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which is affected by load rnagnitudes and available capacityof units in operation.

Load changes in chronological order. The generatingunits change their states in consecutive order according tothe probability distributions of the corresponding stateresidence times a nd c urrent comm itted capacity reserveamount.

The system loadis distributed amon g the generating unitsby obeying the following criteria listed according to theirpriority order:

(a) units have to be loaded with outputs that are not belowtheir technical minimums

to the outages of running units, new units are committedfrom the variable cost priority list. Start up failuresof unitsare checked by co mparing the start up failure probabilityto the generated random number uniformly distributedwithin the interval (0,l). The failed unit is immediatelyscheduled for repair and repaired according to the presumedrepair time duration distribution. When repaired, the unitisincluded in the priority waiting list.

If the available committed generation capacity reserveexceeds the planned amount, owing to load decrease, theunits with the highest variable cost are decommitted andplaced in the priority waiting list. However, if thedecomm itment of an unit decreases the capacity reservebelow the amount planned, this unit is kept running.

For the purpose of this paper which is devoted to theanalysis of the IEEE RTS, the hydro-units are generallypresumed to continuously work with their full availablecapacity dur ing the corresponding part of the year until theenergy available for this part of the yearis exhausted. Themodel developed allows for a more detailed description of

the hydro - units.B. Systerri Load

The system load is represented by its chronologicalhourly diagram. Th e load is changed discretely every hourand considered b eing constant throughout the hour.

The load peak has been treated as a random variabledefined by the expression:

Lni =Lmo( 1 + a 6 ) (1)

where LmO is the predicted mean value. whilea is themaximum expected relative declination from the meanvalue. Parameter6 is a normally distributed random variablewith zero mean and dispersion being equal to1.

The hourly load magnitudes have been taken to beproportional to L, for allLnl magnitudes. Parameter6 isgenerated at the beginning of every hour in courseof thesimulation flow.

C. Sirnulation Flow

The calculation is carried out in such a way torealistically simulate the behavior of the system during ayear when operating witha specified committed generationcapacity reserve whichis distributed among the generatingunits by obeying relevant economical and technical criteriaand limitations.

Events changing system state are load changes whichoccur every hour, generating units outages and generatingunits commitments and decommitrnents undertaken tomaintain the prescribed cominittedcapacity reserve amount

(b) planned generation capacity reserve h as to be committed

(c) minimum total system variable cost(hiel and variableO&M cost) is to be achieved.

The year under considerationis consecutively simulated

many times in order to achieve satisfactorlily exact resultsfor system adequacy indices and operating cost. The gradeof convergenceof the results to exact values can be assessedby analyzing the change in meanof relevant indices andparameters during several consecutive yeairs[4]. If thischange in mean does not exceed the acceptable limits, thecalculationflow is terminated.

D. ystem aclequacuv inc1ice:i. and total operating cost

The following major adequacy indices are determined bysimulation:

LOEE - loss of energy expectation dur ing a year of systemoperation in MWlUyr

LOLE - loss of load espectaltion in h/yr

F - number of load interruptions per year i n int/yr

E - average loss of energy per interruption in MWh/yr

ELL - expected lossof load per interruption in MW /int

ELL - expected loss of load per year in MW/yr

D - average interruption duration in MintSystem variable cost per year is

CFOM = 4 Z;W v v (2)

Indcs I applies to all system generating units while index]specifies unit output levels. W v s the energy producedby

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unit 1 with output levelj duringa year. Paraineterc,, denotesthe variable cost of uniti per uiiit of produced energy whenoperating with power ou tput levelj .

Total system operating cost per year can be approxi-mately determined as:

V = CFOM+c

LOEE (31with c denoting the estimated cost per undelivered unit ofenergy.

increase for higher commited capacityresereve while associated undelivered energy cost decrease.The optimal amount of the commited capacity reserve is thatproviding minimum V. This optimal solution can bedeterminated by screening various options.

Costs CFoM

111. APPLICATIONXAMPLE

Th e simulation model developed has been applied to theIEE E RTS to analyze the effectsof committed generation

capacity reserve upon the total system operating cost forvarious costs per unitof undclivered energy.

TABLE IGENERATINGUNIT VARIABLECOST DATA AND COhlhfITMENT

PRIORITY LIST

Size Number Output Variable PrioiityMW ofunits YO $lM Wh raiik

50 6 1400 2 25 7 8 3

50 6 79 I80 6 40

100 6.30350 1 40 12 94

65 12.22 280 12 10

100 12 1015 5 4 35 14 24

60 12 92 280 12 56

100 124476 4 20 19 62

50 16 3 8 280 15 18

100 15.30197 3 35 25 42

60 23 '3 5 380 23 33

100 22 7810 0 3 25 30 70

55 25 18 480 24 03

100 2 3 . 8 0

12 5 20 36 7850 30 57 580 28 27

100 28 50

100 48.5020 4 80 50.00 6

Table I quotes the variable cost of system generatingunits for various output levels. Technical minimum s ounits have been taken to be equal to the correspondinglowest output power levels quoted in TableI. The priorityrank list has classified the gene ratin g unit s into6 classesregarding average cost. Thislist serves as a basis for unit

coiiimitinent. When committed, units are loaded to achievminimum system variable cost.The generation capacity of the IEEE RTS is3405 MW

and its peak loadis assumed tobe 2850 MW . Start up fail-ure probability i s takento be 0.01. Other relevant parametersare adopted from[1,2].

Several casesof system operation an d structure have beenexamined:

Case 1. is the base case in which all units areplanned tobe continuously in operation.No available loadand energy liinitations are assumed for hydro units.

Case 2. This is the sameas Case 1. except that availableload and energy resources limitations for hydro units artaken into account.

Case 3. Coiiiiiiitted capacity reserve is20% of the systemload The 20 MW combustion oil turbine units are notcommitted in any situation

Case 4 This the same as Case3 except that20 MW unitsare committed when needed

Case 5 This is the same as Case4 but with th e commit-ted capacity reserve being30% of the system load.

Case 6. This is the samea s Case 4 but with the com-mitted capacity reserve being 10 % of the system load.

Case 7 This is the sameas Case 4 but with the com-mitted capacity reserve being5% of the system load.

Case 8 This is the same as Case 1 except thata loadprediction uncertainity w itha = 0 05 is assumed

A comparison of the results obtained for the adequacyindices for Case1 by applying various models are pre-scnted tn Table I1 ME is the simulation model described111 this paper assuming the esponential distributionofgenerating units state residence times.MF is the samemodel but with state residence times taken to bdeterministic and equal to the espected meansof residencetimes. The chronological diagramof state transitionsof agenerating unit in theMF model is presented in Fig.1. The

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TABLE I1BASE CASE ADEQUACY INDICES CALCULATED BYVARIOUS

MODELS

Indices 121 131 [ 5 ] MF MELOEE,MWh/yr 1176 1122.05 1182 1174.29 1161.16

LOLE,Wyr- 9.39418 9.3413 9.212 9.4436 8.660F, i nVy 1.9249 1.83 1.887 1.771

E, MWWint 582.911 646.4 622.235 655.553z D, Mint 4.85284 5.03 5.004 4.89

ELL, M W h t 80.5525 82.66 80.687 74.326ELL, MWlyr 155.057 151.3 152 256 160.517

cyclic flow of state transitions is randomly initialized at thebeginning of the first year of simulation process. The statetransition flow leads for a time intervalz the time instantt = 0 (Fig.1)

t = R T (4)

where T is the cycle duration and R is a randomnumber uniformly distributed within interval(0,i).

Generating

unit state I

t=O t

Fig.1 Generating units stiitetransitions flow in the MFsinirilation niodel

For MF an d ME models the stopping rule criterion has beenused as in [4] with0. 3 % acceptable change in mean for3

2 o 1\-1 5 4 \

consecutive years. TheM F model has converged after133years. For theME model. the stopping rules have beenfulfilled after 188 years. Fig.2 displays ithe convergenceprocess forLOLE indes, for base case, as realized by theMF model.

A reasonably good agreement of the results calculatedby h4F an d ME simulation models with the results obtainedby other modelsis observable. Th e resulls from [2] arecalculated by ap plyi ng the analy tical sl.ate enum eratio napproach that yields, for the case under consideration,practically exact results. Results obatined by simulationdepend on the number of years of simulation and on theconvergence criterion applied.

Table 111 presents the: expected energy production ofgenerating units and associated variable cost for all systemoperation cases under consideration. It is noteworthily toremark that in Case 1 (Case8) a water sp illage equivalent toan energy production of63 .527 GW h (72.7'76 GWh) occurs,

which clearly indicates that sucha system operation is farfrom an economical one. The water spillage makes itpossible to load all thernio and nuclear units above theirtechnical minimums. Water spillage equivalentto an energyproduction of 6 . 5 6 8 GWhl and0 . 5 5 6 MW h occurs in Case 2and Case5 also, for th e same reason. In remaining casesthe water spillage was riot found to be necessary due to thereduced numberof units bein g committed.

Table IV quotes the adequacy indices calculated bysimulation for all cases under examination.As observablefrom Table 111, the liowest system variable cost isassociated with system operation Case7. However, due to arelatively low committed capacity reserve, the systemadequacy in Case 7 is considerably worse than in theremaining cases. It is interesting to note that Case3 haslower system variable cost than Case4 but worse adequacyperformances.

Table V quotes total system operation c:ost in operationcases being studied including both the system variable costand the cost associated with undelivered energy, forvarious cost per undelivered kWh.As observable fromTable V. Case 7 is the most favorable option for c= 0 .5$/kWh, Case3 Tor c = 1, 2 an d 3 $/kWh, Case5 for c = 4and 5 $/kWh and Case2 for c = 6 $/kWh. For relativelyhigh c values system adequacy performances considerably

affect the total operating cost and require a higherpercentageof comm itted capacity reserve.

Fig.2 LOLEvalues in ternis of siinulation years obtainedusing the MF model

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Size Total avcapacity

MW MWThenno

400 800350 350155 62076 304

197 591100 300

12 60

TA BL E I11EXPECTED ENERGY OUTPUT OF GENERATING UNlTS AND VARIABLE COST

Case 1Energy Costs Seiviceoutput durationGWh 1000 $ Idyr

4710 30441 58881809 14911 51672584 34816 4168

676 3171 22231759 45061 2977636 19476 2121

86 35 1437

Case 2

20 801 503 14812 6293Subtokil 3105

Case 3

output durationGW h 1000$ Wyr

output durationGWh 1000$ h iy r

50 3001 1199 0 3997Total 34051 15286 1638 49

1192 0 397515292 167590

TABLE IV

1199 0 399715244 155696

Hydro50 300

rota1 34052531 0 8437

15295 162724

526220262933

80 41835648

8 750 4

1199 0 3997 1199 0 399715186 158780 I 15244 145424

337551929738841

566546687197343505

10 6

2531 0 8437I 15306 163124

65775790473 126453104216114576296

Case 6Energy Costs Setviceoutput durationGWh 1000$ Idyr

5904 37599 73802337 25536 66773566 46139 57521077 10960 3554982 35569 1661

19 536 620 0 0

101 2440 1266

5775 36829 72192249 23822 64263402 44247 5487

992 9295 32631483 37236 2509

140 4140 4683 128 560 0 0

Case 7Energy Costs Serviceoutput durationGW h 1000 $ ldvr

5936 37786 74202361 25998 67453608 46616 58191124 11852 3699830 20526 1405

4 116 140 0 0

88 2529 1102

Size Total av.capacity

MW MWThenno

400 800350 350155 62076 304

197 591100 300

12 6020 80

3105

7

Case 5Energy Costs Serviceoutput durationGWh 1000 $ ldyr

5642 36032 70522179 22394 62273250 42492 5242

886 7271 29131685 42760 2851322 9739 1074

18 77 294105 3084 1313

I

cases LOEE LOLE F E D EL LMWldyr h/yr idyr MWldi t i t Idint M W h t

Case 1 1174.29 9.4436 1.8872 622.235 5.0040 80.687Case 2 4094.98 28.6466 5.4286 754.338 5.2770 72.126Case 3 52562.49 311.4662 56.2481 934.475 5 .5374100.455Case 4 33163.80 207.1955 36.9023 898.693 5.6147 91.565Case 5 10740.29 76.9323 15.3534 699.539 5.0108 72.363Case6 110707.70 611.3008 98.82711120.216 6.1856 116.315Case 7 146435.40 722.7895 113.7068 1287.834 6.7963 123.513Case 8 1920.86 13.9173 6.9323 277.0879 2.0076 87.661

I

Energy Costs ServiceOlitpllt duration

577922513404

9671428

1353

9 7

36851 722323847 643044266 5490

8846 318236022 2417

4034 45127 54

2826 1208

1199 0 399715263 156720

Case 8Energy Costs Serviceoutput durationG W h l b 0 0 $ Wyr

4697 30362 58711811 14922 42632587 34853 4172

686 3365 25661767 45236 2990638 19521 2127

86 51 1433503 14814 6287

SYSTEM ADEQUACY INDICES TOTA L SYSTEM OPERATION COST FOR VARIOUS COMM ITTED

Cases

Case 3c a s e 4Case 5

Case 7

CAPACITY RESERVE

Total svstetii opetation cost, 1000$Cost pe r uiidelivered kWh, $ kW h

0.5 1 2 3 4 5 6167790 168000 168405 168818 16922 8 169637 I170047157354 1159012 1162328 1165 6441 1689 60 172276 175592158378 160360 163352 166668 168984 173300 176616164386 164923 166000 167071 1168145 1169219 1170293164315 169851 180922 191993 203064 214135 225206132745 I160067 174710 189353 203996 218639 233285

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[5] Allan, R.N., and Romian,J., "Reliabilily assessment ofgeneration systems containing multiple hydro plant usingsimulation techniques".IEEE Trans. PWRS-4, No.3,1989,pp. 1074-1080.

IV. CONCLUSIONS

A simulation model is presented for modeling theoperation of mixed hydro- thermo generating systems andvariable cost evaluation. A criterion aimed at minimizingthe system total operating cost including both the generatingunits variable cost and the undelivered energy costissuggested for a rational committed capacity reserveplanning. The approach outlined has been appliedlo theIEEE RTS, for illustration.

V. REFERENCES

[11 IEEE Committee Report, "IEEE Reliability TestSystem", IEEE Trans. PAS-98, 1979, pp. 2047-2054

[2] Allan, R.N., Billinton,R. and Abdel-Gawad, N.M.K.."The IEEE Reliability Test System- Extensions to andEvaluation of the Generating System",IEEE Trans..PWRS-1, N0.4, 1986, pp. 1-7

[3 ] Billinton, R. a nd A llan R.N..Relinbili?v A.s.ses.srirent ofLarge Electric Power Svsteins, Kluwer Academic Pu blishers,Boston 1988.

[4] Ghajar, R. and Billinton, R.," A Monte C arlo simulationmodel for the adequacy evaluation of generating systems",Reliability Engineering arid Systeiii Safe@. Vol 20, 1988.pp.173-186

Jovan M. Nahman was born in Belgrade, Yugoslavia. Hereceived his Dip1 Eng . grade in Electric Power Engineeringfrom the Faculty of Elcctrical Engineering. University ofBelgrade, in 1960. and T echD from the sam e Universityin 1969. In 1960 he joined the Facultyof ElectricalEngineering. Belgrade. where he is employed as a Professorat the Power Systcm Departmen t. During the past severalyears Dr Nahman was activeas a consultant to the industrywhere he led some research in grounding systems andneutral grounding and power system planning andreliability.

Svctislav B, Bdiltoj4c was born in Skopje, Yugoslavia.He received his DiplXng. grade in Electric Power

Engineering from the Facultyof Electrical Engineering,University of Belgrade. in 1981, and M.Sc. from the sameUniversity in 1988. In1981 he joined the Yugo slav ElectricPower Industry, where he is employed in DispatchingService. Since 1993 he is with Electricity CoordinatingCenter in Belgrade. His main interest is in the fieldofcontrol and planning of power systems.