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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)
The Basic Reliability Calculations
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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: