odreĐivanje funkcije raspoloŽivosti …

ODREĐIVANJE FUNKCIJE RASPOLOŽIVOSTI TERMOENERGETSKOG

SISTEMA TERMOELEKTRANE NIKOLA TESLA BLOK A4

Dragan V Kalaba Milan Lj Đorđević

Zoran J Radaković

Snežana D Kirin

Fakultet tehničkih nauka Univerzitet u Prištini Kneza Miloša 7 Kosovska Mitrovica Srbija

Mašinski fakultet Univerzitet u Beogradu Kraljice Marije 16 Beograd Srbija

Inovacioni centar Mašinskog fakulteta Univerzitet u Beogradu Kraljice Marije 16 Beograd

Srbija

Apstrakt Verovatnosna analiza i procena raspoloživosti termoenergetskih sistema tokom

normalnog radnog veka su značajne za smanjenje broja neplaniranih zastoja i optimizaciju rada

sistema U ovom radu je razmatrana termoelektrana čiji se termoenergetski sistem sastoji od tri

podsistema a procena raspoloživosti i pouzdanosti vršena je na osnovu trinaestogodišnje baze

podataka kvarova Na osnovu eksploatacionog istraživanja raspoloživosti i implementacijom

primenjene matematičke teorije pouzdanosti zasnovane na statistici i zakonima verovatnoće

definisana je funkcija odnosno zakon verovatnoće kojom se karakteriše ponašanje slučajno

promenjive (pojava neplaniranog zastoja) Polazna hipoteza da se verovatnosna raspodela

posmatrane slučajno promenjive veličine matematički približava eksponencijalnoj raspodeli je

potvrđena Dobijeni rezultati pružaju bolji uvid u tekuće stanje sistema kao i mogućnost procene

ponašanja sistema tokom buduće eksploatacije Konačna korist je mogućnost za potencijalna

poboljšanja procedura održavanja složenih sistema u cilju smanjenja pojave neplaniranih zastoja

Ključne reči termoenergetski sistem raspoloživost pouzdanost

DETERMINING THE AVAILABILITY FUNCTION OF THE THERMAL

POWER SYSTEM IN POWER PLANT NIKOLA TESLA BLOCK A4

Dragan V Kalaba Milan Lj Đorđević

Zoran J Radaković

Snežana D Kirin

Faculty of Technical Sciences University of Priština Kneza Miloša 7 Kosovska Mitrovica

Serbia

Faculty of Mechanical Engineering University of Belgrade Kraljice Marije 16 Belgrade

Serbia

Innovation Centre of the Faculty of Mechanical Engineering University of Belgrade

Kraljice Marije 16 Belgrade Serbia

Abstract The probabilistic analysis and availability evaluation of the thermal power systems

during useful life period are helpful in minimizing failures of the system and thus to optimize the

system working The present system of thermal power plant under study consists of three

subsystems and the availability and reliability assessment is based on a thirteen-year failure

database By implementation of mathematical application of theory of reliability based on statistics

and theory of possibility exploitation research of the availability has defined the function or the

probabilistic law according to which the random variable behaves (occurrence of complete

unplanned standstill) The initial hypothesis that the distribution of the observed random variable

approaches exponential distribution has been confirmed Obtained results make possible to acquire

a better knowledge of current system state as well as a more accurate assessment of its behavior

during future exploitation Final benefit is opportunity for potential improvement of complex

system maintenance policies aimed at the reduction of unexpected failure occurrences

Key words Thermal power system availability reliability

1 INTRODUCTION

The thermal power system is a major component of the power plant and outages in the process of

the thermal power system directly cause outages of power plant and disruption in the power

system Thus it follows that power plants must have such a technical solution that will work in the

process to give maximum availability and reliability

Despite the use of modern methods of design standard elements (repeatedly proven to work

and tested for a long time) new materials computer applications in process control and the like

with an increase in unit power of the thermal power system the reduction of availability has become

evident Therefore one of the most important tasks imposed on the manufacturers and users of the

thermal power systems is a constant urge to increase its availability as the basic precondition for

good exploitation

This paper presents an exploitation research on the availability of thermal power system in

power plant Nikola Tesla Block A4 (TENT-A4) which is conducted in the period from 1996 to

2008 The applied research and the acquired results are yet another contribution to the methods for

determining the availability of thermal power systems

The thermal power system is represented as a set of three subsystems steam turbines fossil

fuel boiler and three-phase alternator We adopted control limits in order to determine the

transmission limits of the thermal power subsystems within the thermal scheme [1] Simplified

scheme of the thermal power plant with control limits represented in an enclosed border line is

given in fig 1 The control limit that encloses the thermal power system does not encompass

systems for storage and delivery of fuel systems for collecting and treatment of cooling water the

block transformer and the ash dump

Figure 1 Scheme of thermal power plant system

2 AVAILABILITY

In the study of the availability time of the system (hereafter referred to as availability) we shall take

into account only two basic system states 1) operational state (Up state) and 2) state of total

standstill (Down state) caused by repairs (include active repair time logistics and organisational

time) and external influences These two states are in a relation established between the functions of

criteria and working ability resulting in a series of successive changes of both working and total

standstill regimes

In accordance with the definitions given by standard ISO 8402 SRBS [2] we shall determine

both the own and operational availability at some given time interval ΔT The function of own

availability for a given time interval during useful period of life and for continuous changes may be

represented by exponential law (with time independent failure rate as a most common assumption

in such complex systems) [3]

(1)

For interruptible changes it is important to define the time structure of thermal energy system

in order to calculate the function of operational availability at time interval of interest [3]

ii

i

k

jii

k

jii

k

jii

iTnTr

Tr

TnzTpzTrezTa

TrezTa

tA

11

1

(2)

If external influences are not taken into account then the function of own availability is

calculated according to

1 1

1 1 1 1 1 1

1 1

1 1exp

1 1 1 1 1 1

k k

i i

j j

ik k k k k ki

i i i i i i

j j j j j j

Ta Tnzn n

A T T

Ta Tnz Ta Tnz Ta Tnzn n n n n n

(3)

For a sufficient time duration we may calculate the permanent operational availability

according to

Tk

Tn

TnTr

TrA s

ss

s

10

(4)

The power availability at any given time is the ratio between available and maximal

continuous power at i-th time period

i

ii

i

ii

Pt

ezPrPa

Pt

PrPA

1 (5)

The energy availability is defined as the ratio of total energy produced and theoretical

production capacity For a specified interval of observation the following applies

0

Pri i i i

i i i

i i

Ta Trez Pa ezA E A T A P

Tk Pt

ii

iii

ii

ii

ii

ii

PtTk

ezPrPaTrez

PtTk

ezPrTa

PtTk

PaTa

i

i

i

i

i

i

i

i

i

i

Et

Erez

Et

Ea

Et

Ehr

Et

Etr

Ek

Ea ni 21 (6)

exp( ( ))A t t

k

ji TajPajPadtEa

1 (7)

k

ji TkjPtjPtdtEt

1

ki 321 (8)

k

jjji TaezPrezdtPrEtr

1

ni 321 (9)

k

jjji TrezezPrPadtezPrPaEhr

1

k

jjji TrezPtEhr

1 (10)

It is obvious that energy availability takes into account all working states with reduced

capacity for a certain period of time while time availability takes into only complete standstills

21 Determining availability functions of the thermal power system in TENT-A4

Ensuring reliable operation of thermal power system is a complex task since it depends on

numerous components In order to attain a certain pattern in the behaviour of these components

extensive and time consuming research is needed Because this research of the availability and

reliability is based on exploitation investigations it was necessary to possess all relevant data on the

exploitation history of these facilities for determining the actual indicators and characteristics The

main source of information are operational records which are in legal possession of TENT A

Obrenovac The only problem about these operational reports was to determine the active duration

of repairs since reports do not contain time structure of maintenance procedures For this reason the

active duration of repairs in this paper will be equal to the duration of maintenance procedures

The properties and behaviour of all technical systems are by nature highly stochastic

quantities and processes what is one of the most important features of the reliability concept It

means that all information related to the availability of thermal power system in TENT-A4 are

random variables subjected to specific laws of probability Therefore collected data could be

processed only with the help of statistical mathematics Necessary data for determining availability

and reliability indicators for subsystems (turbine boiler generator) and the whole system are

presented in tab 1 2 3 and 4

Operating time intervals that include all data required for system analysis are defined for one

year periods or 8760 working hours for the period from 1996 until 2008

Table 1 Exploitation results Subsystem 1- turbine

i iTk 1Ti iT iTa iTpz iTnz iTrez iTr iNn

n

iiNn

1

iNr if iF iR i sit0

n

isi

t1

0 i

tf 0 i

tO 0 si

[-] [year] h h h h h h h [-] [-] [-] [-] [-] [-] [-] h h [-] [-] [-]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

1 1996 0 8760 5456 219925 2306 108131 653731 1 1 18 005 005 095 00555 2306 2306 01421 01421 00434

2 1997 8760 17520 6962 107838 439 71443 767943 1 2 17 005 01 09 00588 439 2745 00261 01682 02358

3 1998 17520 26280 6756 106225 209 93934 769534 1 3 16 005 015 085 00625 209 2954 00126 01808 04868

4 1999 26280 35040 5894 212636 059 73835 663235 1 4 15 005 02 08 00666 059 3053 00022 01830 16949

5 2000 35040 43800 6584 134510 11203 71847 730247 3 7 12 015 035 065 025 3719 6812 02290 04120 00269

6 2001 43800 52560 6533 73354 6751 142545 795845 1 8 11 005 04 06 00909 6751 10603 04153 08273 00148

7 2002 52560 61320 7176 74601 0 83759 801359 0 8 11 0 04 06 0 0 13554 0 08273 -

8 2003 61320 70080 7234 86217 1936 64407 787807 3 11 8 015 055 045 0375 630 14224 00381 08654 01587

9 2004 70080 78840 7035 116957 10 55403 758903 1 12 7 005 06 04 01428 100 15324 00062 08716 0

10 2005 78840 87600 7172 90845 107 67808 785008 2 14 5 010 07 03 04 034 15358 00012 08728 18182

11 2006 87600 96360 7113 50839 0 113821 825121 0 14 5 0 07 03 0 0 15358 0 08728 -

12 2007 96360 105120 1878 643039 6848 38233 226033 4 18 1 021 091 009 4 1712 16110 01054 09782 00581

13 2008 105120 113880 8443 0 105 31545 875845 1 19 0 005 096 004 +infin 105 16215 00064 09846 09259

Remark 107838 is 1078 hours and 38 minutes

Table 2 Exploitation results Subsystem 2 - boiler


n

iiNn

1

iNr if iF iR i sit0

n

isi

t1

0 i

tf 0 i

tO 0 si

[-] [year] h h h h h h h [-] [-] [-] [-] [-] [-] [-] h h [-] [-] [-]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

1 1996 0 8760 5456 219925 59418 51017 596617 14 14 142 009 009 091 0098 4226 4226 00788 00788 00236

2 1997 8760 17520 6962 107838 52028 19854 716054 10 24 132 006 015 085 0075 5203 9429 00967 01755 00192

3 1998 17520 26280 6756 106225 58711 35425 711025 12 36 120 007 022 078 01 4857 14326 00910 02665 00204

4 1999 26280 35040 5894 212636 23731 50153 639553 7 43 113 004 026 074 0062 3355 17731 00631 03296 00294

5 2000 35040 43800 6584 13451 36522 46528 7054928 12 55 101 007 033 067 0119 2035 19806 00383 03679 00485

6 2001 43800 52560 6533 73354 114052 35314 688614 23 78 78 015 048 052 0295 4937 24743 00922 04601 00202

7 2002 52560 61320 7176 74601 59519 24240 741840 16 94 62 010 058 042 0258 3711 28454 00691 05292 00269

8 2003 61320 70080 7234 86217 38604 27739 751139 10 104 52 006 064 036 0192 3834 32328 00717 06009 00259

9 2004 70080 78840 7035 116957 49723 5740 709240 12 116 40 007 071 029 03 4129 36457 00771 06780 00241

10 2005 78840 87600 7172 90845 39238 28637 745837 12 128 28 007 078 022 0428 3243 39740 00607 07387 00306

11 2006 87600 96360 7113 50839 48510 65311 776611 16 144 12 010 088 012 1333 3018 42758 00562 07949 00330

12 2007 96360 105120 1878 643039 17039 28042 215842 2 146 10 001 089 011 02 8520 51318 01585 09534 00117

13 2008 105120 113880 8443 0 25104 6556 850856 10 156 0 006 095 005 +infin 2505 53823 00465 09999 00399

Table 3 Exploitation results Subsystem 3 - generator

i iTk 1iT iT iTa iTpz iTnz iTrez iTr iNn

n

iiNn

1

iNr if iF iR i sit0

n

isi

t1

0 i

tf 0 i

tO 0 si

[-] [year] h h h h h h h [-] [-] [-] [-] [-] [-] [-] h h [-] [-] [-]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

1 1996 0 8760 5456 219925 0 110435 656035 0 0 16 0 0 1 0 0 0 0 0 -

2 1997 8760 17520 6962 107838 431 71458 767653 2 2 14 012 012 088 0143 216 216 00082 00082 04348

3 1998 17520 26280 6756 106225 134 94001 769601 1 3 13 006 018 082 0077 134 350 00136 00218 06250

4 1999 26280 35040 5894 212636 13408 60516 649916 1 4 12 006 024 076 0083 13408 13458 04173 04391 00074

5 2000 35040 43800 6584 13451 0 83050 741450 0 4 12 0 024 076 0 0 13458 0 04391 -

6 2001 43800 52560 6533 73354 414 148852 802152 2 6 10 012 036 064 02 207 13705 00077 04468 04695

7 2002 52560 61320 7176 74601 237 83522 801122 1 7 9 006 042 058 0111 237 13942 00095 04563 03846

8 2003 61320 70080 7234 86217 129 66214 789614 1 8 8 006 048 052 0125 129 14111 00054 04617 06667

9 2004 70080 78840 7035 116957 4849 50614 754114 1 9 7 006 054 046 0143 4849 19000 01742 06359 00205

10 2005 78840 87600 7172 90845 3050 64825 782025 1 10 6 006 06 04 0166 3050 22050 01100 07459 00324

11 2006 87600 96360 7113 50839 5437 108344 819644 1 11 5 006 066 034 02 5437 27527 01949 09408 00183

12 2007 96360 105120 1878 643039 0 45121 232921 0 11 5 0 066 034 0 0 27527 0 09408 -

13 2008 105120 113880 8443 0 2153 29507 873807 5 16 0 031 097 003 +infin 445 28012 00164 09572 02174

Table 4 Exploitation results System

i iTk 1iT iT iTa iTpz iTnz iTrez iTr iTpz

n

iiNn

1

iNr if iF iR i iPA iEA

[-] [year] h h h h h h h h [-] [-] [-] [-] [-] [-] [MW]

[GWh]

1 2 3 4 5 6 7 8 9 10 12 13 14 15 16 17 18 19

1 1996 0 8760 5456 219925 61724 15 48711 594311 15 176 008 008 092 00852 2329 1384171

2 1997 8760 17520 6962 107838 52938 13 18944 715144 28 163 007 015 085 00800 24486 1751165

3 1998 17520 26280 6756 106225 59054 14 35041 710641 42 149 007 022 078 00940 24297 1721025

4 1999 26280 35040 5894 212636 37238 9 36646 626046 51 140 005 027 073 00643 23376 1463325

5 2000 35040 43800 6584 13451 47725 15 35325 693725 66 125 008 035 065 01200 23821 1652338

6 2001 43800 52560 6533 73354 121257 26 28009 681309 92 99 014 049 051 02626 23941 1631136

7 2002 52560 61320 7176 74601 59756 17 24003 741603 109 82 009 058 042 02073 23120 1714595

8 2003 61320 70080 7234 86217 40509 14 25834 749234 123 68 007 065 035 02059 23500 1760754

9 2004 70080 78840 7035 116957 54712 14 751 704251 137 54 007 072 028 02593 22609 1592329

10 2005 78840 87600 7172 90845 42435 15 25440 742640 152 39 008 080 020 03846 23599 1752617

11 2006 87600 96360 7113 50839 99349 17 14432 725732 169 22 009 089 011 07727 23468 1703202

12 2007 96360 105120 1878 643039 23927 6 21154 208954 175 16 003 092 008 0375 23675 494791

13 2008 105120 113880 8443 0 27257 16 4403 848703 191 0 008 100 0 +infin 26318 2233622

22 Plotting availability factors and indicators

Graphical representation of availability indicators obtained from exploitation research results are

given in Figures 2 3 4 and 5

Figure 2 Empirical reliability and unreliability

Figure 3 Empirical mainainability

Figure 4 Number of delays in the i ndash th period

Figure 5 Failure density distribution

Figure 6 Failure rate distribution

23 Determination of mean availability indices and maintainability

Based on data listed in tab 1 2 3 and 4 these values shall be determined according to the

following functions [4] (for calculated values see tab 5)

mean operating time without outages

n

i

k

jjjs NnTa

knTa

1 1

11

(11)

mean value of failure rate sn

sTa

1

(12)

median duration of maintenance interventions 0 0

1

1n

s si

int t

(13)

median intensity of maintenance interventions s

st0

1

(14)

mean available time

n

iis Tr

nTr

1

1

(15)

Table 5 Calculated values of mean availability indices and maintainability

No Component sTa 510xs 0st 310xs sTr

h 1h h 1h h

1 Subsystem 1 - turbine 538655 186 1230 813 724951

2 Subsystem 2 - boiler 60815 1644 4122 242 680631

3 Subsystem 3 - generator 568137 176 2525 394 726145

4 System 45419 2200 3447 288 672456

24 Determination of availability functions

Using data given in tab 5 following functions will be determined

own availability

exp( )s ss ss

s s s s

A T T

(16)

permanent operating availability

Tk

Tn

TnTr

TrA s

ss

s

10

(17)

1) Subsystem 1 - turbine

09976 00023exp( 008018 )A T T (18)

A0 = 08276

2) Subsystem 2 - boiler

09368 00632exp( 0025844 )A T T (19)

A0 = 0777

3) Subsystem 3 - generator

09956 0 0044exp( 0039578 )A T T (20)

A0 = 0829

4) System

09287 00713exp( 0 0310 )A T T (21)

A0 = 07677

Figure 7 Own availability functions

Figure 8 Power availability

Figure 9 Energy availability

25 Determination of the maintainability function

Based on data given in Table 5 the maintainability function is determined by

0 01 exp( )O t ts (22)

subsystem 1ndashturbine 0 01 exp( 0 0813 )O t t (23)

subsystem 1ndashboiler 0 01 exp( 0 0242 )O t t (24)

subsystem 1ndashgenerator 0 01 exp( 0 0394 )O t t (25)

system 0 01 exp( 0 0288 )O t t (26)

Figure 10 Maintainability functions

3 DETERMINING THE THEORETICAL RELIABILITY FUNCTION

The highest level of output information is made by selection of distribution law for a random

variable For this purpose we have chosen the two-parameter Weibull distribution [5] and

appropriate graphical method Principles of constructing probability plotting graph paper and

empirical data entry are described by many authors [6] so that it will not be described

Figure 11 Weibull probability ploting paper for two-parameter distribution

0

02 03 04 0806 2 3 4 5 6 7 8 20 40 60 8030

02

03

05

1

2

3

5

10

20

30

40

50

60632

70

80

999

99b

90

1

2

3

4

5

7

8

9

01P

15133

70731

01 1 10 100

t 102 h

F(t)

According to obtained shape and scale parameters (η = 70731 β = 15133) and values given

in table next to plotting paper (fig 11) we can determine the total operational time of system Tur

15133b 0908Tur

0908 70731 64224Tur years

and analytical expressions which represent the distribution laws of the observed random variable

[7]

reliability 15133exp 19307R t t (27)

unreliability 151331 exp 19307F t t (28)

failure density 05133 1513300784 exp 19307f t t t (29)

failure rate 0513300784t t

(30)

After plotting times and their corresponding rank values in Weibull probabilistic paper

(fig 8) it could be noted that those points approximately fit a straight line what confirms the

starting hypothesis that the distribution of the observed random variable approaches the Weibull

distribution with satisfactory accuracy Moreover due to the value of scale parameter β = 15133

the Weibull distribution approaches the exponential distribution Aside to the theoretical basis this

completely justifies the relation to the exponential model

Comparison of exploitation and selected theoretical form of reliability and unreliability

functions is shown in fig 12

Figure 12 Exploitation e and theoretical t forms of system reliability function

4 CONCLUSIONS

Processed data along with determined exploitation and theoretical characteristics of availability and

reliability have led us to the following conclusions

thermal power system in TENT-А4 has a high degree of availability and reliability

determined by functions

09287 00713exp( 0 0310 )A T T

15133exp 19307R t t

where the long-term operational availability is 767700 A

the system is fit for maintenance the maintenance service is efficient in failures eliminating

the mean time to repair is determined to be 3447 hours and the maintainability function is

0 01 exp( 0 0288 )O t t

based on the analysis of the failures intensity we conclude that the mean time to failure for

the system is 45419 hours the most influential causes for standstills are the outages of the

boiler installation amounting to 82 of all down times

total operational time (life) determined for thermal power system in TENT-A4 according to

selected theoretical failure distribution is 64224 years or 43145 hours due to the fact that

the period between two major overhauls was almost 8-years (1996ndash2004) or 51838 hours of

operation the obtained results are in full congruence with the maintenance interventions in the

observed period

the initial hypothesis that the distribution of the observed random variable approaches

exponential distribution has been confirmed

according to exploitation research the mean available energy of thermal power system in

TENT-А4 is

2361604EA s GWh

NOMENCLATURE

si

A P - mean power available [MW]

A(E)si - mean energy available (=A(P)siTrsi) [GWh]

Fi - unrealiability ( 1

nfi

i ) [-]

fi - failure density ( 1

nNn Nni i

i

) [-]

MR - medial rang (=(j-03)(n+04)) [-]

n - total number of failures in the reported period [-]

Nn - total number of failures [-]

1

n

i

i

Nn

- cumulative sum of failures (1

n

i

i

j Nn

)[-]

Nt - reverse cumulative sum of failures [-]

Ri - reliability (=1-Fi ) [-]

Ta - engaged time [h]

Tk - calendar time [year]

Tnz - total time of unplanned outages [h]

Tpz - total time of planned outages [h]

Tr - mean time available (=Ta+Trez) [h]

Trez - total time in storage state (=Tk-(Ta+Tpz+Tnz)) [h]

0sit

- mean duration of maintenance (=1

nTnz j

j

Nn j ) [h]

0t i - empirical maintainability ( 01

nf t

ii

) [-]

Greek letters

β - shape parameter [-]

η - scale parameter [-]

λ - failure rate [-]

μ - repair rate [-]

Subscripts

i - number of operating intervals of the system

e - exploitation

t - theoretical

REFERENCES

[1] Kalaba D Thermal power system reliability (in Serbian) University of Priština Faculty of

Tehnical Sciences Kosovska Mitrovica Kosovska Mitrovica Serbia 2011

[2] SRPS АА2005

[3] Ebeling C An Introduction to Reliability and Maintainability Engineering McGraw-Hill

New York USA 1997

[4] Barlow R Clarotti C Spizzichino F Reliability and decision making Chapman and Hall

New York USA 1993

[5] Kalaba D Đorđević M Contribution to methods for determining the theoretical reliability

function of thermal power systems (in Serbian) Proceedings Strategic Managemant 2012

Bor Serbia May 25-27 pp 677-686

[6] Zio E An Introduction to the Basics of Reliability and Risk Analysis World Scientific

Publishing Co Inc Singapore 2007

[7] Milčić D Reliability of mechanical systems (in Serbian) Faculty of Mechanical Engineering

University of Niš Niš Serbia 2005

[8] Milčić D et al Exploitation researches of the thermo ndash energetic systems availability

Proceedings 15th

Symposium on Thermal Science and Engineering of Serbia Sokobanja

Serbia 2011 pp 905-917

[9] Kalaba D et al Determining the reliability of thermal power system in bdquoGackoldquo thermal

power Plant (in Serbian) Elektroprivreda 3 (2010) pp 222-232

1 INTRODUCTION

The thermal power system is a major component of the power plant and outages in the process of

the thermal power system directly cause outages of power plant and disruption in the power

system Thus it follows that power plants must have such a technical solution that will work in the

process to give maximum availability and reliability

Despite the use of modern methods of design standard elements (repeatedly proven to work

and tested for a long time) new materials computer applications in process control and the like

with an increase in unit power of the thermal power system the reduction of availability has become

evident Therefore one of the most important tasks imposed on the manufacturers and users of the

thermal power systems is a constant urge to increase its availability as the basic precondition for

good exploitation

This paper presents an exploitation research on the availability of thermal power system in

power plant Nikola Tesla Block A4 (TENT-A4) which is conducted in the period from 1996 to

2008 The applied research and the acquired results are yet another contribution to the methods for

determining the availability of thermal power systems

The thermal power system is represented as a set of three subsystems steam turbines fossil

fuel boiler and three-phase alternator We adopted control limits in order to determine the

transmission limits of the thermal power subsystems within the thermal scheme [1] Simplified

scheme of the thermal power plant with control limits represented in an enclosed border line is

given in fig 1 The control limit that encloses the thermal power system does not encompass

systems for storage and delivery of fuel systems for collecting and treatment of cooling water the

block transformer and the ash dump

Figure 1 Scheme of thermal power plant system

2 AVAILABILITY

In the study of the availability time of the system (hereafter referred to as availability) we shall take

into account only two basic system states 1) operational state (Up state) and 2) state of total

standstill (Down state) caused by repairs (include active repair time logistics and organisational

time) and external influences These two states are in a relation established between the functions of


standstill regimes






(1)



ii

i

k

jii

k

jii

k

jii

iTnTr

Tr

TnzTpzTrezTa

TrezTa

tA

11

1

(2)



1 1

1 1 1 1 1 1

1 1

1 1exp

1 1 1 1 1 1

k k

i i

j j

ik k k k k ki

i i i i i i

j j j j j j

Ta Tnzn n

A T T


(3)


according to

Tk

Tn

TnTr

TrA s

ss

s

10

(4)



i

ii

i

ii

Pt

ezPrPa

Pt

PrPA

1 (5)



0

Pri i i i

i i i

i i


Tk Pt

ii

iii

ii

ii

ii

ii

PtTk

ezPrPaTrez

PtTk

ezPrTa

PtTk

PaTa

i

i

i

i

i

i

i

i

i

i

Et

Erez

Et

Ea

Et

Ehr

Et

Etr

Ek

Ea ni 21 (6)

exp( ( ))A t t

k

ji TajPajPadtEa

1 (7)

k

ji TkjPtjPtdtEt

1

ki 321 (8)

k


1

ni 321 (9)

k


1

k

jjji TrezPtEhr

1 (10)
























n

iiNn

1

iNr if iF iR i sit0

n

isi

t1

0 i

tf 0 i

tO 0 si

[-] [year] h h h h h h h [-] [-] [-] [-] [-] [-] [-] h h [-] [-] [-]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

1 1996 0 8760 5456 219925 2306 108131 653731 1 1 18 005 005 095 00555 2306 2306 01421 01421 00434

2 1997 8760 17520 6962 107838 439 71443 767943 1 2 17 005 01 09 00588 439 2745 00261 01682 02358

3 1998 17520 26280 6756 106225 209 93934 769534 1 3 16 005 015 085 00625 209 2954 00126 01808 04868

4 1999 26280 35040 5894 212636 059 73835 663235 1 4 15 005 02 08 00666 059 3053 00022 01830 16949

5 2000 35040 43800 6584 134510 11203 71847 730247 3 7 12 015 035 065 025 3719 6812 02290 04120 00269

6 2001 43800 52560 6533 73354 6751 142545 795845 1 8 11 005 04 06 00909 6751 10603 04153 08273 00148

7 2002 52560 61320 7176 74601 0 83759 801359 0 8 11 0 04 06 0 0 13554 0 08273 -

8 2003 61320 70080 7234 86217 1936 64407 787807 3 11 8 015 055 045 0375 630 14224 00381 08654 01587

9 2004 70080 78840 7035 116957 10 55403 758903 1 12 7 005 06 04 01428 100 15324 00062 08716 0

10 2005 78840 87600 7172 90845 107 67808 785008 2 14 5 010 07 03 04 034 15358 00012 08728 18182

11 2006 87600 96360 7113 50839 0 113821 825121 0 14 5 0 07 03 0 0 15358 0 08728 -

12 2007 96360 105120 1878 643039 6848 38233 226033 4 18 1 021 091 009 4 1712 16110 01054 09782 00581

13 2008 105120 113880 8443 0 105 31545 875845 1 19 0 005 096 004 +infin 105 16215 00064 09846 09259




n

iiNn

1

iNr if iF iR i sit0

n

isi

t1

0 i

tf 0 i

tO 0 si

[-] [year] h h h h h h h [-] [-] [-] [-] [-] [-] [-] h h [-] [-] [-]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

1 1996 0 8760 5456 219925 59418 51017 596617 14 14 142 009 009 091 0098 4226 4226 00788 00788 00236

2 1997 8760 17520 6962 107838 52028 19854 716054 10 24 132 006 015 085 0075 5203 9429 00967 01755 00192

3 1998 17520 26280 6756 106225 58711 35425 711025 12 36 120 007 022 078 01 4857 14326 00910 02665 00204

4 1999 26280 35040 5894 212636 23731 50153 639553 7 43 113 004 026 074 0062 3355 17731 00631 03296 00294

5 2000 35040 43800 6584 13451 36522 46528 7054928 12 55 101 007 033 067 0119 2035 19806 00383 03679 00485

6 2001 43800 52560 6533 73354 114052 35314 688614 23 78 78 015 048 052 0295 4937 24743 00922 04601 00202

7 2002 52560 61320 7176 74601 59519 24240 741840 16 94 62 010 058 042 0258 3711 28454 00691 05292 00269

8 2003 61320 70080 7234 86217 38604 27739 751139 10 104 52 006 064 036 0192 3834 32328 00717 06009 00259

9 2004 70080 78840 7035 116957 49723 5740 709240 12 116 40 007 071 029 03 4129 36457 00771 06780 00241

10 2005 78840 87600 7172 90845 39238 28637 745837 12 128 28 007 078 022 0428 3243 39740 00607 07387 00306

11 2006 87600 96360 7113 50839 48510 65311 776611 16 144 12 010 088 012 1333 3018 42758 00562 07949 00330

12 2007 96360 105120 1878 643039 17039 28042 215842 2 146 10 001 089 011 02 8520 51318 01585 09534 00117

13 2008 105120 113880 8443 0 25104 6556 850856 10 156 0 006 095 005 +infin 2505 53823 00465 09999 00399



n

iiNn

1

iNr if iF iR i sit0

n

isi

t1

0 i

tf 0 i

tO 0 si

[-] [year] h h h h h h h [-] [-] [-] [-] [-] [-] [-] h h [-] [-] [-]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

1 1996 0 8760 5456 219925 0 110435 656035 0 0 16 0 0 1 0 0 0 0 0 -

2 1997 8760 17520 6962 107838 431 71458 767653 2 2 14 012 012 088 0143 216 216 00082 00082 04348

3 1998 17520 26280 6756 106225 134 94001 769601 1 3 13 006 018 082 0077 134 350 00136 00218 06250

4 1999 26280 35040 5894 212636 13408 60516 649916 1 4 12 006 024 076 0083 13408 13458 04173 04391 00074

5 2000 35040 43800 6584 13451 0 83050 741450 0 4 12 0 024 076 0 0 13458 0 04391 -

6 2001 43800 52560 6533 73354 414 148852 802152 2 6 10 012 036 064 02 207 13705 00077 04468 04695

7 2002 52560 61320 7176 74601 237 83522 801122 1 7 9 006 042 058 0111 237 13942 00095 04563 03846

8 2003 61320 70080 7234 86217 129 66214 789614 1 8 8 006 048 052 0125 129 14111 00054 04617 06667

9 2004 70080 78840 7035 116957 4849 50614 754114 1 9 7 006 054 046 0143 4849 19000 01742 06359 00205

10 2005 78840 87600 7172 90845 3050 64825 782025 1 10 6 006 06 04 0166 3050 22050 01100 07459 00324

11 2006 87600 96360 7113 50839 5437 108344 819644 1 11 5 006 066 034 02 5437 27527 01949 09408 00183

12 2007 96360 105120 1878 643039 0 45121 232921 0 11 5 0 066 034 0 0 27527 0 09408 -

13 2008 105120 113880 8443 0 2153 29507 873807 5 16 0 031 097 003 +infin 445 28012 00164 09572 02174



n

iiNn

1


[-] [year] h h h h h h h h [-] [-] [-] [-] [-] [-] [MW]

[GWh]

1 2 3 4 5 6 7 8 9 10 12 13 14 15 16 17 18 19

1 1996 0 8760 5456 219925 61724 15 48711 594311 15 176 008 008 092 00852 2329 1384171

2 1997 8760 17520 6962 107838 52938 13 18944 715144 28 163 007 015 085 00800 24486 1751165

3 1998 17520 26280 6756 106225 59054 14 35041 710641 42 149 007 022 078 00940 24297 1721025

4 1999 26280 35040 5894 212636 37238 9 36646 626046 51 140 005 027 073 00643 23376 1463325

5 2000 35040 43800 6584 13451 47725 15 35325 693725 66 125 008 035 065 01200 23821 1652338

6 2001 43800 52560 6533 73354 121257 26 28009 681309 92 99 014 049 051 02626 23941 1631136

7 2002 52560 61320 7176 74601 59756 17 24003 741603 109 82 009 058 042 02073 23120 1714595

8 2003 61320 70080 7234 86217 40509 14 25834 749234 123 68 007 065 035 02059 23500 1760754

9 2004 70080 78840 7035 116957 54712 14 751 704251 137 54 007 072 028 02593 22609 1592329

10 2005 78840 87600 7172 90845 42435 15 25440 742640 152 39 008 080 020 03846 23599 1752617

11 2006 87600 96360 7113 50839 99349 17 14432 725732 169 22 009 089 011 07727 23468 1703202

12 2007 96360 105120 1878 643039 23927 6 21154 208954 175 16 003 092 008 0375 23675 494791

13 2008 105120 113880 8443 0 27257 16 4403 848703 191 0 008 100 0 +infin 26318 2233622













n

i

k

jjjs NnTa

knTa

1 1

11

(11)


sTa

1

(12)


1

1n

s si

int t

(13)


st0

1

(14)

mean available time

n

iis Tr

nTr

1

1

(15)



h 1h h 1h h




4 System 45419 2200 3447 288 672456



own availability

exp( )s ss ss

s s s s

A T T

(16)


Tk

Tn

TnTr

TrA s

ss

s

10

(17)


09976 00023exp( 008018 )A T T (18)

A0 = 08276


09368 00632exp( 0025844 )A T T (19)

A0 = 0777


09956 0 0044exp( 0039578 )A T T (20)

A0 = 0829

4) System

09287 00713exp( 0 0310 )A T T (21)

A0 = 07677






0 01 exp( )O t ts (22)




system 0 01 exp( 0 0288 )O t t (26)








0

02 03 04 0806 2 3 4 5 6 7 8 20 40 60 8030

02

03

05

1

2

3

5

10

20

30

40

50

60632

70

80

999

99b

90

1

2

3

4

5

7

8

9

01P

15133

70731

01 1 10 100

t 102 h

F(t)



15133b 0908Tur

0908 70731 64224Tur years


[7]





(30)










4 CONCLUSIONS





09287 00713exp( 0 0310 )A T T

15133exp 19307R t t




0 01 exp( 0 0288 )O t t








observed period




TENT-А4 is

2361604EA s GWh

NOMENCLATURE

si




nfi

i ) [-]


nNn Nni i

i

) [-]

MR - medial rang (=(j-03)(n+04)) [-]



1

n

i

i

Nn


n

i

i

j Nn

)[-]









0sit


nTnz j

j

Nn j ) [h]


nf t

ii

) [-]

Greek letters





Subscripts


e - exploitation

t - theoretical

REFERENCES



[2] SRPS АА2005


New York USA 1997


New York USA 1993









Proceedings 15th


Serbia 2011 pp 905-917




standstill regimes






(1)



ii

i

k

jii

k

jii

k

jii

iTnTr

Tr

TnzTpzTrezTa

TrezTa

tA

11

1

(2)



1 1

1 1 1 1 1 1

1 1

1 1exp

1 1 1 1 1 1

k k

i i

j j

ik k k k k ki

i i i i i i

j j j j j j

Ta Tnzn n

A T T


(3)


according to

Tk

Tn

TnTr

TrA s

ss

s

10

(4)



i

ii

i

ii

Pt

ezPrPa

Pt

PrPA

1 (5)



0

Pri i i i

i i i

i i


Tk Pt

ii

iii

ii

ii

ii

ii

PtTk

ezPrPaTrez

PtTk

ezPrTa

PtTk

PaTa

i

i

i

i

i

i

i

i

i

i

Et

Erez

Et

Ea

Et

Ehr

Et

Etr

Ek

Ea ni 21 (6)

exp( ( ))A t t

k

ji TajPajPadtEa

1 (7)

k

ji TkjPtjPtdtEt

1

ki 321 (8)

k


1

ni 321 (9)

k


1

k

jjji TrezPtEhr

1 (10)
























n

iiNn

1

iNr if iF iR i sit0

n

isi

t1

0 i

tf 0 i

tO 0 si

[-] [year] h h h h h h h [-] [-] [-] [-] [-] [-] [-] h h [-] [-] [-]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

1 1996 0 8760 5456 219925 2306 108131 653731 1 1 18 005 005 095 00555 2306 2306 01421 01421 00434

2 1997 8760 17520 6962 107838 439 71443 767943 1 2 17 005 01 09 00588 439 2745 00261 01682 02358

3 1998 17520 26280 6756 106225 209 93934 769534 1 3 16 005 015 085 00625 209 2954 00126 01808 04868

4 1999 26280 35040 5894 212636 059 73835 663235 1 4 15 005 02 08 00666 059 3053 00022 01830 16949

5 2000 35040 43800 6584 134510 11203 71847 730247 3 7 12 015 035 065 025 3719 6812 02290 04120 00269

6 2001 43800 52560 6533 73354 6751 142545 795845 1 8 11 005 04 06 00909 6751 10603 04153 08273 00148

7 2002 52560 61320 7176 74601 0 83759 801359 0 8 11 0 04 06 0 0 13554 0 08273 -

8 2003 61320 70080 7234 86217 1936 64407 787807 3 11 8 015 055 045 0375 630 14224 00381 08654 01587

9 2004 70080 78840 7035 116957 10 55403 758903 1 12 7 005 06 04 01428 100 15324 00062 08716 0

10 2005 78840 87600 7172 90845 107 67808 785008 2 14 5 010 07 03 04 034 15358 00012 08728 18182

11 2006 87600 96360 7113 50839 0 113821 825121 0 14 5 0 07 03 0 0 15358 0 08728 -

12 2007 96360 105120 1878 643039 6848 38233 226033 4 18 1 021 091 009 4 1712 16110 01054 09782 00581

13 2008 105120 113880 8443 0 105 31545 875845 1 19 0 005 096 004 +infin 105 16215 00064 09846 09259




n

iiNn

1

iNr if iF iR i sit0

n

isi

t1

0 i

tf 0 i

tO 0 si

[-] [year] h h h h h h h [-] [-] [-] [-] [-] [-] [-] h h [-] [-] [-]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

1 1996 0 8760 5456 219925 59418 51017 596617 14 14 142 009 009 091 0098 4226 4226 00788 00788 00236

2 1997 8760 17520 6962 107838 52028 19854 716054 10 24 132 006 015 085 0075 5203 9429 00967 01755 00192

3 1998 17520 26280 6756 106225 58711 35425 711025 12 36 120 007 022 078 01 4857 14326 00910 02665 00204

4 1999 26280 35040 5894 212636 23731 50153 639553 7 43 113 004 026 074 0062 3355 17731 00631 03296 00294

5 2000 35040 43800 6584 13451 36522 46528 7054928 12 55 101 007 033 067 0119 2035 19806 00383 03679 00485

6 2001 43800 52560 6533 73354 114052 35314 688614 23 78 78 015 048 052 0295 4937 24743 00922 04601 00202

7 2002 52560 61320 7176 74601 59519 24240 741840 16 94 62 010 058 042 0258 3711 28454 00691 05292 00269

8 2003 61320 70080 7234 86217 38604 27739 751139 10 104 52 006 064 036 0192 3834 32328 00717 06009 00259

9 2004 70080 78840 7035 116957 49723 5740 709240 12 116 40 007 071 029 03 4129 36457 00771 06780 00241

10 2005 78840 87600 7172 90845 39238 28637 745837 12 128 28 007 078 022 0428 3243 39740 00607 07387 00306

11 2006 87600 96360 7113 50839 48510 65311 776611 16 144 12 010 088 012 1333 3018 42758 00562 07949 00330

12 2007 96360 105120 1878 643039 17039 28042 215842 2 146 10 001 089 011 02 8520 51318 01585 09534 00117

13 2008 105120 113880 8443 0 25104 6556 850856 10 156 0 006 095 005 +infin 2505 53823 00465 09999 00399



n

iiNn

1

iNr if iF iR i sit0

n

isi

t1

0 i

tf 0 i

tO 0 si

[-] [year] h h h h h h h [-] [-] [-] [-] [-] [-] [-] h h [-] [-] [-]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

1 1996 0 8760 5456 219925 0 110435 656035 0 0 16 0 0 1 0 0 0 0 0 -

2 1997 8760 17520 6962 107838 431 71458 767653 2 2 14 012 012 088 0143 216 216 00082 00082 04348

3 1998 17520 26280 6756 106225 134 94001 769601 1 3 13 006 018 082 0077 134 350 00136 00218 06250

4 1999 26280 35040 5894 212636 13408 60516 649916 1 4 12 006 024 076 0083 13408 13458 04173 04391 00074

5 2000 35040 43800 6584 13451 0 83050 741450 0 4 12 0 024 076 0 0 13458 0 04391 -

6 2001 43800 52560 6533 73354 414 148852 802152 2 6 10 012 036 064 02 207 13705 00077 04468 04695

7 2002 52560 61320 7176 74601 237 83522 801122 1 7 9 006 042 058 0111 237 13942 00095 04563 03846

8 2003 61320 70080 7234 86217 129 66214 789614 1 8 8 006 048 052 0125 129 14111 00054 04617 06667

9 2004 70080 78840 7035 116957 4849 50614 754114 1 9 7 006 054 046 0143 4849 19000 01742 06359 00205

10 2005 78840 87600 7172 90845 3050 64825 782025 1 10 6 006 06 04 0166 3050 22050 01100 07459 00324

11 2006 87600 96360 7113 50839 5437 108344 819644 1 11 5 006 066 034 02 5437 27527 01949 09408 00183

12 2007 96360 105120 1878 643039 0 45121 232921 0 11 5 0 066 034 0 0 27527 0 09408 -

13 2008 105120 113880 8443 0 2153 29507 873807 5 16 0 031 097 003 +infin 445 28012 00164 09572 02174



n

iiNn

1


[-] [year] h h h h h h h h [-] [-] [-] [-] [-] [-] [MW]

[GWh]

1 2 3 4 5 6 7 8 9 10 12 13 14 15 16 17 18 19

1 1996 0 8760 5456 219925 61724 15 48711 594311 15 176 008 008 092 00852 2329 1384171

2 1997 8760 17520 6962 107838 52938 13 18944 715144 28 163 007 015 085 00800 24486 1751165

3 1998 17520 26280 6756 106225 59054 14 35041 710641 42 149 007 022 078 00940 24297 1721025

4 1999 26280 35040 5894 212636 37238 9 36646 626046 51 140 005 027 073 00643 23376 1463325

5 2000 35040 43800 6584 13451 47725 15 35325 693725 66 125 008 035 065 01200 23821 1652338

6 2001 43800 52560 6533 73354 121257 26 28009 681309 92 99 014 049 051 02626 23941 1631136

7 2002 52560 61320 7176 74601 59756 17 24003 741603 109 82 009 058 042 02073 23120 1714595

8 2003 61320 70080 7234 86217 40509 14 25834 749234 123 68 007 065 035 02059 23500 1760754

9 2004 70080 78840 7035 116957 54712 14 751 704251 137 54 007 072 028 02593 22609 1592329

10 2005 78840 87600 7172 90845 42435 15 25440 742640 152 39 008 080 020 03846 23599 1752617

11 2006 87600 96360 7113 50839 99349 17 14432 725732 169 22 009 089 011 07727 23468 1703202

12 2007 96360 105120 1878 643039 23927 6 21154 208954 175 16 003 092 008 0375 23675 494791

13 2008 105120 113880 8443 0 27257 16 4403 848703 191 0 008 100 0 +infin 26318 2233622













n

i

k

jjjs NnTa

knTa

1 1

11

(11)


sTa

1

(12)


1

1n

s si

int t

(13)


st0

1

(14)

mean available time

n

iis Tr

nTr

1

1

(15)



h 1h h 1h h




4 System 45419 2200 3447 288 672456



own availability

exp( )s ss ss

s s s s

A T T

(16)


Tk

Tn

TnTr

TrA s

ss

s

10

(17)


09976 00023exp( 008018 )A T T (18)

A0 = 08276


09368 00632exp( 0025844 )A T T (19)

A0 = 0777


09956 0 0044exp( 0039578 )A T T (20)

A0 = 0829

4) System

09287 00713exp( 0 0310 )A T T (21)

A0 = 07677






0 01 exp( )O t ts (22)




system 0 01 exp( 0 0288 )O t t (26)








0

02 03 04 0806 2 3 4 5 6 7 8 20 40 60 8030

02

03

05

1

2

3

5

10

20

30

40

50

60632

70

80

999

99b

90

1

2

3

4

5

7

8

9

01P

15133

70731

01 1 10 100

t 102 h

F(t)



15133b 0908Tur

0908 70731 64224Tur years


[7]





(30)










4 CONCLUSIONS





09287 00713exp( 0 0310 )A T T

15133exp 19307R t t




0 01 exp( 0 0288 )O t t








observed period




TENT-А4 is

2361604EA s GWh

NOMENCLATURE

si




nfi

i ) [-]


nNn Nni i

i

) [-]

MR - medial rang (=(j-03)(n+04)) [-]



1

n

i

i

Nn


n

i

i

j Nn

)[-]









0sit


nTnz j

j

Nn j ) [h]


nf t

ii

) [-]

Greek letters





Subscripts


e - exploitation

t - theoretical

REFERENCES



[2] SRPS АА2005


New York USA 1997


New York USA 1993









Proceedings 15th


Serbia 2011 pp 905-917



k

ji TajPajPadtEa

1 (7)

k

ji TkjPtjPtdtEt

1

ki 321 (8)

k


1

ni 321 (9)

k


1

k

jjji TrezPtEhr

1 (10)
























n

iiNn

1

iNr if iF iR i sit0

n

isi

t1

0 i

tf 0 i

tO 0 si

[-] [year] h h h h h h h [-] [-] [-] [-] [-] [-] [-] h h [-] [-] [-]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

1 1996 0 8760 5456 219925 2306 108131 653731 1 1 18 005 005 095 00555 2306 2306 01421 01421 00434

2 1997 8760 17520 6962 107838 439 71443 767943 1 2 17 005 01 09 00588 439 2745 00261 01682 02358

3 1998 17520 26280 6756 106225 209 93934 769534 1 3 16 005 015 085 00625 209 2954 00126 01808 04868

4 1999 26280 35040 5894 212636 059 73835 663235 1 4 15 005 02 08 00666 059 3053 00022 01830 16949

5 2000 35040 43800 6584 134510 11203 71847 730247 3 7 12 015 035 065 025 3719 6812 02290 04120 00269

6 2001 43800 52560 6533 73354 6751 142545 795845 1 8 11 005 04 06 00909 6751 10603 04153 08273 00148

7 2002 52560 61320 7176 74601 0 83759 801359 0 8 11 0 04 06 0 0 13554 0 08273 -

8 2003 61320 70080 7234 86217 1936 64407 787807 3 11 8 015 055 045 0375 630 14224 00381 08654 01587

9 2004 70080 78840 7035 116957 10 55403 758903 1 12 7 005 06 04 01428 100 15324 00062 08716 0

10 2005 78840 87600 7172 90845 107 67808 785008 2 14 5 010 07 03 04 034 15358 00012 08728 18182

11 2006 87600 96360 7113 50839 0 113821 825121 0 14 5 0 07 03 0 0 15358 0 08728 -

12 2007 96360 105120 1878 643039 6848 38233 226033 4 18 1 021 091 009 4 1712 16110 01054 09782 00581

13 2008 105120 113880 8443 0 105 31545 875845 1 19 0 005 096 004 +infin 105 16215 00064 09846 09259




n

iiNn

1

iNr if iF iR i sit0

n

isi

t1

0 i

tf 0 i

tO 0 si

[-] [year] h h h h h h h [-] [-] [-] [-] [-] [-] [-] h h [-] [-] [-]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

1 1996 0 8760 5456 219925 59418 51017 596617 14 14 142 009 009 091 0098 4226 4226 00788 00788 00236

2 1997 8760 17520 6962 107838 52028 19854 716054 10 24 132 006 015 085 0075 5203 9429 00967 01755 00192

3 1998 17520 26280 6756 106225 58711 35425 711025 12 36 120 007 022 078 01 4857 14326 00910 02665 00204

4 1999 26280 35040 5894 212636 23731 50153 639553 7 43 113 004 026 074 0062 3355 17731 00631 03296 00294

5 2000 35040 43800 6584 13451 36522 46528 7054928 12 55 101 007 033 067 0119 2035 19806 00383 03679 00485

6 2001 43800 52560 6533 73354 114052 35314 688614 23 78 78 015 048 052 0295 4937 24743 00922 04601 00202

7 2002 52560 61320 7176 74601 59519 24240 741840 16 94 62 010 058 042 0258 3711 28454 00691 05292 00269

8 2003 61320 70080 7234 86217 38604 27739 751139 10 104 52 006 064 036 0192 3834 32328 00717 06009 00259

9 2004 70080 78840 7035 116957 49723 5740 709240 12 116 40 007 071 029 03 4129 36457 00771 06780 00241

10 2005 78840 87600 7172 90845 39238 28637 745837 12 128 28 007 078 022 0428 3243 39740 00607 07387 00306

11 2006 87600 96360 7113 50839 48510 65311 776611 16 144 12 010 088 012 1333 3018 42758 00562 07949 00330

12 2007 96360 105120 1878 643039 17039 28042 215842 2 146 10 001 089 011 02 8520 51318 01585 09534 00117

13 2008 105120 113880 8443 0 25104 6556 850856 10 156 0 006 095 005 +infin 2505 53823 00465 09999 00399



n

iiNn

1

iNr if iF iR i sit0

n

isi

t1

0 i

tf 0 i

tO 0 si

[-] [year] h h h h h h h [-] [-] [-] [-] [-] [-] [-] h h [-] [-] [-]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

1 1996 0 8760 5456 219925 0 110435 656035 0 0 16 0 0 1 0 0 0 0 0 -

2 1997 8760 17520 6962 107838 431 71458 767653 2 2 14 012 012 088 0143 216 216 00082 00082 04348

3 1998 17520 26280 6756 106225 134 94001 769601 1 3 13 006 018 082 0077 134 350 00136 00218 06250

4 1999 26280 35040 5894 212636 13408 60516 649916 1 4 12 006 024 076 0083 13408 13458 04173 04391 00074

5 2000 35040 43800 6584 13451 0 83050 741450 0 4 12 0 024 076 0 0 13458 0 04391 -

6 2001 43800 52560 6533 73354 414 148852 802152 2 6 10 012 036 064 02 207 13705 00077 04468 04695

7 2002 52560 61320 7176 74601 237 83522 801122 1 7 9 006 042 058 0111 237 13942 00095 04563 03846

8 2003 61320 70080 7234 86217 129 66214 789614 1 8 8 006 048 052 0125 129 14111 00054 04617 06667

9 2004 70080 78840 7035 116957 4849 50614 754114 1 9 7 006 054 046 0143 4849 19000 01742 06359 00205

10 2005 78840 87600 7172 90845 3050 64825 782025 1 10 6 006 06 04 0166 3050 22050 01100 07459 00324

11 2006 87600 96360 7113 50839 5437 108344 819644 1 11 5 006 066 034 02 5437 27527 01949 09408 00183

12 2007 96360 105120 1878 643039 0 45121 232921 0 11 5 0 066 034 0 0 27527 0 09408 -

13 2008 105120 113880 8443 0 2153 29507 873807 5 16 0 031 097 003 +infin 445 28012 00164 09572 02174



n

iiNn

1


[-] [year] h h h h h h h h [-] [-] [-] [-] [-] [-] [MW]

[GWh]

1 2 3 4 5 6 7 8 9 10 12 13 14 15 16 17 18 19

1 1996 0 8760 5456 219925 61724 15 48711 594311 15 176 008 008 092 00852 2329 1384171

2 1997 8760 17520 6962 107838 52938 13 18944 715144 28 163 007 015 085 00800 24486 1751165

3 1998 17520 26280 6756 106225 59054 14 35041 710641 42 149 007 022 078 00940 24297 1721025

4 1999 26280 35040 5894 212636 37238 9 36646 626046 51 140 005 027 073 00643 23376 1463325

5 2000 35040 43800 6584 13451 47725 15 35325 693725 66 125 008 035 065 01200 23821 1652338

6 2001 43800 52560 6533 73354 121257 26 28009 681309 92 99 014 049 051 02626 23941 1631136

7 2002 52560 61320 7176 74601 59756 17 24003 741603 109 82 009 058 042 02073 23120 1714595

8 2003 61320 70080 7234 86217 40509 14 25834 749234 123 68 007 065 035 02059 23500 1760754

9 2004 70080 78840 7035 116957 54712 14 751 704251 137 54 007 072 028 02593 22609 1592329

10 2005 78840 87600 7172 90845 42435 15 25440 742640 152 39 008 080 020 03846 23599 1752617

11 2006 87600 96360 7113 50839 99349 17 14432 725732 169 22 009 089 011 07727 23468 1703202

12 2007 96360 105120 1878 643039 23927 6 21154 208954 175 16 003 092 008 0375 23675 494791

13 2008 105120 113880 8443 0 27257 16 4403 848703 191 0 008 100 0 +infin 26318 2233622













n

i

k

jjjs NnTa

knTa

1 1

11

(11)


sTa

1

(12)


1

1n

s si

int t

(13)


st0

1

(14)

mean available time

n

iis Tr

nTr

1

1

(15)



h 1h h 1h h




4 System 45419 2200 3447 288 672456



own availability

exp( )s ss ss

s s s s

A T T

(16)


Tk

Tn

TnTr

TrA s

ss

s

10

(17)


09976 00023exp( 008018 )A T T (18)

A0 = 08276


09368 00632exp( 0025844 )A T T (19)

A0 = 0777


09956 0 0044exp( 0039578 )A T T (20)

A0 = 0829

4) System

09287 00713exp( 0 0310 )A T T (21)

A0 = 07677






0 01 exp( )O t ts (22)




system 0 01 exp( 0 0288 )O t t (26)








0

02 03 04 0806 2 3 4 5 6 7 8 20 40 60 8030

02

03

05

1

2

3

5

10

20

30

40

50

60632

70

80

999

99b

90

1

2

3

4

5

7

8

9

01P

15133

70731

01 1 10 100

t 102 h

F(t)



15133b 0908Tur

0908 70731 64224Tur years


[7]





(30)










4 CONCLUSIONS





09287 00713exp( 0 0310 )A T T

15133exp 19307R t t




0 01 exp( 0 0288 )O t t








observed period




TENT-А4 is

2361604EA s GWh

NOMENCLATURE

si




nfi

i ) [-]


nNn Nni i

i

) [-]

MR - medial rang (=(j-03)(n+04)) [-]



1

n

i

i

Nn


n

i

i

j Nn

)[-]









0sit


nTnz j

j

Nn j ) [h]


nf t

ii

) [-]

Greek letters





Subscripts


e - exploitation

t - theoretical

REFERENCES



[2] SRPS АА2005


New York USA 1997


New York USA 1993









Proceedings 15th


Serbia 2011 pp 905-917





n

iiNn

1

iNr if iF iR i sit0

n

isi

t1

0 i

tf 0 i

tO 0 si

[-] [year] h h h h h h h [-] [-] [-] [-] [-] [-] [-] h h [-] [-] [-]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

1 1996 0 8760 5456 219925 2306 108131 653731 1 1 18 005 005 095 00555 2306 2306 01421 01421 00434

2 1997 8760 17520 6962 107838 439 71443 767943 1 2 17 005 01 09 00588 439 2745 00261 01682 02358

3 1998 17520 26280 6756 106225 209 93934 769534 1 3 16 005 015 085 00625 209 2954 00126 01808 04868

4 1999 26280 35040 5894 212636 059 73835 663235 1 4 15 005 02 08 00666 059 3053 00022 01830 16949

5 2000 35040 43800 6584 134510 11203 71847 730247 3 7 12 015 035 065 025 3719 6812 02290 04120 00269

6 2001 43800 52560 6533 73354 6751 142545 795845 1 8 11 005 04 06 00909 6751 10603 04153 08273 00148

7 2002 52560 61320 7176 74601 0 83759 801359 0 8 11 0 04 06 0 0 13554 0 08273 -

8 2003 61320 70080 7234 86217 1936 64407 787807 3 11 8 015 055 045 0375 630 14224 00381 08654 01587

9 2004 70080 78840 7035 116957 10 55403 758903 1 12 7 005 06 04 01428 100 15324 00062 08716 0

10 2005 78840 87600 7172 90845 107 67808 785008 2 14 5 010 07 03 04 034 15358 00012 08728 18182

11 2006 87600 96360 7113 50839 0 113821 825121 0 14 5 0 07 03 0 0 15358 0 08728 -

12 2007 96360 105120 1878 643039 6848 38233 226033 4 18 1 021 091 009 4 1712 16110 01054 09782 00581

13 2008 105120 113880 8443 0 105 31545 875845 1 19 0 005 096 004 +infin 105 16215 00064 09846 09259




n

iiNn

1

iNr if iF iR i sit0

n

isi

t1

0 i

tf 0 i

tO 0 si

[-] [year] h h h h h h h [-] [-] [-] [-] [-] [-] [-] h h [-] [-] [-]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

1 1996 0 8760 5456 219925 59418 51017 596617 14 14 142 009 009 091 0098 4226 4226 00788 00788 00236

2 1997 8760 17520 6962 107838 52028 19854 716054 10 24 132 006 015 085 0075 5203 9429 00967 01755 00192

3 1998 17520 26280 6756 106225 58711 35425 711025 12 36 120 007 022 078 01 4857 14326 00910 02665 00204

4 1999 26280 35040 5894 212636 23731 50153 639553 7 43 113 004 026 074 0062 3355 17731 00631 03296 00294

5 2000 35040 43800 6584 13451 36522 46528 7054928 12 55 101 007 033 067 0119 2035 19806 00383 03679 00485

6 2001 43800 52560 6533 73354 114052 35314 688614 23 78 78 015 048 052 0295 4937 24743 00922 04601 00202

7 2002 52560 61320 7176 74601 59519 24240 741840 16 94 62 010 058 042 0258 3711 28454 00691 05292 00269

8 2003 61320 70080 7234 86217 38604 27739 751139 10 104 52 006 064 036 0192 3834 32328 00717 06009 00259

9 2004 70080 78840 7035 116957 49723 5740 709240 12 116 40 007 071 029 03 4129 36457 00771 06780 00241

10 2005 78840 87600 7172 90845 39238 28637 745837 12 128 28 007 078 022 0428 3243 39740 00607 07387 00306

11 2006 87600 96360 7113 50839 48510 65311 776611 16 144 12 010 088 012 1333 3018 42758 00562 07949 00330

12 2007 96360 105120 1878 643039 17039 28042 215842 2 146 10 001 089 011 02 8520 51318 01585 09534 00117

13 2008 105120 113880 8443 0 25104 6556 850856 10 156 0 006 095 005 +infin 2505 53823 00465 09999 00399



n

iiNn

1

iNr if iF iR i sit0

n

isi

t1

0 i

tf 0 i

tO 0 si

[-] [year] h h h h h h h [-] [-] [-] [-] [-] [-] [-] h h [-] [-] [-]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

1 1996 0 8760 5456 219925 0 110435 656035 0 0 16 0 0 1 0 0 0 0 0 -

2 1997 8760 17520 6962 107838 431 71458 767653 2 2 14 012 012 088 0143 216 216 00082 00082 04348

3 1998 17520 26280 6756 106225 134 94001 769601 1 3 13 006 018 082 0077 134 350 00136 00218 06250

4 1999 26280 35040 5894 212636 13408 60516 649916 1 4 12 006 024 076 0083 13408 13458 04173 04391 00074

5 2000 35040 43800 6584 13451 0 83050 741450 0 4 12 0 024 076 0 0 13458 0 04391 -

6 2001 43800 52560 6533 73354 414 148852 802152 2 6 10 012 036 064 02 207 13705 00077 04468 04695

7 2002 52560 61320 7176 74601 237 83522 801122 1 7 9 006 042 058 0111 237 13942 00095 04563 03846

8 2003 61320 70080 7234 86217 129 66214 789614 1 8 8 006 048 052 0125 129 14111 00054 04617 06667

9 2004 70080 78840 7035 116957 4849 50614 754114 1 9 7 006 054 046 0143 4849 19000 01742 06359 00205

10 2005 78840 87600 7172 90845 3050 64825 782025 1 10 6 006 06 04 0166 3050 22050 01100 07459 00324

11 2006 87600 96360 7113 50839 5437 108344 819644 1 11 5 006 066 034 02 5437 27527 01949 09408 00183

12 2007 96360 105120 1878 643039 0 45121 232921 0 11 5 0 066 034 0 0 27527 0 09408 -

13 2008 105120 113880 8443 0 2153 29507 873807 5 16 0 031 097 003 +infin 445 28012 00164 09572 02174



n

iiNn

1


[-] [year] h h h h h h h h [-] [-] [-] [-] [-] [-] [MW]

[GWh]

1 2 3 4 5 6 7 8 9 10 12 13 14 15 16 17 18 19

1 1996 0 8760 5456 219925 61724 15 48711 594311 15 176 008 008 092 00852 2329 1384171

2 1997 8760 17520 6962 107838 52938 13 18944 715144 28 163 007 015 085 00800 24486 1751165

3 1998 17520 26280 6756 106225 59054 14 35041 710641 42 149 007 022 078 00940 24297 1721025

4 1999 26280 35040 5894 212636 37238 9 36646 626046 51 140 005 027 073 00643 23376 1463325

5 2000 35040 43800 6584 13451 47725 15 35325 693725 66 125 008 035 065 01200 23821 1652338

6 2001 43800 52560 6533 73354 121257 26 28009 681309 92 99 014 049 051 02626 23941 1631136

7 2002 52560 61320 7176 74601 59756 17 24003 741603 109 82 009 058 042 02073 23120 1714595

8 2003 61320 70080 7234 86217 40509 14 25834 749234 123 68 007 065 035 02059 23500 1760754

9 2004 70080 78840 7035 116957 54712 14 751 704251 137 54 007 072 028 02593 22609 1592329

10 2005 78840 87600 7172 90845 42435 15 25440 742640 152 39 008 080 020 03846 23599 1752617

11 2006 87600 96360 7113 50839 99349 17 14432 725732 169 22 009 089 011 07727 23468 1703202

12 2007 96360 105120 1878 643039 23927 6 21154 208954 175 16 003 092 008 0375 23675 494791

13 2008 105120 113880 8443 0 27257 16 4403 848703 191 0 008 100 0 +infin 26318 2233622













n

i

k

jjjs NnTa

knTa

1 1

11

(11)


sTa

1

(12)


1

1n

s si

int t

(13)


st0

1

(14)

mean available time

n

iis Tr

nTr

1

1

(15)



h 1h h 1h h




4 System 45419 2200 3447 288 672456



own availability

exp( )s ss ss

s s s s

A T T

(16)


Tk

Tn

TnTr

TrA s

ss

s

10

(17)


09976 00023exp( 008018 )A T T (18)

A0 = 08276


09368 00632exp( 0025844 )A T T (19)

A0 = 0777


09956 0 0044exp( 0039578 )A T T (20)

A0 = 0829

4) System

09287 00713exp( 0 0310 )A T T (21)

A0 = 07677






0 01 exp( )O t ts (22)




system 0 01 exp( 0 0288 )O t t (26)








0

02 03 04 0806 2 3 4 5 6 7 8 20 40 60 8030

02

03

05

1

2

3

5

10

20

30

40

50

60632

70

80

999

99b

90

1

2

3

4

5

7

8

9

01P

15133

70731

01 1 10 100

t 102 h

F(t)



15133b 0908Tur

0908 70731 64224Tur years


[7]





(30)










4 CONCLUSIONS





09287 00713exp( 0 0310 )A T T

15133exp 19307R t t




0 01 exp( 0 0288 )O t t








observed period




TENT-А4 is

2361604EA s GWh

NOMENCLATURE

si




nfi

i ) [-]


nNn Nni i

i

) [-]

MR - medial rang (=(j-03)(n+04)) [-]



1

n

i

i

Nn


n

i

i

j Nn

)[-]









0sit


nTnz j

j

Nn j ) [h]


nf t

ii

) [-]

Greek letters





Subscripts


e - exploitation

t - theoretical

REFERENCES



[2] SRPS АА2005


New York USA 1997


New York USA 1993









Proceedings 15th


Serbia 2011 pp 905-917





n

iiNn

1

iNr if iF iR i sit0

n

isi

t1

0 i

tf 0 i

tO 0 si

[-] [year] h h h h h h h [-] [-] [-] [-] [-] [-] [-] h h [-] [-] [-]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

1 1996 0 8760 5456 219925 59418 51017 596617 14 14 142 009 009 091 0098 4226 4226 00788 00788 00236

2 1997 8760 17520 6962 107838 52028 19854 716054 10 24 132 006 015 085 0075 5203 9429 00967 01755 00192

3 1998 17520 26280 6756 106225 58711 35425 711025 12 36 120 007 022 078 01 4857 14326 00910 02665 00204

4 1999 26280 35040 5894 212636 23731 50153 639553 7 43 113 004 026 074 0062 3355 17731 00631 03296 00294

5 2000 35040 43800 6584 13451 36522 46528 7054928 12 55 101 007 033 067 0119 2035 19806 00383 03679 00485

6 2001 43800 52560 6533 73354 114052 35314 688614 23 78 78 015 048 052 0295 4937 24743 00922 04601 00202

7 2002 52560 61320 7176 74601 59519 24240 741840 16 94 62 010 058 042 0258 3711 28454 00691 05292 00269

8 2003 61320 70080 7234 86217 38604 27739 751139 10 104 52 006 064 036 0192 3834 32328 00717 06009 00259

9 2004 70080 78840 7035 116957 49723 5740 709240 12 116 40 007 071 029 03 4129 36457 00771 06780 00241

10 2005 78840 87600 7172 90845 39238 28637 745837 12 128 28 007 078 022 0428 3243 39740 00607 07387 00306

11 2006 87600 96360 7113 50839 48510 65311 776611 16 144 12 010 088 012 1333 3018 42758 00562 07949 00330

12 2007 96360 105120 1878 643039 17039 28042 215842 2 146 10 001 089 011 02 8520 51318 01585 09534 00117

13 2008 105120 113880 8443 0 25104 6556 850856 10 156 0 006 095 005 +infin 2505 53823 00465 09999 00399



n

iiNn

1

iNr if iF iR i sit0

n

isi

t1

0 i

tf 0 i

tO 0 si

[-] [year] h h h h h h h [-] [-] [-] [-] [-] [-] [-] h h [-] [-] [-]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

1 1996 0 8760 5456 219925 0 110435 656035 0 0 16 0 0 1 0 0 0 0 0 -

2 1997 8760 17520 6962 107838 431 71458 767653 2 2 14 012 012 088 0143 216 216 00082 00082 04348

3 1998 17520 26280 6756 106225 134 94001 769601 1 3 13 006 018 082 0077 134 350 00136 00218 06250

4 1999 26280 35040 5894 212636 13408 60516 649916 1 4 12 006 024 076 0083 13408 13458 04173 04391 00074

5 2000 35040 43800 6584 13451 0 83050 741450 0 4 12 0 024 076 0 0 13458 0 04391 -

6 2001 43800 52560 6533 73354 414 148852 802152 2 6 10 012 036 064 02 207 13705 00077 04468 04695

7 2002 52560 61320 7176 74601 237 83522 801122 1 7 9 006 042 058 0111 237 13942 00095 04563 03846

8 2003 61320 70080 7234 86217 129 66214 789614 1 8 8 006 048 052 0125 129 14111 00054 04617 06667

9 2004 70080 78840 7035 116957 4849 50614 754114 1 9 7 006 054 046 0143 4849 19000 01742 06359 00205

10 2005 78840 87600 7172 90845 3050 64825 782025 1 10 6 006 06 04 0166 3050 22050 01100 07459 00324

11 2006 87600 96360 7113 50839 5437 108344 819644 1 11 5 006 066 034 02 5437 27527 01949 09408 00183

12 2007 96360 105120 1878 643039 0 45121 232921 0 11 5 0 066 034 0 0 27527 0 09408 -

13 2008 105120 113880 8443 0 2153 29507 873807 5 16 0 031 097 003 +infin 445 28012 00164 09572 02174



n

iiNn

1


[-] [year] h h h h h h h h [-] [-] [-] [-] [-] [-] [MW]

[GWh]

1 2 3 4 5 6 7 8 9 10 12 13 14 15 16 17 18 19

1 1996 0 8760 5456 219925 61724 15 48711 594311 15 176 008 008 092 00852 2329 1384171

2 1997 8760 17520 6962 107838 52938 13 18944 715144 28 163 007 015 085 00800 24486 1751165

3 1998 17520 26280 6756 106225 59054 14 35041 710641 42 149 007 022 078 00940 24297 1721025

4 1999 26280 35040 5894 212636 37238 9 36646 626046 51 140 005 027 073 00643 23376 1463325

5 2000 35040 43800 6584 13451 47725 15 35325 693725 66 125 008 035 065 01200 23821 1652338

6 2001 43800 52560 6533 73354 121257 26 28009 681309 92 99 014 049 051 02626 23941 1631136

7 2002 52560 61320 7176 74601 59756 17 24003 741603 109 82 009 058 042 02073 23120 1714595

8 2003 61320 70080 7234 86217 40509 14 25834 749234 123 68 007 065 035 02059 23500 1760754

9 2004 70080 78840 7035 116957 54712 14 751 704251 137 54 007 072 028 02593 22609 1592329

10 2005 78840 87600 7172 90845 42435 15 25440 742640 152 39 008 080 020 03846 23599 1752617

11 2006 87600 96360 7113 50839 99349 17 14432 725732 169 22 009 089 011 07727 23468 1703202

12 2007 96360 105120 1878 643039 23927 6 21154 208954 175 16 003 092 008 0375 23675 494791

13 2008 105120 113880 8443 0 27257 16 4403 848703 191 0 008 100 0 +infin 26318 2233622













n

i

k

jjjs NnTa

knTa

1 1

11

(11)


sTa

1

(12)


1

1n

s si

int t

(13)


st0

1

(14)

mean available time

n

iis Tr

nTr

1

1

(15)



h 1h h 1h h




4 System 45419 2200 3447 288 672456



own availability

exp( )s ss ss

s s s s

A T T

(16)


Tk

Tn

TnTr

TrA s

ss

s

10

(17)


09976 00023exp( 008018 )A T T (18)

A0 = 08276


09368 00632exp( 0025844 )A T T (19)

A0 = 0777


09956 0 0044exp( 0039578 )A T T (20)

A0 = 0829

4) System

09287 00713exp( 0 0310 )A T T (21)

A0 = 07677






0 01 exp( )O t ts (22)




system 0 01 exp( 0 0288 )O t t (26)








0

02 03 04 0806 2 3 4 5 6 7 8 20 40 60 8030

02

03

05

1

2

3

5

10

20

30

40

50

60632

70

80

999

99b

90

1

2

3

4

5

7

8

9

01P

15133

70731

01 1 10 100

t 102 h

F(t)



15133b 0908Tur

0908 70731 64224Tur years


[7]





(30)










4 CONCLUSIONS





09287 00713exp( 0 0310 )A T T

15133exp 19307R t t




0 01 exp( 0 0288 )O t t








observed period




TENT-А4 is

2361604EA s GWh

NOMENCLATURE

si




nfi

i ) [-]


nNn Nni i

i

) [-]

MR - medial rang (=(j-03)(n+04)) [-]



1

n

i

i

Nn


n

i

i

j Nn

)[-]









0sit


nTnz j

j

Nn j ) [h]


nf t

ii

) [-]

Greek letters





Subscripts


e - exploitation

t - theoretical

REFERENCES



[2] SRPS АА2005


New York USA 1997


New York USA 1993









Proceedings 15th


Serbia 2011 pp 905-917





n

iiNn

1

iNr if iF iR i sit0

n

isi

t1

0 i

tf 0 i

tO 0 si

[-] [year] h h h h h h h [-] [-] [-] [-] [-] [-] [-] h h [-] [-] [-]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

1 1996 0 8760 5456 219925 0 110435 656035 0 0 16 0 0 1 0 0 0 0 0 -

2 1997 8760 17520 6962 107838 431 71458 767653 2 2 14 012 012 088 0143 216 216 00082 00082 04348

3 1998 17520 26280 6756 106225 134 94001 769601 1 3 13 006 018 082 0077 134 350 00136 00218 06250

4 1999 26280 35040 5894 212636 13408 60516 649916 1 4 12 006 024 076 0083 13408 13458 04173 04391 00074

5 2000 35040 43800 6584 13451 0 83050 741450 0 4 12 0 024 076 0 0 13458 0 04391 -

6 2001 43800 52560 6533 73354 414 148852 802152 2 6 10 012 036 064 02 207 13705 00077 04468 04695

7 2002 52560 61320 7176 74601 237 83522 801122 1 7 9 006 042 058 0111 237 13942 00095 04563 03846

8 2003 61320 70080 7234 86217 129 66214 789614 1 8 8 006 048 052 0125 129 14111 00054 04617 06667

9 2004 70080 78840 7035 116957 4849 50614 754114 1 9 7 006 054 046 0143 4849 19000 01742 06359 00205

10 2005 78840 87600 7172 90845 3050 64825 782025 1 10 6 006 06 04 0166 3050 22050 01100 07459 00324

11 2006 87600 96360 7113 50839 5437 108344 819644 1 11 5 006 066 034 02 5437 27527 01949 09408 00183

12 2007 96360 105120 1878 643039 0 45121 232921 0 11 5 0 066 034 0 0 27527 0 09408 -

13 2008 105120 113880 8443 0 2153 29507 873807 5 16 0 031 097 003 +infin 445 28012 00164 09572 02174



n

iiNn

1


[-] [year] h h h h h h h h [-] [-] [-] [-] [-] [-] [MW]

[GWh]

1 2 3 4 5 6 7 8 9 10 12 13 14 15 16 17 18 19

1 1996 0 8760 5456 219925 61724 15 48711 594311 15 176 008 008 092 00852 2329 1384171

2 1997 8760 17520 6962 107838 52938 13 18944 715144 28 163 007 015 085 00800 24486 1751165

3 1998 17520 26280 6756 106225 59054 14 35041 710641 42 149 007 022 078 00940 24297 1721025

4 1999 26280 35040 5894 212636 37238 9 36646 626046 51 140 005 027 073 00643 23376 1463325

5 2000 35040 43800 6584 13451 47725 15 35325 693725 66 125 008 035 065 01200 23821 1652338

6 2001 43800 52560 6533 73354 121257 26 28009 681309 92 99 014 049 051 02626 23941 1631136

7 2002 52560 61320 7176 74601 59756 17 24003 741603 109 82 009 058 042 02073 23120 1714595

8 2003 61320 70080 7234 86217 40509 14 25834 749234 123 68 007 065 035 02059 23500 1760754

9 2004 70080 78840 7035 116957 54712 14 751 704251 137 54 007 072 028 02593 22609 1592329

10 2005 78840 87600 7172 90845 42435 15 25440 742640 152 39 008 080 020 03846 23599 1752617

11 2006 87600 96360 7113 50839 99349 17 14432 725732 169 22 009 089 011 07727 23468 1703202

12 2007 96360 105120 1878 643039 23927 6 21154 208954 175 16 003 092 008 0375 23675 494791

13 2008 105120 113880 8443 0 27257 16 4403 848703 191 0 008 100 0 +infin 26318 2233622













n

i

k

jjjs NnTa

knTa

1 1

11

(11)


sTa

1

(12)


1

1n

s si

int t

(13)


st0

1

(14)

mean available time

n

iis Tr

nTr

1

1

(15)



h 1h h 1h h




4 System 45419 2200 3447 288 672456



own availability

exp( )s ss ss

s s s s

A T T

(16)


Tk

Tn

TnTr

TrA s

ss

s

10

(17)


09976 00023exp( 008018 )A T T (18)

A0 = 08276


09368 00632exp( 0025844 )A T T (19)

A0 = 0777


09956 0 0044exp( 0039578 )A T T (20)

A0 = 0829

4) System

09287 00713exp( 0 0310 )A T T (21)

A0 = 07677






0 01 exp( )O t ts (22)




system 0 01 exp( 0 0288 )O t t (26)








0

02 03 04 0806 2 3 4 5 6 7 8 20 40 60 8030

02

03

05

1

2

3

5

10

20

30

40

50

60632

70

80

999

99b

90

1

2

3

4

5

7

8

9

01P

15133

70731

01 1 10 100

t 102 h

F(t)



15133b 0908Tur

0908 70731 64224Tur years


[7]





(30)










4 CONCLUSIONS





09287 00713exp( 0 0310 )A T T

15133exp 19307R t t




0 01 exp( 0 0288 )O t t








observed period




TENT-А4 is

2361604EA s GWh

NOMENCLATURE

si




nfi

i ) [-]


nNn Nni i

i

) [-]

MR - medial rang (=(j-03)(n+04)) [-]



1

n

i

i

Nn


n

i

i

j Nn

)[-]









0sit


nTnz j

j

Nn j ) [h]


nf t

ii

) [-]

Greek letters





Subscripts


e - exploitation

t - theoretical

REFERENCES



[2] SRPS АА2005


New York USA 1997


New York USA 1993









Proceedings 15th


Serbia 2011 pp 905-917





n

iiNn

1


[-] [year] h h h h h h h h [-] [-] [-] [-] [-] [-] [MW]

[GWh]

1 2 3 4 5 6 7 8 9 10 12 13 14 15 16 17 18 19

1 1996 0 8760 5456 219925 61724 15 48711 594311 15 176 008 008 092 00852 2329 1384171

2 1997 8760 17520 6962 107838 52938 13 18944 715144 28 163 007 015 085 00800 24486 1751165

3 1998 17520 26280 6756 106225 59054 14 35041 710641 42 149 007 022 078 00940 24297 1721025

4 1999 26280 35040 5894 212636 37238 9 36646 626046 51 140 005 027 073 00643 23376 1463325

5 2000 35040 43800 6584 13451 47725 15 35325 693725 66 125 008 035 065 01200 23821 1652338

6 2001 43800 52560 6533 73354 121257 26 28009 681309 92 99 014 049 051 02626 23941 1631136

7 2002 52560 61320 7176 74601 59756 17 24003 741603 109 82 009 058 042 02073 23120 1714595

8 2003 61320 70080 7234 86217 40509 14 25834 749234 123 68 007 065 035 02059 23500 1760754

9 2004 70080 78840 7035 116957 54712 14 751 704251 137 54 007 072 028 02593 22609 1592329

10 2005 78840 87600 7172 90845 42435 15 25440 742640 152 39 008 080 020 03846 23599 1752617

11 2006 87600 96360 7113 50839 99349 17 14432 725732 169 22 009 089 011 07727 23468 1703202

12 2007 96360 105120 1878 643039 23927 6 21154 208954 175 16 003 092 008 0375 23675 494791

13 2008 105120 113880 8443 0 27257 16 4403 848703 191 0 008 100 0 +infin 26318 2233622













n

i

k

jjjs NnTa

knTa

1 1

11

(11)


sTa

1

(12)


1

1n

s si

int t

(13)


st0

1

(14)

mean available time

n

iis Tr

nTr

1

1

(15)



h 1h h 1h h




4 System 45419 2200 3447 288 672456



own availability

exp( )s ss ss

s s s s

A T T

(16)


Tk

Tn

TnTr

TrA s

ss

s

10

(17)


09976 00023exp( 008018 )A T T (18)

A0 = 08276


09368 00632exp( 0025844 )A T T (19)

A0 = 0777


09956 0 0044exp( 0039578 )A T T (20)

A0 = 0829

4) System

09287 00713exp( 0 0310 )A T T (21)

A0 = 07677






0 01 exp( )O t ts (22)




system 0 01 exp( 0 0288 )O t t (26)








0

02 03 04 0806 2 3 4 5 6 7 8 20 40 60 8030

02

03

05

1

2

3

5

10

20

30

40

50

60632

70

80

999

99b

90

1

2

3

4

5

7

8

9

01P

15133

70731

01 1 10 100

t 102 h

F(t)



15133b 0908Tur

0908 70731 64224Tur years


[7]





(30)










4 CONCLUSIONS





09287 00713exp( 0 0310 )A T T

15133exp 19307R t t




0 01 exp( 0 0288 )O t t








observed period




TENT-А4 is

2361604EA s GWh

NOMENCLATURE

si




nfi

i ) [-]


nNn Nni i

i

) [-]

MR - medial rang (=(j-03)(n+04)) [-]



1

n

i

i

Nn


n

i

i

j Nn

)[-]









0sit


nTnz j

j

Nn j ) [h]


nf t

ii

) [-]

Greek letters





Subscripts


e - exploitation

t - theoretical

REFERENCES



[2] SRPS АА2005


New York USA 1997


New York USA 1993









Proceedings 15th


Serbia 2011 pp 905-917















n

i

k

jjjs NnTa

knTa

1 1

11

(11)


sTa

1

(12)


1

1n

s si

int t

(13)


st0

1

(14)

mean available time

n

iis Tr

nTr

1

1

(15)



h 1h h 1h h




4 System 45419 2200 3447 288 672456



own availability

exp( )s ss ss

s s s s

A T T

(16)


Tk

Tn

TnTr

TrA s

ss

s

10

(17)


09976 00023exp( 008018 )A T T (18)

A0 = 08276


09368 00632exp( 0025844 )A T T (19)

A0 = 0777


09956 0 0044exp( 0039578 )A T T (20)

A0 = 0829

4) System

09287 00713exp( 0 0310 )A T T (21)

A0 = 07677






0 01 exp( )O t ts (22)




system 0 01 exp( 0 0288 )O t t (26)








0

02 03 04 0806 2 3 4 5 6 7 8 20 40 60 8030

02

03

05

1

2

3

5

10

20

30

40

50

60632

70

80

999

99b

90

1

2

3

4

5

7

8

9

01P

15133

70731

01 1 10 100

t 102 h

F(t)



15133b 0908Tur

0908 70731 64224Tur years


[7]





(30)










4 CONCLUSIONS





09287 00713exp( 0 0310 )A T T

15133exp 19307R t t




0 01 exp( 0 0288 )O t t








observed period




TENT-А4 is

2361604EA s GWh

NOMENCLATURE

si




nfi

i ) [-]


nNn Nni i

i

) [-]

MR - medial rang (=(j-03)(n+04)) [-]



1

n

i

i

Nn


n

i

i

j Nn

)[-]









0sit


nTnz j

j

Nn j ) [h]


nf t

ii

) [-]

Greek letters





Subscripts


e - exploitation

t - theoretical

REFERENCES



[2] SRPS АА2005


New York USA 1997


New York USA 1993









Proceedings 15th


Serbia 2011 pp 905-917





h 1h h 1h h




4 System 45419 2200 3447 288 672456



own availability

exp( )s ss ss

s s s s

A T T

(16)


Tk

Tn

TnTr

TrA s

ss

s

10

(17)


09976 00023exp( 008018 )A T T (18)

A0 = 08276


09368 00632exp( 0025844 )A T T (19)

A0 = 0777


09956 0 0044exp( 0039578 )A T T (20)

A0 = 0829

4) System

09287 00713exp( 0 0310 )A T T (21)

A0 = 07677






0 01 exp( )O t ts (22)




system 0 01 exp( 0 0288 )O t t (26)








0

02 03 04 0806 2 3 4 5 6 7 8 20 40 60 8030

02

03

05

1

2

3

5

10

20

30

40

50

60632

70

80

999

99b

90

1

2

3

4

5

7

8

9

01P

15133

70731

01 1 10 100

t 102 h

F(t)



15133b 0908Tur

0908 70731 64224Tur years


[7]





(30)










4 CONCLUSIONS





09287 00713exp( 0 0310 )A T T

15133exp 19307R t t




0 01 exp( 0 0288 )O t t








observed period




TENT-А4 is

2361604EA s GWh

NOMENCLATURE

si




nfi

i ) [-]


nNn Nni i

i

) [-]

MR - medial rang (=(j-03)(n+04)) [-]



1

n

i

i

Nn


n

i

i

j Nn

)[-]









0sit


nTnz j

j

Nn j ) [h]


nf t

ii

) [-]

Greek letters





Subscripts


e - exploitation

t - theoretical

REFERENCES



[2] SRPS АА2005


New York USA 1997


New York USA 1993









Proceedings 15th


Serbia 2011 pp 905-917







0 01 exp( )O t ts (22)




system 0 01 exp( 0 0288 )O t t (26)








0

02 03 04 0806 2 3 4 5 6 7 8 20 40 60 8030

02

03

05

1

2

3

5

10

20

30

40

50

60632

70

80

999

99b

90

1

2

3

4

5

7

8

9

01P

15133

70731

01 1 10 100

t 102 h

F(t)



15133b 0908Tur

0908 70731 64224Tur years


[7]





(30)










4 CONCLUSIONS





09287 00713exp( 0 0310 )A T T

15133exp 19307R t t




0 01 exp( 0 0288 )O t t








observed period




TENT-А4 is

2361604EA s GWh

NOMENCLATURE

si




nfi

i ) [-]


nNn Nni i

i

) [-]

MR - medial rang (=(j-03)(n+04)) [-]



1

n

i

i

Nn


n

i

i

j Nn

)[-]









0sit


nTnz j

j

Nn j ) [h]


nf t

ii

) [-]

Greek letters





Subscripts


e - exploitation

t - theoretical

REFERENCES



[2] SRPS АА2005


New York USA 1997


New York USA 1993









Proceedings 15th


Serbia 2011 pp 905-917










0

02 03 04 0806 2 3 4 5 6 7 8 20 40 60 8030

02

03

05

1

2

3

5

10

20

30

40

50

60632

70

80

999

99b

90

1

2

3

4

5

7

8

9

01P

15133

70731

01 1 10 100

t 102 h

F(t)



15133b 0908Tur

0908 70731 64224Tur years


[7]





(30)










4 CONCLUSIONS





09287 00713exp( 0 0310 )A T T

15133exp 19307R t t




0 01 exp( 0 0288 )O t t








observed period




TENT-А4 is

2361604EA s GWh

NOMENCLATURE

si




nfi

i ) [-]


nNn Nni i

i

) [-]

MR - medial rang (=(j-03)(n+04)) [-]



1

n

i

i

Nn


n

i

i

j Nn

)[-]









0sit


nTnz j

j

Nn j ) [h]


nf t

ii

) [-]

Greek letters





Subscripts


e - exploitation

t - theoretical

REFERENCES



[2] SRPS АА2005


New York USA 1997


New York USA 1993









Proceedings 15th


Serbia 2011 pp 905-917





15133b 0908Tur

0908 70731 64224Tur years


[7]





(30)










4 CONCLUSIONS





09287 00713exp( 0 0310 )A T T

15133exp 19307R t t




0 01 exp( 0 0288 )O t t








observed period




TENT-А4 is

2361604EA s GWh

NOMENCLATURE

si




nfi

i ) [-]


nNn Nni i

i

) [-]

MR - medial rang (=(j-03)(n+04)) [-]



1

n

i

i

Nn


n

i

i

j Nn

)[-]









0sit


nTnz j

j

Nn j ) [h]


nf t

ii

) [-]

Greek letters





Subscripts


e - exploitation

t - theoretical

REFERENCES



[2] SRPS АА2005


New York USA 1997


New York USA 1993









Proceedings 15th


Serbia 2011 pp 905-917



15133exp 19307R t t




0 01 exp( 0 0288 )O t t








observed period




TENT-А4 is

2361604EA s GWh

NOMENCLATURE

si




nfi

i ) [-]


nNn Nni i

i

) [-]

MR - medial rang (=(j-03)(n+04)) [-]



1

n

i

i

Nn


n

i

i

j Nn

)[-]









0sit


nTnz j

j

Nn j ) [h]


nf t

ii

) [-]

Greek letters





Subscripts


e - exploitation

t - theoretical

REFERENCES



[2] SRPS АА2005


New York USA 1997


New York USA 1993









Proceedings 15th


Serbia 2011 pp 905-917




nf t

ii

) [-]

Greek letters





Subscripts


e - exploitation

t - theoretical

REFERENCES



[2] SRPS АА2005


New York USA 1997


New York USA 1993









Proceedings 15th


Serbia 2011 pp 905-917



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