294 IEEE Transactions on Power Systems, Vol. 3 , No. 1 , February 1988

FYedN. Lse Mantxr

Univexsity of Oklahoma N o m , OK 73069

AEsTRAcr

Joint dispatch, in which all the generating

dispatched, can result in signficant pmduction cost savings as campared with independent area dispatch. This paper presents a three-area production simulation model w h i c h evaluates :

o The expec td unit energy generation.

o The expeAed area u~lserved energy.

o The expect& pool-wide production cost savings and the e area production cost savings. Randcw unit forced outages, unit joint awnershi P I andtransrm 'ssion interconnection constraints are considered in this proposed model. In this paper, the simulation results of a q l e three-area system are also presented.

- in an interco- "4"" are centrally

llmRf3MJcrIm

Backsround

There are two ccnmnoriiy used methods for single-area prduction simulation in a probabilistic environment - Monte-carlo approach and analytical probabilistic approa?: The Monte-Carlo approach uses a deterrrrrm stic production simulation algorithm to compute the prcduction indices for a given realization ofsystem states. The realizations of system states are generated randcnnly via a Monte-Carlo front end. Since the number of passible system states is usually very large, the amputation time required to obtain reasonably accurate estimates are thus very large. ? h e high carrpxltational requirements limit its application.

m e single-area probabilistic approach was intnxiuce3 by Baleriaux and Booth [1,2]. This approach is formulated based upon an equivalent load duration curve. This approach is cumputationally very efficient.

Joint dispatch of generating resources amrq interconnected utilities is receiving increases attention as a viable alternative to reduce service costs without sacrificing service reliability. Consequently, my researchers have attempted to develop methcdologies in the area of joint dispatch proftuction simulation. Ihe reported multi-area models are basically direct extensions of single-area models. Ihese models are :

This paper was sponsored by the IEEE Power Engineering Society for presentation at the IEEE Power Industry Computer Applica- tion Conference, Montreal, Canada, May 18-21, 1987. Manuscript was published in the 1987 PICA Conference Record.

o Direct simulation model (GE model) [3] - For a given system capacity state and load level, this model perfom a deterministic dispatch simulation

appropriately consider random unit forced outages in the simulation, a Monte-carlo front e& is requked . The high cumputational -9 associated with Monte-carlo simulation may l m t its application.

o Heuristic simulation model [4] - In this model, the exyct+ p e r - p l i n g production cost savings are heuristically assessed based upon two extreme cases, indeperdent area dispatch and joint dispatch without transrm 'ssion constraints. The consistency of its results may be open to question.

o mpbabilistic simulation models -- ?his type of models has been limited to two-area models. The models proposed in references [5, 6, 71 use a bivariate Gramihalier series expansion to approbte the joint area load p-ility function. This methodolq can be viewed as direct extension of the Baleriaux-Booth approach. ~n [8], Ahsan et al. proposed a two-area prcduction simulation model based upon the segmentation method. To the author's knowledge, all the probabilistic two-area models have inherent problems in being extended to a threearea model :

0 The formulation of a trivariate Gram-Charlier series to accurately approximate a joint probability density function is questionable [9].

o The implementation of a three dimensional segmentation method requires excessive carputer memory.

Amroach

A theoretically sound and camputationally efficient three-area model is proposed in this paper. To avoid approximating a three dimensional load duration surface, this model employs a discrete load/proMilistic generation capacity approach with transmission constraints imbeded in the probabilistic generation capacity model. This model accounts for randm unit forced outages via an analytical probabilistic approach (i.e. in contrast to the Monte-Carlo simulation in [ 3 ] ) . ?his model explicitly considers transrm ssion interconnection constraints (i.e. in contrast to the heuristic approach in [4]) in the production simulation. It is believed that the proposed three-area approach is novel and has not been reported before.

One notable differ- between a two-area probabilistic model and a three-area probabilistic model is the added Oamplexity in p e r transfer arrangenm-~ts. In a two-area simulation, the power transfer arrangement is unique. In a three-area simulation, there can be same variations. In this paper, the impact of power transfer arrangements upon the expected energy generation and unserved energies in a multi-area joint dispatch environment is discus-. This discussion offers considerable insight into a multi-area prduction simulation P-.

via a linear p r q r a m h g technique. To

0885-8950/88/0200-0294$01 .WO 1988 IEEE

295

L(i) :

S(i) :

s(i) :

NOTATION

Demand at area i.

A R.V. which represents the generating capacity at area i.

A R.V. which represents the dispatchable generating capcity at area i.

M(i) : Transn 'ssion

IM(i) : Transmi ssion

T(i,j): Tramxu * ssion j.

Pr(.) : mbability.

export limit f m area i.

import limit into area i.

flaw limit f m area i to area

E( .) : Expect& value.

E{.l.): Conditional expect& value.

m : Exp=t&Unsenredenerqy.

MFMoIxIL(x;Y

Transmission Interconnection Representation ccsnpared to a single-area production simulation model, the added complexity in a multi-area proctudion simulation model is the consideration of transmission interconnection constraints. The in*-area energy transfers have to be within the capability of the available transmi ssion interconnections. merefore, the criterion for a viable transnu 'ssion interconnection representation in a multi-area production sirmilation model is the ability to enforce the p e r transfer limits with the least amount of ccarpxltational requirements rather than the ability to rigorously corrpxte transmission flaws. With th is criterion in mind, a linear flaw network represntation is used in the proposed three-area model. ?he general topology for a three-node 1- flow network is shm in Figure 1. Eachtransnu 'ssion link is characterized by two uni-directional flow limits.

The general delta connected topolosy of a three-area network can be converted into an equivalent wye connected topology [lo] with the addition of a super node at the junction. This conversion transforms o o u p ~ ~ - 'ssion constraints into locdl transrmssion constraints. The transmission import limit m(i) and the transnu 'ssion export limit m(i) at node i relate to the uni-directional flm limits as follaws :

m(i) = 2 T(j,i) j=1; j+i i = 1 , 2 , 3 <I>

At a given denwd level L(i) at area i, the dispatchable area capacity $(i) can be determined fm the available area capacity S(i), the area trahsmission export limit M(i) , and the area demand level L(i).

S(i) = h(S(i); L(i)+M(i)): i = 1 , 2 , 3 <2>

?he supply will balance the demand in the three-area network (i.e. no unserved energy) if and only if the fQlh4ing hold :

h

&1) 1 L(1) - IM(1)

3 2 ) 2 L(2) - IM(2)

G(3) 2 L(3) - IM(3)

<3>

<4>

<5>

<6> z(1) + g(2) + g ( 3 ) 2 L(1) + L(2) +L(3)

mese sinple demand-supply feasibility conditions are the basis of the proposed three-m model. For a higher dimensional system (i.e. system with more areas), a set of d e n w d y l y feasibility conditions, in which the transrm ssion constraints are imbeded, also exist. Unfortunately, the mesh-star conversion is generally not valid for an interconnected system with more than three areas. In [ I l l , the author proposed an efficient multi-area reliability evaluation method via a reduced set of demand-supply feasibility inequalities. The author believes that similar approach can be used to extend the proposed produdion simulation method to a higher dimensional system.

Unit Lmdinq O r d e r

?he philosophy upon w h i c h the three-area joint dispatch production simulation model is developd can be statd as follaws :

o Maximize pool-wide production cost savings (i.e. utilize all the generating resources in the interconnc?cted network in the most ecodcdl mer).

o Allocate produdion cost savings fairly to each participating area.

To maximize the exp+~3 pl-wide production cost savings, generating wts are loaded in the order of their average incremental costs. The most efficient generating unit in the interconneded system is the one with the lawest average -tal cost; this generating unit is loaded first. The next unit to be dispatched is the unit with the second lawest average incremntal cost and so on.

At present, each unit in the interconnected three area system is representd as one loading block and is dispatched according to its respective merit Order. Must-run units, multi-block unit representation, and dispatch modifiers can be easily inplernentd in this proposed evaluation model.

Figwe 1 Emected herqv Generation

With the philosophy of maximizing the expecbd

296

pool-wide production cost savings, a generating unit in the intermnnectd system is dispatched to maximize its expected energy generation constrained by the follcwing :

o System demands.

o Transmission constraints.

o Its own capacity and availability rate.

o Its loading order.

With fixed system demands, transrm ' ssion constraints, unit characteristics, ancl Unit loading order, the

en- generation of the subject unit is invariant to the irm-area energy transrer arrangement. This can be illustrate3 by a simple -le. Consider the dispatch of an area 1 generating unit with 5 Mw capacity in a three-area system described in Table 1.

Table 1

Area1 Area2 Area3 ------ ----- - WW) 2 3 2

Import Limit (Mw) 2 2 2

Export Limit (Mw) 3 3 3

After serving the 2 MW demand at area 1, there is 3 MW surplus capacity which can be transferred to area 2 and area 3. Consider the following two transfer al-rargements :

o Area 2 has the priority to receive the surplus capacity -- Area 2 can only i m p r t 2 MW because of its mrt limit. The raining 1 Mw will then go to area 3. The p e r generation of this unit is then 5 Mw.

o rea 3 has the priority to receive the surplus capacity -- &ea 3 only needs 2 Mw. ?he remaining 1 ~w will then go to area 2. The p e r generation of this unit is still 5 Mw.

It can be visualized that for any other transfer scheme which is a cambination of the two extreme cases, the p e r generation of this subject unit is still 5 Mw.

In this three-area d e l , the expeded energy generation of a given unit is computed as the difference between the expected system unserved energies before and after the subject unit is dispatched. The key to this evaluation is an efficient algorithm to compute the expected system unserved energy. For a given set of area demands (i.e. area 1 demand, area 2 demand, area 3 demand), a joint area dispatchable capacity state is feasible (i.e. no system unserved energy) if and only if this capacity state satisfies the inecpalities <3>, <4>, <5>, and <6>. It is conceptually clear that the expectsd system unserved energy can be evaluated by checkuq the feasiblity of every possible joint area dispatchable capacity states (i.e. enmerating over the entire $(I), sh(2), 3(3) space). This pmcedwe is too cumbersome f m a computational point of view. A much more efficient algorithm can be formulated by observing the following :

o A joint area dispatchable capacity state will result in system unserved energy if and only if it violates at least one of the inequalities <3>, <4>, <5>, and <6>.

o These four s-le inequalities directly define the infeasible region in the three-dimensional area dispatchable capacity space.

&sed upon these observations, an efficient algorithm is developed by directly accumulating the expected system unserved energy frcnn the infeasible region. Ihe system unserved energy is the sum of the follcwmg camponents :

o Expcted unserved energy due to violating a local ineguality -- For example, area 1 will have expeded unserved energy if <3> is violated. This expected unserved energy is :

EUEl = E([L(l)-IM(l)-S(l)] I [L(l)-IM(l)-

S^(l)]>O) * Prl[L(l)-IM(l)-~(l)]>O) <7>

m e local expected unserved energies at area 2 and area 3 can be similarly evaluated.

o Esrpeded unserved energy due to violation of the pol inequality -- Expxted system unserved energy will result if <6> is violated. This expect& unserved energy is :

RTEs = E [ L( 1) +L( 2) +L( 3) -X ( 1) -X (2) -X (3) I

X(l)+X(2)+X(3) < L(l)+L(2)+L(3) ] * Pr[X(l)

+X(2)+X(3) < L(l)+L(2)+L(3) 3 <8>

Where :

x(i) = Max(Z(i); L(i)-IM(i)); i = 1, 2, 3

The expected system unserved energy is the sum of all the components :

E m = m 1 + m 2 + m 3 + EUES <9>

mis camputation procedure does not require linear flow solutions to verify the feasibility of transmission flows. As a matter of fact, the transmission constraints are imbeded in the area capacity models.

m e d Area Unserved hemy

Unlike the energy generation which is transfer scheme Invariant, the expected area unserved energy depends heavily upon the energy tranfer schene employed. As a CO--, two distinct computation approaches are employed in this three-area model:

1) The expected unit energy generation is evaluated on a system-wide basis, and not on a specific energy transfer schm.

2) The expected area unserved e n q has to be evaluated based upon a specific energy transfer scheme which is fair to all the participating areas.

In this model, the energy transfer schm assumed in the expected area unserved energy evaluation can be stated as follows :

o The capacity of each generating unit will be dispatched first to meet the demand of the m e r ( s ) . surplus capacity, if available, will then be transferred to other areas.

o Exported energy is shared by receiving areas according to area derrand ratio if transmi ssion interconnection permits arid area needs prevail.

This scheme can be clarified by a simple example. In this example, it is assured that there is 20 MW surplus capacity available at area 1, and the area 1 export limit permits a 20 MW export. &ea 2 and area 3 are described in Table 2.

Table 2

Import Limit (MW) 10 10

Area Need (MW) 8 20

Based upon the demand ratio, area 2 is entitled to receive 5 MW while area 3 is entitled to receive 15 MW. Ihe to the transrm 'ssion import limit, area 3 can only import 10 MW. Out of the remaining 10 MW, area 2 needs only 8 MW. Therefore, area 1 exports 18 MW: area 2 receives 8 MW: area 3 receives 10 MW.

As pointed out earlier the expeded pol-wide unserved energy results f m violation of inequalites <3>, <4>, <5>, and <6>. The expected unserved energies resulted f m violating <3>, <4>, and <5> (i.e. as shown in equation <7>) can be directly attributed to specific areas, and do not depend upon assumed energy transfer schm. 'Ihe e x p e c t d unserved energy d t e d f m violating <6> (i.e. as shown in equation <8>) needs to be attributed to the participating areas according to the a s d energy transfer scheme. Various eneqy transfer schemes can be reflected by appropriately allocating the expeded unserved energy, a m e d f m violating <6>, among the participating areas.

Joint Unit Ownership

In an interconnected system, large base-load unit(s) are often jointly m e d by several participating utilities in order to minimize the individual capital investment. To appropriately assess the expected area cost benefits accrued from joint dispatch, jointawnership of generating units has to be considered. In a multi-area joint dispatch prcduction simulation, each unit's expected energy generation is invariant to the energy transfer arrarqenent, the expeded energy generation of a jointly m e d unit can thus be computed considering that this unit is solely m e d by the area where it is located. ?his expectd energy generation can be attributed to each owner simply by using awnership percentages. U n l i k e the energy generation, joint mership does complicate the evaluation of the expeded area unserved energies. This added camplaity is a result of the capacity correlation m n g participating areas intrcduced through joint crwnership. This difficulty can be overcome by evaluating the area unserved energy conditional upon jolntly m e d area capacity states. It is important to point out that the area expxt/import limits have to be modified to reflect a specific jointly owned capacity state. This can be illustrated by considering a simple jointly m e d capacity state (ml , m2, m3) (i.e. area 1 cwns m l MW, area 2 owns m2 MW and so on) from a iointlv m e d

unit located at area 1. The area limits conditional upon this state are

Ex(l)l = Ex(1) - (m2 + m3)

IM(1)' = IM(1) + (m2 + m3)

Ex(2)' = M(2) + m2

IM(2)' = IM(2) - m2

M(3) ' = M(3) + m3

IM(3) ' = IM(3) - m3

297

import/export

<lo>

<11>

<12>

<13>

<14>

<15>

Based upon these modified transrm 'ssion limits, the conditional expect& area ullser~ed energy can be evaluated by the same procedure as outlined before. ?he area unserved energy is then the sum of the conditional expected area unserved eneqies weighted by the associated probabilities of jointly m e d capacity states.

Allocation of Cost Savimrs

mere is no universal rule governing cost benefits allocation in a joint dispatch operation. The cost allocation policy used in this p a p is a practicing policy in the U.S. [ U ] . This policy can be stated as follm :

0 Each participating area delivering power and energy to the p m l will be wmpensated for its increased operation costs.

o The total savings accrued from joint dispatch will be computed as the difference between the sum of the prcduction costs incurred to each area in inaependent dispatch and the total system production costs in joint dispatch.

o mese savings will be split equally between the importing area(s) and the exporting area(s) . o m e saving which an exporting area receives is one half of the difference between the average decrenmtal cost of the pol imported energy and the average incrmtal cost of the area expo- energy multiplied by the expect4 area en- expo~t. The saving which an importing area receives is one half of the difference between the average decremental cost of the imported energy and the average incremental cost of the pool exported energy multiplied by the expect4 area energy

III a probabilistic simulation where Landom unit forced outages are considered, an arm is defined as an exporting area if the expeded area energy generation plus the expeded area unserved en- exceeds the area en- demand. An importing area is defined accordingly. In th is three-area model, the following are required at each participating area to allocate the expect& production cost savings :

o The expected energy generation from each unit m e d by the subject area.

o The expected unserved energy at the subject area.

SAElPIE S r n Y

This proposed model is used to simulate a sample three-area system on a typical Summer normal weeMay. This sample system is defined in the Appendix. There are a total of 45 generating units

298

with 44 un i t s being solely owned and 1 unit being jointly med. The installed area capacity and capacity mix are summarized in Table 3.

Table 3 Area capacity

rea capacity ~uclear codl Oil ---- ---___-- ---_--- -I--- ---- ------ 1 3,400 MW 5.9% 73.5% 11.8% 8.8% 2 3,400 MW 26.5% 35.3% 23.5% 14.7% 3 3,100 MW 16.1% 19.4% 58.1% 6.4%

Among the three areas, area 1 has the highest percentage of econdcdl capacity, and area 3 has the lowest percentage of economical capacity. The bi-hourly area loads used in this sample study are given in Table 4.

Table 4 Area Loads

Hour

1 - 2 3 - 4 5 - 6 7 - 8 9 -10 11 -12 13 -14 15 -16 17 -18 19 -20 21 -22 23 -24

Area l(MW) I--------

1,600 1,450 1,400 1,750

2,450 2,550 2,550 2,500 2 , 300 2,250 1,900

2 , 200

Area i(MW) _____----- 1,750 1,600 1,550 1,750 2 , 150 2,600 2 , 700 2,750 2,700 2 , 500 2,450 2,150

Area 3(MW)

1,500 1,350 1,350 1,700 2 , 300 2 , 550 2 , 550 2,500 2 , 500 2,350 2,350 1 , 950

The en- demands of areas 1, 2, 3 are 49,800 MWH, 53,300 and 49,900 MWH respectively.

The expeded en- generations at area 1, area 2, and area 3 are summarized and presented in Table 5, Table 6, and Table 7 respectively.

Table 5 rea 1 Expected @neration

Unit ID Expectd Jh- Generation(MWH)

(Joint Dispatch) (Indep. Dispatch)

1 2 - 3 4

5 - 8 9 -10 11

12 -17 Unserved

3 , 600 23 , 040 8,112 15,303 1,760 4,638 826 <286>

--------- 3 , 600 23 , 040 7,249 11 , 440

904 2 , 077 898 <592>

Table 6 Area 2 Expected Generation

Expected Jheryy Generation(MWH) (Joint Dispatch) (Indep. Dispatch) Unit ID -------- ---____----___- --------_-------

1 5,400 5,400 2 11,520 11,520

3 - 4 23,040 21,555 5 5,461 5,783

6 - 7 3 , 458 4,377

Unsenred <644> <1,439> 8-172 , 628 3,226

Table 7 kea 3 Esrpected Generation

Unit ID

1 2 3 4 5

6 - 9 10 -13

U n s e r v e d

Expected J h q Generation(-) (Joint Dispatch) (Idep. Dispatch) ------r_------- ------------_-_

9,000 9,000 7,870 8 , 160 3 , 624 4 , 320 8,692 10,663 5,591 6,327 7,214 8,908 845 1,094 <442> <1,428>

The generation cost over this 24 hour period is $ 2,928,316. The expeded system saving is $ 280,240 which is 9.57% of the expzted system generation cast. 1 has an expedxd net export of 7,497 MWH while area 2 and area 3 have expected net imports of 1,703 MWH and 7,064 MWH respectively. M s result i s consistent with the fact that area 1 has the highest percentage of txoncnnical capacity and area 3 has the lawest percentage of econanical capacity. 'Ihe average incremental cost for area 1

energy is $ 16.05/mH. The average decremmtal cost for area 2 imported energy is $ 86.7/MWH. The average decremental cost for area 3 imported energy is $ 35.8m. Based on the afore-cited allocation policy, area 1 is entitled to 50% of the expcted system saving while area 2 and area 3 are entitled to 24.1% and 26.9% respectively.

The area loads listed in Table 4 indicate that all the participating areas have coincident peaks. To illustrate the impact of load diversity on the

shifted to earlier hours (e.g. 2,300 MW is shifted from hours 9-10 to hours 7-8 and so on ) to create non-coincident peaks. The impact of this load shifting is presented in Figure 2. It can be noted from Figure 2 that the exycted system cost savings increase as the area load &versity increaseS.

expected system cost savings, area 3 loads are

w $2 9% 1 2 3 4 5 6 7 a

Shift of Area 3 Load in Hour

Figure 2

To illustrate the impact of transrm 'ssion capability on the expe+$i system cost sayings, the import/export lmts at area 1 are varied locally. men thowp v y change in transnu * ssion intenmnnection will usually alter transnu * ssion limits at mare than one areas, the local change at

299

13% w 5 12% ' eL 5 11% m v>

area 1 is assumed because it is simple to illustrate the effect. ?he impad of varying transrm 'ssion import/exprt l i m i t a t area 1 on the expect& system cost savings is presented i n Figure 3.

?he lcrwer limit is chosen to be 200 MW because 200 MW is the minimum transrm 'ssion capability required t o accammodate the jointly awned generating capacity.

L

Area 1 Imnort/Exuort Limit in 100 W4

Figure 3

Cumutation Time

This sample system i s s imulated on a Compaq Deskpm Mkm-ampter using a 50 MW k e m n t in area capacity modeling. 'Ihe oomputation time for the 24 hour simulation is in the neighborhod of 2 minutes.

(?oNcLLTs1oN

A novel -area joint dispatch production simulation methcd is presented in this paper. Based upon t h i s methcd, an ~ h n e n t a l canputer model has been successfully implemented on an INTEL 8086 based ifl ANSI Fortran 77. This model considers transrm ssion import/ e x p r t constraints, random outages of generation units, joint unit awnership, and area cost benefit allocation. Tnis model can aid system planners in evaluating the viabil i ty of joint dispatch from a cost effectiveness pint of view. It can also aid system planners i n assess i~~ the econcsnic value of transmission interconnections. Furthermre, the inpact of energy transfer arrangements upon the expectd energy generation and the e x p e c t d area unserved energy has k e n discussed. Tnis discussion form a valuable basis for evaluating the expectd energy generation and area unserved enerqy in a miLti-area joint dispatch production simulation model.

REFERENCES

[l] H. Baleriaux, H. Jamoulle, F'r. L. de Guertechm , ttSimulation de l'exploitation d'un parc de machines thenniques de production d'electricite couples a des station de pampage81, Revue E, (edition S.R.B.E.), Vol. 5, No. 7, 1967.

[2] R. R. Booth, Vuwer System Simulation Mcdel Based on Probability Analysisvg,IEEE Transactions on PAS, Vol. 91, 1972.

[3] A. M. Adamson, A. L. Desell, J. F. Kenney, and L. L. m e r , ftInclusion of Inter-- Transmi ssion

-

i n production costing s ~ a t i o n l ~ , on PAS, Vol. 97, No. 5, 1978.

IEEE Transactions

[4] S . U. Khan, and S. T. Lee, l%stimtion of power-pooling -fits Fran procfudion Simulationst8, IEEE Transactions on PAS, Vol. 100, No. 4, 1981.

[5] N.S. mu, C. Necsulescu, K. F. Schenk, and R. B. Misra, "A Methcd To M u a t e Econcwic Benefits in Interconneded Systems", IEEE Transactions on PAS, Vol. 102, No. 2, 1983.

[6] L. R. N o y e s , TWo-Area FYoMilist ic Fmxiuction Costing By ?he Methd of Bi-Var ian t Cumulantsfl, Transadions on PAS, Vol. 102, No. 2, 1983.

[7] Q. Ahsan, K.F. Schenk, and R. B. Misra, "Expcted E n r g y proaudion cost of WO Interconnected Systems W i t h Correlated Demands11, IEEE Transactions on PAS, Vol. 102, No. 7, 1983.

[8] Q. Ahsan, and K. F. Schenk, ttTWo A r e a produdion C o s t Evaluation By The Segmentation Methodt1, IEEE PES 85 Win* Meeting Paper NO. 85 WM 009-6.

[9] J. B i c k e l , and K j e l l A. Doksum, Mathemtical Stat is t ics : Basic Ideas and Selected Tmics, page 34, Holden-my, 1977.

[lo] H. T. Spears, Kenneth L. H i c k s , and Stephen T. Y. Lee, lProkability of Loss of Lead For 'Ihree Areas", IEEE Transactions on PAS, Vol. 89, No. 4, 1970.

[ll] F. N. Lee, Wulti-Area Reliability -- A New A p p c a c h ~ ~ , IEEE PES 1986 Summer Meeting Paper, No. 86 SM 352-9.

[12] A. J. W c c d , and B. F. Wollenbeq, pawer Generation opera t ion & Control, John Wiley & Sons, 1984.

APPENDIX

DescriWion of Area 1

U n i t I D Type Size(MW)

1(*) Nuclear 200 2 - 3 coal 600 4 cml 400

5 - 8 coal 200 9 -10 coal 50 11 O i l 400

12 -17 CT 50

--I- -- -~ sm 8.5 10.0 11.0 13.0 17.3 31.8 70.0

F.O.R.

.25

.20

.15

.10

.05

.15

.05

(*) U n i t 1 is a part of a jointly owned 1000 MW nuclear u n i t locatd a t area 3.

The total generating capacity a t area 1 is 3,400 MW. The transrm 'ssion import and export limits are both 700 MW. The cost of unserved energy is assumed t o be $ lOO/MWH.

300

k x r i p t i o n of Area 2

Unit I D Type Size(MW) $p F.O.R. I----- -I--- -_--I__ -_I_ ------

1(*) Nuclear 300 8.5 .25 2 Nuclear 600 7.5 .20

3 - 4 Cm1 600 10.5 .20 5 O i l 400 30.0 .15

6 - 7 O i l 200 35.0 .10 8 -17 CT 50 70.0 .05

(*) Unit 1 i s a part of a jointly awned 1,000 MW nuclear unit locate3 a t area 3.

The to t a l generating capacity a t area 2 is 3,400 MW. The transnu 'ssion import and export l i m i t s are both 700 MW. The cast of unserved enerqy is assumed to be $ lOO/MWH.

Descriwtion of Area 3

Unit I D Type ------- 1(*) Nuclear 2 coal 3 c o d l 4 O i l 5 oil

6 - 9 O i l 10 -13 CF

Size(MW) F.O.R.

500 400 2 00 600 400 200 50

8.5 12.0 14.0 24.3 27.3 33.0 70.0

-25 .15 .10 .20 .15 .10 .05

(*) Unit 1 is a jointly owned 1000 nuclear unit. Area 1, area 2, and area 3 m 200 MW, 300 MW, and 500 MW respectively.

Ihe total generation capacity a t area 3 is 3,100 MW. 'Ihe transrm 'ssion import and export limits a t area 3 are both 650 MW. 'Ihe cost of unserved energy is assumed t o be $ l o o p .