Document 2jEg8EqRnm8w52ExNMz2bV6Ga

Ilf. X Probability Theory Can Predict Frequency of Future Events | j too 3 Percent total tu/trine cutoff** with duration* ffraoter then Indicated volue by preuuro clast and by yoars 1939-44 5 Clow Offreemenr Of Colculat*d end octuof dlttribullcvi of awnblnotlon turbine forced outoge* volldotes uss of probability theory for engineering applications WotaO'Afrs'Jbn c/ bat txart c* " Ttecopacl hr between itatloni marked- 4 4 Probability of lood lost increases ot ly effects group reserve requirements II occeieroted pace with dolly lood ratio O.OOOOQI 11 i II11111M II11 i I i 1111111111 Igysg 300 390 400 450 SOO 990 600 Reserve, rrq* 4 A Probability of lood loss decreases I m w|th growing system reserve capacity them into subgroup* of simitar unit* and calculate the outage probabilities of cad) subgroup, then combine the calculations for each subgroup as shown in Tabic l, p 104. From Table 1 a summary of outage probabilities in terms of mw out of sendee .instead of number of units can be calculated as shown in Table II. - Results of such a study for the Con* solidsted Edison system are shown in Fig. 2. Curve A represents 60 units on the system in 1938 that aggregated 2592 mw with a turbine outage of 0.03, nag* lecting effect of boilers. Curve B repre sents expected experience for 1968 with estimated capacity of 3770 mw for the following outage rates: below 1000*psig pressure, turbines 0.01, boilers, 0.01S; 1000 psig and above, boilers and tur bines, 0.03. While these outages are expressed as a given fraction of time, they must not bo Interpreted to mean that this exact fraction will occur every year. Rather, over a long term of years the various values of outage time will average at the calculated magnitudes. Outage DaroHoa. Probability calcu lations give no information on the dura-, lions of individual outages. This can only be obtained from past experience. Fig. 3 and 4 summarize experience on a large number of units canvassed by the EEI. This type of Information U of importance to the planning engineer, especially where hydro plants with storage reservoirs are involved. Once the outage rate is known it be# comes possible by means of the bln*y mial formula to calculate the expected! duration ol limultaneous outages. Vi\g lidlty of the method can be against actual experience as shown Fig. 5. These curves demonstrate edequacy of the method for use in eoirj] nearing planning, provided the dsUj are properly interpreted. Lea of Load. Having calcoloted mathematical relationship of magnitudes and their probability occurrence, next step is to compute probability of loss of load for a system of reserve. This is done appropriate correlation of the prob*j bilitiea of outage (Fig. 2) with load-duration curve (such as Fig. 6); 102 |42*4) FOWEt July l,4j For a discussion of this correlation see A1EE paper No. 47-248, "Generating Reserve Capacity Determined by the Probability Method,** by G Calabrese. Service Reliability. Having calculated the outage and load-loss probabilities, n* step Involves choosing a suitable iadei sad fixing the value that will .*** desired degree of service re liability. Tbcae indexes can be ex- Pre****l *: the number of days outage #r *** * load per peak season or per as one day outage or loos of load k u raan^ P*a^ seasons; expected loss per peak season (or year) | f Installed capacity; expected , ,r 081 per year per kw of maximum , The probability' method assumes t the calculated outages can occur at any time of the year. But the peak load usually oiurs at only one lime during a year as shown in Fig. 6, 7 and 8; henco the probability of losing capacity in excess of the reserve at peak time Is much smaller than if the peak load persisted throughout the year, On the other hand, equipment must be taken out of service over extended periods for overhauling, so that at times the reserve provided over the peak load U all that is available at lower loads. In view of these considerations it is reeommended that the index of reliability be chosen with due regard to the nature of the load-duration curve and overhaul schedule. For a discussion of indexes see AIEE paper referred to previously in this article. Level of Reliability. Level of relia bility chosen depends on local condi tions, importance of load, effect of voltage drop, aha of system end, last but not least, personal judgment A useful guide to selecting the level is past experience with outages and cor rective measures that can be provided to reduce load when needed. There are other problems that re quire evaluation of relative reliability of alternate methods of system develop ment The probability technique lends Itself readily to arriving at an exact economic evaluation from this stand point- Problems might be of the fol lowing nature: What reliability-is lost or gained by decreasing or increasing system reserve? By changing the aha FOWEr July 1944 {4?S1 10)