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Generation Adequacy Planning LOLE/LOLP Study Seminar by Gene Preston December 6, 2002.

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Presentation on theme: "Generation Adequacy Planning LOLE/LOLP Study Seminar by Gene Preston December 6, 2002."— Presentation transcript:

1 Generation Adequacy Planning LOLE/LOLP Study Seminar by Gene Preston g.preston@ieee.org December 6, 2002

2 Seminar Purpose Show the methodology for calculating the reliability indices using graphics and examples Define terms used in reliability studies such as LOLE, LOLP, EUE, FOR, PFOR, pdf, etc. Provide information to stakeholders concerning input data and interpretation of study results for single area and multi-area studies

3 Generation Adequacy Study Objectives Ensure installed generation reserve is sufficient Test the sensitivity of study parameters

4 pdf = probabilistic density function of a typical generator forced out of service f(x)f(x) x - megawatts (MW) total area = 1 0Pmax f(x) ~ Pmax time at each MW level See notes for each slide for more information.

5 Cumulative distribution function of the pdf   random variables x 1 f(x)f(x)F(x)F(x) expected value or mean value 1- area = value F(x) = 1 - Pr[generation MW ≤ x] = Pr[generation MW > x].5

6 Combination of two generator pdfs using convolution  

7 Representation of pdfs with discrete states x1x1 gen 1 Prx2x2 gen 2 Pr.125.25.125.1653.375.25.375.2123.625.25.625.2725.875.25.875.3499

8 Take all combinations of Pr’s and MW’s X Pr 0.25 0.0413250 0.50 0.0944000 0.75 0.1625250 1.00 0.2500000 1.25 0.2086750 1.50 0.1556000 1.75 0.0874750

9 Representation of pdfs with discrete states (one generator with states: 0, Derated, Pmax) f(x)f(x) x - MW 0Derated Pmax.8.1 PFOR.1 FOR

10 Generator failure as an exponential function of time probability of failure = 1 t = 0 probability of failure = 1/λ mean time to failure 1 – exp(–λt)

11 Steady state FOR (forced outage rate) derived from λ and µ up down λµ λ = failure rate µ = repair rate Pr[unit is up] = P 1 Pr[unit is down] = P 0 and P 0 + P 1 = 1 µP 0 = λP 1 gives P 0 = λ / (λ + µ) also FOR = P 0 = Pr[ down ] FOR = per unit down time

12 Markov representation of a 3-state generator P max MW 0 MW λ1λ1 µ1µ1 P1P1 P der MW P3P3 P2P2 µ2µ2 µ3µ3 λ2λ2 λ3λ3 λ 1 +λ 2 –µ 2 –µ 1 –λ 2 µ 2 +λ 3 –µ 3 1 1 1 P1P2P3P1P2P3 001001 FOR = per unit down time PFOR = per unit derated time (partial forced outage rate)

13 Use of the Markov process to represent three two-state generators U D 9 1 unit 1 FOR=.1 10 MW U D 4 1 unit 2 FOR=.2 15 MW U D 2.33 1 unit 3 FOR=.3 20 MW

14 Markov representation of three generators P 3 UDU P 2 UUD P 1 UUU P 5 DUU P 6 DUD P 4 UDD P 8 DDD P 7 DDU 2.33 9 9 9 4 4 4 4 1 1 1 1 1 1 1 1 1 9 1 1

15 Markov representation of three generators P1P2P3P4P5P6P7P8P1P2P3P4P5P6P7P8 0000000100000001 3 -2.3 -4 0 -9 0 0 0 -1 4.3 0 -4 0 -9 0 0 -1 0 6 -2.3 0 0 -9 0 0 -1 -1 7.3 0 0 0 -9 -1 0 0 0 11 -2.3 -4 0 0 -1 0 0 -1 12.3 0 -4 0 0 -1 0 -1 0 14 -2.3 1 1 1 1 1 1 1 1

16 Markov representation of three generators P1P2P3P4P5P6P7P8P1P2P3P4P5P6P7P8.504 45 MW.216 25 MW.126 30 MW.054 10 MW.056 35 MW.024 15 MW.014 20 MW.006 0 MW

17 Use of a binary tree for the three generators to perform the convolution process Individual States Cumulative Gen 1 Gen 2 Gen 3 MW Pr MW Pr ΣPr 20.7 -- 45.504 45.504.504 15.8 0.3 -- 25.216 35.056.560 10.9 0.2 20.7 -- 30.126 30.126.686 0.3 -- 10.054 sort 25.216.902 20.7 -- 35.056 20.014.916 0.1 15.8 0.3 -- 15.024 15.024.940 0.2 20.7 -- 20.014 10.054.994 0.3 -- 0.006 0.006 1.000

18 Graph of the 3 generator cumulative distribution for the probability that generation MW is > x) 1.0.9.8.7.6.5.4.3.2.1 0 0 5 10 15 20 25 30 35 40 45 50 x (MW) Pr.994.940.916.902.686.560.504.000 load not served generation

19 Unsuitability of the binary tree and Markov methods for large systems A system with 400 two-state generators has a total of: 400 120 2  10 states (combinations) This is greater than the number of atoms in the universe (~10 80 )!

20 The same cumulative distribution can be created one generator at a time. The function is updated as each generator is added. 1.0.9.8.7.6.5.4.3.2.1 0 0 5 10 15 20 25 30 35 40 45 50 x (MW) Pr.994.940.916.902.686.560.504.000 load not served generation

21 Starting with a blank distribution 1.0.9.8.7.6.5.4.3.2.1 0 0 5 10 15 20 25 30 35 40 45 50 x (MW) Pr load not served

22 Cumulative distribution for generator 1 generator 1 = {10 MW, FOR=.1} Pr 1.0.9.8.7.6.5.4.3.2.1 0 0 5 10 15 20 25 30 35 40 45 50 x (MW).900 load not served.000 ∞

23 Adding generator 2 scales and shifts the initial distribution for Pr=.8 (up) and Pr=.2 (down) generator 2 = {15 MW, FOR=.2} 1.0.9.8.7.6.5.4.3.2.1 0 0 5 10 15 20 25 30 35 40 45 50 x (MW) Pr.900 x.2 =.18.900 x.8 =.72 1.00 x.8 =.80

24 Summing the two curves gives the combined generators 1 and 2 cumulative distribution 1.0.9.8.7.6.5.4.3.2.1 0 0 5 10 15 20 25 30 35 40 45 50 x (MW) Pr load not served.000.72.80+.18=.98.80 generation

25 Adding generator 3 scales and shifts the distribution for Pr=.7 (up) and Pr=.3 (down) generator 3 = {20 MW, FOR=.3} 1.0.9.8.7.6.5.4.3.2.1 0 0 5 10 15 20 25 30 35 40 45 50 x (MW) Pr.98x.3=.294.80x.3=.24.72x.3=.216.98x.7=.686.80x.7=.56.72x.7=.504 1.00x.7=.700

26 Summing the two curves gives the combined generators 1, 2, and 3 cumulative distribution (same curve as the one using a binary tree) 1.0.9.8.7.6.5.4.3.2.1 0 0 5 10 15 20 25 30 35 40 45 50 x (MW) Pr.294+.700=.994.24+.70=.940.216+.7=.916.686.560.504.000 load not served generation.216+.686=.902

27 Binary tree graph of the 3 generator cumulative distribution for the probability that generation is available at x MW 1.0.9.8.7.6.5.4.3.2.1 0 0 5 10 15 20 25 30 35 40 45 50 x (MW) Pr.994.940.916.902.686.560.504.000 load not served generation

28 Cumulative distribution Pr[generation is up] represented in discrete 1 MW steps 1.0.9.8.7.6.5.4.3.2.1 0 0 5 10 15 20 25 30 35 40 45 50 x (MW) Pr load not served generation

29 Flip the function over and backwards and the distribution represents Pr[generation out of svc] This is the COPT or Capacity Outage Probability Table 1.0.9.8.7.6.5.4.3.2.1 0 45 40 35 30 25 20 15 10 5 0 x (MW) Pr load not served.496.440.314.098.084.060.006.000

30 Representation of Pr[gen out of service] as piecewise linear increments 1.0.9.8.7.6.5.4.3.2.1 0 0 5 10 15 20 25 30 35 40 45 50 x (MW) Pr load not served

31 Representation of Pr[gen out of service] as piecewise quadratic increments 1.0.9.8.7.6.5.4.3.2.1 0 0 5 10 15 20 25 30 35 40 45 50 x (MW) Pr load not served for any 3 points, interpolate between the left two points

32 Relative per unit error introduced by numerous interpolations of piecewise linear (PL) and piecewise quadratic (PQ) distributions PL x=30% PQ x=30% PQ x=20%

33 LOLE – loss of load expectation EUE – expected unserved energy 1.0.9.8.7.6.5.4.3.2.1 0 0 5 10 15 20 25 30 35 40 45 50 MW x – MW (daily or hourly) Pr EUE = MWH not served (for each hour in the study) generation LOLE for one day = 1 - Pr[gen up] = Pr[load loss] = 1-.56 =.44 d/y.686.560.504.994.940.916.902

34 LOLP – loss of load probability 1.0.9.8.7.6.5.4.3.2.1 0 0 5 10 15 20 25 30 35 40 45 50 MW x – MW weekly peak demand Pr generation LOLP (for a week) = 1 - Pr[gen up] = Pr[load loss] = 1-.56 =.44.686.560.504.994.940.916.902 annual LOLP = 1-  i (Pr[gen up] i ) for all i weeks

35 Representing load uncertainty (each hour is a Normal distribution of MW values) 1.0.9.8.7.6.5.4.3.2.1 0 0 5 10 15 20 25 30 35 40 45 50 MW x – MW (daily or hourly) Pr generation.686.560.504.994.940.916.902

36 Generation scheduled maintenance 1 xxx 2 xxx 3 4 xxxxx 5 6 xxx 7 8 xxxx 9 xxx 10 xxxx 11 1 5 10 15 20 25 30 35 40 45 50 52 week # during the year generator # summer insufficient reserve?

37 Generation scheduled maintenance reduces available generation – increases LOLE 1 5 10 15 20 25 30 35 40 45 50 52 week # during the year generator installed MW before maintenance MW demand insufficient reserve planning reserve with maint

38 Generation scheduled maintenance to minimize overall LOLE 1 5 10 15 20 25 30 35 40 45 50 52 week # during the year generator installed MW before maintenance MW demand planning reserve with maint

39 Automatic scheduled maintenance methodology to minimize LOLE 1.Sort the MW unit sizes from largest to smallest. 2.Place the largest MW generator in a time slot with the greatest unused reserve margin. 3.Place the next largest generator in a time slot with the greatest unused reserve margin. 4.Repeat step 3 until all units are scheduled.

40 1999 load shape

41

42

43 ERCOT generation (MW) forced out of service and derated 0 2000 4000 6000 8000 10000 12000 ~5000 MW ~9000 MW ~6% ~11% 12.5% actual more generators

44 DC tie considerations probability of a DC tie failure is nearly 0 probability of generation supply being available in the other region is expected to be nearly 1 transmission constraints in the other region may reduce the probability of DC tie capability to less than 1 DC tie capacity can be included or excluded from the LOLP calculations (affects the LOLE) DC tie capacity may or may not be used to serve firm load in ERCOT (affects the reserve)

45 DC tie considerations DC tie with X MW firm generation DC tie with 0 MW firm generation DC tie in LOLP calculations Yes No LOLP:100% DC MW CDR : X MW gen 11% x=0 to 12.5% for x=all firm LOLP: X MW DC CDR : X MW gen 12.5% reserve LOLP:100% DC MW CDR : 0 MW gen 11% reserve LOLP: 0 MW DC CDR : 0 MW gen 12.5% reserve

46 Switchable generation considerations Switchable generation capability must be available to ERCOT when called upon. The same switchable MWs must be used in both the reserve calculation and the LOLP calculation.

47 Self-serve generation considerations Currently, both the self serve generation and self serve load (840 MW in the previous study) are omitted from the CDR and the LOLP calculations. Alternately, the self serve generation and load could be included with the CDR and LOLP calculations with a negligible effect on LOLE. Currently, self serve generation and load are included in the transmission load flow analysis as fixed MW values with 100% availability.

48 Interruptible load considerations The load can be modeled as two components, firm plus interruptible (i.e. two forecasts) The LOLE for serving firm load can be calculated by using only the forecast for firm load in the computer simulation. The LOLE for interruptible load can be calculated by using a forecast of firm load plus interruptible load in the computer simulation and then subtracting the LOLE results obtained for the firm load forecast.

49 Data needed to perform single-area LOLP studies hourly ERCOT loads for the (annual) study period (historical year hourly loads are scaled) the annual peak demand forecast and the percentage of interruptible load percentage of load forecast uncertainty each generator’s seasonal MW (Pmax) capability, fuel type, type of unit, and maintenance periods (by beginning and ending week numbers or by total weeks needed) FOR and DFOR of generator types such as gas, coal, nuclear, hydro, wind, etc. identification of self-serve MW by generator

50 Single Area Output Reports – Input Data SINGLE AREA GENERATOR DATA: SEASONAL CAPACITIES CDR FORCED PARTIAL-OUTAG SCHEDULED UNIT AREA WINT SPNG SUMM FALL CAP OUTAGE RATE DERATNG UNAVAILABLE NAME NAME MW MW MW MW % RATE % % % B1 D1 B2 D2 -------- -------- ---- ---- ---- ---- --- ------ ------ ------ -- -- -- -- STP1 ERCOT 1311 1311 1311 1311 100 6.90 2.30 5.50 5 4 0 0 STP2 ERCOT 1311 1311 1311 1311 100 6.90 2.30 5.50 4 4 0 0 CMPK 1 G ERCOT 1161 1161 1161 1161 100 6.90 2.30 5.50 11 4 0 0 CMPK 2 G ERCOT 1161 1161 1161 1161 100 6.90 2.30 5.50 3 12 0 0 DOW1 ERCOT 986 986 986 986 100 10.00 0.00 0.00 7 4 0 0 DOW2 ERCOT 917 917 917 917 100 10.00 0.00 0.00 3 12 0 0 DEC 1 G ERCOT 818 818 818 818 100 6.70 0.00 0.00 4 12 0 0 THSE 2 G ERCOT 818 818 818 818 100 6.70 0.00 0.00 48 4 0 0 LIM1 ERCOT 744 744 744 744 100 4.22 2.90 19.00 13 4 0 0 LIM2 ERCOT 744 744 744 744 100 4.22 2.90 19.00 3 12 0 0 MTNLK 1G ERCOT 727 727 727 727 100 4.22 2.90 19.00 43 4 0 0 MTNLK 2G ERCOT 727 727 727 727 100 4.22 2.90 19.00 48 4 0 0 MTNLK 3G ERCOT 727 727 727 727 100 4.22 2.90 19.00 49 4 1 8 MOSES3 G ERCOT 726 726 726 726 100 4.22 2.90 19.00 43 4 0 0 CB 3 ERCOT 703 703 703 703 100 6.70 0.00 0.00 13 4 0 0 DC-EAST ERCOT 700 700 700 700 0 0.01 0.00 0.00 3 12 0 0 Weeks 1-9 49-52 Weeks 10-21 Weeks 22-37 Weeks 38-48

51 Single Area Output Reports – Maintenance AUTOMATIC MAINTENANCE OF 12 LONG & 4 SHORT WEEKS SCHEDULED UNAVAILABLE: -WINTER- ---SPRING--- ----SUMMER---- ----FALL--- WIN UNIT AREA JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC NAME NAME week: 1111111111222222222233333333334444444444555 -------- -------- 1234567890123456789012345678901234567890123456789012 PB 5 G ERCOT ooooooo........ ooooo PB 6 G ERCOT........ oooo. MRGN 6 G ERCOT........ oooo. MRGN 2 G ERCOT oo........ oooooooooo MRGN 4 G ERCOT....... oooo.. MRGN 5 G ERCOT........ oooo. MRGN 3 G ERCOT oo........ oooooooooo

52 Single Area Output Reports – CDR WEEK CAPACITY OUT-OF-SVC AVAILABLE PEAK LOAD RESERVE RESERVE WEEK MW MW MW MW MW % BEGINS ---- -------- -------- -------- -------- -------- ------- ------ 16 80223. 0. 80223. 0. 80223. 0.0 APR 18 17 80223. 0. 80223. 35344. 44879. 127.0 APR 25 18 80223. 0. 80223. 49251. 30972. 62.9 MAY 2 19 80223. 0. 80223. 52755. 27468. 52.1 MAY 9 20 80223. 0. 80223. 53323. 26900. 50.4 MAY 16 21 80223. 0. 80223. 54975. 25248. 45.9 MAY 23 22 80223. 0. 80223. 60222. 20001. 33.2 MAY 30 23 80223. 0. 80223. 57907. 22316. 38.5 JUN 6 24 80223. 0. 80223. 55546. 24676. 44.4 JUN 13 25 80223. 0. 80223. 57007. 23216. 40.7 JUN 20 26 80223. 0. 80223. 63446. 16777. 26.4 JUN 27 27 80223. 0. 80223. 62549. 17673. 28.3 JUL 4 28 80223. 0. 80223. 62641. 17582. 28.1 JUL 11 29 80223. 0. 80223. 64447. 15776. 24.5 JUL 18 30 80223. 0. 80223. 67662. 12561. 18.6 JUL 25 31 80223. 0. 80223. 67691. 12532. 18.5 AUG 1 32 80223. 0. 80223. 70378. 9845. 14.0 AUG 8 33 80223. 0. 80223. 69615. 10607. 15.2 AUG 15 34 80223. 0. 80223. 70535. 9688. 13.7 AUG 22 35 80223. 0. 80223. 67195. 13027. 19.4 AUG 29 36 80223. 0. 80223. 63388. 16835. 26.6 SEP 5 37 80223. 0. 80223. 58919. 21303. 36.2 SEP 12 38 80223. 0. 80223. 61987. 18236. 29.4 SEP 19 39 80223. 0. 80223. 59018. 21205. 35.9 SEP 26 40 80223. 0. 80223. 0. 80223. 0.0 OCT 3

53 Single Area Output Reports – LOLE Results WEEK PEAK LOAD RESERVE WEEKLY PROBABILITY HOURLY UNSERVED WEEK MW % LOAD>GENR MWH BEGINS ---- -------- ------- -.--3--6--9-12-15- ----.--3--6--9- ------ 16 0. 0.0 0.0000000000000000 0.0000000000 APR 18 17 35344. 127.0 0.0000000000000000 0.0000000000 APR 25 18 49251. 62.9 0.0000000000000000 0.0000000000 MAY 2 19 52755. 52.1 0.0000000000000000 0.0000000000 MAY 9 20 53323. 50.4 0.0000000000000000 0.0000000000 MAY 16 21 54975. 45.9 0.0000000000000000 0.0000000000 MAY 23 22 60222. 33.2 0.0000000000000692 0.0000000000 MAY 30 23 57907. 38.5 0.0000000000000000 0.0000000000 JUN 6 24 55546. 44.4 0.0000000000000000 0.0000000000 JUN 13 25 57007. 40.7 0.0000000000000000 0.0000000000 JUN 20 26 63446. 26.4 0.0000000013815166 0.0000009830 JUN 27 27 62549. 28.3 0.0000000001051571 0.0000000560 JUL 4 28 62641. 28.1 0.0000000001375059 0.0000000719 JUL 11 29 64447. 24.5 0.0000000208146472 0.0000123400 JUL 18 30 67662. 18.6 0.0000393594360814 0.0782425020 JUL 25 31 67691. 18.5 0.0000418127666276 0.0886081361 AUG 1 32 70378. 14.0 0.0053711529435669 11.2483312958 AUG 8 33 69615. 15.2 0.0015578843676685 2.7090544949 AUG 15 34 70535. 13.7 0.0068264952639734 7.4071353617 AUG 22 35 67195. 19.4 0.0000147424748045 0.0100945754 AUG 29 36 63388. 26.6 0.0000000011738335 0.0000010857 SEP 5 37 58919. 36.2 0.0000000000000008 0.0000000000 SEP 12 38 61987. 29.4 0.0000000000194574 0.0000000072 SEP 19 39 59018. 35.9 0.0000000000000011 0.0000000000 SEP 26 40 0. 0.0 0.0000000000000000 0.0000000000 OCT 3 ANNUAL 70535. 13.7* 0.0137945421779943 21.5414809098 (* INSTALLED) LOSS OF LOAD EXPECTATION = 0.019290 DAYS/YR USING DAILY PEAK LOADS AND NO LOAD UNCERTAINTY LOSS OF LOAD EXPECTATION = 0.001565 DAYS/YR USING HOURLY LOADS AND NO LOAD UNCERTAINTY

54 Transmission model considerations Simplified transmission network (NARP) –requires the development of an equivalent –computationally fast –questionable circuit flow results Full transmission network (PLF) –eliminates the need to develop an equivalent –computationally fast if PDFs are used –results are in agreement with AC load flow

55 Transmission PDFs from AC load flows PDF = power distribution factor =  MW ckt flow /  MW power transfer  difference in two shift factors gen  flow load buses

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57

58 Harmful Generators for Austrop-Sandow Ckts PDFs for ckt: 3429 SANDOW 345 - 7040 AUSTRO34 345 1 221 LOSTPN 2 -0.1734601 load flow bus 7008 222 LOSTPN 3 -0.1734599 load flow bus 7009 220 LOSTPN 1 -0.1734593 load flow bus 7007 257 BEP GT2 -0.1689710 load flow bus 7808 256 BEP GT1 -0.1689707 load flow bus 7807 258 BEP ST1 -0.1689678 load flow bus 7809 223 FPP G1 -0.1501281 load flow bus 7010 224 FPP G2 -0.1501194 load flow bus 7011 225 FPP G3 -0.1498940 load flow bus 7012 229 HAYSN 4 -0.1423499 load flow bus 7017 228 HAYSN 3 -0.1423486 load flow bus 7016 226 HAYSN 1 -0.1423371 load flow bus 7014 227 HAYSN 2 -0.1423371 load flow bus 7015 247 MCQUEE06 -0.1342581 load flow bus 7605 322 SANDH G1 -0.1341542 load flow bus 9016 323 SANDH G2 -0.1341542 load flow bus 9017 325 SANDH G4 -0.1341535 load flow bus 9019 324 SANDH G3 -0.1341533 load flow bus 9018 246 CANYHY06 -0.1338861 load flow bus 7487 313 DECKR G2 -0.1316094 load flow bus 9001 312 DECKR G1 -0.1315037 load flow bus 9000

59 More Generator PDFs for Austrop-Sandow 252 GUALUP 3 -0.1303046 load flow bus 7802 250 GUALUP 1 -0.1303038 load flow bus 7800 251 GUALUP 2 -0.1303038 load flow bus 7801 248 SCHUMA13 -0.1302463 load flow bus 7609 253 GUALUP 4 -0.1302456 load flow bus 7805 254 GUALUP 5 -0.1302456 load flow bus 7805 255 GUALUP 6 -0.1302456 load flow bus 7805 261 RIONO G3 -0.1293995 load flow bus 7812 259 RIONO G1 -0.1293991 load flow bus 7810 260 RIONO G2 -0.1293990 load flow bus 7811 315 DECKR G4 -0.1291926 load flow bus 9003 316 DECKR G5 -0.1291926 load flow bus 9004 317 DECKR G6 -0.1291926 load flow bus 9005 314 DECKR G3 -0.1291925 load flow bus 9002 263 RIONO G5 -0.1291662 load flow bus 7814 262 RIONO G4 -0.1291648 load flow bus 7813 264 RIONO G6 -0.1291633 load flow bus 7815 249 LAKEWD06 -0.1285502 load flow bus 7624 276 LAR #3 -0.1281178 load flow bus 8288 153 SAND 4 G 0.1279722 load flow bus 3432 SOUTH -0.1045032 load flow area 4 NORTH 0.0786292 load flow area 2 WEST 0.0504448 load flow area 1 HOUSTON -0.0243481 load flow area 3

60 Maximum Flows for Austrop-Sandow Ckts MAXIMUM +/- LINE FLOWS FROM SUMS OF INCREMENTAL GENERATOR FLOWS -------FROM------ -------TO-------- RATG BASE +MW -MW %ADJ 3429 SANDOW 345 7040 AUSTRO34 345 716 -356.0 2840.0 -3269.3 -2.2 3429 SANDOW 345 7040 AUSTRO34 345 789 -356.0 2840.0 -3269.3 -2.2 average weighted scale factor = 2.24 % sum of flows from helpers sum of flows from harmers

61 Maximum Flow Sources for Austrop-Sandow MAXIMUM CIRCUIT FLOWS WITH ALL CIRCUITS IN SERVICE -------FROM------ -------TO-------- ID RATG PCT -GENERATION-to-LOAD- DIST 3429 SANDOW 345 7040 AUSTRO34 345 1 716 -446 LOSTPN 2 18->NORTH.252 3429 SANDOW 345 7040 AUSTRO34 345 2 789 -405 LOSTPN 2 18->NORTH.252 3429 SANDOW 345 7040 AUSTRO34 345 1 716 397 SAND 4 G 22->SOUTH.232 3429 SANDOW 345 7040 AUSTRO34 345 2 789 360 SAND 4 G 22->SOUTH.232

62 0 MW Pr [ flow>x ] 0 1 ckt rating static base case flow overload Probabilistic flows on a circuit (in preparation to remove the overloaded portion)

63 Removing a transmission overload ckt overload states p p p Pr Pr[loss of gen>x] Pr[ckt MW>x] p = Pr[of an individual generation state] generation states one circuit’s flows MW shift a binary tree of generation states circuit rating

64 Correlating the removal of a transmission overload with the generation distribution line overload states F(x,y) surface as a set of discrete points 1 0 Pr F(x) generation distribution circuit distribution

65 Load shedding to remove Austrop- Sandow circuit overloads LINE-GENERATOR-AREA LOAD SHEDDING REPORT: BUS# BUS NAME BUS# BUS NAME ID MW MWH GENERATOR > LOAD AREA PDF 3429 SANDOW 345 - 7040 AUSTRO34 345 1 167. 0.114381 LOSTPN 2 NORTH 0.25209 3429 SANDOW 345 - 7040 AUSTRO34 345 1 167. 0.043348 LOSTPN 3 NORTH 0.25209 3429 SANDOW 345 - 7040 AUSTRO34 345 1 167. 0.016571 LOSTPN 1 NORTH 0.25209 3429 SANDOW 345 - 7040 AUSTRO34 345 1 167. 0.006372 BEP GT2 NORTH 0.24760 3429 SANDOW 345 - 7040 AUSTRO34 345 1 167. 0.002422 BEP GT1 NORTH 0.24760 3429 SANDOW 345 - 7040 AUSTRO34 345 1 166. 0.000880 BEP ST1 NORTH 0.24760 3429 SANDOW 345 - 7040 AUSTRO34 345 1 584. 0.000473 FPP G1 NORTH 0.22876 3429 SANDOW 345 - 7040 AUSTRO34 345 1 584. 0.000009 FPP G2 NORTH 0.22875 3429 SANDOW 345 - 7040 AUSTRO34 345 2 167. 0.022171 LOSTPN 2 NORTH 0.25209 3429 SANDOW 345 - 7040 AUSTRO34 345 2 167. 0.010692 LOSTPN 3 NORTH 0.25209 3429 SANDOW 345 - 7040 AUSTRO34 345 2 167. 0.004809 LOSTPN 1 NORTH 0.25209 3429 SANDOW 345 - 7040 AUSTRO34 345 2 167. 0.002008 BEP GT2 NORTH 0.24760 3429 SANDOW 345 - 7040 AUSTRO34 345 2 167. 0.000778 BEP GT1 NORTH 0.24760 3429 SANDOW 345 - 7040 AUSTRO34 345 2 166. 0.000277 BEP ST1 NORTH 0.24760 3429 SANDOW 345 - 7040 AUSTRO34 345 2 584. 0.000138 FPP G1 NORTH 0.22876 3429 SANDOW 345 - 7040 AUSTRO34 345 2 584. 0.000002 FPP G2 NORTH 0.22875 0.225331 MWH for one hour (with all gens at Pmax)

66 Load shedding to remove Austrop-Sandow circuit overloads AREA 2 NORTH AREA 2 TOTAL SYS RESV% LOAD-MW LOLP TLOP EUE-MWh TEUE-MWh TEUE-MWh 26.8 24556.70 0.0000000 0.0000000 0.000000 0.000001 0.000000 25.8 24747.19 0.0000000 0.0000000 0.000000 0.000002 0.000000 24.9 24937.68 0.0000000 0.0000000 0.000001 0.000003 0.000000 23.9 25128.17 0.0000000 0.0000000 0.000005 0.000006 0.000000 23.0 25318.67 0.0000001 0.0000001 0.000017 0.000011 0.000000 22.1 25509.16 0.0000004 0.0000001 0.000060 0.000019 0.000000 21.2 25699.65 0.0000012 0.0000002 0.000200 0.000033 0.000000 20.3 25890.14 0.0000039 0.0000004 0.000642 0.000057 0.000000 19.4 26080.63 0.0000115 0.0000006 0.001982 0.000095 0.000000 18.5 26271.13 0.0000328 0.0000010 0.005868 0.000157 0.000000 17.7 26461.62 0.0000894 0.0000017 0.016656 0.000254 0.000000 16.9 26652.11 0.0002330 0.0000026 0.045318 0.000408 0.000000 16.0 26842.60 0.0005806 0.0000041 0.118123 0.000646 0.000001 15.2 27033.09 0.0013812 0.0000062 0.294801 0.001011 0.000002 14.4 27223.58 0.0031339 0.0000093 0.703970 0.001559 0.000007 13.6 27414.08 0.0067733 0.0000139 1.607262 0.002374 0.000019 12.8 27604.57 0.0139248 0.0000203 3.505661 0.003567 0.000049 12.0 27795.06 0.0271876 0.0000293 7.298278 0.005290 0.000123 11.3 27985.55 0.0503270 0.0000418 14.489008 0.007744 0.000297 10.5 28176.04 0.0881587 0.0000588 27.404648 0.011197 0.000684 9.8 28366.54 0.1458544 0.0000817 49.340149 0.016000 0.001510 9.1 28557.03 0.2274701 0.0001123 84.498868 0.022601 0.003175 8.3 28747.52 0.3338294 0.0001524 137.585140 0.031555 0.006356 7.6 28938.01 0.4604444 0.0002029 212.981405 0.043481 0.012050 6.9 29128.50 0.5966979 0.0002636 313.627661 0.058973 0.021579 6.2 29319.00 0.7275037 0.0003300 439.966399 0.078365 0.036333 5.5 29509.49 0.8376617 0.0003927 589.470300 0.101443 0.057332 4.9 29699.98 0.9172952 0.0004368 757.143111 0.127114 0.084476 4.2 29890.47 0.9653328 0.0004466 936.921174 0.153360 0.116035 3.5 30080.96 0.9886289 0.0004117 1123.342538 0.177556 0.148519 2.9 30271.46 0.9972702 0.0003356 1312.648220 0.197277 0.177645 2.2 30461.95 0.9995617 0.0002363 1502.893099 0.211163 0.199933 1.6 30652.44 0.9999568 0.0001397 1693.351411 0.219370 0.214090 1.0 30842.93 0.9999959 0.0000674 1883.840375 0.223328 0.221365 0.4 31033.42 0.9999987 0.0000254 2074.331880 0.224820 0.224271 note the differences in TEUE area and system load levels --------------- warning - load sheds can appear to occur at different % load levels generation Pr [out of svc] transmission constraints

67 Load shedding to remove Austrop-Sandow circuit overloads RESV% LOAD-MW LOLP TLOP GLOL-D/Y TLOL-D/Y TOTL-D/Y 22.1 66956.00 0.0000004 0.0000001 0.000001 0.000000 0.000001 21.2 67456.00 0.0000012 0.0000001 0.000003 0.000001 0.000004 20.3 67956.00 0.0000039 0.0000002 0.000010 0.000001 0.000011 19.4 68456.00 0.0000115 0.0000004 0.000029 0.000002 0.000031 18.5 68956.00 0.0000328 0.0000006 0.000084 0.000003 0.000086 17.7 69456.00 0.0000894 0.0000010 0.000232 0.000004 0.000236 16.9 69956.00 0.0002330 0.0000015 0.000615 0.000007 0.000622 16.0 70456.00 0.0005806 0.0000024 0.001563 0.000011 0.001574 15.2 70956.00 0.0013812 0.0000036 0.003799 0.000017 0.003816 14.4 71456.00 0.0031339 0.0000055 0.008833 0.000027 0.008860 13.6 71956.00 0.0067733 0.0000082 0.019635 0.000041 0.019676 12.8 72456.00 0.0139248 0.0000120 0.041690 0.000062 0.041752 12.0 72956.00 0.0271876 0.0000173 0.084488 0.000092 0.084580 11.3 73456.00 0.0503270 0.0000246 0.163376 0.000135 0.163511 10.5 73956.00 0.0881587 0.0000345 0.301211 0.000195 0.301406 9.8 74456.00 0.1458544 0.0000472 0.529378 0.000277 0.529655 9.1 74956.00 0.2274701 0.0000641 0.886719 0.000390 0.887109 8.3 75456.00 0.3338294 0.0000847 1.416075 0.000539 1.416615 7.6 75956.00 0.4604444 0.0001094 2.158461 0.000733 2.159193 6.9 76456.00 0.5966979 0.0001386 3.146670 0.000982 3.147652 6.2 76956.00 0.7275037 0.0001670 4.400033 0.001284 4.401317 5.5 77456.00 0.8376617 0.0001914 5.922297 0.001641 5.923937 4.9 77956.00 0.9172952 0.0002067 7.703882 0.002040 7.705923 4.2 78456.00 0.9653328 0.0002070 9.723858 0.002472 9.726330 3.5 78956.00 0.9886289 0.0001889 11.947046 0.002903 11.949949 2.9 79456.00 0.9972702 0.0001498 14.317933 0.003325 14.321258 2.2 79956.00 0.9995617 0.0001027 16.754972 0.003700 16.758673 1.6 80456.00 0.9999568 0.0000594 19.161745 0.004023 19.165768 1.0 80956.00 0.9999959 0.0000280 21.463148 0.004293 21.467442 0.4 81456.00 0.9999987 0.0000104 23.621519 0.004478 23.625998 generation transmission LOLE LOLE

68 Overall effect of removing all transmission overloads on the LOLE single area unserved load 0 0 1 x MW load additional unserved load due to a transmission constraint Pr [gen is in service]

69 Overall effect of removing all transmission overloads on the LOLE Pr [gen is out of service] 0 1 Generation MW 0 Capability  increasing load single area unserved load additional unserved load due to a transmission constraint

70

71 See my dissertation on egpreston.com for more details. The End


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