Power Transformers Reliability Estimation Study - … · Power Transformers Reliability Estimation Study Cristinel POPESCU1, Mircea GRIGORIU2, Marius-Constantin POPESCU3, Luminita

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


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)


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.


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%


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%


Power transformer 19.80%

Switch 59.73%

11: Change indicator relative unavailability

duration on equipment.

4.2. Indicators of Reliability of Electric

Power Transformers


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-


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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Simulations of Oil-filled Transformer Loss-of-Life

Models, Proceedings of the 11th International

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Computational Techniques in Electrical

Engineering (MMACTEE'09), Published by

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[2] Mastorakis, N.. Bulucea, C.A., Popescu M.C.,

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ISSN: 1790-5095 154 ISBN: 978-960-474-181-6

Documents

Power Transformers Reliability Estimation Study - … · Power Transformers Reliability Estimation Study Cristinel POPESCU1, Mircea GRIGORIU2, Marius-Constantin POPESCU3, Luminita