DGR-Based Investment Decision Model of Generation Expansion Planning

Copyright © IFAC Power Plants and Power Systems Control, Seoul, Korea, 2003

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DGR-BASED INVESTMENT DECISION MODEL OF GENERATION EXPANSION PLANNING Yu Cheng

LiZi Zhang

Dept. ofElectrical Engineering, North China Electric Power University, Beijing 102206, China

Abstract: In deregulated power markets, we must pay enough attention to generation expansion planning. This article applies degree of gray relationship theory to analyze investment decision of generation expansion planning. At last, according to proper practical case to show that DGR (degree of gray relationship) is really effective in analyzing investment decision of generation expansion planning. Copyright © 2003 IFA C Keywords: generation expansion planning, investment decision model, degree of gray relationship.

1. INTRODUCTION

means electricity generation, transmission, distribution and supply is integral. Relevant generation expansion planning and grid planning could work in line and share the information and drive for the common interests. In market environment, power generation, transmission, distribution and supply deregulated gradually and introduce competition so the interests of every segments have their own independency.

Due to the natural monopolization of electricity transportation and distribution, most countries introduce competition into electricity generation side and supply side. As we know, most countries' deregulated power market is developed from generation market. The crisis of California deregulated power market advise us that we must attach importance to generation expansion planning to avoid the lack of capacity during the construction of deregulated power market.

2) Goals of generation expansion planning is changed. In monopolization pattern, goals of generation expansion planning must be consistent with whole power system planning. The core goals of . generation expansion planning is to make sure when, where, what kind of and how much capacity of power plant to construct within the planning period. Generation expansion planning also must meet the needs of the development of power load that is constrained by many restriction condition and technical economy targets of least expend of national economy. But in marketing environment each generation company take part in competition generation market independently. Interests of generation expansion planning are in common with generation investor. Generation expansion planning should still try to improve the power supply ability, security and reliability to meet the needs of power customers. But investors' core goal is to improve their profits by generation expansion planning. So the

Under monopolization environment, Generation expansion planning pays much attention to technology than the market itself. But in competition environment, generation expansion planning should pay much attention to markets and utilize the economic signals produced by electricity price to improve the benefits of generation expansion planning. So investment decision of generation expansion planning should be regarded day by day.

2.

PROBLEM

In deregulated power market, investment decision of generation expansion planning faces many new problems such as: I) Independency of generation expansion planning. Traditional management pattern is vertical that 1061

frame of generation expansion planning must improve the profits of investors and also improve social benefits. 3) More investment risk. In the past, generation expansion planning is an integrate resource planning of electricity generation, transmission, distribution and supply and based on the "least expend of equal profits" rule. The planning could guarantee the return of generation equipments investment and operation costs. But in market environment, introduction of competition brings many uncertain factors. Profits of future investment are in deep relation with competition level of generation market and influenced by the fluctuation of electricity price. So it is very hard to make sure that investments could return. During the decision of generation expansion planning, paying more attention to the investment return is very important. 4) Difficulty of load forecast. The basic information of generation expansion planning that derived from long-term load forecasting is not enough. Traditional long-term load forecasting only focuses on the development of load itself and also involves the development of national economy. But it doesn't think of the response of end-users to the power market. In today's deregulated market environment, end-users have much more choices. When facing the fluctuation of electricity price, they will choose a proper power supplier to make expend least. So the relationship of load and electricity price is not only rigid but also elastic. This elastic relationship of load and electricity price will influence electricity generation and the operation and benefit of new planning capacity. 5) Importance of electricity price forecast. The function and characteristic of electricity price determine that electricity price is the relevancy of power enterprises and power end-users. Electricity price forecast is previsional and must forecast the development of electricity price. In investment decision process of generation expansion planning, unsuccessful electricity price forecast will make the whole investment scheme balance distortion. So electricity price forecast is very crucial to generation expansion planning. Generally speaking, electricity price forecast must think of such factors as: capacity cost, depreciation rate, fuel price, system load rate, interest rate, investment risk, exchange rate, technology and management level and electricity demand price elasticity.

3. DEGREE OF GRAY RELATIONSHIP (DGR) Thinking of investment decision of generation expansion planning is a "gray system", this article uses degree of gray relationship theory (DGR) to set up the investment decision model of generation expansion planning. The basic concept of degree of gray relationship theory, see (Marco, et al., 1996), is such:

In the above formula, X is a serial, if X has such characters as: 1) Data of X are approachable; 2) Data of X are proportional; 3) non-negative; then X is called degree of gray relationship factors set.

Suppose that X is a degree of gray relationship factor set,

X =

kli E N,N = (lA m),m ~ 2F xj

= (xj (1),A x j (n)~

(2)

Xj(h)E xj,h E H,H

= {1,2A n},n ~ 3;

Make X o E X is reference row, x j E X is compare row, Xo (h) and Xj (h) is the data of Xo and Xj in the point h. Define that R(xo ,xJ is the degree of gray relationship ofXj to xo, calculation formula is below:

In formula (3), r(xo (h), Xj(h)) is the compare estimation of Xo (h) to Xj (h), defined as below: r(x o(h),x j (h))

=

min minlxo(h)- Xi (h)1 + A. max maxlxo(h)- xj(h)1 jeN heH

jeN

heH

(4) r(xo (h), Xj (h)) satisfies such conditions as follows: 1)

Criterion:

2)

Integrity:

0< r(xo (h), Xj (h))<=1; r(xbyj<>r(Yj,xJ, xj,Yj EX;

3 ) Even symmetry: r(x,y)=r(y,x), if X={x,y};

Based on the analysis of context, generation expansion planning involves many factors. In the actual implement process, these factors are uncertain and fuzzy. Some rational index will exhibit some extent uncertainty and fuzzy. And also we must think of the psychological and physical condition of investors. So many uncertain factors make investors hard to make a successful decision. Thus, generation expansion planning investment decision system is a "gray system" that means information of the system is partly known and partly unknown.

4)

Approachability: I

r(xo (h)-x; (h)) 1 oc r(xo (h), Xi (h)).

From above we can get degree of gray relationship space that is the combination of distance space and point set topological space. In formula (4), I r(xo (h)-Xi(h))! is the estimation of distance, minlxo (h) - Xi (h)l, max maxlxo (h) - Xi (h)l] is [ min ieN heH jeN heH the compare condition of Xi and xo, it includes point set topological information. In this formula, Il. which 1062

is a constant, A. E [0,1], is the differentiate coefficient of DGR, its function is to adjust compare condition. When A. =0, no compare condition, when A. = 1, compare condition keep unchanged. Usually we setA. =0.5. 4. INVESEMENT DECISION MODEL In the process of investment decision, we must consider many indexes. These indexes associate and influence each other and weight of each index is different. The magnitude of each weight reflects the importance of the corresponding index. Each index has its own meanings and dimension, so it is very hard to make a compare among different indexes. Thus we should initialize these indexes fIrst. In practical, it is crucial to identify weight of each index. Common methods include Delphi technique, AHP and relative entropy method etc.

4. J Model construction based on DGR

Suppose that S={ S], •• •,Srn } is the set of m decision-making objects. Every object is described by n index systems P={ PJ, ... , Pn } which have different meaning and dimension. Thus, we can obtain a m x n dimension decision indexes matrix. After standardization of this matrix, we obtain a new index matrix [R]:

=

Wi

,i = 1,A. .n

n

(8)

Lr(Pi,Pi) j=1

In the format of matrix: [W] =[wi ,A. , W n f, that means that [W] is the weight matrix of index system. The construction of investment decision model is:

= [R]mxn

[Y]mxI

(9)

• [W]nxl

[Y] is the result matrix of investment decision.

4.2 Model Construction based on fuzzy DGR

Models of fuzzy DGR perform fuzzy reasoning considering the fuzzy characteristic of some indexes that can simulate the reasoning ability of human nature. To construct a model, fIrstly we should defme fuzzy

-

-

cluster DGR r(pi' pj) as below:

(10)

m

[R]=

-(

SI

Xl,l

X 1,2

A.

X 1,n

S2

X 2 ,I

X 2,2

A.

XI,n

M

M

Xm,l

X m ,2

M Sm

~.:cX h,j

Pn

PI

M A.

r Pj'Pj

/\

X h,j )

h=1

=..:;m'-=------

L

(5)

(11)

(Xh,j V Xh,j)

h=1

M Xm,n

)

" /\" and "v" is fuzzy less operator and greater operator.

mxn

-

According to the same reasons, rep i , P j) also reflects the fuzzy influence of Pi to other indexes.

represents the jth index of the ith object. It is obvious that [R] has the characteristic ofDGR factor sequence.

Xij

Wj

=

,i = 1,A. ,n

n

(12)

L~(Pj,Pj)

(6)

j=1

,;n

[W] =[;i ,A. f is the matrix format of[W], that means [W] is the weight matrix of index systems. Investment decision model could be constructed as below:

In the formula (6), r(Pi,Pi) is the cluster DGR of

Pi to other indexes, shown below:

[Y]mxl

= [R]mxn

• [W]nxl

(13)

[Y] is the result matrix after decision-making. rep i ' Pi) reflects the influence of Pi to other indexes in some extent. If certain index has great influence to other indexes, we can draw the conclusion that the information contained in this index is great and vice versa. After standardization of these n DGRs, we could obtain every relative weights of each index. That is:

From what we have discussed above, we can obtain the DGR based investment decision algorithm as below: I) Set up index system, then initialize and standardize of index matrix; 2) According to formula (7) and (11) to calculate DGR of any two indexes; 3)

Calculate

the

cluster

DGR

r(pi' Pi) or

rep i ' P j ) of each index;

4) 1063

Calculate the relative weight of each index;

5)

Perform decision-making process using formula (9) and formula (13).

RL

=RL c N

+ RL p

NG)

I I

5.MODEL APPLICATION RL We choose investment decision of generation expansion planning as the analytical object. There are three generation expansion plans to implement which are expressed as 51, 52, 53. Decision-maker will take into account three indexes, which are investment cost, operation cost and investment return. The first two indexes are cost-type index that should be the least and the last index is benefit-type index that should be the biggest.

c

(17)

= j=\

GC"j,k - 1

k=\ D

(18)

max

N

NG)

"L..J "GC L..J t,J,. k k=\

= j=\

RL

-

H ',J,. k

-1

P

(19)

RL -- reliability level coefficient; RL c - reserve capacity coefficient; RL p

Calculation of each index is shown below, see (Wang, 1990; Zhang and He, 1989): 1) Calculation of investment cost (thermal power plant).

--

reserve power coefficient;

Dma.t -- the max load forecasted of the tth planning year; PDma.t -- the max power demand forecasted of the tth planning year.

N NG)

Z=""C L..J L..J ',J,'k- G',J,'k j=l

(14)

k=\

According the formula above, we can obtain every index's numerical value of each scheme. As shown in table 1. .

Z - investment cost;

Table 1 Indexes' value for each scheme

N -- numbers of power plants; NGj -- the unit numbers of the

jth generating unit C,j,k - the current value of the tth year the jth power plant the kth unit investment cost; Gtj,k -- 0-1 variable, means whether the tth year the jth power plant the kth unit will be constructed (Gtj,k=l, construct; Gtj,k=O, not construct).

Factor

OC =

Investment return rate (%)

Reliability level (%)

1150

600

12%

18%

1000

500

10%

22%

1150

550

10%

25%

51

Scheme 52

Scheme 53

The calculation of index weight matrix (showed in table 2) is based on the decision ofDGR:

NG)

Ij=\ IpC"j,k - GC"j,k - H"j,k k=\

Operation cost (money)

Scheme

2) Calculation of operation cost (thermal power plant). N

Investmet cost (money)

[W]4x\ = [O.318,O.217,O.344,O.l21f

(15)

Table 2 Decision results based on DGR OC -- operation cost; PCtj,k -- the current value of the tth year the jth power plant the kth unit generation cost; GCtj,k -- the capacity of the tth year the jth power plant the kth unit. Htj,k -- the tth year the jth power plant the kth unit expectational generation hours.

Scheme [Y]

( I I pt -GC"j,k -H"j,k)-OC-Z j=1 k=1 Z

34.65%

[W]4xl = [O.331,O.225,0.305,O.139f Table 3 Decision results based on fuzzy DGR

N NG)

=

37.06%

The calculation of index weight matrix (Showed in table 3) is based on the decision of fuzzy DGR:

3) Calculation of investment return rate.

F

28.29%

Scheme

(16)

[Y]

F -- investment return rate;

31.18%

35.74%

33.08%

From the results of these two decision methods, we can draw the consistent conclusion that the best scheme is 52.

Pt -- electricity price forecasted of the tth planning year. 4) Calculation of reliability level This article uses reserve capacity coefficient and reserve power coefficient to reflect reliability level.

6. CONCLUSION There are many uncertain and fuzzy factors in practical investment decision of generation 1064

expansion planning; these factors will influence the decision-makers' final decision results. Gray system theory is the right and feasible method to solve this problem. This article attempts to apply degree of gray relationship theory to construct models of investment decision of generation expansion planning. According to the detailed analysis, this article draw the conclusion that models based on DGR or fuzzy DGR is an effective way to provide successful investment decision for generation expansion planning.

REFERENCES Marco Dorigo, Vittorio Maniezzo and Alberto Colorni( 1996). Optimization by Acolony of Cooperating Agents. Journal of IEEE Transactions on System, 1, 29-41. Wang Xifan(1990). Power System Planning. Hydraulic Power Press, Beijing. Zhang ben and He Dayu(1989).Generation Expansion Planning. Energy Press, Beijing.

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