Power Transformers Reliability Estimation Study

Power Transformers Reliability Estimation Study Cristinel POPESCU 1, Mircea GRIGORIU 2, Marius-Constantin POPESCU 3, Luminita Georgeta POPESCU 1, Constantina Liliana GROFU 4 1 University Constantin Brancusi of Targu Jiu, ROMANIA University POLITEHNICA Bucharest, 313 Spl.Independentei, zipcode 060042, Bucharest-6 3 University of Craiova, ROMANIA, 13, A.I.Cuza Street, zipcode 200585, Craiova popescu67pop@yahoo.com, popescu.marius.c@gmail.com, luminita@utgjiu.ro, 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. 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]: 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.The graph states for simplified analysis for safety of 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]: Fig.Simplified equivalent diagram of the power transformer. where: SSM-magnetic subsystem, SSE-electrical subsystem, SSI - insulation subsystem, SSCM- ISSN: 1790-5095 148 ISBN: 978-960-474-181-6

Fig. 3: Defining characteristic sizes are available electrical where sizes represented are as follows. Sizes characteristic time: T A duration of the analysis, T F -duration of the load and warm reserve, T RS -period of stagnation as a reserve static (cold), T d, T MP duration of the downtime caused by failures in damage (T d ) and the preventive maintenance works (T MP ). Sizes characteristic of power: P N -rated power of transformer, P T -power throughput, P RC - reduction power (power no transported T-F) due to operation as hot backup, P RF -forced reduction in power due to un-catastrophic unavailability of subsystems (SSM, SSE, SSR). Sizes characteristic energy: W T - energy throughput, W RC, W RS no transiting energy during the backup (RC, RS), W RC,RC W, W RC - 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: f 1 - 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; f 2 - 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; f 3 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; f 4 - transit load (power) required under the term;. The functions f 3 and f 4 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 f and [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. Sub Elements system 0 1 SSM ESS Failure mode U D S C I N 2 3 4 5 6 7 Columns X D p Clamps X D p Indicators affected Primary Winding X X, D p 8 Secondary Winding X X, D p ISSN: 1790-5095 149 ISBN: 978-960-474-181-6

SSI Switch plots X X X X, D p Input Elements (electrical leg. primary windings) X X X, D p Output Elements (electrical leg. secondary windings) X X X, D p The link switch plots X X X, D p Connections between windings X, D p Invalid link X, D p Tightening bolts of insulation Clamps Carcasses windings Distance end of the winding X View of the winding insulation X Insulators for connection to primary Insulators for connection to secondary X X X X X Insulating oil X X SSCM Staging lower yoke X D T D p Flag minimum oil X S Screen Protectors X 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 - 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): Staging upper yoke X D T Tightening Bolts Clamps X Thrusts of building magnetic circuit Thrusts of support elements in the transformer tank Fasteners on pedestal X X X D t SSR Grip and manoeuvre elements (ear, rings, gauges. Pt. Lifting trolley on wheels) X -- Transformer oil X D p Tank X X Radiators X X SSP Conservatory of oil X X D t Gaskets (vat, Isolated) X X 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 Oil sampling valve X Faucet drying oil X for emptying X Oil level indicator X D t Forced Air Cooling X D p Spark gap X S Gas relay X S Safety valve X S 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: R i, F i, µ i, ie M i. 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: λ λi[ %] FTP =, Fi = FTP, λ+µ 100 (1) νi[ %] µ i t r µ i = µ, M i = 1 e β % i [ ] ISSN: 1790-5095 150 ISBN: 978-960-474-181-6

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 6 Tree of electric power transformer of events reported in catastrophic failure of the cooling subsystem Number of incidents 321 340 285 378 380 330 324 350 339 360 Total period 1124 1215 1090 1321 1378 1276 1250 1220 1230 1311 of downtime where λ, µ - basic indicators of reliability of power transformers; F PT - probability of failure of power transformers; υ i, β i - weighting number of falls and fall duration subsystem (i) the total value of these indicators at the level of power transformers; t r =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 T 7 Tantareni Sub system le 3 The values of reliability indicators for the transformer T 7 Tantareni subsystems. 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 M i 0.59 0.48 0.58 0.61 0, 62 0.69 R i 0.95 0.94 0.96 0.98 0.97 0.95 Graph evolution in time of global indicators. respectively Fig.shows the evolution of the indicator "number of incidents" in the categories of equipment: Year 5: Evolution in time of the indicator "number of incidents" in the categories of plants. 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 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. 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. 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, ISSN: 1790-5095 151 ISBN: 978-960-474-181-6

(%) 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% 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% 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% 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 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 (T a ) the time of statistical analysis for the population studied. 13: Graph hierarchically elements impacting on the 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 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% 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 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% Fig. 14: Chart percentage of cases of failure of 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. References [1] Ilie F., Bulucea C.A., Popescu M.C., Simulations of Oil-filled Transformer Loss-of-Life Models, Proceedings of the 11 th International Conference on Mathematical Methods and Computational Techniques in Electrical Engineering (MMACTEE'09), Published by WSEAS Press, pp.195-202, Vouliagmeni Beach, Greece, September 2009. [2] Mastorakis, N.. Bulucea, C.A., Popescu M.C., Transformer Electromagnetic and Thermal Models, Proceedings of the 9 th WSEAS International Conference on Power Systems (PS`09): Advances in Power Systems, pp.108-117, Budapest, Hungary, September 2009. [3] Mastorakis N., Bulucea C.A., Manolea Gh., Popescu M.C., Perescu-Popescu L., Model for Predictive Control of Temperature in Oil-filled Transformers, Proceedings of the 11 th WSEAS International Conference on Automatic Control, Modelling and Simulation, pp.157-165, Istanbul, Turkey, May -June 2009. [4] Mastorakis N., Bulucea C.A., Popescu M.C., Manolea Gh., Perescu L., Electromagnetic and Thermal Model Parameters of Oil-Filled Transformers, WSEAS Transactions on Circuits and Systems, Issue 6, Vol.8, pp.475-486, June 2009. [5] Popescu M.C., Manolea Gh., Bulucea C.A., Boteanu N., Perescu-Popescu L., Muntean I.O., Transformer Model Extension for Variation of Additional Losses with Frequency, Proceedings of the 11 th WSEAS International Conference on Automatic Control, Modelling and Simulation, pp.166-171, Istanbul, Turkey, May -June 2009. [6] Popescu, M.C., Manolea, Gh., Bulucea, C.A., Perescu-Popescu, L., Drighiciu, M.A., Modelling of Ambient Temperature Profiles in Transformer, Proceedings of the 13 th WSEAS International Conference on Circuits, (part of the 13 th WSEAS CSCC Multiconference), pp.128-137, Rodos, Greece, July 2009. [7] Popescu M.C., Mastorakis N., Manolea Gh., Thermal Model Parameters Transformers, WSEAS Transactions on Power Systems, Issue 6, Vol.4, pp.199-209, June 2009. [8] Popescu M.C., Bulucea C.A., Perescu L., Improved Transformer Thermal Models, WSEAS Transactions on Heat and Mass Transfer, Issue 4, Vol.4, pp. 87-97, October 2009. [9] Popescu M.C., Mastorakis N.. Popescu- Perescu L., New Aspects Providing Transformer Models, International Journal of Systems Applications, Engineering & Development, Issue 2, Vol.3, pp.53-63, 2009. [10] Popescu M.C., Mastorakis N., Bulucea C.A., Popescu-Perescu L., Modelling of Oil-filled Transformer, International Journal of Mathematical Models and Methods in Applied Sciences, Issue 4, Vol.3, pp.346-355, 2009. [11] Popescu M.C., Mastorakis N., Popescu- Perescu L., Electromagnetic and Thermal Model Parameters, International Journal of Energy, Issue 4, Vol.2, pp.51-65, 2008. [12] Popescu M.C., Manolea Gh., Perescu L., Parameters Modelling of Transformer, WSEAS Transactions on Circuits and Systems, pp.661-675, Issue 8, Vol.8, August 2009. [13] Popescu M.C., Mastorakis N., Bulucea C.A., Manolea Gh., Perescu L., Non-Linear Thermal Model for Transformers Study, WSEAS Transactions on Circuits and Systems, Issue 6, Vol.8, pp.487-497, June 2009. [14] Popescu M.C., Popescu C., Functional Parameters Modelling of Transformer, Journal of Mechanical Engieenering Research, pp.001-037, November 2009. [15] Popescu M.C., Popescu C., Transformer Thermal and Loss of Life Models, Journal Electrical and Electronics Engineering Research, pp.001-022, November 2009. ISSN: 1790-5095 154 ISBN: 978-960-474-181-6