fo hil mp s fo e frequency of SBO is under predicted by a factor of �2 by approximate time BO durations of 8 h and 16 h. The time dependent cutset evaluation method is ede for to study the SBO frequency time correlation. SBO is defined as the total loss of AC electrical power to the esse electrical buses in a nuclear power plant (B ower s nt. Fas menta ch, Kal offsite et sup ation of cutsets for on-site emergency AC power supply system. (3) SBO frequency time correlation by combing results from steps 1 to thu et al., 2000). Step 2 is carried out by Fault Tree method using DG units start automatically and feed both the buses. Provision ex- ists to connect any one of the DGs to both the emergency buses. 3. LOSP frequency time correlation For FBTR which has two redundant feeders and transformers, the time independent frequency of loss of offsite power is 4.7/y. The objective is to estimate the frequency of LOSP events, whose duration is greater than or equal to a specified value. The frequency of LOSP (kLOSP (tP T)) due to grid failure exceeding specified Abbreviations: AC, alternating current; ASBT, auto startup andbus transfer logic; BC, bus coupler; CCF, common cause failures; DCS, DC supply; DG, diesel generator; DGBHW, DG breaker hardware; DGBHWM, DG breaker hardware manual; EF, error factor; FBTR, fast breeder test reactor; H, human operation; IGCAR, Indira Gandhi Centre for Atomic Research; INCB, incoming breakers; LOSP, loss of offsite power; MAPS, Madras Atomic Power Station; SBO, station blackout; TDCE, time dependent cutset evaluation; UVR, under voltage relay. * Corresponding author. Annals of Nuclear Energy 35 (2008) 2332–2337 Contents lists availab Annals of Nuc journal homepage: www.els E-mail address:
[email protected] (M. Ramakrishnan). and two 100% emergency diesel generator (DG) sets. For FBTR, SBO is defined as the loss of power in two or more of the four class III bus sections. The broad conditions under which SBO occurs at FBTR are: (i) 2 out of 2 DGs fail (2/2:F) after loss of off-site power. (ii) Fault in two or more bus sections. Although less likely, the sec- ond condition directly leads to blackout irrespective of availability of resources. The estimation of SBO frequency proceeds in three steps. (1) Loss of off-site power (LOSP) frequency time correlation. (2) Gener- The major factors contributing to the loss of off-site power are: (i) Failures in the grid, (ii) failures in the feeder, and (iii) trans- former failures. The schematic of off-site power distribution at FBTR is shown in Fig. 1. From the schematic diagram it is clear that the failure of one feeder or transformer does not lead to LOSP be- cause of redundancy. Emergency power is provided by two DGs. Each DG unit sup- plies an independent bus, which is in two sections. Each of these bus sections is normally fed by an independent transformer from offsite power supply. When offsite power supply fails, both the occurs when onsite emergency AC p during a loss of off-site power eve (FBTR) is a loop type, 40 MWt experi ira Gandhi Centre for Atomic Resear class IV power buses are supplied by pendent feeders and class III buses g 0306-4549/$ - see front matter � 2008 Elsevier Ltd. A doi:10.1016/j.anucene.2008.08.001 ntial and non-essential aranowsky, 1988). SBO ystems are unavailable t Breeder Test Reactor l reactor located at Ind- pakkam, India. In FBTR power through 2 inde- ply from class IV buses RISK SPECTRUM software. Step 3 is carried out by time dependent cutset evaluation (TDCE) method (Baranowsky,1988; IAEA-TEC- DOC-593, 1991; Battle and Campbell, 1983). 2. Description of off-site and onsite emergency power distribution scheme at FBTR Station black out (SBO) is one of the initiating events for poten- tial accidents at nuclear power plants. In this context it is necessary has been arrived at after a detailed study of loss of offsite power phenomena in various plant sites (John Arul et al., 2003; Marimu- Estimation of station blackout frequency M. Ramakrishnan a,*, A. John Arul a, S. Usha b, C. Sent aReactor Physics Division, IGCAR, Kalpakkam, Tamil Nadu 603 102, India b Technical Services Division, IGCAR, Kalpakkam 603 102, India cAERB Safety Research Institute, Kalpakkam 603 102, India a r t i c l e i n f o Article history: Received 15 February 2008 Received in revised form 30 July 2008 Accepted 1 August 2008 Available online 16 September 2008 a b s t r a c t This paper presents the co time averaged expression method. It is found that th averaged expressions for S applied for offsite power fe of the feeders is taken out 1. Introduction ll rights reserved. r outage management by treating the change in SBO frequency when one maintenance for ‘n’ days, as the risk measure. � 2008 Elsevier Ltd. All rights reserved. 2. Based on the observed data available at FBTR, step 1 is carried out by fitting the LOSP data with the help of a power law, which r Indian fast breeder test reactor Kumar c arison of station blackout (SBO) frequency computed with approximate r diesel generator unavailability and time dependent cutset evaluation le at ScienceDirect lear Energy evier .com/ locate/anucene N istri Nuc Grid Supply 33kV IGCAR Feeder-2 33kV IGCAR Feeder-1 M A PS 2 30 k V B us O 33kV bus Fig. 1. Off-site power d 10-1 100 101 102 10-2 10-1 100 101 Fr eq ue nc y (/y r) Duration (hr) Grid data Fit - (t) = 0 /(1+t) c 0 = 4.4, c = 1.234+0.08 Λ λ λ M. Ramakrishnan et al. / Annals of duration as derived from FBTR data, is shown in Fig. 2 as points. Detailed analysis of offsite power failure data (Marimuthu et al., 2000) has shown that the frequency non-recovery time correlation is characterized by a power law (John Arul et al., 2003). The follow- ing equation is fitted to the data: kgridðt P TÞ ¼ k0=ð1þ TÞc; ð1Þ where k0 = 4.4 and c = 1.235. The power law fit for the LOSP data re- corded at FBTR is shown in Fig. 2. The LOSP frequency at FBTR class IV bus level is obtained by adding the respective feeder and transformer failure rates with exponential non-recovery times as follows. With only one feeder-transformer, kð1ÞLOSPðtP TÞ ¼ kgridðtP TÞ þ kF � expð�T=TFRÞ þ kT � expð�T=TTRÞ ð2Þ When both feeders and transformers are available, kð2ÞLOSPðt P TÞ ¼ kgridðt P TÞ þ 2 � ½kF � expð�T=TFRÞ þ kT � expð�T=TTRÞ� � ½UF þ UT� ð3Þ where kF, kT – failure rates of feeder and transformer, respectively. UF, UT – unavailabilites of feeder and transformer. TFR, TTR – mean time to repair of feeder and transformer. 4. Evaluation ofon-site emergency power system unavailability In this study, the DGs and their configuration, auxiliaries and support systems, all important breakers and startup and bus trans- fer relay logics have been considered. The reliability of the emer- gency power supply system is evaluated using fault tree method. Immediate cause approach is followed as far as practicable. The Fig. 2. Loss of offsite power frequency as a function of power loss duration. fault tree is developed using RISK SPECTRUM software. Compo- nents for which data from FBTR is not available, data from litera- ture is used (IAEA-TECDOC-478, 1988; IAEA-TECDOC-636, 1992). The generated cutsets are evaluated by TDCE method as described in the next section. The reliability parameters calculated for DG from FBTR data are given in Table 1. The reliability block diagram for on-site emergency power system is shown in Fig. 3. The abbre- viations for components in Fig. 3 are described in abbreviations list. 5. Station blackout frequency time correlation The frequency of station blackout events exceeding a specified duration (kSBO(T)) is obtained by combining the model for the fre- quency of LOSP (kLOP(T)) with the unavailability of DG over the duration of interest (UDG(T)), i.e., kSBOðt P TÞ ¼ kLOSPðTÞ � UDGðTÞ ð4Þ where kLOSP (T) is given by Eq. (3), UDGðTÞ ¼ UDG � e�2T=Tr; 33kV / 6.6 kV FBTR Transformer-1 (TMtb 001) 33kV / 6.6 kV FBTR Transformer-2 (TMtb 002) To the loads of FBTR & SGTF, ITG To the loads of FBTR NC 6.6kV bus bution system at FBTR. Table 1 Calculated reliability parameters for DG Sl. no. Parameter DG-1 DG-2 1 Fail to start probability 1.7e�03/de 5.0e�03/de 2 Fail to run rate 3.2e�03/h 3.2e�03/h 3 Unavailability 9.1e�02 7.7e�02 lear Energy 35 (2008) 2332–2337 2333 and Tr, the mean time taken to repair a DG, is taken as 8 h. The parameter UDG is evaluated with fault tree method. However, Eq. (4) is only an approximate time averaged expres- sion. There are several methods available to calculate the SBO fre- quency like fault tree method, time dependent cutset evaluation method and Markov method (IAEA-TECDOC-593,1991; Senthil Ku- mar et al., 2005) treating the time dependence more realistically. Here the time dependent cutset evaluation method is applied as follows. In the time dependent cutset evaluation method for obtaining SBO frequency duration correlation, the cutsets gener- ated by fault tree method for DG unavailability are assigned time dependence based on the event combinations and then multiplied with LOSP frequency correlation function and integrated. The de- tails of the method are explained below. From the analysis of cutsets generated from fault tree analysis it is observed that cutsets of order greater than three are not contrib- uting significantly to the onsite emergency power system unavail- ability. So, cutsets which are of order up to three only have been considered further for time dependent cutset evaluation. The cut- sets generated are in general in one of the following event combinations. Case 1: The systems/components appearing in the cutset are unavailable at the instant of occurrence of LOSP. The integration rule for this case is a simple multiplication as given below: DG1 INCB DGBHW H ASBT1 277A DGBHWM H 187A NCB UVR1 127 B 67 for o 2334 M. Ramakrishnan et al. / Annals of Nuc DG2 H ASBT2 117 B DGBHWM H 217 B DGBHW IUVR2 2 Fig. 3. Reliability block diagram kSBOðt P TÞ ¼ kLOSPðTÞ � U1 � e�l1T � U2 � e�l2T � U3 � e�l3T ; ð5Þ where U1, U2, U3 are unavailabilities and l1, l2, l3 are respective re- pair rates. Case 2: Two systems/components appearing in the cutset are unavailable at the instant of occurrence of LOSP and the third sys- tem/component is available at the instant of LOSP occurrence and subsequently fails during the LOSP interval. This form is best illus- trated with the help of Fig. 4. The SBO frequency contribution from this event combination is kSBOðt P TÞ ¼ Z 1 0 kLOSPðT þ t1Þ � U1 � e�l1ðTþt1Þ � U2 � e�l2ðTþt1Þ � ð1� PftsÞ:kre�kr t1 � e�lTdt1 ð6Þ At t = 0, LOSP occurs. One of the DGs and one of the components are unavailable at t = 0. The other DG started successfully but failed Time 1 0 t1 t=0 T recovery Fig. 4. State diagram for UUR case. INCB DCS1 DCS2 287 A BC 197 A 100 B 100 A INCB BC 200 B 200 A 177 A A 227 B nsite emergency power supply. lear Energy 35 (2008) 2332–2337 at time t1. For this condition to persist for a duration of T or more the following conditions are to be satisfied. (a) LOSP does not recover for a duration of t1 + T(kLOSP(T + t1)). (b) One of the DGs and the other component which are unavail- able at t = 0, do not recover for a duration t1 + T (U1 � e�l1ðTþt1Þ � U2 � e�l2ðTþt1Þ). (c) The DG which has started successfully and subsequently failed at t1 does not recover for a duration T. (ð1� PftsÞ� kre�krt1 � e�lT). If the above conditions are satisfied then we can say that the SBO has occurred for a duration of T or more. Case 3: A system/component appearing in the cutset is unavail- able at the instant of LOSP occurrence and the other two systems/ components which are available at the instant of LOSP occurrence, subsequently failed at different instants during the LOSP interval. This condition is illustrated with the help of Fig. 5. The SBO frequency contribution from this event combination is kSBOðt P TÞ ¼ Z 1 0 Z 1 t1 kLOSPðT þ t2Þ � U1 � e�l1ðTþt2Þ � fð1� PftsÞ:kr1e�kr1 t1dt1g � e�l2ðTþðt2�t1ÞÞ � ð1� PftsÞ � kr2 � e�kr2 t2 � e�l3Tdt2 ð7Þ At t = 0 LOSP occurs and one of the components is unavailable. Both the DGs started successfully on demand and one of the DGs failed at time t1 and the other DG failed at time t2 (t2 > t1). For this condition to persist for a duration of T or more, the following con- ditions are to be satisfied. (a) LOSP does not recover for a duration t2 + T (kLOSPðT þ t2Þ). (b) The component which is unavailable at t = 0, does not recover for a duration t2 þ TðU1 � e�l1ðTþt2ÞÞ. Since 415V bus section failure rates are very low of the order of 1e�8/h, events of type 4 have not been considered. 6. Analysis of SBO results A program in C++ was developed to carry out the time depen- dent cutset evaluation method by Simpson’s 1/3 rule. This program takes the cutsets generated from fault tree and data for basic events as input and generates the results as SBO frequency vs. duration. The SBO frequency calculated by time averaged expres- sions are 5.42e�4/ry for SBO duration of 8 h and 4.81e�5/ry for SBO duration of 16 h. By this TDCE method the SBO frequency is 9.26e�4/ry for SBO duration of 8 h and 1.05e�4/ry for SBO dura- tion of 16 h. The comparison of SBO frequency between TDCE method and approximate time averaged expressions are shown in Fig. 6. From Fig. 6 it is clear that the time averaged expression under predicts the SBO frequency by a factor of �2 for SBO dura- tion of 8 h and 16 h. The SBO frequency for FBTR, if one of the feeders is taken out for maintenance for an additional period of ‘n’ days in a year is ob- tained by increasing the feeder’s maintenance unavailability by T recovery 1 Table 3 CCF values used in sensitivity study Sl. no. Event ID Independent failure rate/ unavailability Common cause failure rate/ unavailability b = 5% b = 10% b = 20% M. Ramakrishnan et al. / Annals of Nuclear Energy 35 (2008) 2332–2337 2335 Time t1 t=0 t2 0 Fig. 5. State diagram for URR case. SBO Frequency Vs Duration 1.00E-05 1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 SB O F re qu en cy (/ yr ) Double feeder-TDCE Double feeder-Time Averaged (c) The DG which has failed at t2 does not recover for a duration T. (ð1� PftsÞ � kr2 � e�kr2t2 � e�l3T ). (d) The DG which has failed at t1 does not recover for a duration (t2 � t1 + T). (ð1� PftsÞ � kr1 � e�kr1t1 � e�l2ðTþðt2�t1ÞÞ). Case 4: SBO is initiated by common cause failure of redundant components or failure of common elements/components in the distribution system. In this case the frequency of SBO of duration T or more is, kSBOðt >¼ TÞ ¼ fsysðTÞ ð8Þ where fsys (T) is the system failure frequency-time duration correla- tion function. The significant, maximum cutset order encountered in this problem is three and minimum order is one. The expressions for the second and first order cutsets are obtained from the above expressions applicable for third order cutset by setting the irrele- vant unavailability equal to 1 and repair rate equal to 0. The total SBO frequency is the sum of contributions from the four major types of event combinations defined above. For FBTR, events of type 4 could occur, for instance, due to failures in 415V bus sections. Table 2 SBO frequency if one of the feeders is unavailable for an additional 14 days in a year SBO duration (h) kSBO frequency (/y) Single feeder system (kSF) Double feeder system (kDF) Double feeder – one feeder unavailable days additional period/year (TDCE) 2 1.9E�2 6.1E�3 6.72E�3 4 1.1E�2 3.1E�3 3.41E�3 8 3.6E�3 9.3E�4 1.05E�3 16 4.6E�4 1.1E�4 1.21E�4 0 2 4 6 8 10 12 14 16 18 20 Duration (hr) Fig. 6. Comparison of SBO frequency by TDCE and time averaged expressions. 1 Auto startup and bus transfer logic common cause failure 7.36E�04 3.68E�05 7.36E�05 1.47E�04 2 Station battery bank common cause failure 9.2E�05 4.60E�06 9.2E�06 1.84E�05 3 Buses hardware common cause failure 8.0E�08 4.00E�09 8.0E�09 1.60E�08 4 DG fail to run common cause failure 3.2E�03 1.60E�04 3.2E�04 6.40E�04 5 DG fail to start common cause failure 4.17E�03 2.09E�04 4.17E�04 8.34E�04 1.00E+00 for 14 Fractional increase (kSF/kDF � 1)/365 Double feeder – one feeder unavailable for 14 days additional period/year (extrapolation) 5.8E�03 6.6E�03 7.0E�03 3.4E�03 1.00E-05 1.00E-04 1.00E-03 1.00E-02 1.00E-01 0 2 4 6 8 10 12 14 16 18 20 Duration (hr) SB O F re q (/y r) Double Feeder beta=10% Double feeder beta=20% Fig. 7. Station blackout frequency vs. the duration for different beta values. 7.9E�03 1.0E�03 8.7E�03 1.2E�04 SBO frequency for one feeder non-availability for n-additional 31 ncy Nuc days/year is k0DF (n) = kDF (1 + (r � 1)/365 � n). From Table 2 it is clear that the extrapolation technique and TDCE technique predicts the SBO results closely for ‘n’ days of additional outage in a year. 7. Uncertainty and sensitivity analysis Sensitivity analysis: The SBO frequency has been computed by varying CCF factor for important components. The components for which b factor variation is studied are shown in Table 3. Increasing beta value increases the SBO frequency without chang- an additional period of ‘n’ days. If one of the feeders is taken out for maintenance for an additional period of 14 days in a year, the SBO frequency increases by 10% for 4 h duration and by 13% for 8 h duration. The ratio (r = kSF/kDF) of single feeder blackout frequency to double feeder blackout frequency is about 3.1 (for 2 h) to 4.2 (for 16 h duration). The results are given in Table 2. The extrapolated 26% 21% 7% Fig. 8. Pie chart of onsite emerge 5% 5% 3% 1%1% 2336 M. Ramakrishnan et al. / Annals of ing the shape of the curve. The results are shown in Fig. 7. Uncertainty analysis: Uncertainty analysis of SBO frequency is done by Monte Carlo Method. All basic event data are sampled using lognormal distribution constructed from available median failure rate (x0) and error factor (EF). Box-Muller method (Box and Muller, 1958) is used for generating log-normal samples. The following equations are used: U1 ¼ sqrtð�2lnðr1ÞÞ� sinð2pr2Þ ð9Þ U2 ¼ sqrtð�2lnðr1ÞÞ� cosð2pr2Þ ð10Þ k1 ¼ x0 expðsU1Þ; k2 ¼ x0 expðsU2Þ ð11Þ In these equations, k1 and k2 are the simulated values of two independent log normal variables with parameters (s, x0), and s = ln (EF)/1.645, and r1 and r2 are uniformly distributed random numbers. The uncertainty analysis indicates that the results in the magnitude of SBO could be uncertain by a factor of 3. 8. Discussion of the results The frequency of offsite power loss is 4.7 ± 0.3/y. The onsite emergency power system unavailability calculated by Fault Tree method is 8.1E�3. It is dominated by the second order cutset with run failure of a DG as one event and the unavailability of another due to breakdown or preventive maintenance as the other event. The percentage contribution due to this is (26 + 21 = 47%) and is followed by CCF of DG to run (31%) as shown in Fig. 8. The increase in SBO frequency, if one of the feeders is taken out for maintenance for 14 days over the parallel operation of two feeders case, is about 10% for SBO duration of 2 h and 16 h. The simple time averaged method under predicts the SBO frequency by a factor of �2 for SBO duration of 8 h and 16 h. The contribution to SBO frequency from explicit common elements such as bus sec- tion failures is negligible. 9. Conclusion The frequency of loss of offsite power (LOSP) at FBTR is found to be 4.7/y. Onsite data on the LOSP and failure data on feeders and transformers at FBTR are used to arrive at the frequency of LOSP as a function of down time. The non-recovery probability of offsite power failure with time is represented by a power law. The cutsets % CL3-DGA-FR-RCCF CL3-DGA-FR-DG02 CL3-DGA- UM-DG01 CL3-DGA-FR-DG01 CL3-DGA- UM-DG02 CL3-DGA-FR-DG01 CL3-DGA- FR-DG02 CL3-DGA-FS-DG02 CL3-DGA- UM-DG01 CL3-DGA-FS-SCCF CL3-DGA-FS-DG01 CL3-DGA- UM-DG02 CL3-DGA-FR-DG01 CL3-DGA- FS-DG02 CL3-DGA-FR-DG02 CL3-DGA- FS-DG01 power sub-system contributions. lear Energy 35 (2008) 2332–2337 and unavailability of onsite emergency power supply are evaluated with the Fault Tree method. The cutsets were transformed to time dependent form, and integrated with LOSP frequency duration cor- relation to get the SBO frequency duration correlation at FBTR. These results are compared with the results arrived at by using simple time averaged expressions. The increase in SBO frequency for one feeder outage of ‘n’ days was also analyzed. The sensitivity with respect to common cause failure parameter (b) is also ana- lyzed. The time dependent cutset method is found to be accurate compared with the time average method for making decisions on allowed outage time of equipment where errors of factor 2 are significant. Acknowledgements The authors are thankful to Director IGCAR, Director REG, Direc- tor ROMG for their guidance and active support. The authors acknowledge the support and motivation received from Associate Director (Operation & Maintenance, ROMG) and Head, RPD. References Baranowsky, P.W., 1988. Evaluation of Station Blackout Accidents at Nuclear Power Plants, NUREG-1032. Battle, R.E., Campbell, D.J., 1983. Reliability of Emergency AC Power Systems at Nuclear Power Plants, NUREG/CR-2989, ORNL/TM-8545. ORNL, USA. Box, G.E.P., Muller, M.E., 1958. Annals of mathematical statistics 29, 610. IAEA-TECDOC-478, 1988. Component Reliability Data for use in Probabilistic Safety Analysis, IAEA, Vienna. IAEA-TECDOC-593, 1991. Case Study on the Use of PSA Methods: Station Blackout Risk at Millstone Unit 3, IAEA, Vienna. IAEA-TECDOC-636, 1992. Manual on Reliability Data Collection for Research Reactor PSAs, IAEA, Vienna. John Arul, A., Senthil Kumar, C., Marimuthu, S., Om Pal Singh, 2003. The power law character of offsite power failures. Annals of Nuclear Energy 30, 1401–1408. Marimuthu, S., Theivarajan, N., Senthil Kumar, C., 2000. Statistics of Off-Site Power Failure at Kalpakkam, REV-A, PFBR/01160/DN/1000. Senthil Kumar, C., John Arul, A., Om Pal Singh, 2005. New Methodologies for Station Blackout Studies in Nuclear Power Plants, ICRESH05, Mumbai. M. Ramakrishnan et al. / Annals of Nuclear Energy 35 (2008) 2332–2337 2337 Estimation of station blackout frequency for indian Indian fast breeder test reactor Introduction Description of Off-Site And Onsite Emergency Power Distribution Scheme At off-site and onsite emergency power distribution scheme at FBTR LOSP Frequency Time Correlationfrequency time correlation Evaluation of On-Site Emergency Power System Unavailabilityon-site emergency power system unavailability Station Blackout Frequency Time Correlationblackout frequency time correlation Analysis of SBO Resultsresults Uncertainty and Sensitivity Analysissensitivity analysis Discussion of the Resultsresults Conclusion Acknowledgements References