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

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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

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

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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.

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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

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Combination of two generator pdfs using convolution

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

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Take all combinations of Pr’s and MW’s X Pr

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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

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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)

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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

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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 P1P2P3P1P2P FOR = per unit down time PFOR = per unit derated time (partial forced outage rate)

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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 unit 3 FOR=.3 20 MW

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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

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Markov representation of three generators P1P2P3P4P5P6P7P8P1P2P3P4P5P6P7P

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Markov representation of three generators P1P2P3P4P5P6P7P8P1P2P3P4P5P6P7P MW MW MW MW MW MW MW MW

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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 sort

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Graph of the 3 generator cumulative distribution for the probability that generation MW is > x) x (MW) Pr load not served generation

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

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The same cumulative distribution can be created one generator at a time. The function is updated as each generator is added x (MW) Pr load not served generation

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Starting with a blank distribution x (MW) Pr load not served

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Cumulative distribution for generator 1 generator 1 = {10 MW, FOR=.1} Pr x (MW).900 load not served.000 ∞

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Adding generator 2 scales and shifts the initial distribution for Pr=.8 (up) and Pr=.2 (down) generator 2 = {15 MW, FOR=.2} x (MW) Pr.900 x.2 = x.8 = x.8 =.80

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Summing the two curves gives the combined generators 1 and 2 cumulative distribution x (MW) Pr load not served = generation

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Adding generator 3 scales and shifts the distribution for Pr=.7 (up) and Pr=.3 (down) generator 3 = {20 MW, FOR=.3} x (MW) Pr.98x.3= x.3=.24.72x.3= x.7= x.7=.56.72x.7= x.7=.700

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Summing the two curves gives the combined generators 1, 2, and 3 cumulative distribution (same curve as the one using a binary tree) x (MW) Pr = = = load not served generation =.902

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Binary tree graph of the 3 generator cumulative distribution for the probability that generation is available at x MW x (MW) Pr load not served generation

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Cumulative distribution Pr[generation is up] represented in discrete 1 MW steps x (MW) Pr load not served generation

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Flip the function over and backwards and the distribution represents Pr[generation out of svc] This is the COPT or Capacity Outage Probability Table x (MW) Pr load not served

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Representation of Pr[gen out of service] as piecewise linear increments x (MW) Pr load not served

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Representation of Pr[gen out of service] as piecewise quadratic increments x (MW) Pr load not served for any 3 points, interpolate between the left two points

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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%

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LOLE – loss of load expectation EUE – expected unserved energy 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] = =.44 d/y

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LOLP – loss of load probability MW x – MW weekly peak demand Pr generation LOLP (for a week) = 1 - Pr[gen up] = Pr[load loss] = = annual LOLP = 1- i (Pr[gen up] i ) for all i weeks

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Representing load uncertainty (each hour is a Normal distribution of MW values) MW x – MW (daily or hourly) Pr generation

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Generation scheduled maintenance 1 xxx 2 xxx 3 4 xxxxx 5 6 xxx 7 8 xxxx 9 xxx 10 xxxx week # during the year generator # summer insufficient reserve?

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Generation scheduled maintenance reduces available generation – increases LOLE week # during the year generator installed MW before maintenance MW demand insufficient reserve planning reserve with maint

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Generation scheduled maintenance to minimize overall LOLE week # during the year generator installed MW before maintenance MW demand planning reserve with maint

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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.

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1999 load shape

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ERCOT generation (MW) forced out of service and derated ~5000 MW ~9000 MW ~6% ~11% 12.5% actual more generators

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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)

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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

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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.

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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.

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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.

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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

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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 D STP1 ERCOT STP2 ERCOT CMPK 1 G ERCOT CMPK 2 G ERCOT DOW1 ERCOT DOW2 ERCOT DEC 1 G ERCOT THSE 2 G ERCOT LIM1 ERCOT LIM2 ERCOT MTNLK 1G ERCOT MTNLK 2G ERCOT MTNLK 3G ERCOT MOSES3 G ERCOT CB 3 ERCOT DC-EAST ERCOT Weeks Weeks Weeks Weeks 38-48

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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: 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

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Single Area Output Reports – CDR WEEK CAPACITY OUT-OF-SVC AVAILABLE PEAK LOAD RESERVE RESERVE WEEK MW MW MW MW MW % BEGINS APR APR MAY MAY MAY MAY MAY JUN JUN JUN JUN JUL JUL JUL JUL AUG AUG AUG AUG AUG SEP SEP SEP SEP OCT 3

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Single Area Output Reports – LOLE Results WEEK PEAK LOAD RESERVE WEEKLY PROBABILITY HOURLY UNSERVED WEEK MW % LOAD>GENR MWH BEGINS APR APR MAY MAY MAY MAY MAY JUN JUN JUN JUN JUL JUL JUL JUL AUG AUG AUG AUG AUG SEP SEP SEP SEP OCT 3 ANNUAL * (* INSTALLED) LOSS OF LOAD EXPECTATION = DAYS/YR USING DAILY PEAK LOADS AND NO LOAD UNCERTAINTY LOSS OF LOAD EXPECTATION = DAYS/YR USING HOURLY LOADS AND NO LOAD UNCERTAINTY

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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

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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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Harmful Generators for Austrop-Sandow Ckts PDFs for ckt: 3429 SANDOW AUSTRO LOSTPN load flow bus LOSTPN load flow bus LOSTPN load flow bus BEP GT load flow bus BEP GT load flow bus BEP ST load flow bus FPP G load flow bus FPP G load flow bus FPP G load flow bus HAYSN load flow bus HAYSN load flow bus HAYSN load flow bus HAYSN load flow bus MCQUEE load flow bus SANDH G load flow bus SANDH G load flow bus SANDH G load flow bus SANDH G load flow bus CANYHY load flow bus DECKR G load flow bus DECKR G load flow bus 9000

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More Generator PDFs for Austrop-Sandow 252 GUALUP load flow bus GUALUP load flow bus GUALUP load flow bus SCHUMA load flow bus GUALUP load flow bus GUALUP load flow bus GUALUP load flow bus RIONO G load flow bus RIONO G load flow bus RIONO G load flow bus DECKR G load flow bus DECKR G load flow bus DECKR G load flow bus DECKR G load flow bus RIONO G load flow bus RIONO G load flow bus RIONO G load flow bus LAKEWD load flow bus LAR # load flow bus SAND 4 G load flow bus 3432 SOUTH load flow area 4 NORTH load flow area 2 WEST load flow area 1 HOUSTON load flow area 3

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Maximum Flows for Austrop-Sandow Ckts MAXIMUM +/- LINE FLOWS FROM SUMS OF INCREMENTAL GENERATOR FLOWS FROM TO RATG BASE +MW -MW %ADJ 3429 SANDOW AUSTRO SANDOW AUSTRO average weighted scale factor = 2.24 % sum of flows from helpers sum of flows from harmers

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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 AUSTRO LOSTPN 2 18->NORTH SANDOW AUSTRO LOSTPN 2 18->NORTH SANDOW AUSTRO SAND 4 G 22->SOUTH SANDOW AUSTRO SAND 4 G 22->SOUTH.232

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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)

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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

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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

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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 AUSTRO LOSTPN 2 NORTH SANDOW AUSTRO LOSTPN 3 NORTH SANDOW AUSTRO LOSTPN 1 NORTH SANDOW AUSTRO BEP GT2 NORTH SANDOW AUSTRO BEP GT1 NORTH SANDOW AUSTRO BEP ST1 NORTH SANDOW AUSTRO FPP G1 NORTH SANDOW AUSTRO FPP G2 NORTH SANDOW AUSTRO LOSTPN 2 NORTH SANDOW AUSTRO LOSTPN 3 NORTH SANDOW AUSTRO LOSTPN 1 NORTH SANDOW AUSTRO BEP GT2 NORTH SANDOW AUSTRO BEP GT1 NORTH SANDOW AUSTRO BEP ST1 NORTH SANDOW AUSTRO FPP G1 NORTH SANDOW AUSTRO FPP G2 NORTH MWH for one hour (with all gens at Pmax)

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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 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

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Load shedding to remove Austrop-Sandow circuit overloads RESV% LOAD-MW LOLP TLOP GLOL-D/Y TLOL-D/Y TOTL-D/Y generation transmission LOLE LOLE

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

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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

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

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