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Power Transformers Reliability Estimation Study
Cristinel POPESCU1, Mircea GRIGORIU
2, Marius-Constantin POPESCU
3,
Luminita Georgeta POPESCU1, Constantina Liliana GROFU
4
1University “Constantin Brancusi” of Targu Jiu, ROMANIA
University POLITEHNICA Bucharest, 313 Spl.Independentei, zipcode 060042, Bucharest-6 3University of Craiova, ROMANIA, 13, A.I.Cuza Street, zipcode 200585, Craiova
[email protected], [email protected], [email protected],
http://www.hydrop.pub.ro, http://www.ucv.ro
ROMANIA
Abstract - The paper refers to the electrical power transformers as objects of analysis of reliability.
Analysis of the reliability forecast is made based on the structure of the power electric transformers
and on their functions in an electric power system of Romania (SEE).
Key-words: Reliability, Diagrams, Power transformers.
1 Introduction
Study of power transformer reliability of forecast
starts from the idea that although the processor to
other devices appear to be the most reliable while
still being a key component of power system, can
have a major impact on overall system reliability
of which is part. Transformer can be considered as
a bivalent element [3], [5], [6], [7] with two states
in terms of reliability: F-functioning and D-
defects.
Analysis of forecast reliability can be achieved on
the transformer structure or on the function based
on which it has a power system.
2 Structure Analyses to Forecast Reliability
of Power Transformers
An analysis of the reliability of the power
transformers can be made using the indicators of
reliability, either on the simplified equivalent
diagram or on the graph states and the method of
Markov chains [2], [3], [4], [6], [11], [15].
In this regard, processor power is considered a set
system consisting on the following subsystems:
Fig.Simplified equivalent diagram of the power
transformer.
where: SSM-magnetic subsystem, SSE-electrical
subsystem, SSI - insulation subsystem, SSCM-
subsystem to enhance mechanical SSR-cooling
subsystem, SSP-self-protection subsystem.
Knowing the specific indicators of reliability and
the serial character as the processor system, it can
be achieved the graph states for the simplified
analysis of safety while the power transformer, in
which the state 0 is successful, and i=1→6 state of
failure (when one of the subsystems may be
damaged) [16]:
Fig.The graph states for simplified analysis for
safety of power transformers.
Availability of power transformer can be analyzed
using the time and power variables on which it
made the power-time diagram of the power
transformer [5], [7]:
Proceedings of the International Conference on ENERGY and ENVIRONMENT TECHNOLOGIES and EQUIPMENT
ISSN: 1790-5095 148 ISBN: 978-960-474-181-6
Fig. 3: Defining characteristic sizes are available
electrical power transformers.
where sizes represented are as follows.
Sizes characteristic time:
TA–duration of the analysis, TF-duration of the
load and warm reserve, TRS-period of stagnation
as a reserve static (cold), Td, TMP–duration of the
downtime caused by failures in damage (Td) and
the preventive maintenance works (TMP).
Sizes characteristic of power: PN-rated power of
transformer, PT-power throughput, ∆PRC-
reduction power (power no transported T-F) due
to operation as hot backup, ∆PRF-forced reduction
in power due to un-catastrophic unavailability of
subsystems (SSM, SSE, SSR).
Sizes characteristic energy: WT - energy
throughput, ∆W RC, ∆WRS – no transiting energy
during the backup (RC, RS), ∆WRC,RC ∆W, ∆WRC -
unavailable energy in electric power transformer
secondary due to the un-catastrophic
unavailability, that the catastrophic defects and
preventive maintenance works.
Forecast reliability analysis based on electric
power transformer structure has in mind the safety
of time, availability of time , the power and the
energy transformer on the base station through
which the processor in operation and on the single
function of the transformer, the power required
transit the secondary.
3 Analysis of the Forecast Reliability
of Power Transformers in the EEA-
Based Functions Forecast reliability analysis based on functions
that satisfy each of the subsystems of the electrical
power transformer has the following functions:
f1 - self-processor; it refers to the possibility that
the electric power transformer provides intrinsic
safety by appropriate reaction of the elements of
the structure of SPP;
f2 - galvanic isolation and separation; it refers to
the retention performance of dielectric stiffness
under tension between the elements of electrical
power and earth transformer and between the
elements of power electrical transformer at the
different voltages;
f3 – the conservation of the quality of the
electrical throughput energy; it means that by the
state that certain elements of electrical power
transformer are, it should not be a source of
deforming or lop-sided arrangement;
f4 - transit load (power) required under the term;.
The functions f3 and f4 are considering the
possibilities of adjusting the voltage by the
switching plots of electrical power transformer.
Table 1 shows the relevant functions and
subsystems of the electric power transformer
which contribute to achieving these features:
Table 1 Encoding functions of subsystems state electric
power transformer.
Function Subsystems Function Subsystems
f 1 SSP f 3 SS, SSM, SSE
f 2 SSCM, SSI f 4 SS, SSR
With the functions coded above, it can be
performed the graph states of the electric power
transformer reported to the functions of his
subsystems, using as indicators the state and
transition probabilities as follows: N-normal, be -
the state of failure relative to the functions fand [1],
[7], [8], [10].
4: The graph of states of electrical power
transformer functions related to its subsystems.
An analysis of reliability of the electric power
transformer can be made by analysis of failure
modes of its components specifying the indicators
presented in Table [9, 14.11].
Table Defects in electrical power transformer.
Failure mode Sub
system Elements
U
D
S
C
I N
Indicators
affected
0 1 2
3
4
5
6
7
8
Columns X D p SSM
Clamps X D p
Primary Winding X X S t, D p ESS
Secondary Winding X X S t, D p
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ISSN: 1790-5095 149 ISBN: 978-960-474-181-6
Switch plots X X X X S t, D p
Input Elements (electrical leg. primary windings)
X X X S t, D p
Output Elements (electrical leg. secondary windings)
X X X S t, D p
The link switch plots X X X S t, D p
Connections between windings X S t, D p
Invalid link X S t, D p
Tightening bolts of insulation
Clamps X D p
Carcasses windings S t
Distance end of the winding X S t
View of the winding insulation X S t
Insulators for connection to
primary X X S t
Insulators for connection to
secondary X X S t
SSI
Insulating oil X X S t
Staging lower yoke X D T
Staging upper yoke X D T
Tightening Bolts Clamps X S t
Thrusts of building magnetic
circuit X S t
Thrusts of support elements in the
transformer tank X S t
Fasteners on pedestal X D t
SSCM
Grip and manoeuvre elements
(ear, rings, gauges. Pt. Lifting
trolley on wheels) X --
Transformer oil X D p
Tank X X S t
Radiators X X S t
Conservatory of oil X X D t
Gaskets (vat, Isolated) X X S t
Filter X D t
Cap conservative oil filling X --
Clear Conservative X --
Faucet conservative separation X D t
filling tank X D t
Drain vane X S t
Oil sampling valve X S t
Faucet drying oil X S t
for emptying X S t
Oil level indicator X D t
SSR
Forced Air Cooling X D p
Spark gap X S
Gas relay X S
SSP
Safety valve X S
Flag minimum oil X S
Screen Protectors X S t
Earth elements X s
The tables use the following notations: U- wear, D
- derives (change parameters), S - Breakdown C -
corrosion, I - interruption, N - unidentified, S–the
security of the transformer or of the personnel St -
safety time. Event three of the electrical power
transformer can be achieved in relation to various
undesirable events such as: lack of features,
uncertainty time, unavailable power or energy of a
the failure of a subsystem of electric power
transformer.
For example event tree was developed in relation
to the event "failure function galvanic isolation
and separation" (Fig. 5) and "catastrophic failure
of the cooling subsystem (Fig. 6):
5 Tree event of electrical power transformer failure
event reported to galvanic isolation and separation
function.
Based on data obtained from monitoring the
operation of power transformers within the EEA
were evaluated indicators of reliability of the
subsystems of the power transformers: Ri, Fi, µi, ie
Mi.
The evaluation of these indicators was made by
considering the exponential distribution of
random variables TBF and TMC.
Relations are calculated using the relationship 1:
[ ]
[ ][ ]
ri ti
i
ii
TPi
iTP
eM
FFF
µ−=µ
β
ν=µ
λ=
µ+λ
λ=
1,%
%
,100
%,
(1)
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ISSN: 1790-5095 150 ISBN: 978-960-474-181-6
6 Tree of electric power transformer of events
reported in catastrophic failure of the cooling
subsystem
where λ, µ - basic indicators of reliability of
power transformers;
FPT - probability of failure of power transformers;
υi, βi - weighting number of falls and fall duration
subsystem (i) the total value of these indicators at
the level of power transformers; tr=MTMC - the
time the works were completed in corrective
maintenance, considered within 16 hours.
With these relations were obtained the following
values of reliability indices calculated for the
station transformer T7 Tantareni
le 3 The values of reliability indicators for the
transformer T 7 Tantareni subsystems.
Sub
system SSM ESS SSI SSCM SSR SSP
Be 105 2.951 26.1 29.1 2.95 29.07 46.75
µi [h -1] 0.062 0.034 0.054 0.068 0.057 0.087
Mi 0.59 0.48 0.58 0.61 0, 62 0.69
Ri 0.95 0.94 0.96 0.98 0.97 0.95
4 The Operational Reliability Study
SEEA this part of the paper is presented a statistical
reliability of key global indicators by which we
can evaluate the behaviour in time of equipment
and hence power transformers as parts of
electrical equipment.
4.1 Number of Incidents and Duration
of Availability Evolution of the indicators "number of incidents"
and "total time of unavailability" in the EEA is
represented for the period 1996 - 2006 in Tab. 5,
that graph in Fig.statistical processing was done
with reference to the total electrical power
transformers within the EEA. 4: Evolution of indicators "number of incidents",
"Duration of unavailability.
Year 1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
Num-
ber of
inci-
dents
321 340 285 378 380 330 324 350 339 360
Total
period
of
down-
time
1124
1215
1090
1321
1378
1276
1250
1220
1230
1311
Graph evolution in time of global indicators.
respectively Fig.shows the evolution of the
indicator "number of incidents" in the categories
of equipment:
5: Evolution in time of the indicator "number of
incidents" in the categories of plants.
Year 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005
LEA 123 197 145 168 156 172 134 181 175 162
LES 110 115 125 108 118 123 130 112 134 153
PT 34 25 43 52 20 39 30 42 19 20
SE 22 34 28 41 18 20 11 36 24 25
From the causes for the occurrence of defects,
may be a statistic by which we can judge in each
case the total weight, and the frequency of
occurrence of a fault.
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ISSN: 1790-5095 151 ISBN: 978-960-474-181-6
8: Graph evolution whiles the number of incidents
on installations. We take into consideration the normal operating
conditions, the weather conditions, the moisture,
and other causes.
In the category of other causes may be considered
throwing foreign objects, variations of
temperature, tree falls, and extreme weather
conditions. As Table respectively Fig.presents a
ranking of the causes that led to defects facilities:
7: Chain of causes defects facilities.
Case Percent
Normal operating load 67.7%
Wind, storm 12.1%
Downloads atmospheric 12%
Penetration of moisture 2.44%
Other 5.67%
9: Graph hierarchically causes defects facilities.
Also, statistical data processing can provide an
assessment of the weight that the power
transformers in the equipment have.
This assessment can be made by the two
indicators' relative number of falls "and" relative
duration of unavailability.
7: Assessing the indicator "number of falls relative" to
the equipment.
Equipment Relative number of failures
(%)
DRV 0.34%
Secondary circuit 1.52%
Separator 7.12%
Current transformer 11.87%
Current transformer 12.46%
Power transformer 27.86%
Switch 38.83%
10: Change the indicator "number of falls relative"
to the equipment. 8: Evaluation indicator relative unavailability duration
"on equipment.
Equipment Relative duration of
unavailability (%)
DRV 0.51%
Secondary circuit 2.49%
Separator 2.70%
Voltage transformer 5.06%
Current transformer 9.71%
Power transformer 19.80%
Switch 59.73%
11: Change indicator relative unavailability
duration on equipment.
4.2. Indicators of Reliability of Electric
Power Transformers
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ISSN: 1790-5095 152 ISBN: 978-960-474-181-6
Study of operational reliability of power
transformers within the EEA has been made for
the period 1996 - 2005, on the volumes of
population (n) divided by the power game.
Table 6 presents the values of the indicator
"number of failures" υ (Ta) the time of statistical
analysis for the population studied.
12: Change the indicator "number of failures" in the
range of powers in the period 1998 to 2005.
A hierarchy of elements in terms of impact on the
power transformers is presented in Tab. 9,
respectively Fig. 13:
9: Chain of evidence in terms of impact of failure of
power transformers.
Item Percent
Primary Winding 59.9%
Secondary Winding 14.68%
Winding case 0.83%
Insulation between windings 4.62%
Insulators crossing 4.62%
Electrical contacts 3.6%
Gaskets 5.25%
Unclassified 6.21%
13: Graph hierarchically elements impacting on the
power transformers.
A statistic with the reasons behind the failure of
power transformers is presented in Table ,
respectively Fig.
10: Rating percentage of cases resulting failure of
power transformers.
Case Percent
Insulation aging 15.5%
Quality materials 35%
Surge 8%
Constructive solutions inadequate 2%
Maintenance failure 13.5%
Uncontrolled actions of Foreigners 4%
Other 22.5%
Fig. 14: Chart percentage of cases of failure of
power transformers.
By both, the summary of the table and the graphic
representation, one may note that a major
influence in the behaviour of power transformers
have a winding insulation, that poor quality
material.
Distribution of random variables and fundamental
indicators of reliability of electrical equipment can
be studied with the following specifications:
- Statistical processing can be made with
reference to the following random variables: TBF
good time running between two successive
failures, during fault TMC - during corrective
maintenance works and the annual number of
falls.
- Electrical equipment can be classified in terms
of operational reliability fall into two categories:
Equipments with a satisfactory level of reliability
that NFS which have the failure intensity of the
order (10-4
h-1
), category containing the falling
power transformers, the high voltage circuit
breakers and medium voltage circuit breakers;
Equipments with good reliability level of NFB
which have a failure intensity of the order (10-5
h-
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ISSN: 1790-5095 153 ISBN: 978-960-474-181-6
1), category falling separators, transformers and
the dischargers measure of protection.
Following the studies it was found that the law of
distribution model with minimum error statistics
of power transformers for TBF parameters and the
TMC is Weibull distribution.
Conclusions Following the studies carried out on the power
reliability transformers, he following conclusions
can be drawn:
In the analysis of the estimate reliability, the
electrical transformers should be considered as
complex systems consisting in many subsystems
(magnetic, electric, insulation, building
mechanical cooling and self-protection. In terms
of the operational analysis, with a strong
correlation between the rated power transformers
and the level of operational reliability, it has been
required the treatment of the categories of power
transformers, resulting in an analysis for power
transformers, respectively for the average power.
Following the studies it was found that the items
with the greatest impact on the reliability of
electric power transformers are windings. The
main cause in the failure of the electric power
transformers is the poor quality of materials such
as insulating materials. At thereliability analysis
of the electrical transformers must be considered
the maintenance terms, the availability and the
security of time.
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Proceedings of the International Conference on ENERGY and ENVIRONMENT TECHNOLOGIES and EQUIPMENT
ISSN: 1790-5095 154 ISBN: 978-960-474-181-6