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1724 IEEE Transactions on Power Systems, Vol. 11, No. 4, November 1996 PERATING COST AND COMMITTED GENERATION CAPACITY PLANNING JNahman University of Belgrade Yugoslavia Abstract: A realistic simulation model is presented for the evaluation of generating units variable cost and cost df undelivered energy taking into account existing limitations and uncertainties. A criterion for committed capacity rewrve planning is also suggested aimed at minimizing the total system operating cost. Thc model and the committed capacity reserve planning criterion are applied to the IEEE HTS, for demonstration. I. INTRODUCTION The committed generating capacity reserve adopted aects both the operating cost and the adequacy indices of a power system. For a proper reserve coininitment it is necessary to evaluate the variable generating units costs, depending in a discrete manner on uiiits power output levels, as well as to consider the espected cost due to the load curtailment in possible system deficiency situations However, to evaluate both these costs a very comples analysis of the espected system operation during the planning period has to be performed owing to existing technical constraints and limitations and, particularly, to the stochastic nature of many events and circunistances affecting the system operation The sequential chronological simulation of the system operation treated as a stochastic process is the only approach providing a realistic evaluation of required parameters and costs by taking into account all relevant limitations, uncertainties and procedures 96 WM 179-2 PWRS A paper recommended and approved by the IEEE Power System Engineering Committee of the IEEE Power Engineering Society for presentation at the 1996 IEEEiPES Winter Meeting, January 21- 25, 1996, Baltimore, MD. Manuscript submitted July 31, 1995, made available for printing November 16, 1995 S. Bulatovic Electricity Coordinating Center Yugoslavia A system simulation model has been successfully developed and used for evaluating the effects of spinning reserve margins upon the IEEE RTS adequacy indices 1.2,3. A versatile simulation model has been also applied for the analysis of peaking units impacts on the adequacy indices of IEEE RTS 4 A simulation approach including a very detailed model of hydro-units and associated water resources has been also presented recently tjl. This paper uses a sequential sirnulation power system model for evaluating the operating system cost taking into account its dependence on unit power output levels Limitations regarding minimum acceptable loads for thermo units as well as regarding available water resources for hydro units are incorporated in the model. The model implies the most economical loading of units by simulating the loading of the individual units. A criterion is also proposed for committed capacity reserve planning aimed at minimizing the total generating units variable and undelivered energy cost. 11. POWER SYSTEM MODEL A. Geiierating units The ninning generating units are simulated by two-state models. The simulation software developed allows for arbitrary distributions of units state residence times. Units are committed with respect to their fuel and variable 0 & M cost depending on their outputs, to achieve minimum system variable cost for a given system load. The planned committed generating capacity reserve is distributed among the running units according to the minimum cost criterion. The loading of thermo and nuclear units is kept above the corresponding lowest technically acceptable limits for normal operation (technical minimums) If an output being equal or higher than the technical minimum can not be provided for an unit, this unit is decorrimitted. In the case when the available committed capacity reserve is lower than planned, owing to the load increase or 0885-8950/96/$05.00 0 1996 IEEE Authorized licensed use limited to: NORTH CHINA ELECTRIC POWER UNIVERSITY. Downloaded on October 5, 2009 at 21:02 from IEEE Xplore. Restrictions apply. 1725 which is affected by load rnagnitudes and available capacity of units in operation. Load changes in chronological order. The generating units change their states in consecutive order according to the probability distributions of the corresponding state residence times and current committed capacity reserve amount. The system load is distributed among the generating units by obeying the following criteria listed according to their priority order: (a) units have to be loaded with outputs that are not below their technical minimums to the outages of running units, new units are committed from the variable cost priority list. Start up failures of units are checked by comparing the start up failure probability to the generated random number uniformly distributed within the interval (0,l). The failed unit is immediately scheduled for repair and repaired according to the presumed repair time duration distribution. When repaired, the unit is included in the priority waiting list. If the available committed generation capacity reserve exceeds the planned amount, owing to load decrease, the units with the highest variable cost are decommitted and placed in the priority waiting list. However, if the decommitment of an unit decreases the capacity reserve below the amount planned, this unit is kept running. For the purpose of this paper which is devoted to the analysis of the IEEE RTS, the hydro-units are generally presumed to continuously work with their full available capacity during the corresponding part of the year until the energy available for this part of the year is exhausted. The model developed allows for a more detailed description of the hydro - units. B. Systerri Load The system load is represented by its chronological hourly diagram. The load is changed discretely every hour and considered being constant throughout the hour. The load peak has been treated as a random variable defined by the expression: Lni =Lmo ( 1 + a 6 ) (1) where LmO is the predicted mean value. while a is the maximum expected relative declination from the mean value. Parameter 6 is a normally distributed random variable with zero mean and dispersion being equal to 1. The hourly load magnitudes have been taken to be proportional to L, for all Lnl magnitudes. Parameter 6 is generated at the beginning of every hour in course of the simulation flow. C. Sirnulation Flow The calculation is carried out in such a way to realistically simulate the behavior of the system during a year when operating with a specified committed generation capacity reserve which is distributed among the generating units by obeying relevant economical and technical criteria and limitations. Events changing system state are load changes which occur every hour, generating units outages and generating units commitments and decommitrnents undertaken to maintain the prescribed cominitted capacity reserve amount (b) planned generation capacity reserve has to be committed (c) minimum total system variable cost (hiel and variable O&M cost) is to be achieved. The year under consideration is consecutively simulated many times in order to achieve satisfactorlily exact results for system adequacy indices and operating cost. The grade of convergence of the results to exact values can be assessed by analyzing the change in mean of relevant indices and parameters during several consecutive yeairs 4. If this change in mean does not exceed the acceptable limits, the calculation flow is terminated. D. System aclequacuv inc1ice:i. and total operating cost The following major adequacy indices are determined by simulation: LOEE - loss of energy expectation during a year of system operation in MWlUyr LOLE - loss of load espectaltion in h/yr F - number of load interruptions per year in int/yr E - average loss of energy per interruption in MWh/yr ELL - expected loss of load per interruption in MW/int ELL - expected loss of load per year in MW/yr D - average interruption duration in Mint System variable cost per year is CFOM = 4 Z; Wv cv (2) Indcs I applies to all system generating units while index specifies unit output levels. Wv is the energy produced by Authorized licensed use limited to: NORTH CHINA ELECTRIC POWER UNIVERSITY. Downloaded on October 5, 2009 at 21:02 from IEEE Xplore. Restrictions apply. 1726 unit 1 with output levelj during a year. Paraineter c, denotes the variable cost of unit i per uiiit of produced energy when operating with power output level j . Total system operating cost per year can be approxi- mately determined as: V = CFOM + c LOEE (3 1 with c denoting the estimated cost per undelivered unit of energy. increase for higher commited capacity resereve while associated undelivered energy cost decrease. The optimal amount of the commited capacity reserve is that providing minimum V. This optimal solution can be determinated by screening various options. Costs CFoM 111. APPLICATION EXAMPLE The simulation model developed has been applied to the IEEE RTS to analyze the effects of committed generation capacity reserve upon the total system operating cost for various costs per unit of undclivered energy. TABLE I GENERATING UNIT VARIABLE COST DATA AND COhlhfITMENT PRIORITY LIST Size Number Output Variable Prioi ity MW ofunits Y O $lM Wh raiik 50 6 1 400 2 25 783 50 6 79 I 80 6 40 100 6.30 350 1 40 12 94 65 12.22 2 80 12 10 100 12 10 155 4 35 14 24 60 12 92 2 80 12 56 100 12 44 76 4 20 19 62 50 16 38 2 80 15 18 100 15.30 197 3 35 25 42 60 23 35 3 80 23 33 100 22 78 100 3 25 30 70 55 25 18 4 80 24 03 100 23.80 12 5 20 36 78 50 30 57 5 80 28 27 100 28 50 100 48.50 20 4 80 50.00 6 Table I quotes the variable cost of system generating units for various output levels. Technical minimums of units have been taken to be equal to the corresponding lowest output power levels quoted in Table I. The priority rank list has classified the generating units into 6 classes regarding average cost. This list serves as a basis for unit coiiimitinent. When committed, units are loaded to achieve minimum system variable cost. The generation capacity of the IEEE RTS is 3405 MW and its peak load is assumed to be 2850 MW. Start up fail- ure probability is taken to be 0.01. Other relevant parameters are adopted from 1,2. Several cases of system operation and structure have been examined: Case 1. is the base case in which all units are planned to be continuously in operation. No available load and energy liinitations are assumed for hydro units. Case 2. This is the same as Case 1. except that available load and energy resources limitations for hydro units are taken into account. Case 3. Coiiiiiiitted capacity reserve is 20% of the system load The 20 MW combustion oil turbine units are not committed in any situation Case 4 This the same as Case 3 except that 20 MW units are committed when needed Case 5 This is the same as Case 4 but with the commit- ted capacity reserve being 30% of the system load. Case 6. This is the same as Case 4 but with the com- mitted capacity reserve being 10% of the system load. Case 7 This is the same as Case 4 but with the com- mitted capacity reserve being 5% of the system load. Case 8 This is the same as Case 1 except that a load prediction uncertainity with a = 0 05 is assumed A comparison of the results obtained for the adequacy indices for Case 1 by applying various models are pre- scnted tn Table I1 ME is the simulation model described 111 this paper assuming the esponential distribution of generating units state residence times. MF is the same model but with state residence times taken to be deterministic and equal to the espected means of residence times. The chronological diagram of state transitions of a generating unit in the MF model is presented in Fig.1. The Authorized licensed use limited to: NORTH CHINA ELECTRIC POWER UNIVERSITY. Downloaded on October 5, 2009 at 21:02 from IEEE Xplore. Restrictions apply. 1727 TABLE I1 BASE CASE ADEQUACY INDICES CALCULATED BY VARIOUS MODELS Indices 121 131 5 MF ME LOEE,MWh/yr 1176 1122.05 1182 1174.29 1161.16 LOLE,Wyr- 9.39418 9.3413 9.212 9.4436 8.660 F, inVy 1.9249 1.83 1.887 1.771 E, MWWint 582.911 646.4 622.235 655.553 z D, Mint 4.85284 5.03 5.004 4.89 ELL, MWht 80.5525 82.66 80.687 74.326 ELL, MWlyr 155.057 151.3 152 256 160.517 cyclic flow of state transitions is randomly initialized at the beginning of the first year of simulation process. The state transition flow leads for a time interval z the time instant t = 0 (Fig.1) t = R T (4) where T is the cycle duration and R is a random number uniformly distributed within interval (0,i). Generating unit state I t=O t Fig.1 Generating units stiite transitions flow in the MF sinirilation niodel For MF and ME models the stopping rule criterion has been used as in 4 with 0.3 % acceptable change in mean for 3 2o 1 - 1 5 4 consecutive years. The MF model has converged after 133 years. For the ME model. the stopping rules have been fulfilled after 188 years. Fig.2 displays ithe convergence process for LOLE indes, for base case, as realized by the MF model. A reasonably good agreement of the results calculated by h4F and ME simulation models with the results obtained by other models is observable. The resulls from 2 are calculated by applying the analytical sl.ate enumeration approach that yields, for the case under consideration, practically exact results. Results obatined by simulation depend on the number of years of simulation and on the convergence criterion applied. Table 111 presents the: expected energy production of generating units and associated variable cost for all system operation cases under consideration. It is noteworthily to remark that in Case 1 (Case 8) a water spillage equivalent to an energy production of 63.527 GWh (72.776 GWh) occurs, which clearly indicates that such a system operation is far from an economical one. The water spillage makes it possible to load all thernio and nuclear units above their technical minimums. Water spillage equivalent to an energy production of 6.568 GWhl and 0.556 MWh occurs in Case 2 and Case 5 also, for the same reason. In remaining cases the water spillage was riot found to be necessary due to the reduced number of units being committed. Table IV quotes the adequacy indices calculated by simulation for all cases under examination. As observable from Table 111, the liowest system variable cost is associated with system operation Case 7. However, due to a relatively low committed capacity reserve, the system adequacy in Case 7 is considerably worse than in the remaining cases. It is interesting to note that Case 3 has lower system variable cost than Case 4 but worse adequacy performances. Table V quotes total system operation c:ost in operation cases being studied including both the system variable cost and the cost associated with undelivered energy, for various cost per undelivered kWh. As observable from Table V. Case 7 is the most favorable option for c = 0.5 $/kWh, Case 3 Tor c = 1, 2 and 3 $/kWh, Case 5 for c = 4 and 5 $/kWh and Case 2 for c = 6 $/kWh. For relatively high c values system adequacy performances considerably affect the total operating cost and require a higher percentage of committed capacity reserve. Fig.2 LOLE values in ternis of siinulation years obtained using the MF model Authorized licensed use limited to: NORTH CHINA ELECTRIC POWER UNIVERSITY. Downloaded on October 5, 2009 at 21:02 from IEEE Xplore. Restrictions apply. 1728 Size Total av capacity MW MW Thenno 400 800 350 350 155 620 76 304 197 591 100 300 12 60 TABLE I11 EXPECTED ENERGY OUTPUT OF GENERATING UNlTS AND VARIABLE COST Case 1 Energy Costs Seivice output duration GWh 1000$ Idyr 4710 30441 5888 1809 14911 5167 2584 34816 4168 676 3171 2223 1759 45061 2977 636 19476 2121 86 35 1437 Case 2 20 801 503 14812 6293 Subtokil 3105 Case 3 output duration GWh 1000$ Wyr output duration GWh 1000$ hiyr 50 3001 1199 0 3997 Total 34051 15286 163849 1192 0 3975 15292 167590 TABLE IV 1199 0 3997 15244 155696 Hydro 50 300 rota1 3405 2531 0 8437 15295 162724 5262 2026 2933 804 1835 648 87 504 1199 0 3997 1199 0 3997 15186 158780 I 15244 145424 33755 19297 38841 5665 46687 19734 3505 106 2531 0 8437 I 15306 163124 6577 5790 473 1 2645 3104 2161 1457 6296 Case 6 Energy Costs Setvice output duration GWh 1000 $ Idyr 5904 37599 7380 2337 25536 6677 3566 46139 5752 1077 10960 3554 982 35569 1661 19 536 62 0 00 101 2440 1266 5775 36829 7219 2249 23822 6426 3402 44247 5487 992 9295 3263 1483 37236 2509 140 4140 468 3 128 56 0 00 Case 7 Energy Costs Service output duration GWh 1000 $ ldvr 5936 37786 7420 2361 25998 6745 3608 46616 5819 1124 11852 3699 830 20526 1405 4 116 14 0 00 88 2529 1102 Size Total av. capacity MW MW Thenno 400 800 350 350 155 620 76 304 197 591 100 300 12 60 20 80 3105 7 Case 5 Energy Costs Service output duration GWh 1000$ ldyr 5642 36032 7052 2179 22394 6227 3250 42492 5242 886 7271 2913 1685 42760 2851 322 9739 1074 18 77 294 105 3084 1313 I cases LOEE LOLE F E D ELL MWldyr h/yr idyr MWlditit Idint MWht Case 1 1174.29 9.4436 1.8872 622.235 5.0040 80.687 Case 2 4094.98 28.6466 5.4286 754.338 5.2770 72.126 Case 3 52562.49 311.4662 56.2481 934.475 5.5374 100.455 Case 4 33163.80 207.1955 36.9023 898.693 5.6147 91.565 Case 5 10740.29 76.9323 15.3534 699.539 5.0108 72.363 Case6 110707.70 611.3008 98.8271 1120.216 6.1856 116.315 Case 7 146435.40 722.7895 113.7068 1287.834 6.7963 123.513 Case 8 1920.86 13.9173 6.9323 277.0879 2.0076 87.661 I Energy Costs Service Olitpllt duration 5779 2251 3404 967 1428 135 3 97 36851 7223 23847 6430 44266 5490 8846 3182 36022 2417 4034 451 27 54 2826 1208 1199 0 3997 15263 156720 Case 8 Energy Costs Service output duration GWh lb00$ Wyr 4697 30362 5871 1811 14922 4263 2587 34853 4172 686 3365 2566 1767 45236 2990 638 19521 2127 86 51 1433 503 14814 6287 SYSTEM ADEQUACY INDICES TOTAL SYSTEM OPERATION COST FOR VARIOUS COMMITTED Cases Case 3 case 4 Case 5 Case 7 CAPACITY RESERVE Total svstetii opetation cost, 1000 $ Cost per uiidelivered kWh, $kWh 0.5 1 2 3 4 5 6 167790 168000 168405 168818 169228 169637 I170047 157354 1159012 1162328 11656441168960 172276 175592 158378 160360 163352 166668 168984 173300 176616 164386 164923 166000 167071 1168145 1169219 1170293 164315 169851 180922 191993 203064 214135 225206 132745 I160067 174710 189353 203996 218639 233285 Authorized licensed use limited to: NORTH CHINA ELECTRIC POWER UNIVERSITY. Downloaded on October 5, 2009 at 21:02 from IEEE Xplore. Restrictions apply. 1729 5 Allan, R.N., and Romian, J., Reliabilily assessment of generation systems containing multiple hydro plant using simulation techniques. IEEE Trans. PWRS-4, No.3,1989, pp. 1074-1080. IV. CONCLUSIONS A simulation model is presented for modeling the operation of mixed hydro - thermo generating systems and variable cost evaluation
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