Power System and Cogeneration: An Optimal Expansion Planning

Co pyright © IFAC Power Systems a nd Power Pla nt Cont rol. Seou l. 'Ko rea. 1989

POWER SYSTEM AND COGENERATION: AN OPTIMAL EXPANSION PLANNING Y. H. Kwun K orea Electrotechnolog)' R esearch Institute, Changwon, K orea

Abst~t.

Cogenerati~n technology became an attractive power generation option. In th1S study , ~ optlmal po~er system expansion planning model that integrate ~e supply plann1ng of potent1al cogenerators with that of host electric utilities lS presen~ed • . ~e . first step is to derive the optimal capacity expansion plans o~ electrlc u~lltles and cogenerators independently, and the second step is to flnd most deslrable supply plan of both the utilities and cogenerators in order to meet total electric ity and thermal demand of a region.

Keywords. Cogeneration, optimization, ecOl'lCllllics, power system expansion, modeling

INTRDUCl'IOO Due to the potential energy and cost saving to both electric utilities and industrial users from efficient use of some energy that would otherwise wasted, cogeneration plays an important role in the electric power and thennal energy supply planning. its nature, cogeneration produces a joint product - process heat/ steam and electricity. Thus, cogeneration represents an alternative to the electricity-only production technologies that normally employed by electric utilities. Cogeneration also represents an alternative to the steam/heat-on!y production technologies that normally used in the industrial and cOlllllercial sectors. Thus, both potential cogenerators and electric utilities should be included in the power system planning framework,if cogeneration potential of the study region is not negligible.

By

and cogeneration. Benefits from cogeneration can be analyzed by comparing the cost with that of without-cogeneration case. The final step is to find most desirable plan when total system is concerned. The planning goal of this step is to minimize overall cost of producing electricity and thennal energy required in a study region . In this formulation cogeneration technologies would be selected in place of the electricity-only and/or heat-only plants whenever it is economical to do so. The savings of this case may be regarded as the maximum societal benefit from cogeneration. 'IHE

~EL

The model fonwlated in this section represent the technical alternatives for producing thermal energy in the industrial sector and electricity in the utility sector. Specifically included are a variety of cogeneration options, as well as conventional heat-only and electricity-only production technologies . A special attention should be paid to grouping of indi vidual industries. A resonalable grouping might be done by the size of steam demand of each industry in order to reflect the economies of scale effect. Also , electricity-to-heat demand ratio and fuel type is considered. Followings are description of the model when linear progrBIIIDing technique is used.

Since many cogeneators are also large industrial customers of electric utility , the future growth of cogeneration influences both the demand and supply patterns of the utilities. This makes the role of cogeneration quite complicated. Several cogeneration planning models have been developed to evaluate cogeneration ventures . '!bese are usually designed to help industry to find the "best" cogeneration option . In these models, however , the effects of cogeneration on electric utilities are not explicitly considered. In this study, several alternative formulations presented that vary according to the planning objectives . The analysis starts wi th separate optimization models for individual potential cogenerators and utilities in which cogeneration is absent .

Cogeneration can influence both the operation schedule ofexisting plants of the utility and industries, and future capacity expansion schedules. '!be formulation is divided into two parts, one for the industry sector and the other for the utility sector, and they are linked by cogeneration activities. Following set specifications are used as the indices of the parameters and variables in the model .

are

In the second model, the cogenerators plan their optimal steam and electricity supply schdeules with both conventional heat-only production and and cogeneration technologies assuming that the utilities' future generation schdule is known . In this case, the planning objective of the industries is to mimimize cost of heat-only production, electricity purchase from utilities

tET

wEW lEI

Time periods in the study time horizon Time bands during each time period.

Industries or groups of industries that are potential cogenerators.

243

244

Y. H. Kwun

pEP,PU,FQ Plant technologies. PU is subset for utility and FQ the subset for industry • Input and output materials. HR • EM,HR,HS,ME is the subset of M for raw materials, MS the subset for process heat (or steam), and ME the subset for electricity. cE C Process control options for industrial plants representing different power-toheat production ratios .

exceed the produced electricity in any tu.e band, ZI , w,t + ei , w, t::; L

L dp , c L b. ,c Up , I , c ,w , t

for

IEI ,wEW, and tET

Also, power self-use is restricted so as not to exceed the industry's own demand for electricity. for

Cogenerator sector constraints The decision variables of a potential cogenerator are defined as:

(4)

c

p

(5)

lEI,wEW , and tET

Finally, if upper bounds on the new plant addition are desirable, they can be accommodated through

Up,c,I,w,t: Thermal energy production level by each process (Ton/hr) Vp , l,t New capacity additions of each type of plant (Ton/hr) Cogenerated power sales to utility (MW) Zi , w,t Industrial self-use of cogenerated et I W,t power (MW) The industrial cogenerator is represented as using both thermal and electric energy for its industrial process. It produces the thermal energy in its own plants. It can obtain its electrical energy either by purchasing it from the electric utility and/or by cogenerating it by its own plants. The by,

capacity

utilization

~

Vi • P • t

Vi

I

I: Vi

or

P•t

u,v,z,e

. P•t

~

Vi

I

(6)

t

~O

Utili ty sector const.raints The decision include :

variables

of the utility sector

Xp,w , t:Power generation level of plant type p(MW) YP , t : New capacity additions of plant type p( MW) The capacity constraint of each plant is;

constraint is given

Xp

I

::;

w. t

8 p, w (!{Up, t + L YP, t I

(7)

t

for

::; 8 p , w(Kq p . I • t + L Vp . I , tl ,

Ldp , c Up , c , l , w,t c

t

(1)

for pEFQ, I E I ,wEW,t ET where 8 p ,w is the availability factor and Kqp,l , t is the existing capacity(Ton/hr). The plant utilization coefficient , dp,c,is defined as : dp , c

o

if c is an available cogeneration process control type of plant p otherwise

L (Kq p , 1 ,t + L Vp , I , tl

~

(1 + rQ 11 HP I , t

1

where the future peak thennal demands, HP I , t , and, the minimtDll reserve margin, rQI , are exogenous parameter of each industry. Demand constraint for thennal energy production expressed as follows. In the expression, b.,c is production coefficient matrix.

•

p

~

HI , w , t

(1+ r U) ( LPt - Lel,wP,tl

The demand constraint and upper bounds are; L (xp,w , t + L Zl ,w, t) p I

( 3)

The values of the thennal energy demands in each time band, Hl , w,t,can be determined by multiplying peak demand, HPi , t, by the ratio of the demand at the time band to the peak demand . This ratio might be used to represent the thennal load shape of the industry, Next constraints are included in order to express the energy balances of cogenerated electricity, These state that the Stml of power shipped to the utility and that retained for self-use cannot

(8)

where fl ( 0 ::; fl <; 1 is a parameter designed to represent the degree of firmness, ru is the minimum reserve margin of the utility, LPt is the exogeneously projected electricity peak load of the area, and WP(subset of W) stands for the peak load time band.

for

C

for .EMS, IEI,wEW, and tET

for tET

I

(2 )

E I and t ET

LLdp , c Lb.,c Up,l,c , w, t

L(!{UP,t + iyp,r) + Lflzi,wP , t ~

P

for

Next,the cogeneration made available during each time period allows the utility to avoid or to delay new plant construction . The power supply available from industries increase the utility ' s available capacity,while self-generation reduces the utility ' s supply obligation. Thus, the capaci ty expansion constraint is expressed as : p

Next, capacity expansion constraint is ; t

where 8 p , w is the availability factor of each plant and KUp,t existing capacity.

YP, t

~Lw,t

- Lei ,w,t

(9)

I

wEW, andtET or

::; YP, t

L YP, t x,y

::; yt

(10)

~O

Cost functions are expressed as follows . capital cost of utility, ykt and that of industry, Zkl , t, are given by,

The

( 11)

vtl,

t

L

L P

a qI , p

k p , t Vp, I , t

(12)

Power System and Cogeneration

where a "p and a q1. p are capital recovery factors, kp, t are unit capital costs, and yo t is the utility's fixed capital charge on existing plants, Material costs, ytt and Zfl,t,are given by, yt t

= L fU.,

LChLBa,pXp,w,t)

t

•

(13)

p

•

LChLdp,CLba,c Up,c,1,w,tl p

(14)

c

245

that cannot be exceeded when cogeneration is included, Moreover,the utility's avoided cost is the difference between the costs in the two solutions with- and without- cogeneration, The Solutions are used for cost/benefit analyses of cogeneration . Next formulation is for the case in which the industries maximize their benefits by introducing the cogeneration technology without considering the utility's power supply schedule. In this case, the industrial sector model includes cogeneration option, but is independent of the utility sector.

where fU., t and fq 1 ,. ,t are uni t material costs of each sector (S/Ton), and 0 w is duration of each time band (hrs)

The objective function of industrial sector of this case is expressed as

Next, the operation and maintenance costs, and ZI 1 , t are calculated by,

21

ylt

t

yll,t = L [ lfp,dk"p,t P

+ LYP , tl + IVp,dLCh Xp,w,t»)

ZI 1 , t

=L

(15)

[ If p, t{ \t'Ip, 1 ,t + L vp , i , t )

p

t

+ IVp , t!Ldp,c LOw Xp,c,l,w,tl)

(16)

c

where lfp,t is unit fixed O&M cost and IVp,t is unit variable O&M cost (S/MWh or S/Ton) , Next, when an industry cogenerate power, the revenue from power sale and the reduction in payment for the power purchase are included in the objective function of the problem, It is given by ; zP 1 ,t

=

Z

t LOw Zl, w, t

(17) where Zt is the buyback rate and e t the price of electricity, Sector models If cogeneration technologies are excluded from above fonoulation, the two sectors are independent of each other, Each party will find its optimal supply plan by minimizing total costs to supply its awn demand with steam-only or with electrici tyonly production technologies, The solutions of these sectoral models are used as a basis for determining the benefits of cogeneration, Objective function of electric utility, y, and that of each industry, ZI when cogeneration option is excluded are 1

y = L-----[yc t + yf t + ylt 1 t (1+k)t ZI

L

1 L-----[ZCI,t + Zfi,t + ZII,t») t (l+k)t

(18)

where k is the discount rate and cost functions are found in Eq, (11) through Eq, (17), Constraint set can be fonaed from ( 1) to ( 6 ) for industrial sector, and from (7) to (10) for electric utility sector, respectively, However, in this sector models, all the cogenerationrelated expressions should be excluded from the constraints,

The minimum costs found in these sectoral models provide an upper bound on the production costs

(

20 )

The cogeneation schedule found in the solution can be considered as the "best" cogeneration option of industries under the given economic and technical environment, and known electricity price. This solution can be further analyzed by comparing with the solution of the "global" model discussed below. After the industy sector probelm is solved, the utility sector problem may be reoptimized to check the effect of cogeneration on the electric utility supply plan. Here, cogeneration of industries are a..-sumed to be known. Global model The objective of the "global" model is to find the supply mix that mInImIzes the total cost of energy supply in order to meet the exogenous thermal and electricity demands in the whole study region. The value that the objective function takes on represents the global cost, or the sum of the combined costs of the electric utility and the industrial users during the planning horizon. In this formulation, each party is assumed to behave as a global cost minimizer and not as the individual cost minimizer, The solution of this model is highly significant from public policy perspective because it represents an optimal utilization of resources from a societal viewpoint. The objective function of the fonnulation is shown below, and all the constraints from (1) to (10) are included in the formulation. L-----[yc t + ytt + ylt + t (l+k)t

OBJ

+ (19)

[ZC i ,t + Zf I , t + ZI i , t - zP i , tl (1 +k) t

L (ZC i ,t + Zf I

,t

+ ZI I , t ) )

(21)

i

The solution of this model represents a joint optimal supply pattern, Though cogeneration technologies can produce electricity more efficiently than conventional electricity-only generation technologies, there exist a limit on the amount of cogeneration needed to achieve minimum overall cost of production, since the cost savings do not grow monotonically with the quantity of cogeneration. The decreasing marginal benefit is attributable to the following. As an utility purchases more power from cogenerators, less of its own generation is required. As more cogenerated

Y. H.Kwun

246

energy is purchased, it displaces more efficient plants of utility, and consequently,the marginal cost savings of cogeneration per kWh decrease wi th increasing quantity. Moreover, in the industries, as cogeneration power sales increase, less efficient cogeneration plant must be brought into production. 'Ihus, the marginal costs of electricity increase as the industry increases its cogeneration output. CASE SWDY

'Ihis section discusses an application of the .odel described above. 'Ihe primary objective of this section is to analyze an optimal capacity expansion schedules of conventional power system and industrial cogeneration in the example area. As the sample region for the example study, Korea is selected. In this study region, electricity consumption in 1987 was 64,000 GWh and is expected to grow up to more than 160,000 GWh in 2000. But ,due to the insufficient domestic energy resoureces, conservation and effifient utilization of energy has been one of the most important issues in energy JDBnBgement policy. In 1987,

total cogeneration capacity in the region was about 731 MW, and its electricity generation corresponded to about 4 % of national total electricity demand. In this section, the analysis focusses on the optimal capacity expansion pattern and effects of the cogeneration developments on the supply of the electric utility. Special attention is given to the overall costs and benefits of the cogeneration development and the global cost minimizing power system expansion plan.

Industries are classified into three groups based on the size of steam demand and type of industry, and plant technology set includes eleven types, four for electric utility and seven for industry. Cogeneration technologies are charaterized by heat/electricity ratio, size of unit plant and fuel type. A time period is divided into five time bands l •

Table 1 presents the optimal electric utility capacity expansion and cogeneration expansion patterns of three different problems. 'Ihe first problem is of the case in which cogeneration is excluded. 'Ihe second case is when cogeneration is included, but it is solved independently of the utility. 'Ihe last case is the solution of global problem. Also given are the present worth of cost savings that result in when cogeneration is allowed in the available technology mix. The results show that, when comparing the with-cogeneration case and the without-cogeneration case, the costs of the utili ty sector decrease (because it produces less electricity when cogeneration is allowed) and the costs of the industry sector increase (because they produce both steam and electricity when cogenerating). 1 'Ihe case study is done for the illustrative purpose of the proposed model. 'Ihus, the representation of electric utility and potential cogeneration systems are simplified.

Table 1 The Optimal Solutions (unit : GW ) Year

89/90 91/92 93/94 95/96 96/98 99/00 total

Utility New ttl

Electriciy Capacity Ind 1 In d-2 In d-3 New tU New tU New tU

When Cogeneration is excluded 21.1 .23 - .4!! - 22.0 .48 .23 - 25.0 .48 - .23 3.4 27.8 .48 .23 2.7 30.8 - .48 - .23 .23 3.6 34.1 .48 9.7 -

-

.U7

.07 .07 .07 .07 .07

89/90 91/92 93/94 95/96 97/98 99/00 total

When Utility System expansion is given 21.1 .07 .50 .01 .24 - :M - 22.0 .04 .93 .02 .26 - .07 - 25.0 .06 .49 .03 .29 - .07 2.5 27.5 .08 .24 .03 .32 .07 2.7 30.2 .09 .14 .04 .36 - .07 3.5 33.6 .11 .25 .05 .41 .07 8.7 .45 .18 Cost sav1ngs(H$) Energy: 292, otsl:505

89/90 91/92 93/94 95/96 97/98 99/00 total

Global optimal Solution 210 .07 .55 .23 - .07 - 219 .04 .59 .23 - .07 - 249 .06 .65 - .23 - .07 2.6 269 .11 .76 - .23 - .07 - .07 2.6 299 .15 .90 .23 - .07 3.5 330 .17 1.08 .23 8.7 .60 Cost saV1ngs(H$) Energy: 152, Total: 551

(Note)

Gf: Fuel cost real escallation rate Gc : Capital cost real escalltion rate Ind-i : industry group i Cost savings : cost savings (1987 $)

shown in the table, in without-cogeneration case, the utility expand 9,700 MW of new coal and nuclear plants to meet increasing peak load, and the industries expand only conventional steam production plant. As

If cogeneration is included and the behaviors of the industries are independent of the utility, 630 MW of total cogeneration capacity is built during the time horizon. As a result, this amount can be regarded as the economic potential of industrial cogeneration. If cogeneration are to be installed as above, the utility's capacity addition will be reduced due to the decreased supply obligation to the cogenerating industries. 'Ihe cost savings compared wi th the first case was 505 million dollars (present worth) of total. In this case, industry group 1 and group 2 (relatively large industries) introduced cogeneration, but industry group 3 (relatively small industries) was found to install only the steam-only production plants that might be more more economical than cogeneration plants due to the scale effect. Next, in the global model, if both the utility to behave in order to minimize overall cost of producing electricity and thennal energy, the optimal solution is different from that of the above case. 'Ihat is, total cogeneration plant addition decreased from 630 MW to 600 MW and industry group 2 did not install any cogeneration plant. As a result, total cost savings are increased from 505 to 551 million dollars, and cogenerated energy proportion is smaller than the above case. and industries assl.UOOd

247

Power System and Cogeneration

a whole, however, the econ
Aa

In the global model, the results simply shows the role that cogeneration can play in the optimal power plant mix when it is assumed that the two sectors cooperatate canpletely. industrial sectors. And, public policy makers may find energy policy tools to induce the level of cogeneration development to the most desirable level. The policy option may be the level of buyback rate, financial incentives and so on. a:t
There may be many of ways in which the model could be improved. They include more detailed classification of potential cogenerator groups, and better treatment of steam losd pattern. Also, some nonlinear representation of the problem may be introduced.

1laugbMn, M.L. and others (1987).

Cogeneration in ~. The University of Texas, Austin, Texas. pp. 53-128. Brown, D.H.(1982) . Cogeneration Potential of Energy Constervation System. IEEE Trans. on Power Apparatus and SYStems,Vol.PAS-101, No.8, pp. 2597-2601 . Hu, D.(1986). Cogeneration . Reston Publishing Inc. Reston. Harkins, H.L.(1981) . PURPA new horizons for electric utilities and industry.IEEE Trans. on Power Apparatus and SYStems.Vol.PAS-100, No.6, pp. 2784-2789. Kendrick, D. and Stoutjesdijk, A. (1978). The planning of industrial investment programs. The World Bank, John Hopkins Press, Baltimore Korea Elecric Power Corporation(1989).A study on the prospect of self-generation.Seoul,Korea

Cogenerator sector

Electric utility sector

Potential cogenerators Energy Use Analysis (Steam, Electricity)

I Steam 8nd electricity analysis/forecast

I

Electric Utility Demand and

Solve conventional system expansion problem wi thout cogeneration option

Technology representation

I

I

I Solve optimal steam prod. problem w/o cogeneration

Solve optimal steam prod. problem w/ cogeneration

I Cost/benefit sensitivity I--analysis Fig. 1

Res~

Forecast

Solve optimal power supply problem when cogen . is known

Solve Globally Optimal Power and Steam production Problem

Basic structure of analysis