METHOD AND ALGORITHM OF RANGING OF RELIABILITY OBJECTS OF THE POWER SUPPLY SYSTEM

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1 Farzalye Y.. METHOD AND ALGORITHM OF RANGING OF RELIABILITY OBJECTS OF THE POWER SUPPLY SYSTEM METHOD AND ALGORITHM OF RANGING OF RELIABILITY OBJECTS OF THE POWER SUPPLY SYSTEM Farzalye Y.. Azerbajan Scentfc-Research and Desgn-Prospectng Insttute of Energetc ABSTRACT Rangng of objects s wdely appled at the decson of operatonal problems. Howeer, t s spent manly ntutely. There are deeloped method and algorthm of rangng of objects of a power supply system on ndependent parameters of relablty and proftablty of work wth the recommendaton of the basc drectons of mproement of these parameters. INTRODUCTION Rangng of the equpment and deces (objects) of an electro power system on relablty and proftablty of work s wdely used at the decson of many operatonal problems, ncludng at the organzaton of mantenance serce and repar. Known, that relablty and proftablty of work of objects characterzed by a number of parameters (for example, factor of readness, specfc charge of condtonal fuel, etc.). To group objects by way of ncrease of ther relablty and proftablty on each of these parameters does not represent dffculty. Howeer, often the stuaton when these parameters contradct each other obsered. For example, on sze specfc the charge of fuel the power unt can exceed aerage alue on power staton. At the same tme, under the charge of the electrc power n system of own needs - to be t s less, than aerage alue. As an example n table 1 some monthly aerage parameters of eght power unts 300 МWt are resulted. Table 1. Data on work of power unts of power staton N Parameter Index number of the power unt Operatng rato of the 62,8 27,9 68,6 71,3 80,0 76,8 75,9 78,9 establshed capacty, % 2 Aerage loadng, мwт The charge el. energy 4,1 4,4 4,0 3,9 3,5 4,0 3,7 3,5 on own needs, % 4 The specfc charge of condtonal fuel, q/(кwт.c) 374,6 371,0 368,4 369,7 336,7 373,9 363,0 374,2 We wll use these data n the further for an llustraton of methodology of rangng of objects. They concern to a class of dscrete multarate data wth a nomnal scale of measurement [1] as each of noted aboe parameters consdered as an attrbute wth a quanttate scale of measurement of contnuous szes. It s necessary to note, that alongsde wth dscrete multarate data there are also multarate data of contnuous random arables. For example, ntal nformaton for calculaton of parameters of nddual relablty. Features of classfcaton of these data are 78

2 Farzalye Y.. METHOD AND ALGORITHM OF RANGING OF RELIABILITY OBJECTS OF THE POWER SUPPLY SYSTEM consdered n [2,3]. Practcal realzaton of algorthm of rangng of objects s preceded wth transformaton of ntal data Transformaton of ntal data prodes oercomng the dffcultes connected wth natural dstncton of unts of measure and a scale of quanttate estmatons of parameters, dstncton of ther orentaton of change, wth elmnaton of nterrelaton of these parameters. For example, the charge of the electrc power on own needs dffers from the specfc charge of condtonal fuel both on unts of measure, and on scale. The nterconnected parameters at rangng ntal data result not only n ncrease n labour nput of calculatons, but also to erroneous result. Therefore, classfcaton of used parameters on ndependent groups makes one of the prmary goals of transformaton of data. Oercomng of dstncton of unts and scales of measurement of parameters s reached by normalzaton (standardzaton). Normalzaton n practce spent on one of followng formulas: X X 1 ; 2 ; X 3 X (X) ; X X 4 ; X X 5 ; X X 6 L (X) X (X) L (X) where X and -quanttate estmatons of parameters before transformaton; m 1 X m X ; 1 2 (X X ) L (X) (Xmax Xmn ) ; (X) ; Xmax X 1,X2,... Xm; Xmn X 1,X2,... Xm; m- m 1 number of objects. Comparate estmaton of expedency of these transformatons has shown [4]: 1. Transton as a result of the certan transformatons to szes 1, 2 and 3 (unlke 4, 5 and 6 ) does not sole a problem of dstncton of scale of measurement; 2. Szes (X) and L(X) are correlated. The factor of correlaton s sgnfcant, but the sze of scope L(X) demands less calculatons, than an aerage quadratc deaton (X). The sze (X) prodes presence of general populaton of random arables. Real statstcal data concern to statstcal data of multarate type and are small. Data on dstrbuton of realzatons of attrbutes are absent. The nformaton on attrbutes s concentrated n statstcal functon of dstrbuton (s.f.d.) realzatons of attrbutes F ). Adantages of scope L(X) cause expedency of ts applcaton; 3. Comparson of transformatons 5 X X also X X X shows, that factor of correlaton L (X) 6 between ( X X) and X t s essental below, than between (X X ) and L(X); X X Thus, the most effecte should consder transformaton 6. L (X) As follows from table 1, the ector of parameters has a arous orentaton. If operatng rato of the establshed capacty (К E ) and aerage loadng of one power unt (Р A ) smlar parameters for other power unt wth the mnmal rsk of the erroneous decson t s possble to conclude, that exceed relablty and proftablty of work of the frst power unt aboe. The concluson wll be erroneous for the charge electrc power on own needs (E ON ) and the specfc charge of condtonal fuel (S F ). Heurstc character of dscusson of ths queston demands formalzaton of the decson. For what take adantage of concepts and methods of the correlaton analyss. Results of calculatons of factors of correlaton (r) between K E, P A, E ON and S F are resulted n table 2. Calculatons spent under the formula [5] 79

3 Farzalye Y.. METHOD AND ALGORITHM OF RANGING OF RELIABILITY OBJECTS OF THE POWER SUPPLY SYSTEM m 1 r m [П M )][П M )] [ ) ), j1 k1 jk,j k,j Whch, n partcular, testfes to ndependence of factor of correlaton of an orentaton of change of a parameter Table 2. Estmatons of factors of correlaton of parameters Parameters К E Р A E ON S F К E - 0,59-0,83-0,30 P A 0, ,77-0,84 E ON -0,83-0,77-0,52 S F -0,30-0,84 0,52 - Analyss of data of table 2 confrms the dstncton of an orentaton of ectors of attrbutes noted aboe. Orentaton K E and P A dffers from orentaton E ON and S F. Factors of correlaton on sze are sgnfcant and allow assumng nterrelaton of consdered parameters. Casual character of realzatons of parameters causes casual character of obserable nterrelaton. To consder ths feature, crtcal alues of factors of correlaton [ r;r] pay off wth the set sgnfcance alue. Ths problem soled as follows: 1. Two samples of random arables are modeled wth unform dstrbuton n an nteral [0,1]. Number of elements of the frst and the second samples we shall desgnate through m ; 2. Calculate factor of correlaton r between realzatons samples; 3. Items 1 and 2 repeat N tme; 4. On realzatons of factor of correlaton s under constructon s.f.d. F(r) crtcal alues r and r (1 ) for of some sgnfcance alues also are defned ; 5. Under standard programs are establshed n ew of symmetry F(r) dependences r f (m ). These dependences wth the bg assurance look lke of factors R 2, A, B, m, X and r are resulted n table 3 k B r( 1 ) AmV Table 3. Results of calculatons of factors of the equaton r f (m ) k. Some results of calculaton (1-2) R 2 A B Estmatons r at m equal ,990 0,992 0,995 0,999 0,690 0,811 0,880 0,927 0,507 0,624 0,712 0,774 0,442 0,549 0,629 0,700 0,397 0,379 0,444 0,499 0,240 0,310 0,360 0,410 0,168 0,240 0,281 0,320 As follows from table 3 at n5 to establsh dependence between two parameters t s practcally mpossble, snce een at =0,05 absolute alues of factors of correlaton ndependent samples random arables ( r ) r not less than 0,81. At m =8 and =0,05 accordng to table 2 t s possble to approe presence of dependence between K E and E ON, P A and E ON, P A and S F (table.2). At the same tme dependence between K E and P A, K E and S F, and also E ON and S F can be casual. A graphc llustraton of dependence r f (m ) at =0,025 t s resulted n fgure 1. V V 80

4 Farzalye Y.. METHOD AND ALGORITHM OF RANGING OF RELIABILITY OBJECTS OF THE POWER SUPPLY SYSTEM Fg.1. A graphc llustraton of change of crtcal alues of factor of correlaton ndependent samples random arables These cures show, what een at m =50 absolute sze of crtcal alues r and r wth a sgnfcance alue =0,05 not less than 0,2. To elmnate dstncton n an orentaton of ectors of parameters we shall enter nto consderaton an opposte parameter on sense «factor of underexplotaton of the establshed capacty», calculated as К U =1-К E, and nstead of P A we shall enter sze Р A = Р NOM Р A. At small number of objects, probably essental nfluence of casual character of factor of correlaton on result of the analyss of nterrelaton of attrbutes. Valdty of the analyss s proded by comparson of an estmaton r wth bottom nterrelaton of parameters wth probablty takes place ether at r and top (1 ) crtcal alues. Absence of r r r or at r r (1 ). Algorthm rankng objects. Rankng of objects of a power supply system spent n followng sequence: 1. Realzatons of each of the parameters descrbng relablty and proftablty of object, we shall consder as populaton of random arables { ; П } m 2. Let's calculate a number of ther statstcal parameters. Namely, aerage arthmetc alue M ), the mnmal П, mn and maxmal alues П, max, scope L ) under formulas: M П П 1 m 1 ) m П,j j1, mn mn{п } m, max max{п } m L ) [П,max П, mn ] where =1,n ; n - number of parameters Lst of parameters s caused by necessty of representaton of each populaton two samples as ersons of - th attrbute (parameter) wth =1,n ; 3. Realzatons for whch П > M ), we carry to the frst sample (to the frst erson -th an attrbute). Realzatons, for whch П < M ) -(to the second the second erson --th an attrbute). Such classfcaton s wdely used n practce, physcally proed; 81

5 Farzalye Y.. METHOD AND ALGORITHM OF RANGING OF RELIABILITY OBJECTS OF THE POWER SUPPLY SYSTEM 4. For both samples () each data populaton aerage arthmetc alues M,1 ) and M,2 ) wth =1,n are calculated. Thus, the mnmal alue of realzatons - th a parameter of the frst sample П, and the maxmal alue n the second sample- П,2, max. Notce, that essental,1, mn dstncton M,1 ) and M,2 ) are caused by dstncton of number of realzatons samples {m, 1m, 2 }; 5. Under formulas M ) [M ) M )] L ) M V,1,2 ) [M ) M,1,2 )] are calculated normalzaton alues of absolute sze of aerage alue of a relate deaton; 6. The greatest absolute sze of aerage alue of a relate deaton under the formula s defned M,max ) max{ M,j )} j1,2, That defnes sample, whch to the greatest degree dffers from correspondng set. It s necessary to note, that as П M ) П both consdered samples are unpreentable (not,2, max,1, mn representate). In other words, the group of objects that ersons to the greatest degree dffer from other objects on j-oh - th an attrbute allocated; 7. Further from ths group of objects, the subgroup for whch dstncton on - th to an attrbute from the alue aerage on set s een more allocated. Ths subgroup can be allocated under condton of a fndng of the second sgnfcant attrbute. Recognton of a subgroup s spent as follows: 7.1. For the allocated group of objects the matrx of realzatons j-oh ersons к- th an attrbute, where k=1,n, j, and k;n, j, number of realzatons of sample on j-oh ersons - th an attrbute; 7.2. Each realzaton к- th an attrbute wth k=1,n,j, and k n a matrx t s replaced wth realzaton correspondng eeryone object - th an attrbute; 7.3. Accordng to the transformed matrx aerage arthmetc alues of realzatons к-го an attrbute wth k=1,n,j, and k are calculated; 7.4. The greatest sze among these aerage alues defned; 7.5. Ths greatest alue s normalzed and compared wth M, max. If at j=1 t s more, and at j=2 t s less, than M,max classfcaton of data on - th to an attrbute s expedent. Otherwse t s nexpedent; 7.6. If the lead classfcaton has appeared nexpedent: In a bass data on preous stage of classfcaton undertake; From the general lst of objects the objects hang essental features (by results of expedent classfcaton) wthdrawn; We pass to classfcaton of the remaned lst of objects wth constant sequence of the analyss. Control crteron representatty of samples. Aboe at the analyss representate samples we started wth uncondtonal poston conformty wth whch sample t s consdered not representate f at M ) M ) sze П,mn as would exceed M ), and at M ) M ) sze П,max would be less M ) wth =1,n. It has made meanng to not dstract from algorthm of classfcaton of data. Actually the crteron of the control representate samples s more strct, snce a place of condtons П M ) and П M ) partes M ) M ), mn, max L 1,n ), and M,(1 ) ) M ), where M, ) П, mn are checked, and M,(1 ) ) П, max ; 82

6 Farzalye Y.. METHOD AND ALGORITHM OF RANGING OF RELIABILITY OBJECTS OF THE POWER SUPPLY SYSTEM M, ) and M,(1 ) ) - cantl dstrbutons F {M )} for F {M )} 0, 05 and F {M )} 1 0,95 ; M ) - modeled on F ) estmatons of aerage arthmetc alues n realzatons П; n number of realzatons of sample. CONCLUSIONS 1. The method and algorthm of rankng of objects by way of ncrease of relablty and proftablty of ther work s deeloped; 2. In real condtons when the number of the factors nfluencng relablty and proftablty of work of objects s great, classfcaton of objects at an ntute leel leads to essental rsk of the erroneous decson; 3. The automated rankng of objects allows: 3.1. To classfy objects on two groups. Proded that wth ncrease n quanttate alue of parameters of relablty and proftablty of work of objects ther relablty and proftablty ncreases - The frst group ncludes "bad" objects for whch the quanttate estmaton of the most sgnfcant parameters exceeds ther aerage alue on all objects; - The second group ncludes "good" objects, for whch quanttate estmaton of the most sgnfcant parameters less ther aerage alue on all objects; 3.2. To defne the basc ways of ncrease of relablty and proftablty of work REFERENCES 1. Lbo G.S., Method's foreheads of processng of polytypc expermental data. Noosbrsk. A scence, 1981, 160с 2. Farhadzadeh E.M., Farzalye Y.., Muradalye A.. Method and algorthm of the choce optmum number attrbutes descrbng relablty of the equpment of electro nstallatons. Journal: «Relablty: Theory&applcatons». R&RATA (Vol.9 No.2 (33) 2014, June, USA, p Farhadzadeh E.M., Farzalye Y.., Muradalye A.. Some feature of calculaton of parameters of nddual relablty of the equpment and deces of electro nstallatons. Ke, Electronc modelng, Farzalye Y.., Comparson of normalzaton ways at classfcaton ntal data. Journal: «Relablty: Theory&applcatons+. R&RATA (Vol.9 No.2 ( , September, USA, p Lukomsky Y.I., Theory of correlaton and ts applcaton to the analyss of manufacture. State comty ssue,