This is the same system as MC4 however the program that created this output report is a program called MC4i.txt which can handle 3 state generators and much larger systems, more than a million MW peak demand and more than 10,000 generators easily. Note that this run is not exactly the same as MC4 because the random number draw sequence had to be made different. This program shows a number of interesting features about the direct solution and Monte Carlo. Single area means the total system made up of a smaller Area 1 and the rest of the system outside Area 1 is called Area 0. TOTAL SYSTEM HOURLY LOADS: (no transmission constraints) (note this is winter peaking) WINTER SUMMER OFF PEAK HR MW LOLP MW LOLP MW LOLP 1 5904. 0.00000000 5344. 0.00000000 2544. 0.00000000 2 6224. 0.00000000 5624. 0.00000000 2624. 0.00000000 3 6544. 0.00000000 5904. 0.00000000 2704. 0.00000000 4 6864. 0.00000000 6184. 0.00000000 2784. 0.00000000 5 7184. 0.00000000 6464. 0.00000000 2864. 0.00000000 6 7504. 0.00000000 6744. 0.00000000 2944. 0.00000000 7 7824. 0.00000000 7024. 0.00000000 3024. 0.00000000 8 8144. 0.00000035 7304. 0.00000000 3104. 0.00000000 9 8464. 0.00000663 7584. 0.00000000 3184. 0.00000000 10 8784. 0.00009990 7864. 0.00000000 3264. 0.00000000 11 9104. 0.00116223 8144. 0.00000035 3344. 0.00000000 12 9424. 0.00998912 8424. 0.00000465 3424. 0.00000000 13 9424. 0.00998912 8424. 0.00000465 3424. 0.00000000 14 9104. 0.00116223 8144. 0.00000035 3344. 0.00000000 15 8784. 0.00009990 7864. 0.00000000 3264. 0.00000000 16 8464. 0.00000663 7584. 0.00000000 3184. 0.00000000 17 8144. 0.00000035 7304. 0.00000000 3104. 0.00000000 18 7824. 0.00000000 7024. 0.00000000 3024. 0.00000000 19 7504. 0.00000000 6744. 0.00000000 2944. 0.00000000 20 7184. 0.00000000 6464. 0.00000000 2864. 0.00000000 21 6864. 0.00000000 6184. 0.00000000 2784. 0.00000000 22 6544. 0.00000000 5904. 0.00000000 2704. 0.00000000 23 6224. 0.00000000 5624. 0.00000000 2624. 0.00000000 24 5904. 0.00000000 5344. 0.00000000 2544. 0.00000000 D1 MIN, D2 WIN, D3 SUM, D4 ADD = 2000 8000 7000 1424 AREA 1 HOURLY LOADS: (LOLPs are without the 300 MW tie lines) (note Area 1 is slightly summer peaking) WINTER SUMMER OFF PEAK HR MW LOLP MW LOLP MW LOLP 1 392. 0.00019059 473. 0.00199813 168. 0.00000281 2 420. 0.00038873 507. 0.00346375 180. 0.00000308 3 448. 0.00097081 541. 0.00476578 192. 0.00000408 4 476. 0.00200443 575. 0.00503447 204. 0.00000687 5 504. 0.00338983 609. 0.00658280 216. 0.00000927 6 532. 0.00470413 642. 0.01003925 228. 0.00001038 7 560. 0.00486112 676. 0.01771949 240. 0.00001831 8 588. 0.00533541 710. 0.05166797 252. 0.00006419 9 616. 0.00682649 744. 0.08406298 264. 0.00006423 10 644. 0.01004867 778. 0.11537263 276. 0.00006449 11 672. 0.01488440 812. 0.11613750 288. 0.00006555 12 700. 0.04923480 846. 0.11979800 300. 0.00006810 13 700. 0.04923480 846. 0.11979800 300. 0.00006810 14 672. 0.01488440 812. 0.11613750 288. 0.00006555 15 644. 0.01004867 778. 0.11537263 276. 0.00006449 16 616. 0.00682649 744. 0.08406298 264. 0.00006423 17 588. 0.00533541 710. 0.05166797 252. 0.00006419 18 560. 0.00486112 676. 0.01771949 240. 0.00001831 19 532. 0.00470413 642. 0.01003925 228. 0.00001038 20 504. 0.00338983 609. 0.00658280 216. 0.00000927 21 476. 0.00200443 575. 0.00503447 204. 0.00000687 22 448. 0.00097081 541. 0.00476578 192. 0.00000408 23 420. 0.00038873 507. 0.00346375 180. 0.00000308 24 392. 0.00019059 473. 0.00199813 168. 0.00000281 D5 MIN, D6 WIN, D7 SUM = 300 700 846 (Its useful to compare the direct solution with Monte Carlo, see ^ pointers.) SINGLE AREA SA DIRECT SOLUTN TIME = 0.01 SEC (see DC.txt for solution method) -------------------------------------------- LOLH LOLE ALLR ~ALOLP 0.225304 0.099956 0.095577 0.026220 ^ ^ MWHEUE MWHTOTAL puEUEppm 33.39405 28573440. 1.16871 <- Australia has a 20 ppm standard ^ RESERVE MARGIN = 13.57 % <- close to ERCOT's desired reserve 2 AREA INTERCONNECTION +MW=IMPORT -MW=EXPORT ATCMW PROBLTY (the 300 MW tie was sized to match the largest generator) 300 0.99000 <- small 846 MW peaking system with 300 MW tie 200 0.01000 <- N-1 outage state has ATC of 200 MW, FOR=1% -300 1.00000 <- export state ATC is not used +0 0.00000 <- we could have a probability of 0 MW tie ATCs (islanding) -0 0.00000 AREA 1 A1 DIRECT SOLUTION TIME = 0.19 SEC -------------------------------------------- LOLH LOLE ALLR ~ALOLP 0.462914 0.120807 0.114066 0.031690 ^ ^ MWHEUE MWHTOTAL puEUEppm 26.02041 2267660. 11.47457 ^ RESERVE MARGIN = 15.01 % <- Area 1 has 973 MW internal generation with 15% reserve AREA 0 A0 DIRECT SOLUTION TIME = 0.22 SEC -------------------------------------------- LOLH LOLE ALLR ~ALOLP 0.255615 0.112015 0.106533 0.029383 MWHEUE MWHTOTAL puEUEppm 37.97683 26305780. 1.44367 RESERVE MARGIN = 11.53 % FD SEQUENTIAL MONTECARLO SOLUTION TRANSMISSION MTTR = 0.333 DAYS GENERATION MTTR = 28.375 DAYS (A WEIGHTED AVERAGE) (the numbers below are sensitive to the starting seed) --------------------------------------------------------- LOLH SD% LOLE SD% ALOLP SD% MWHEUE SD% 0.314000 41 0.133000 41 0.027000 31 49.085 45 SA 0.488000 63 0.124000 57 0.017000 40 29.370 60 A1 12.952 ppm A1 ATCS LOSS OF LOAD TRANSMISSION EVENTS # ATCMW PROB LOLTV SD% CALCPR 1 300. 0.9900 386. 72 0.9898 (this is the N-0 state) 2 200. 0.0100 2. 67 0.0102 (FOR=1% and MTTR=8 hrs) 0.29 min 1000 yrs --------------------------------------------------------- LOLH SD% LOLE SD% ALOLP SD% MWHEUE SD% 0.246400 13 0.109600 12 0.024500 10 35.686 18 SA 0.396200 22 0.093000 20 0.014800 16 22.668 22 A1 9.996 ppm A1 ATCS LOSS OF LOAD TRANSMISSION EVENTS # ATCMW PROB LOLTV SD% CALCPR 1 300. 0.9900 3430. 25 0.9899 2 200. 0.0100 66. 45 0.0101 2.91 min 10000 yrs --------------------------------------------------------- LOLH SD% LOLE SD% ALOLP SD% MWHEUE SD% 0.230460 8 0.104030 6 0.023640 6 33.580 13 SA ^ ^ ^ 0.399900 7 0.096590 6 0.015610 5 22.110 8 A1 <- the low ALOLP is misleading, see my writeup **. ^ ^ 9.750 ppm A1 <- Australia has a 20 ppm upper level design target. ATCS LOSS OF LOAD TRANSMISSION EVENTS ^ # ATCMW PROB LOLTV SD% CALCPR 1 300. 0.9900 34436. 8 0.9899 <- the number of events where even the N-0 ties were fully loaded. 2 200. 0.0100 821. 15 0.0101 <- the high SD on transmission is because trans FOR's are very low 29.49 min 100000 yrs --------------------------------------------------------- ** If generator and transmission mean time to repair MTTR is large, such as 6 to 12 months, then its likely the sequential frequency and duration monte carlo model will run many years with these long outage devices in service and no loss of load will be recored in those years. However, when they do have an extended outage, surely the outage will go through a peak load period causing much distress to the system with possible loss of load on many consecutive days. The ALOLP counts only one event each year there is loss of load that year. It makes no distinction between there being one day loss of load and 100 days loss of load. As such, high impact low probability events are glossed over and if we relied on the ALOLP as a measure by which the system is designed, we could be in for a rude shock when one day one of those large plants (nuclear) or transmission element (auto) is outaged and we have no recourse other than to force a load reduction. We can give weight to the number of days outaged within one of those years by multiplying the number of days times the ALOLP number, which is one. But guess what, that is just the LOLE, which already counts the number of days there is loss of load each year. Therefore I would recommend you design your system using the LOLE as a reference rather than the ALOLP. You might use the puEUEppm with a bench reference like Australia does with a .002% loss of load or 20 ppm is maybe easier to remember. It looks like 10 ppm EUE is going to be pretty close to an LOLE of 0.1 days per year, so 20 ppm is going to be slightly higher than 0.1 d/y, but not all that different since the LOLE varies sharply with small changes in the reserve margin. I will post more on this topic as the two area probabilistic ATC model is more fully developed. Gene Preston, PE, PhD 12/19/2015 updated 02/23/2016