of X ð0Þðk þ 1Þ are distributed in the region of the trend curve Y ðkÞ that maybe divided into a convenient number of contiguous intervals. When X ð0Þðk þ 1Þ falls ininterval i, one of S such intervals, it may be regarded as corresponding to a state Ei in an m

order Markov unstable sequence, Ei can be signified as follows:

Ei ¼ ½E1i;E2i�, (8)

where i ¼ 1,2,yS, S is the amount of states.

E1i ¼ Y ðkÞ þ Ai. (9)

E2i ¼ Y ðkÞ þ Bi. (10)

ARTICLE IN PRESSM. Huang et al. / Renewable Energy 32 (2007) 1165–1174 1169

Y ðkÞ is a time function, so E1i and E2i will vary with the time series. It means that the stateEi is dynamic. To establish S (the amount of states), E1i and E2i , depends on the studyobject and the original data series [8].

2.3. Calculate the transition probability P

For Markov-chain series, the transition probability from state Ei to state Ej can beestablished using an equation as follows:

PijðmÞ ¼MijðmÞ

Mi

ði; j ¼ 1; 2; . . . ;SÞ, (11)

where PijðmÞ is the transition probability of state Ej transferred from state Ei for m steps (inthis paper, 1 step stands for 1 year), m is the number of transition steps each time, MijðmÞ isthe number of original data of state Ej transferred from state Ei for m steps, Mi is thenumber of original data points in state Ei.

These PijðmÞ values can be presented as a transition probability matrix R(m).

RðmÞ ¼

p11ðmÞ p12ðmÞ � � � p1jðmÞ

p21ðmÞ p22ðmÞ � � � p2jðmÞ

� � �

pi1ðmÞ pi2ðmÞ � � � pijðmÞ

266664

377775 ði; j ¼ 1; 2; . . . ;SÞ. (12)

The state transition probability PijðmÞ reflects the statistical law of each state transition in asystem, which is the foundation of Markov probability matrix forecast. The future developmentof the system can be forecasted by studying the state transition probability matrix R(m).Generally, it is necessary to observe the one-step transition matrix R(1). Suppose the object tobe forecasted is in state EQð1pQpSÞ, row Q in matrix R(1) should be considered. If maxPQjð1Þ ¼ PQLð1Þðj ¼ 1; 2; . . . ; S; ð1pQpSÞÞ, then what will most probably happen in thesystem at the next moment is the transition from state EQ to state EL. It is difficult to determinethe future transition of the state, if two or more transition probabilities in the row Q of matrixR(1) are the same. Therefore the transition probability matrix of two-step transition matrix R(2)or multi-step transition matrix R(m), where mX3, should be considered [9].

2.4. Calculate the forecasting data

After the determination of the future-state transition of a system, i.e. the determinationof Grey elements E1i, E2i, the changing interval of the forecast value is between E1i and E2i.The most probable forecast value, Y ðk þ 1Þ, is considered to be the middle value of thedetermined state interval, that is

Y ðk þ 1Þ ¼ 1=2ðE1i þ E2iÞ ¼ Y ðkÞ þ 1=2ðAi þ BiÞ. (13)

3. The Grey–Markov forecasting model for the electric-power demand in China

There are many factors which could influence the electric-power demand, such as theeconomy, the industry framework, people’s income level, the weather, the government’s

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Table 1

The Electric-power consumption of China from 1985 to 2004 (unit: TWh)

Number 1 2 3 4 5

Year 1985 1986 1987 1988 1989

Amount 4117.6 4507.0 4985.2 5466.8 5865.3

Number 6 7 8 9 10

Year 1990 1991 1992 1993 1994

Amount 6230.4 6804.0 7589.2 8426.5 9260.4

Number 11 12 13 14 15

Year 1995 1996 1997 1998 1999

Amount 10023.4 10764.3 11284.4 11598.4 12305.2

Number 16 17 18 19 20

Year 2000 2001 2002 2003 2004

Amount 13471.4 14633.5 16200 18910 21735

M. Huang et al. / Renewable Energy 32 (2007) 1165–11741170

policy and so on. Some factors are clear, and others are not clear. So the time series ofelectric-power demand of a country shows large random fluctuations. As Table 1 shows,the historical data series of the electric-power consumption of China from 1985 to 2002 isrising, but fluctuating randomly. So this paper forecasts and analyzes the electric-powerdemand by Grey–Markov forecasting model [10].

3.1. Build the GM(1,1) Grey forecasting model

Based on the historical data of the electric-power consumption in China from 1985 to2001, a trend curve equation is built by GM(1,1) Grey forecasting model. It is as follows:

Y ðkÞ ¼ Xð0Þðk þ 1Þ ¼ 4331:308566e0:078455k ðk ¼ 1; 2; 3; . . . ; nÞ; (14)

where k is the series number of the year, and k ¼ 1 means that it is 1985.The forecast value of 2002 calculated by the equation is 16438.15TWh.

3.2. Partition of states by Markov-chain forecasting model

According to the actual electric-power consumption data, four states, i.e., fourcontiguous intervals are established about the curve of X

ð0Þðk þ 1Þ. According

to(8)–(10), the four states intervals can be got as follows:

E1 : E11 ¼ Y ðkÞ � 0:130Y ; E21 ¼ Y ðkÞ � 0:045Y ;

E2 : E12 ¼ Y ðkÞ � 0:045Y ; E22 ¼ Y ðkÞ;

E3 : E13 ¼ Y ðkÞ; E23 ¼ Y ðkÞ þ 0:045Y ;

E4 : E14 ¼ Y ðkÞ þ 0:045Y ; E24 ¼ Y ðkÞ þ 0:130Y ;

where Y denotes the average value of the historical electric-power consumption from 1985to 2001. The historical data series, the regressed curve and the states intervals are showedin Fig. 1.

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1984 1986 1988 1990 1992 1994 1996 1998 2000 2002

4000

6000

8000

10000

12000

14000

16000Y

Ele

ctric

pow

er r

equi

rem

ent

X Year

Fig. 1. The forecasting curve of the electric-power requirement in China.

M. Huang et al. / Renewable Energy 32 (2007) 1165–1174 1171

3.3. Calculate the transition probability P

After observing the states intervals and the historical data series, the number of thehistorical data in every interval can be got. They are as follows:

M1 ¼ 3 M2 ¼ 6 M3 ¼ 3 M4 ¼ 5,

where Mi denotes the number of the historical data in the interval i, and i ¼ 1,2,3,4. Thenumbers of one-step transiting to E1, E2, E3, E4 from E1 are as follows:

M11ð1Þ ¼ 2 M12ð1Þ ¼ 0 M13ð1Þ ¼ 0 M14ð1Þ ¼ 1.

Next Mijð1Þ, where i ¼ 2,3,4 and j ¼ 1,2,3,4 can be calculated in the same way. Thencalculate the one-step transition probability to every states interval and present them in thetransition matrix R(1) as follows:

Rð1Þ ¼

23

03

03

13

05

45

15

05

13

13

03

13

15

05

15

35

266664

377775.

The electric-power consumption of 2001 year is in the E4 state interval, so observe thefourth row of the transition matrix. Because max P4j ¼ P44ðj ¼ 1; 2; 3; 4Þ as the matrix R(1)shows, the electric-power demand of 2002 year is most probably in the E4 state interval,namely between 15,319.28 and 16,894.12TWh.

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Table 2

Forecast values from 2003 to 2013.

Year Forecast Value (TWh)

Grey–Markov GM(1,1)

2003 18541.3 17779.7

2004 20575.7 19230.8

2005 23940.5 20800.4

2006 24498.0 22498.0

2007 26785.1 24334.1

2008 27977.2 26320.2

2009 29032.2 28468.3

2010 31247.5 30791.7

2011 33428.8 33304.7

2012 35865.4 36022.9

2013 38399.3 38962.9

M. Huang et al. / Renewable Energy 32 (2007) 1165–11741172

3.4. Calculate the forecast value

Calculate the most probable forecast value of 2002 year’s electric-power demand by Eq. (13).

Y ð18Þ ¼ 1=2ðE14 þ E24Þ ¼ 1=2ð15; 319:28Þ þ 16; 894:12 ¼ 16; 106:7.

As Table 1 shows, the actual electric-power consumption in China in 2002 is 16,200TWh. Sothe forecasting precision is 99.42%.

3.5. Calculate the forecast value from 2003 to 2013

Calculate the forecast value from 2003 to 2013 by Grey–Markov forecasting modelfollowing the above steps. Table 2 shows the forecasting values which are calculated byGrey-Markov forecasting model and GM(1,1) Grey-forecasting model.

3.6. Comparison of forecast precision between the Grey– Markov forecasting model and the

GM(1,1) Grey forecasting model

As the above, we can get the forecast values from 2002 to 2004 calculated by Grey–Markovforecasting model and GM(1,1) Grey-forecasting model. From Table 1, we can get the realityamount of the electric-power demand in China from 2002 to 2004. We compared the forecastvalues between the two models and the results are presented in Table 3.Table 3 shows that the Grey–Markov forecasting model is better for forecasting the

electric-power demand in China. The forecast values of Grey–Markov forecasting modelsare more precise than GM(1,1) Grey forecasting model, for data sequence with largerandom fluctuation.

4. Conclusions

The Grey–Markov forecasting model can fully utilize the information of the historicaltime-series data with large random fluctuation. As the case study shows that the accuracy

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Table 3

Comparison of forecast results with two different methods.

Year Reality (TWh) GM(1,1) Grey–Markov

Value (TWh) Precision Value (TWh) Precision

2002 16,200 16,438.15 98.53% 16,106.7 99.42%

2003 18,910 17,779.7 94.02% 18,541.3 98.05%

2004 21,735 19,230.8 88.48% 21,204.7 97.56%

M. Huang et al. / Renewable Energy 32 (2007) 1165–1174 1173

of Grey–Markov forecasting model in forecast value from 2002 to 2004 is higher thanthose of GM(1,1) Grey forecasting model in this paper. Based on the above analysis, theGrey–Markov forecasting model appeals to be intrinsically better because it has merits ofboth simplicity of application and high forecasting precision. This model has integrated theadvantages of GM(1,1) Grey forecasting model and Markov-chain forecasting model.

The forecasting result of this forecasting method greatly depends on state-intervalspartitioning. There is no standard rule to divide the states intervals. Generally speaking,the number of states should be decided according to the data and the demands of theproblem. If the historical data are not abundant, the number of states should be fewer, sothat the transition between the states can be clearly revealed. If the data are abundant, thenumber of states should be increased and the forecasting precision would be increasedcorrespondingly.

Because the electric-power demand in China is influenced by many factors such as theeconomy, industry framework, people’s income level, weather and government’s policy,there is a certain development trend for the historical time-series data, and the datafluctuate randomly. So it is suitable to forecast the electric-power demand by theGrey–Markov forecasting model.

The Grey–Markov forecasting model could be applied to forecast other time seriesproblems with large random fluctuation.

Acknowledgements

This study was supported by the Teaching and Research Award Program forOutstanding Young Teachers in Higher Education Institutions of MOE, PRC, NaturalScience Foundation of China (Project No. 30270773), Specialized Research Fund for theDoctoral Program of Higher Education (Project no. 20040335034) and Natural ScienceFoundation of Zhejiang (Project no. RC02067).

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