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Definition

Reliability is a general quality of an object an ability toperform a desired function, sustaining the values of rated

operational indicators in given limits and time according to

given technical conditions.

Reliability is probability that an activity of an appliance ingiven time and given operation conditions will be adequate

to its purpose.

EIA (Electronic Industry Association, USA)

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Reliability Calculations

1. Reliability of single parts of networks in the time of

production of project documentation

2. Reliability of already operated networks

3. Reliability in the area of control of electric power

system operation

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failure rate [ year-1]

mean time of failure [ h ]

probability of failure-free run R [ - ]

probability of failure Q [ - ]

mean time between failures tS [ h ]

Restored x Notrestored objects

Mean time between failures x Mean time to failure

Numerical Representation of Reliability

(Classical - reliability of elements)

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Global Indices of Reliability

Outage rate - SAIFIaverage system outage rate

(number of outages/year/consumer)

Total time of all outages - SAIDIaverage system outage time

(min/year/consumer)

Time of one outage - CAIDIaverage outage time at a customer

(min/outage)

(Reliability of electric energy supply)

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Bathtub curve

I II III t

Early failure

period Constant failure rate periodWear-out failure

period

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The relation between the function of reliability and

failure rate is:

For failure rate it is valid:

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Division of Probability of FailureExponential division

Exponential rule of failure

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Poissons division

Weibulls deal

If k = 0, there is probability of no failure, therefore probability of failure-freerunning.

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Obtaining of input values for reliability calculations

Calculation of Reliability in Electricity

Industry

A priori reliability determination of reliability quantities from data of a producer.

Empirical reliabilitymonitoring of failures in electricity industry.

The empirical method is mostly used for obtaining the input values for reliabilitycalculations, because an application of a priori reliability method requires different

attitude to every element of electricity system.

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Analysis of Distribution Network Failure Databases

Exclusive outage databases had been on the rise since 1975 in theformer Czechoslovakia.

Unfortunately, database building stopped in1990 because of politicaland social changes.

Thanks to the expert group CIRED Czech distributors opted forunified monitoring of global reliability indices and the reliability ofselected pieces of equipment in 1999 again.

Data for the reliability computation is centrally processed andanalyzed at the VSB - Technical University of Ostrava since the year2000.

Collected data are often heterogeneous. It is necessary to solve the storage, indexing, and also transformation

of such data.

We need to create a common relational scheme for the storage of the

data, a new relation makes the querying and analysis possible.

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Database range

Region1 Region2 Region3 Region4 Region5 Region6 Region7 Region82000 - - - 1 - 12 - - 1 - 12 1 - 12

2001 1 - 12 - 1 - 12 1 - 12 - 1 - 12 1 - 12 1 - 12

2002 1 - 12 - 1 - 12 1 - 12 - 1 - 12 1 - 12 1 - 12

2003 1 - 12 - 1 - 12 1 - 12 - 1 - 12 1 - 12 1 - 12

2004 1 - 12 - 1 - 12 1 - 12 1 - 12 1 - 12 1 - 12 1 - 12

2005 - - 1 - 12 1 - 12 1 - 12 1 - 12 1 - 12 1 - 12

2006 - 1 - 12 1 - 12 1 - 12 1 - 12 1 - 12 1 - 12 1 - 122007 - 1 - 12 1 - 12 1 - 12 1 - 12 1 - 12 1 - 12 1 - 12

2008 - 1 - 12 1 - 12 1 - 12 1 - 12 1 - 12 1 - 12 1 - 12

2009 - 1 - 12 1 - 12 1 - 12 1 - 12 1 - 12 1 - 12 1 - 12

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Heterogeneous Data

We developed a common relational schema.

Order Attribute Description

1 Distribution company Unique number of a distributor

2 Outage identification Unique number of an outage

3 Outage type Accidental, planned or forced

4 Distribution point Type of substation: single, double busbar substation, . . .

5 Distribution area Specification of the location

6 Network type Insulated system, resonant grounded neutral system, . ..

7 Network voltage 0.4 kV, 22 kV, . . .8 Equipment voltage 0.4 kV, 22 kV, . . .

9 Original outage identification Unique number of the outage cause

10 Outage cause Foreign influences, causes before starting operation, . . .

11 Equipment type Overhead line, underground line, . . .

12 Failed equipment Specific equipment: conductor, switch, pole, fuse, . . .

13 Type of equipment Further specification: wooden pole, steel pole, . . .

14 Amount of failed equipment

15 Short circuit type One-line-to-ground fault, ground fault, line-to-line grounded fault, . . .

16 Producer Siemens, ABB, . . .

17 Production year Production year of the equipment

18 Outage start time

19 First manipulation Failure limitation start time20 End of manipulations Failure limitation time

21 End of outage Supply renewal time for all consumers

22 End of equipment failure Equipment reparation end time

23 Time of dead earth

24 Unsupplied power at the outage start

25 Unsupplied power at the end of manipulations

26 Unsupplied distribution transformers at the outage start

27 Unsupplied distribution transformers at the end of manipulations

28 Unsupplied customers at the outage start

29 Unsupplied customers at the end of manipulations

30 Number of unsupplied customers multiplied by time of their outage

31 Failure type With or without equipment fail

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Failure rate

(year-1)

N = number of failures (-) Z = number of elements of the given type

in the network (-)

P = the considered period (year)

Results

PZ

N

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Mean duration of the failure

(h)

N = number of failures (-) ti = the considered period (h)

Results

N

t

N

i

i

1

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Results

The value tendency of reliability indices of the22 kV cable

Cable 22 kV

0

1

2

3

4

5

6

7

200020012002 20032004 200520062007 20082009 Total

Meantime

torepair(h)

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

Failurerate(year-1)

(h)

(year

-1

)

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Results

Comparison with methodology EZ 22/80

EZ

22/80

22 kV cable (year

-1)

14.5 5.480 ( 215 4.034

22 kV overhead line (year-1

) 14 3.018 (h) 3 4.163

110 kV overhead line (year-1

) 5.2 0.370 (h) 3.5 3.992

MV/LV transformer (year-1

) 0.03 0.007 (h) 2500 4.315

110 kV/MV transformer (year-1

) 0.04 0.059 ( 1300 0.480

22 kV circuit breaker (year-1

) 0.015 0.016 ( 30 64.179

110 kV circuit breaker (year-1

) 0.01 0.052 ( 100 47.425

Equipment 2000 - 2009

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Results

Division of failures according to their causes

1

2

3

4

8

9

Causes before starting operation

Operation and maintenance causes

Foreign influences

Forced outage

Cause not explainedOther causes

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The Main Calculation Methods of

Reliability

Method of reliabilty schemes

Department of electrical power engineering

Markovs processes

Simulative methods

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- make-up of reliability diagram,

- assignment of relevant reliability quantities to single elements,

- simplification of reliability diagram towards one element,

Advantages:

- considered systems do not have to really exist as yet,

- procedure of solving is well-arranged and not exacting concerningmathematics,

- mathematical procedure does not require iterative calculation,

- accuracy of results depends only on the accuracy of input parameters

of calculation.

Disadvantages:

- it is impossible to pursue power balance of network,

- T type bay can be modelled only approximately.

Method of Reliability Schemes

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Probability of failure-free run:

Rule of Multiplication of Probabilities :

P(A) probability of occurrence ofA

P(B) probability of occurrence ofB

Series systems

A failure of one element leads to a failure of a system.

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A failure of a system occurs when all elements have a failure

Probability of a failure:

Probability of failure-free run:

Parallel Systems

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Simplified

Probability of failure-free run:

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Mean times of outages of a two-elements system:

Series connection of elements

For this circuit with two elements it holds:

P ... Failure rate [year-1]

U ... Maintenance rate [year-1]

... Outage rate (maintenance + repair) [year-1]

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Maintenance outage cannot occur at this connection, because at the failure of one

element maintenance of another element will not begin.

Parallel connection of elements hot reserve

Failure rate:

Mean time of failure:

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Parallel circuit of elements cold reserve

. Manipulation time [h]

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Simulation Methods of Calculation of Reliability

It is necessary to know the intensity of outages and mean time of outages of all the

elements of a system.Simulation - numerical method which resides in experimenting with mathematical

models of real systems on numerical computers.

Advantages:

- considered systems do not have to really exist as yet,

- considered systems can be too complicated for using analytical methods,

- simulation makes possible study of behaviour of systems in real, accelerated, or

retarded time. The second possibility is the most important in this case,

because the processes of outage of elements and their re-introduction into

operation are very slow. It would be very inefficient to study them in any othertime but accelerated.

- with simulation it is possible to verify results obtained by other independant

processes,

- possibility of modelling T type bays- simple power balance of a diagram is carried out, outage is always simulated at

overloaded elements.

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- construction of a useful simulation model is very time-consuming. Mostly

several variants of a model are needed.

- simulation is a numerical method, so a solution of certain problem cannot be

generally transferred on analogous problems.

- the results obtained from stochastic simulation models are values of

accidental quantities, and it would be very computer time-consuming if their

accuracy should be increased

- precision of results depends on the number of iterations,

- the needed number of iterations depends on the extent of the solved

network and on the required precision.

Disadvantages of simulation methods: