Reliability and Availability Analysis Methodology for Power System Protection Schemes

Transcription

1 Reliability and Availability Analysis Methodology fo Powe System Potection Schemes Andé dos Santos Instituto Supeio Técnico, Univesidade de Lisboa Lisboa, Potugal Rede Eléctica Nacional S.A. Sacavém, Potugal P. F. Coeia, M.T. Coeia de Baos, Fellow, IEEE Instituto Supeio Técnico, Univesidade de Lisboa Lisboa, Potugal Abstact A new methodology is pesented, allowing to evaluate potection systems eliability and availability indexes, taking into account equipment failue and epai ates. The potection scheme is tanslated into a eliability gaph, enabling to identify all possible logical occuences in the system, eithe meaning failue o successful opeation. Evaluation of the system eliability and availability indexes is achieved by Monte Calo simulation. The methodology is applied to a typical tansmission line potection bay, fo diffeent time to epai scenaios, and conclusions on asset management options ae dawn. In the eliability gaph, each unit is epesented by a diected banch, wheeas nodes epesent unit connections. The system success is descibed by any path connecting cause to effect. Redundancy will esult into altenative paths; theefoe, system success does not depend on the success of all its units. Keywods powe system potection, automation, eliability, availability, eliability gaph, Monte Calo simulation. I. INTRODUCTION Reliability and availability of powe systems is of stategic impotance fo defining powe utilities CAPEX and OPEX policies. Futhemoe, egulatos ae equiing that utilities comply with objectives in powe system design and opeation, towads fulfillment of a specified Adequate Level of Reliability fo the bulk powe system [1] to [3]. Consequently, utilities ae facing new challenges in edefining equipment life cycles, establishing eliability-centeed and condition-based maintenance pogams, downsizing opeational maintenance teams, outsoucing maintenance, educing spae pat stoage, and edesigning cost effective potection and automation schemes. These ae some of the utilities concens that uge fo a eliability and availability analysis appoach. Reliability and availability analysis of powe system potection schemes is usually addessed by means of fault tee and Makov analysis [4] to [8]. In the pesent pape, an altenative methodology, based on complex system desciption by means of eliability gaphs and solution by Monte Calo simulation, is descibed and applied to a line bay potection system. II. PROPOSED METHODOLOGY A. System Desciption Complex systems ae composed by numeous units opeating in seies, paallel, standby, o a combination of those. The system woking pinciple is epesented by a eliability block diagam, and the coesponding eliability gaph. Fo illustation, a vey simple example is pesented in figue 1. Fig. 1: Example of a system woking pinciple desciption by eliability block diagam a) and eliability gaph b). The eliability of a given unit,, is defined as the pobability of failue-fee opeation up to time t. Unit pefomance is also descibed by a failue ate function, elated to the time ate of unit suvival, : 1 (1) exp (2) Successful opeation of seies-connected units natually equies that all units opeate successfully. Consideing that the defined units do not inteact with each othe, system eliability is given by: (3) In a paallel configuation, the system success occus if any of the units succeeds, the system eliability being: (4) The mean time to fail MTTF is a key pefomance index commonly used to descibe the system eliability: MTTF (5) Anothe impotant system index is its availability. The availability function is defined as the pobability that the

2 system is in opeation at time t. Fo a single non epaiable unit but, if epai is allowed, emains unchanged while is inceased. On edundant systems, unit epai inceases both and. Repai of a unit is chaacteized by the pobability of epai up to time t, and the mean time to epai is used as a key pefomance index to descibe the epai pocess: MTTR (6) B. System Reduction Poblem complexity can be educed by educing the numbe of banches equied to descibe the system woking pinciple. Consideing equations (3) and (4), equivalent units can be defined by meging seies and paallel connected units. Reliability of the espective equivalent units is given by and [9]: exp (7) 11exp (8) whee. Fom an opeational point of view, meging is ecommended only fo units with common epai pocesses. C. Solution Algoithm Reliability gaph analysis allows identifying all possible logical occuences in the system, as well as the subset coesponding to system successful opeation. Each successful event, commonly named tie-set [9], coesponds to a set of ightly oiented banches connecting cause and effect. A tie-set is said minimal when no node is tavesed moe than once. The set of all minimum tie-sets defines the eliability of the oveall system. Consideing a system with i minimum tie-sets (T 1, T 2,, T i ), the system eliability is given by: t T t T t T t (9) Fo the system being used as illustation (figue 1), two minimum tie-sets exist and: T t t t (10) T t t (11) These tie-sets ae descibed as ows in Table 1, whee the columns coespond to the eliability gaph banches. The pobability of occuence of a tie-set is simply the poduct of pobabilities of success of each doted banch. Table 1: TIE-SETS of system composed of a unit in seies with two paallel units. U1 U2 U3 T 1 T 2 Evaluation of the system eliability and availability indexes is achieved by Monte Calo simulation [10]. A stochastic pocess, which descibes the opeation of lage numbe of systems opeating duing a long peiod, is simulated. System failues, suvivals and epais ae egisteed as if they wee the esult of one single expeiment. The simulation time span is divided into an equal numbe of time intevals (tials), such as a second, an hou, o a yea. At each tial, a set of andom numbes is geneated accoding to a unifom distibution ove the inteval 0, 1. The geneated numbes ae compaed with the coesponding unit failue pobability, 1, o epai, duing the tial. If the unit is in opeation at the tial beginning, and the geneated andom numbe is highe than its failue pobability, the unit will fail. If the unit is on a fail state and the geneated andom numbe is highe than its epai pobability, the unit will be epaied. The simulation stats with all units in opeation and, as the simulation evolves, the units state will change accoding to thei fail/epai cycles. Tial esults ae used at the end of the simulation to compute, and. D. Unit Hazad Model A unit hazad model descibes its failue and epai ates. One of the most commonly adopted failue ate models is the constant failue ate. Available field data suggest that this is a good assumption fo powe system equipment [11]. The same applies to equipment epai ates. The coesponding eliability and epai functions ae witten as: (12) (13) whee λ and µ denote the failue and epai ates. E. Statistical analysis The eliability and availability indexes cannot tuly be detemined fom a single Monte Calo simulation. Howeve, when epeated N times, with diffeent andom seeds, the simulations yields a set of values fo eliability and availability indexes. Fo each set one can calculate statistical paametes such as the aveage, the standad deviation o a two side confidence intevals CI on : N N (14) (15) N ; (16) N whee is the fequency of occuence, and is the standad nomal andom vaiable coesponding to 1001 % CI. F. Algoithm Validation A system composed of two edundant units was consideed fo validation of the poposed algoithm. The units ae chaacteized by constant failue and epai ates, failues/hou, epais/hou.

3 Pefomed algoithm validation encompasses checking the computed eliability and availability values, and also checking the adequacy of Monte Calo simulation to descibe the eliability of a single unit. On one hand, as egads availability, fo such simple system, it can be theoetically calculated by [9]: (17) Theefoe, fo the consideed system, 99.99%. On the othe hand, no closed fom exists allowing diect calculation of the eliability. Validation is caied out by compaison with esults obtained by Makov Chain appoach. Using the developed methodology, the system eliability index was calculated by simulating N=300 systems opeating duing hous. Tials ae made on an houly basis and the obtained numbe of system failues and suvivals, ae pesented in table 2, fo each 4000 hous. System eliability values, at the end of each time inteval, shown in figue 2, ae calculated as the coesponding numbe of suvivals, divided by the numbe of simulated systems. Table 2: FAILURES AND SURVIVALS fom a Monte Calo simulation of 300 systems opeating duing hous. Time inteval Failues in the inteval Numbe of suvivals (Hou) Using a Makov Chain appoach, the system eliability and availability indexes ae evaluated by solving m fist ode diffeential equations, m being the numbe of system states [9]. Even if only two states (success/fail) ae possible fo each of the n units in the system, 2. This indicates that, although being a vey poweful method, the Makov Chain appoach apidly explodes in complexity as soon as the numbe of units and states inceases. Fo the simple system being consideed, only 4 equations ae solved. Obtained esults ae pesented in figue 2, and thei matching with esults fom Monte Calo simulation is clea. In ode to calculate the system availability index, unit epai is now taken into account. This index is calculated at the end of the simulated time span, as the pecentage of system successful opeation time. The simulated time span anged fom 10 to hous. Each simulation is epeated 40 times, and statistical analysis of all esults is caied out to assess system availability. Figue 3 pesents the calculated availability, its aveage and the coesponding 95% and 98% confidence intevals, as function of the simulated time. Results clealy show that simulation time span must be defined in accodance to the equied confidence inteval. Fig. 2: Reliability of a system with two edundant units computed afte Monte Calo simulation (histogam). Reliability cuve computed using Makov Chain (solid line). Fig. 3: Availability of a system with two edundant units, calculated afte Monte Calo simulation and as function of the simulation time span. Availability calculated fo each simulation (dots), its aveage (solid line) and its 95% and 98% confidence intevals (shaded aea). The adequacy of the Monte Calo simulation to descibe the eliability of a given unit was also checked. A simulation was caied out, consideing 300 units simultaneously placed in opeation, and thei states wee monitoed fo a time span of hous. Tials wee made, on an houly basis, and the numbe of unit failues and suvivals is pesented in table 3, fo each 1000 hous. Table 3: FAILURES AND SURVIVALS fom a Monte Calo simulation of 300 units opeating duing hous. Time inteval Failues in the inteval Numbe of suvivals (Hou) Using the esults fom Table 2, the coesponding failue ate was calculated using equation (18).

4 1 (18) whee n denotes the numbe of suvivals in the inteval. The coesponding histogam is pesented in figue 4. It shows that the simulation data, while still showing some andomness, espects the unit fault ate. Fig. 4: Unit failue ate computed afte Monte Calo simulation (histogam) with failues/suvivals pe hou (solid line). III. FAILURE RATE OF BASIC COMPONENTS A Adopted Desciption Fomat The failue ate data of the main components of a line bay potection system has been collected fom seveal souces, Unfotunately, the failue ate data do not shae a common fomat and, in ode to combined all these data on the same study, it is necessay to adopt a unique failue ate fomat. In the pesent study, the adopted failue ate index is the numbe of failues pe yea. A thoughtful bibliogaphical suvey on eliability data fo the elevant potection system components was conducted and data wee pocessed in ode to fit the adopted desciption fomat. B Cicuit Beake Data published in CIGRE TB 510 [12], esulting fom a woldwide suvey, wee selected. It includes both Majo and Mino Failues. The cicuit beake components wee gouped into two categoies: i) the components at sevice voltage, and the opeating mechanism; ii) the electic contol and auxiliay cicuits. This classification was adopted, esulting into two sepaate tables, Tables 4 and 5. Pesented data coespond to all Majo Failues in which a fail to open occued afte a fault cleaing command. C Measuing Tansfomes Measuement tansfomes eliability data was collected fom the CIGRE bochue TB 512 [13], also esulting fom a woldwide suvey. The tansfome components ae divided in two categoies egading thei physical connection to the powe system: i) pimay components and ii) seconday components. This classification was adopted and the coesponding failues/yea wee evaluated. Results ae shown in Tables 6 and 7. D Communication System Regading eliability of communication systems, the objective values poposed in the Communications Systems Pefomance Guide fo Potective Relaying Applications wee consideed. This guide was pepaed jointly by the WSCC Telecommunications and IEEE PSRC Relay Wok Goups [14]. The communication systems ae classified accoding to the impotance of the bulk powe system element which they ae applied to. The failue ates wee evaluated consideing the taget values fo availability poposed in [9], and fo diffeent MTTR. Table 4: CB FAILURE RATE - Components at sevice voltage and opeating mechanism. (failues/yea 10 ) Kind of sevice Total Live Tank Dead Tank GIS Ovehead line Tansfome Cable Shunt eacto Capacito Bus couple Table 5: CB FAILURE RATE - electic contol and auxiliay cicuits. (failues/yea 10 ) Kind of sevice Total Live Tank Dead Tank GIS Ovehead line Tansfome Cable Shunt eacto Capacito Bus couple Table 6: MEASURING TRANSFORMERS FAILURE RATE - pimay components. (failues/yea 10 ) Rated Voltage AIS GIS Class MVT CVT CCVT CT VT CT 60<=V<110kV <=V<200kV <=V<300kV <=V<500kV <=V<700kV >=700kV Table 7: MEASURING TRANSFORMERS FAILURE RATE - seconday components. (failues/yea 10 ) Rated Voltage AIS GIS Class MVT CVT CCVT CT VT CT 60<=V<110kV <=V<200kV <=V<300kV <=V<500kV <=V<700kV >=700kV

5 Computed values fo the thee communication system classes ae shown in Table 8. Table 8: COMMUNICATION SYSTEMS FAILURE RATE, accoding to Availability equiement and defined MTTR. Class A (%) MTTR=24h MTTR=48h (failues/yea) MTTR=72h MTTR=168h E Potection Relays It is undestood that eliability of powe system potection schemes encompasses the ability to opeate wheneve equied (dependability) and the ability not to opeate if not equied (secuity). Reliability and availability data fo potection elays ae not common in the liteatue. These ae vey much dependent on the utility philosophy towads: maintenance pactices; availability and teatment of substation SCADA alams; elay type and manufactue. Even so, field data on availability can be found fo diffeent elay technologies [15] [5]. Fo failue ate computation, a MTTR value of 2.5 yeas was consideed fo electomechanical and static technologies. It is commonly accepted that this coesponds to a utility pactice of a 5-yea time-based maintenance pogam. Fo the digital technology, self-supevision was assumed, and a 1-week MTTR was consideed. Results ae pesented in Table 9. Table 9: PROTECTION RELAY FAILURE RATE, accoding to availability field data and typical MTTR. Relay type A MTTR Failue ate (%) (yea) (failues/yea) Electomechanic and static Static Digital with self-supevision F DC Powe Supply The % availability value was consideed fo the DC Powe Supply, esulting fom field data published by Schweitze [5]. This numbe, although vey high, does not seem too fa fom eality, given the substation auxiliay powe supply system achitectue. Indeed, the DC powe supply has multiple edundancy, most of the cases deliveed fom tetiay windings of altenative powe tansfomes, backup batteies and a diesel geneato. Computed esults shown in Table 10 coespond to consideing diffeent values of MTTR, anging fom 1 day to 1 week. Table 10: AUXILIARY DC POWER SUPPLY FAILURE RATE, accoding to A= % and typical MTTR used. (failues/yea 10 ) MTTR 1 day 2 days 3 days 7 days DC powe supply IV. CASE STUDY - RELIABILITY AND AVAILABILITY OF A LINE BAY PROTECTION SYSTEM A typical tansmission line bay potection system is consideed, with full edundancy of most of its components: main potection elays, cuent tansfome coes, voltage tansfome seconday cicuits, cicuit beake tipping coils, and auxiliay powe supply. The study is intended to povide guidance on asset management policy based on potection system availability equiements. Taken fom section III, eliability data of the elevant line bay elements ae shown in Table 11, coesponding to maximum and minimum failue ate values. Table 11: MAXIMUM AND MINIMUM FAILURE RATES of line bay potection system bay elements. (failues/yea 10 ) min max CT Pimay System (CTp) VT Pimay System (VTp) CB Sevice Components (CBs) CT Seconday System (CTs) VT Seconday System (VTs) CB Contol System (CBc) Main Potection elay (M) DC Powe supply system (DCPS) The system eliability gaph and the coesponding educed model ae shown in figues 5 b) and c), espectively. The educed model was obtained accoding to the peviously pesented methodology, consideing a common MTTR fo all seconday system elements, and a simila assumption fo all pimay system elements. These assumptions eflect common maintenance pactices. CB CT VT VTs1 CTs1 DC PS1 Bus DC PS1 M1 VTp M1 CTp M2 U2 U1 U3 CBc1 CBc2 CBs U1 U2 U3 DC PS2 M2 CTs2 DC PS2 VTs2 a) b) c) Fig. 5: Line bay potection system a). Reliability gaph b) educed model c).

6 Fig. 6: (a), (b), (c): Line bay potection system availability, calculated afte Monte Calo simulation consideing seveal scenaios of pimay and seconday systems MTTR. Availability aveage (solid line) and its 95% and 98% confidence intevals (shaded aea). Reliability indices of the equivalent units in the educed model ae given by: U VTP CTP CB (19) U VTS CTS CBC M DCPS (20) U VTS CTS CBC M DCPS (21) The coesponding computed values ae pesented in Table 12. Tie-sets ae identified in Table 13. Given the unit failue ates U, U, and U, the system eliability is evaluated accoding to: U 1 1 U 1 U (22) Results shown in Table 14 coespond to 2, 5 and 10 yeas of system opeation. They ae compaed with the eliability of the main potection elay. These esults ae useful to define equipment waanties and stocking. In ode to evaluate the system availability, the poposed Monte Calo solution algoithm was applied. Seveal scenaios, chaacteized by a combination of diffeent pimay and seconday systems MTTR values, wee consideed: 1 to 6 months, in steps of 1 month, fo the seconday system; and 1, 2 and 3 days, fo the pimay system. The simulations wee caied out consideing 40 systems opeating simultaneously ove 210 hous. Each scenaio was simulated 80 times. The coesponding system availability was evaluated. Statistical analysis of the esults was caied out. Results pesented in figues 6 (a), (b) and (c) coespond to the wost case scenaios egading eliability data (maximum failue ate values in Table 11). The aveage value and the coesponding 95% and 98% confidence intevals of the potection system availability ae shown. Each figue coesponds to a given pimay system MTTR, and the system availability is epesented as a function of the seconday system MTTR. Figue 6 shows that an incease on the pimay o seconday system MTTR impacts negatively on the system availability, this impact being highe as egads the pimay system. This is expected given the edundant design of the seconday system. The poposed methodology allows the quantification of these impacts, thus poviding guidance on system design, while accounting fo maintenance stategies. Table 12: MAXIMUM AND MINIMUM FAILURE RATES of the equivalent units used in the educed model of the line bay potection system. (failues/yea 10 ) min max U U U Table 13: TIE-SETS of the line bay potection system educed model. U1 U2 U3 T 1 T 2 Table 14: RELIABILITY OF LINE BAY PROTECTION SYSTEM AND MAIN PROTECTION, afte 2, 5 and 10 yeas of opeation. Reliability (%) Potection System Main Potection Relays 2 yeas 5 yeas 10 yeas max min max min max min

7 V. DISCUSSION ON ASSET MANAGEMENT Regading asset management, seveal conclusions can be dawn fom Table 14: Afte 10 yeas of opeation, the eliability of the main potection dops to a value between 90.48% to 83.36%. This means that if 100 systems ae placed in sevice, it is expected that 11 to 17 units will fail afte 10 yeas in sevice. Unde these cicumstances, it is easonable to accept a 10-yea waanty peiod fo the equipment if the pice incement is less than 17% of the pice without waanty. If no waanty is puchased and a 10-yea equipment depeciation peiod is defined, it is easonable to establish a spae pats stock in the ange of 11% to17% of the total installed units. Mixed stategies can also be analyzed. Consideing a puchase of 100 main potection units, with 5-yea waanty and 10-yea depeciation peiods, the main potection pice should not be highe than 8% of the pice without waanty, in ode to cove the expected numbe of failues duing the fist 5 yeas of opeation. Indeed, fo the last 5 yeas of opeation, it is expected that 5 to 8 units will fail. Theefoe, this is a easonable numbe fo spae pats stocking. Results depicted in figue 6 allow the following conclusions: The seconday system MTTR anging fom 1 to 6 months does not significantly impact the availability of the potection system. Theefoe, spae pats stocking may be avoided, if the manufactues ae engaged with a time to epai and eplace of a failed element in the consideed time ange % availability is a easonable minimum objective value fo the line bay potection system. This value could be used as an indicato in a egulatoy famewok, although highe values may be intenally tageted by utilities. VI. CONCLUSION The pape pesents a numeical methodology applied to potection systems based on complex system desciption by means of eliability gaphs and solution by Monte Calo simulation. The potection system is divided into numeous individual components, and the coesponding eliability gaph is built accoding to its opeating pinciple. Monte Calo simulation is used to compute system eliability and availability indices, which can be used fo decision making with egad to utmost impotant utility policies, such as equipment waanty equiements, spae pat quantification and mean time to epai specification. An extensive suvey on existing data was caied out, esulting into specification of typical and ealistic eliability indices fo each potection and automation system component: cicuit beake, cuent and voltage tansfomes, auxiliay powe supply and potection elay. The developed methodology is a valuable tool on tacking the opeational pefomance of diffeent potection and automation schemes, thus enhancing system eliabilitycenteed and condition-based maintenance pogams, as well as suppoting life cycle assessment and efubishment decisions. REFERENCES [1] R. Billinton and R. N. Allan, Reliability Evaluation of Powe Systems, Plenum Pess, 2 nd edition [2] NERC, Technical Repot Suppoting Definition of Adequate Level of Reliability, Apil 24, 2012 [3] O. Gjede, G. H. Kjolle, J. Heggset, Reliability of the Potection System and its Impact on the Reliability of Supply, 16 th Powe Systems Computation Confeence, Glasgow, July [4] P. M. Andeson, Reliability modeling of potective systems, IEEE Tans. Powe App. and Syst., vol. PAS-103, no. 8, pp , [5] E.O. Schweitze III et al., Line Potection: Redundancy, Reliability, and Affodability, SEL, [6] P.M. Andeson, G.M. Chintalui, S.M. Magbuhat, R.F. Ghaja, An Impoved Reliability Model fo Redundant Potective Systems Makov Models, IEEE Tans. Powe Syst., vol. 12, no. 2, pp , [7] Y. He, L. Söde, R. N. Allen, Evaluating the Effect of Potection System on Reliability of Automated Distibution System, 14 th Powe Systems Computation Confeence, Sevilla, June [8] G. Theil, Makov Models fo Reliability-Centeed Maintenance Planning, 15 th Powe Systems Computation Confeence, Liege, August [9] M.L. Shooman, Pobabilistic Reliability: an Engineeing Appoch, McGaw-Hill Book Company, [10] R. Billinton and W. Li, Reliability Assessment of Electic Powe Systems Using Monte Calo Methods, Spinge US, 1 st edition [11] WG A3.06, Final Repot of the Int. Enquiy on Reliability of High Voltage Equipment Pat 1 Summay and Geneal Mattes, CIGRE, Octobe [12] WG A3.06, Final Repot of the Int. Enquiy on Reliability of High Voltage Equipment Pat 2 - Reliability of High Voltage SF6 Cicuit Beakes, CIGRE, Octobe [13] WG A3.06, Final Repot of the Int. Enquiy on Reliability of High Voltage Equipment Pat 4 - Instument Tansfomes, CIGRE, Octobe [14] WSCC Telecommunications and Relay Wok Goups, Communications Systems Pefomance Guide fo Potective Relaying Applications, Novembe [15] R. Baone.(2011, Novembe 18). Relay eliability (was WECC availability class definitions). Available powe_system_potection@yahoogoups.com.