68 1997 6 A utom ation of E lectric Pow er System s 21 6 ( 710049 ) 0 (8) EPR I [ 5 6 ] : : (1) : [ 1 ] (2) [ 2 3 ] [ 4 ] : (3) (1) (2) (3) (4) (5) ( ) (6) (7) [ 7 1996-12- 19 ] 1995-2006 Tsinghua Tongfang Optical Disc Co. Ltd. All rights reserved.
g g 69 V (E^ (F ) ) = V (F ) gn S (3) V (F ) F (4) : 1 V^ (F ) = N S 6 N S [F (x i) - E^ (F ) ] 2 (4) i= 1 (3) F V (F ) N S E (F ) E^ (F ) : 1 V (E^ (F ) ) (5) E^ (F ) [ 8 9 ] 111 Β = 3 (3) (5) : : (1) (2) (3) Β = : N S = V (F ) gn S E^ (F ) (6) V (F ) (ΒE^ (F ) ) 2 (7) ( ) 1 3 112 11211 ( ) ( ) x P (x ) F (x ) x (1) : E (F ) = 6 F (x ) g P (x ) x X (1) F E^ (F ) (2) : E^ (F ) = 1 N S 6 N S F (x i) (2) i= 1 E^ (F ) F N S x i i F (x i) i x i (2) E^ (F ) E (F ) [10 ] 1121111 x F (x ) E^ (F ) (E^ (F ) F (x ) N S ) E (F ) E^ (F ) : r : r - 1 1995-2006 Tsinghua Tongfang Optical Disc Co. Ltd. All rights reserved.
70 0101 r = 2 [1 12 ] 1121112 P I 2 P i P I = 6 (8) i P li P i i P li i P I k P I : P I = 5P I B k + (9) 5B k B k k P I : LOL P EPN S F&D [ 4 ] [ 15 18 1121113 ] [13 14 ] 11212 : : 2 N 2 N [ 19 20 ] : : M EX ICO [ 21 ] CON FTRA [ 22 ] TR EL SS [ 23 ] CR EAM [ 24 25 ] [ 21 ] [ 22 ] [ 24 26 ] [ 27 ] 1995-2006 Tsinghua Tongfang Optical Disc Co. Ltd. All rights reserved.
[21 28 ] 211 F F " F Α 90% V (F Α) = 1 [V (F ) + V (F ") + 2COV (F F ") ] (14) 4 F F " COV (F F ") < 0 F Α F F " F F P i F " [27 ] W F SSE (Sou thern2sou theastern) nk [ 29 ] nk (10) : n k = N S g P g k V k [ 24 26 ] (10) 214 6 P k g V k k : Z Z F N S P k k Y : V k k W Y = F - Z + E (Z ) (15) [21 ] [28 ] 200 E (Y ) = E (F ) - E (Z ) + E (E (Z ) ) = E (F ) 600 V (Y ) = V (F ) + V (Z ) - 2COV (F Z ) 50% Z F V (Y ) < V (F ) [ 22 ] 212 : (1) P 3 (x ) : [26 ] F (x ) P (x ) E (F ) = 6 x X P 3 P 3 (x ) (11) (x ) : F 3 F (x ) P (x ) (x ) = P 3 : (x ) UD G i E (F ) = 6 F 3 (x ) P 3 (x ) = E (F 3 ) (12) UD T i x X E (F ) E (F 3 ) P 3 (x ) F 3 E (F 3 ) ( ) F 3 F P 3 (x ) 3 P 3 (x ) 112 [ 30 ] [ 27 ] 213 : F Α = 1 2 g g 71 (F + F ") (13) 1995-2006 Tsinghua Tongfang Optical Disc Co. Ltd. All rights reserved. [ 31 ] :
72 C (x ) C (x ) F (x ) C (x ) F (x ) CPU C lancy D P C (x ) F (x ) [ 32 ] [ 33 34 ] [39 ] ( ) [40 ] [35 ] M R T S (m odified IEEE reliab ility test system ) [ 24 25 36 38 ] L i W enyuan B illin ton R 4 [ 9 ] [24 25 ] [ 41 F (x ) ] [ 9 : ] [ 41 ] [ 42 ] F (x ) = G (x ) + T (x ) + C (x ) (16) G (x ) T (x ) C (x ) [ 43 G (x ) T (x ) ] 1995-2006 Tsinghua Tongfang Optical Disc Co. Ltd. All rights reserved.
g g 73 : (1) [ 44 45 ] [46 ] (2) [47 ] (3) [ 47 48 ] 6 1.. : [49 ] 1991 2 A llan R N B illinton R. Concep ts of Pow er System R eliab ility Evaluation. E lectrical Pow er & Energy System s 1988 10 (3): 139 141 3 T ask Fo rce on Bulk Pow er System R eliability of the IEEE2PES A pp lication of P robab ility M ethods Subcomm ittee. Bu lk Pow er System R eliab ility Concep ts and A pp licationṡ IEEE T rans on PW R S 1988 3 (2): 109 117 [50 ] 4 Pereira M V F Balu N J. Compo site Generationg T ran sm ission R eliab ility Evaluation. P roceedings of the IEEE 1992 80 (4): 470 491 5 EPR İ Compo site System R eliability Evaluation M ethodṡ R epo rt EL 25178 198717 6 EPR İ D evelopm ent of Compo site System R eliability Evaluation P rogram T he CR EAM M odel. R epo rt EL 26926 199018 [ 51 53 ] 7 IEEE. R eliability A ssessm ent of Compo site Generation and T ran sm ission System ṡ IEEE T u to ririal Cou rse 90EH 0311212PW R 199012 [ 50 ] 8 R ubinstein R Y. Sim ulation and the M onte Carlo M ethod. N ew Yo rk: John W iley and Sons 1981 : 9 Kalo s M H. M onte Carlo M ethodṡ N ew Yo rk: John W iley and Sons 1986 10 B illinton R A llan R N. R eliability A ssessm ent of L arge E lectric Pow er System ṡ Bo ston: K luw er A cadem ic Pub lishers 1988 11 B illinton R A llan R N. R eliability Evaluation of Pow er System ṡ L ondon: P itm an A dvanced Publish ing P rogram 1984 12 M iko linnas T A W o llenberg B F. A n A dvanced Con tingency Selection A lgo rithm. IEEE T ran s on PA S 1981 100 (2): 608 617 13 Salvaderi L B illinton R. A Comparison Betw een Tw o 5 Fundam en tally D ifferen t A pp roaches to Com po site System R eliab ility Evaluation. IEEE T ran s on PA S 1985 104 (12): 3486 3492 14 Endrenyi J A lbrench t P F B illinton R et al. Bulk Pow er System s R eliability A ssessm ent W hy and How? IEEE T rans on PA S 1982 101(9): 3439 3456 15 B illinton R Gan L. U se of M onte Carlo Sim ulation in T each ing Generation Capacity A dequacy A ssessm enṫ 1995-2006 Tsinghua Tongfang Optical Disc Co. Ltd. All rights reserved.
74 IEEE T rans on PW R S 1991 6 (4): 1571 1577 16 M elo F C G Pereira M V F Silva A M L D. F requency and D u ration Calcu lation s in Com po site Generation and T ran sm ission R eliab ility Evaluation. IEEE T rans on PW R S 1992 7 (2): 469 476 17 Singh C Chander T P Jun Feng. Convergence Characteristics of Tw o M on te Carlo M odels fo r R eliab ility Evaluation of In terconnected Pow er System ṡ E lectric Pow er System s R esearch 1993 28 (1): 1 9 18 Sankarak rishnan A B illinton R. Sequential M onte Carlo Sim u lation fo r Com po site Pow er System R eliability A nalysis w ith T im e V arying L oadṡ IEEE T rans on PW R S 1995 10 (3): 1540 1545 19 Sch illing M T B illinton R Silva A M L D et al. B ibliography on Compo site System R eliability (1964 1988). IEEE T rans on PW R S 1989 4 (3): 1122 1132 20 A llan R N B illinton R B reiph l A M et al. B ibliography on the A pp lication of P robabilitym ethods in Pow er System R eliability Evaluation (1987 1991). IEEE T rans on PW R S 1994 9 (1): 41 49 21 Dodu J C M erlin A. A n A pp lication of L inear P rogramm ing to the P lann ing of L arge Scale Pow er System s: T he M EX ICO M odel. Cam bridge In P roc. 5th PSCC 197519 22 Cunha S H F Pereira M V F O liverira G C et al. Com po site Generation and T ran sm ission R eliab ility Evaluation L arge Scale H ydroelectric Pow er System ṡ IEEE T rans on PA S 1985 104(10): 2657 2663 23 Bhavaraju M P Balu N J L auby M G. T ransm ission System R eliab ility Evaluation of L arge Scale System ṡ M ontreal: C IGR E Sympo sium 1991 1A g11 24 PereiraM V F P into L M V G. A N ew Computational Too l fo r Compo site R eliability Evaluation. IEEE T rans on PW R S 1992 7 (1): 258 264 25 Pereira M V F M acetra M E P O liverira G C et al. Com b in ing A nalytical M ethods and M on te Carlo T echn iques in P robab ilistic Pow er System A nalysiṡ IEEE T rans on PW R S 1992 7 (1): 265 272 26 O liverira G C Pereira M V F Cunha S H F. A T echnique fo r R educed Computational Effo rt in M onte Carlo Based Com po site R eliab ility Evaluation. IEEE T rans on PW R S 1989 4 (4): 1309 1315 27 A nders G J Endrenyi J Pereira M V F et a l. Fast M onte Carlo Sim ulation T echniques fo r Pow er System R eliab ility Studieṡ Paris: C IGR E Sym po sium 1990: 38 205 28 Pouget J... 1988 29 A ug A H T ang W H. P robability Concep ts in Engineering P lann ing and D esign V o lum e g : D ecision R isk and R eliability. N ew Yo rk: John W iley and Son s 1984 30 EPR İ Comparison of A lgo rithm s fo r Computing Generation System R eliab ility Indiceṡ R epo rt EL 2 2874 198313 31 Sch illing M T F ilho M B D C Silva A M L D et al. A n In tegrated A pp roach to Pow er System R eliab ility A ssessm en ṫ E lectrical Pow er & Energy System s 1995 17 (6): 381 390 32 C lancy D P Gro ss G W u F F. P robabilistic F low s fo r R eliab ility Evaluation of M u lti2a rea Pow er System In terconnection. E lectrical Pow er & Energy System s 1983 5 (2): 101 114 33 EPR İ Compo site System R eliability Evaluation: Phase g : Scop ing Studieṡ R epo rt EL 25290 1987112 34 EPR İ Compo site System R eliability Evaluation M ethodṡ Pepo rt EL 25178 198716 35 F ilho R F Pereira M V F. D evelopm ent of a Com po site R eliab ility P rogram fo r B razilian System P ropo sal and Status of O ngo ing R esearch. San F rancisco: In P roc of 2nd In t P robab ilistic M ethods A pp lied to E lectric Pow er System s 198819 36 B illinton R L i W. H ybrid A pp roach fo r R eliability Evaluation of Com po site Generation and T ran sm ission System s U sing M on te Carlo Sim u lation and Enum eration T echnique. IEE P roc C 1991 138 (3): 233 241 37 B illinton R L i W. A System State T ransm ission Sam p ling M ethod fo r Com po site System R eliab ility Evaluation. IEEE T rans on PW R S 1993 8 (3): 761 767 38 Kum amo to H T anaka K Inoue K el al. State2 T ran sition M on te Carlo fo r Evaluating L arge R epairable System ṡ IEEE T rans on R eliability 1980 29 (12) 39 M ello J C O Pereira M V F Silva A M L D. Evaluation of R eliability W o rth in Compo site System s Based on Peseudo2Sequential M onte Carlo Sim ulation. IEEE T rans on PW R S 1994 9 (3): 1318 1326 40 Khan M E B illinton R. A H ybrid M odel fo r Q uantifying D ifferent Operating States of Compo site Pow er System ṡ IEEE T rans on PW R S 1992 7 (1): 187 193 41 Endrenyii J. R eliability M odel in E lectric Pow er System ṡ N ew Yo rk: John W iley and Son s 1978 42 L iw B illinton R. Effect of Bus L oad U ncertainty and Co rrelation in Com po site System A dequacy Evaluation. IEEE T rans on PW R S 1991 6 (4): 1522 1529 43.. : 1991 44 Zadeh L A. Fuzzy Setṡ Info rm ation and Contro l 1965 8 (3): 338 353 45 Zimm erm ann H J. Fuzzy Sets D ecision M ak ing and Expert System ṡ Bo ston: K luw er A cadem ic Pub lishers 1991 46 Bo les J B Pelaez C E. A pp lication of Fuzzy L ogic to : R eliab ility Engineering. P roc of the IEEE 1995 83 (3): 435 449 47 M moh J A M a X W Tom sovic K. O verview and L iteratu re Su rvey of Fuzzy Sets T heo ry in Pow er 1995-2006 Tsinghua Tongfang Optical Disc Co. Ltd. All rights reserved. System ṡ IEEE T rans on PW R S 1995 10 (3): 1676 1690 48 H aubrich H J Seitz T H Bovy A. Fuzzy Sets in R eliab ility A nalysis of Pow er System ṡ M elbou rne: 1993 Expo rt System A pp lication to Pow er System s 199311: 212 217 49 L ing J M L in C E H uang C L. P robabilitym easure of A dequacy A ssessm en t U sing a Fuzzy A pp roach. E lectric Pow er System R esearch 1995 33 (1): 7 15
g g 75 50 Saraiva J T M iranda V P into L M V G. Generationg T ran sm ission Pow er System R eliab ility Evaluation by M on te Carlo Sim u lation A ssum ing a Fuzzy L oad D escrip tion. IEEE T rans on PW R S 1996 11 (2): 690 695 51 M iranda V M ato s M. D istribution System P lanning w ith Fuzzy M odels and T echniqueṡ B righ ton: P roc of C IR ED 1989 198918: 472 476 52 M iranda V M ato sm Saraiva J T. Fuzzy L oad F low 2 N ew A lgo rithm s Inco rpo rating U ncertain Generation and load R ep resen tation. Graz: P roc of the 10th PSCC 199012 53 M iranda V saraiva J T. Fuzzy M odeling of Pow er System Op tim al L oad F low. IEEE T rans on PW R S 1992 7 (2): 843 849 1970 1936 THE APPL ICATION OF MONTE CARLO M ETHOD TO REL IAB IL ITY EVAL UATION OF POW ER SY STEM S B ie Z haohong ΨW ang X if anx i an J iao tong U niversityκ710049κx i anκch inaγ Abstract T he paper surveys basic p rincip les of M onte Carlo m ethod and its app lication to reliability evaluation of pow er system ṡ By comparison w ith the enum eration app roachκ its features and app lication scope are p resented. Furthermo reκ the app roach fo r imp roving the convergent speedκthe com bination ofm onte Carlo m ethod and the enum eration app roach and load models used in evaluation are summ arized in detail. A t lastκ som e valuable ideas and future w o rk s are p ropo sed. Keywords pow er system reliability M onte Carlo m ethod p lanning ( ) 1997 10 1 2 ( ) ( ) 3500 6000 2000 1400 1998 : 24 11 : (025) 3429900-2438 : 323 : (025) 3421949 : 210003 : 1995-2006 Tsinghua Tongfang Optical Disc Co. Ltd. All rights reserved.