51. IWK Internationales Wissenschaftliches Kolloquium International Scientific Colloquium

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1 51. IWK Internationales Wissenschaftliches Kolloquium International Scientific Colloquium PROCEEDINGS September 26 FACULTY OF ELECTRICAL ENGINEERING AND INFORMATION SCIENCE INFORMATION TECHNOLOGY AND ELECTRICAL ENGINEERING - DEVICES AND SYSTEMS, MATERIALS AND TECHNOLOGIES FOR THE FUTURE Startseite / Inex:

2 Impressum Herausgeber: Reaktion: Der Rektor er Technischen Universität llmenau Univ.-Prof. Dr. rer. nat. habil. Peter Scharff Referat Marketing un Stuentische Angelegenheiten Anrea Schneier Reaktionsschluss: 7. Juli 26 Fakultät für Elektrotechnik un Informationstechnik Susanne Jakob Dipl.-Ing. Helge Drumm Technische Realisierung (CD-Rom-Ausgabe): Institut für Meientechnik an er TU Ilmenau Dipl.-Ing. Christian Weigel Dipl.-Ing. Marco Albrecht Dipl.-Ing. Helge Drumm Technische Realisierung (Online-Ausgabe): Universitätsbibliothek Ilmenau Postfach Ilmenau Verlag: Verlag ISLE, Betriebsstätte es ISLE e.v. Werner-von-Siemens-Str llrnenau Technische Universität llmenau (Thür.) 26 Diese Publikationen un alle in ihr enthaltenen Beiträge un Abbilungen sin urheberrechtlich geschützt. Mit Ausnahme er gesetzlich zugelassenen Fälle ist eine Verwertung ohne Einwilligung er Reaktion strafbar. ISBN (Druckausgabe): ISBN (CD-Rom-Ausgabe): Startseite / Inex:

3 51 st Internationales Wissenschaftliches Kolloquium Technische Universität Ilmenau September 11 15, 26 R. Włoek / Sz. Moskwa Moelling of HV Devices Diagnostic Proceures INTRODUCTION Consequence of asset restructuring are the increasing nees of cost-effective operation, maintenance an iagnostic processes that means the work s reliability of evices/systems shoul be on high level an cost of eventual breakown shoul be as low as possible. Exploitation of high voltage evices has been base till now on specialize traitional tools, typically using "time-base" cyclic maintenance scheuling as a part of all exploitation processes. Increasing importance of iagnostic for supply quality [4] is a reason that iagnostic proceures etermine exploitation processes of high voltage evices. Supply availability epens on technical state of all power electrical evices which participate in transport an istribution process, e.g.: power istribution stations, power an istribution transformers, power electrical lines, etc. In many matters which are consiering uner iagnostic proceure, appear ranom variables epene on parameter (often interprete as a time). Mathematical moels of these occurrences are stochastic processes, e.g. Markov moels. Mathematical moels base on Markov theory are use to stuy of system state if this state in a given moment is enough to etermine probabilistic profiles of future system evelopment The HV evice state can be specifie by evice insulation conition. Result of iagnostic proceure gives information for the classification of insulation states (Tab. 1.). Aitional avantage of iagnostic proceure might be renewal of technical state of evices by corrective maintenance. Preventive maintenance type e.g. CBM inclue a iagnostic proceure. In general, maintenance is either planne. Presente moels below were use to calculation availability of HV evices epens only on time interval of iagnostic proceure or without iagnostic. 1

4 Table 1. The classification of insulation states base on the measuring results PI Polarization Inex DAR Digital Arc Reflection TC Time Constant DD Dielectric Discharge Insulation states 1 minutes 1 minute 6 secons 15 secons resistance x capacity S 3 weak < 1 < 1 < 1 > 4 S 2 inefinite 1 o 2 1 o 1,4 1 o 8 2 o 4 S 1 goo 2 o 4 1,4 o 1,6 8 o 2 < 2 S as new > 4 > 1,6 > 2 ischarge current (after 6s)/(V x C) MODELS DESCRIPTION First moel represents egraation process of insulation. The example use stochastic processes theory to buil mathematical moels of HV evice insulation to estimate probability of failure, what is cheaper then after breakown costs. Moel an appropriate methos for parameter estimation of egraation ata have been evelope [5, 6]. Moel is base on Markov theory of ranom processes. The Markov processes require to subject matter of exploitation an iagnostics probabilistic approach, base on few assumptions. The following assumptions are here taken into account: HV Device might be in six states, where four of them represent egraation state of insulation an two S 4 an S 5 represent amage. Degraation is moeling as the natural one irectional transition between the states, S, S 1, S 2, S 3 etermine by result of iagnostic measurements an tests (Tab. 1). The probability of the transition to the following state in the step (n+1) oes not epen on the probability of the transition from step (n-1) to n. p ij is the probability of transitions between states i an j. Graf of moel is shown on Fig. 1. 2

5 Fig.1. Graph of egraation process For presente example following simplifie probabilities (uring single step) are taking into account: p p p p,2 (1) p p p p,8 (2) p p 1 (3) 3 4 One step n in simulation is equal 1 year. As the result of calculations are limite state probabilities: p 39,5% S (4) p 28,2% S1 (5) p 2,1% S 2 (6) p 4% S 3 (7) p,8% S 4 (8) p 7,3% S 5 (9) Availability is a sum of probability of states S, S 1, S 2 an is equal 87,8%. This mathematical moel coul support the iagnostics ecision process about continuation of evices exploitation or eventually repair. The next moel can be use to simulation an calculation availability of evice in exploitation process with iagnostic maintenance. As the practical application, the optimal time of the iagnostic inspection may be calculate on the basis of such moel. The moel escription has been evelope as a continuous time Markov chain [1, 2]. To ate, in the power system context, continuous parameter Markov chains have been applie most extensively to moel power system an maintenance problems [3]. The following assumptions an approximations have been use for constructing the moel: 3

6 The transitions time (times to occurrence of failures, component repair times, preventive maintenance times an times between subsequent preventive maintenance actions) are Weibull istribute ranom variables. The cumulative istribution function is: α F ( t) 1 exp( βt ) (1) For α 1 equation (1) becomes a function of exponential istributions. If α 1 an β the expecte value of ranom variable can be expresse as: 1 1 EX (11) β Device failures an intermeiate state are inepenent. Moeling evice cannot become efective uring iagnostics an repairs. When evice is own the process can only move to up-state at a corresponing repair rate. After the occurrence of evice failure the process moves to a state in witch the evice is in optimal conition (S state as new ) again. The time neee to carry out preventive maintenance is not neglecte in favor of a state space reuction. When a protection evice exhibits a certain efects this efect might be etecte an correcte uring iagnostic proceure an preventive maintenance. Fig.2. Graph of egraation process with catastrophic amage Graph of exploitation process in this moel (Fig. 2) takes into account the following 4

7 states: S, S 1, S 2 states of insulating system, efine respectively as new, healthy an egrae, S 3, S 4 amage states, X, X 1, X 2 states of iagnostic maintenance. This moel enables the evaluation of optimal interval time between iagnostic proceure an the availability of arrangement as the function of time. Following quantities are efine in this moel: rate of occurrence of potential catastrophic amage, mean lifetime of insulating system without iagnostic proceure 1-1, rate of repair following catastrophic failure µ 4, renewal time of arrangement µ 3-1, time of iagnostic- an repair proceure µ -1, number of intermeiate states, in this case k 3, optimal time interval of iagnostic inspection -1. The equations escribing probability events are in the following matrix forms: P Λ (12) The probability vector P is efine as: ef [ p p1 p2 p3 p4 p5 p6 p7 ] P (13) n p i i 1 1 for n 8 (14 whose element p i enotes the probability that the Markov chain is at state i. Matrix of transition between states has the form: z k1 z k1 z k1 µ µ Λ (15) µ µ µ µ µ µ 4 4 µ 3 µ 3 where: z k1. The solution of equations (12) gives the availability of the moel, which is 5

8 calculate as: A ( t) p + p + p (16) The following example illustrates the implementation of the moel. All time an rate are exponentially istribute. In this case: 1/365, 1 1/365, µ 4 ½, µ 2 an k 3. Thus the equation (16) has a form: 195( , A ( t) (17) (4, , , ,62 1 ) µ 3 ) µ Simulation was taken for renewal time of arrangement µ 3-1 from 1 ay to 7 ays. Availability is calculate for constants µ 3-1 an then epens only on time interval of iagnostic proceure t -1. Plot of whole simulation is shown in Fig. 3. Fig.3. Plot of moel availability A(t) For µ 3 1/7 (renewal in 7 ays) maximum of function A(t) is equal,9851 for t 74 ays. Optimal value of the mean time to iagnostic maintenance (inspection an renewal) is calculate by taking the function A(t) with respect to an then equating it to zero. 6

9 CONCLUSIONS The mathematical simulation an the knowlege of state changing probability or especially probability of evice failure may be applie to increase of preventive effectiveness of iagnostics an HV evice work Availability, in other wors better supply quality. Markov theory is very useful to moel an analyse the iagnostic processes. Propose in this paper, mathematical moels enable e.g. quick an easy way to equal Availability of HV evice. This moel makes it possible to simulate any ranom process with regar to ifferent kin of subject factors. References: [1] Davis M.H.A.: Markov Moels an Optimization, Chapman & Hall, 1993 [2] Filipowicz B.: Moelowanie i optymalizacja systemów kolejkowych - cz. I Systemy markowskie. (in polish) Przesiębiorstwo Poligraficzne Taeusz Rukowski, Kraków 1995 [3] Pukite P., Pukite J., Moeling for Reliability Analysis: Markov Moeling for Reliability, Maintainability, Safety, an Supportability, Wiley-IEEE Press, 1998 [4] Subgroup Quality Aspects within Working Group Network Issues : Quality Aspects, EUROELECTRIC, 2, Belgium [5] Włoek R., Moskwa Sz.: Application of stochastic processes theory to iagnostics of high voltage evices EPE 25 6th International Scientific Conference Electric Power Engineering 25, May 3-June 1, 25, Kouty na Desnou, Czech Republic p. 83 [6] Włoek R., Moskwa Sz.: Zastosowanie proceur probabilistycznych w eksploatacji elektroenergetycznych linii napowietrznych i kablowych Applicability probabilistic proceure in exploitation of power electrical lines an cables lines (in polish) Przeglą Elektrotechniczny, 25 Vol.81 No.4, pp Authors: Prof. Romual Włoek Ing. Szczepan Moskwa, MSc AGH UST Department of Electrical Power, al. Mickiewicza Kraków, POLAND Phone: Fax: gewloek@cyf-kr.eu.pl, szczepan@agh.eu.pl 7