Fundamentals of a Motor Thermal Model and its Applications in Motor Protection

Transcription

1 Fundamenals of a Moor Thermal Model and is Applicaions in Moor Proecion 1. Absrac B.Venkaaraman, B.Godsey Black & Veach Corporaion This paper discusses he fundamenals of a moor hermal model and is mahemaical inerpreaion and physics for he differen sages of moor operaion. (overload, locked roor, oo frequen or prolonged acceleraion, duy cycling applicaions). explains Thermal Model Time Consans and oher echnical parameers ha cause he biasing of he hermal model algorihm. Oher opics covered in his paper show ha (a) deailed moor daa shee informaion, and (b) coordinaion beween he proecion engineer and he moor supplier, can lead o proper selecion of moor hermal proecion parameers. This paper presens a closer look a moor sall, acceleraion and running hermal limi curves. also explains he concep of hermal capaciy and elaboraes on how hermal capaciy is evaluaed in moor proecion devices. The following poins are also covered in his paper: Discusses some addiional mehods, such as volagedependan and slip-dependan moor overload curves, employed o evaluae hermal capaciy in nonsandard moor applicaions, Presens he concep of maching hermal ime consans for moor cyclic loads cases. n addiion, he response of a hermal model algorihm in pracical applicaions is demonsraed. Describes a real case example showing how o apply and fine-une he hermal model in -ineria load applicaion. Explores in his conex, some of he key opics ha will ensure safe operaion of he moor while promoing saisfacory moor design characerisics.. nroducion nducion moors are he workhorses of any indusrial plan. Typical moor applicaions include pumps, fans, compressors, mills, shredders, exruders, de-barkers, refiners, cranes, conveyors, chillers, crushers, and blowers. Saisics have shown ha despie heir reliabiliy and simpliciy of consrucion, annual moor failure rae is conservaively esimaed a 3-5% per year, and in exreme cases, up o W. Premerlani GE Global Research Niskayuna, New York E.Shulman, M.Thakur, R.Midence GE Mulilin Markham, Onario 1%, as in he Pulp and Paper indusry. Downime in a facory can be very expensive and, in some insances, may exceed he cos of moor replacemen. Proper machine proecion is required o minimize he moor failure rae, preven damage o associaed equipmen and o ensure boh personnel safey and producion arges. The documen Repor of Large Moor Reliabiliy Survey of ndusrial and Commercial nsallaions, published by he EEE Moor Reliabiliy Working Group [3] conains he resuls of EEE and EPR surveys on moor reliabiliy and major causes of moor failure. The summary of hese resuls is shown in Table. n spie of differen approaches and crieria (EEE failure groups are formed according o cause of failure and EPR according o failed componen ) boh sudies indicae a very similar failure percenage associaed wih mechanical- and elecrical-relaed machine problems. Analyzing he daa from his able we can conclude ha many failures are direcly or indirecly relaed o, or caused EEE Sudy EPR Sudy Average Failure Conribuor % Failed Componen % % Persisen Overload 4.% Saor Ground nsulaion 3.00 Elecrical Normal Deerioraion 6.40% Turn nsulaion 4.00 Relaed Failures Bracing 3.00 Core 1.00 Cage % Elecrical Relaed Toal 30.60% Elecrical Relaed Toal 36.00% High Vibraion 15.50% Sleeve Bearings Mechanical Poor Lubricaion 15.0% Anifricion Bearings 8.00 Relaed Failures Trus Bearings 5.00 Roar Shaf.00 Roor Core % Mechanical Relaed Toal 30.70% Mechanical Relaed Toal 3.00% High Ambien Temp. 3 Bearing Seals 6.00 Environmenal Abnormal Moisure 5.8 Oil Leakege 3.00 Mainenance & Oher Abnormal Volage 1.5 Frame 1.00 Reasons Abnormal Frequency 0.6 Wedges 1.00 Relaed Failures Abrasive Chemicals 4. Poor Venilaion Cooling 3.9 Oher Reasons 19.7 Oher Componens 1.00 Environmenal Reasons & Oher Reasons Toal 38.70% Mainenance Relaed & Oher Pars Toal 3.00% 35% Table 1. Summary of EEE and EPR Moor Reliabiliy Surveys. Moor Thermal Model Proecion Applicaions 41

2 by, exensive heaing of he differen moor pars involved in machine operaion. Tha is why we find accurae racking of moor hermal saus and adequae response of he moor conrol sysem o abnormal siuaions o be very imporan. Modern rends in moor design and consrucion are moving in he direcion of making moors more compac and efficien. The use of inorganic insulaion maerials such as fiberglass and silicon resins provides improved dielecric moor insulaion properies compared o legacy maerials such as coon and varnish. Bu a he same ime some new maerials are more vulnerable o excessive heaing. Anoher imporan consideraion ha should be consdered in racking he hermal sae of he moor, is heaing overesimaion, which can also cause undesirable moor soppage and hence poenially cosly inerrupion of processes. The saemens above clearly explain he imporance of an accurae hermal esimae of a moor in service. Currenly his ask (precise moor hermal proecion) is srongly suppored by modern echnology. The developed algorihms can be implemened in microprocessor devices, which are capable of providing a desirable level of accuracy and flexibiliy. The hermal algorihm operaes as per he following sequence: Real-ime moor daa is supplied o microprocessor device. This daa is processed according o he firmware hermal algorihm program and compared wih expeced values, sored in memory. The proecion device compues he analog value, which is compared wih he programmed hreshold. The proecion device riggers he digial oupus if he compared analog value exceeds his hreshold. The ideal analog mehod for modeling he hermal image in he Moor Proecion Device (MPD) would be o embed non-inerial emperaure sensors ino he saionary (saor) and roaing (roor) pars of he moor srucure. However, i is no feasible o insall emperaure sensors in he roors for echnical reasons, reliabiliy and cos. An addiional reason o rejec such emperaure sensors as he main basis for hermal proecion, is he fac ha he radiional Resisance Temperaure Deecor (RTD) has a relaively slow reacion ime and can respond adequaely o he speed of he heaing process during moor acceleraion. Saor RTDs acually provide realisic resuls in monioring he emperaure under balanced moor condiions, bu again hey are no suiable for monioring he fas hermal ransiens. Alernaively, a main real-ime inpu hermal model could use 3-phase moor curren. The elecrical energy applied o he moor is parially ransformed ino hea which is sored in he moor. Thus his hea is a funcion of curren and ime. This fac, plus some oher facors and assumpions ha will be covered furher in his paper, are employed o develop and implemen he curren-based hermal model. 3-phase curren values measured in real-ime are also used in special algorihms applied o deec differen sages of moor operaion: sopped, sar, run, overload. n -ineria load applicaions volage monioring can be used in he hermal model algorihm o dynamically mach he hermal limi o differen saring condiions. n some applicaions speed sensors are employed o deec slow roor roaion or moor sall. Anoher imporan par of hermal model implemenaion is Expeced values sored in MPD. This erm implies ha informaion is available from he moor designer and moor manufacurer, ha is relaed o he hermal reserve, allowed performance and hermodynamics of he moor in quesion. The moor is no a homogeneous body and even one componen can be presened as a combinaion of nodes conneced via hermal resisance o each oher and exernal ambien condiions. For example, he saor has slo copper, end-head copper, eeh and a core. Each node is characerized by is own rae of emperaure change. [6] Tha is why in order o do he full analysis and deec a boundary for normal operaion, moor designers always arge he developmen of he mos deailed model including elecrical, mechanical, hermal, and chemical componens. Bu once a moor is properly designed and consruced o is inended specificaions, a less deailed model is adequae o provide hermal proecion by evaluaing hermal risk wih reference o moor daa shees and hermal damage curves. Common sense dicaes reliance on a complee moor analyses o deermine he correspondence of he MPD algorihm variables o he daa ypically available from he moor manufacurer. MPD also incorporaes simplified algorihms modeling physical moor saes and processes. This approach allows us o aain an adequae level of hermal proecion in modern MPD, for any applicaion, by handling he available moor informaion. n rying o keep he algorihm simple we face anoher challenge. is raher difficul o relae he hermodynamic behavior of he moor under seady-sae condiions, wih he rapid saor and roor heaing ha occurs during hermal moor ransiens such as acceleraion, sall and cyclic load change. The algorihm mus also accoun for hea ransfer from he moor s winding o he housing and from he housing o he free (ambien) air. To resolve his issue he ime before rip parameer was seleced as he common crierion for hermal condiion evaluaion. Acually, for moor acceleraion and sall condiions, he safe sall ime specified by moor designers, is he only objecive esimae of he imum allowable moor emperaure, because of he real difficuly of direcly measuring he roor emperaure. [6] Based on he discussion in his secion of he paper, he main moor hermal algorihm requiremens can be summarized as follows: Accuracy. A precise esimae of he hermal moor image. Consideraion of differen moor applicaions, such as variable frequency, volage unbalance, long acceleraion, cyclic loads. Reference o daa specified by moor designers. Simpliciy. The algorihm is easy o undersand. A simple way o calculae he hermal esimae of he moor for he operaional sequence in quesion. Dependabiliy. The capabiliy of monioring he hermal 4 Moor Thermal Model Proecion Applicaions

3 capaciy a any momen of moor operaion. The hermal esimae is mainained and responds adequaely o MPD power failure evens. Compliance o indusry sandards. The algorihm mus mee he requiremens, and should follow he recommendaions lised in, EEE Guide for AC Moor Proecion (Sd C ) [9] and EEE Guide For he Presenaion of Thermal Limi Curves for Squirrel Cage nducion Machines (Sd ) [10]. Easy Seup. The parameers required o se up he hermal model are obained from he sandard se of moor daa readily available from moor manufacurers. Reliabiliy. The model is suppored by alernaive moor emperaure evaluaion mehods, based on RTD s monioring. This backup mehod is exremely useful in cases where he hermal process significanly deviaes from wha was expeced because of abnormal ambien emperaures or moor cooling impairmen. Flexibiliy. The possibiliy of apply he model even in very unusual cases. n addiion o he accurae hermal model he sae of he ar Moor Proecion Device should be equipped wih he enhancemens and addiional funcionaliy lised below. RTD npus for absolue emperaure monioring, alarming and ripping of he moor a emperaures. Temperaure-based saor hermal esimae, capable o correc main hermal model in he abnormal operaional condiions A emperaure-based saor hermal esimae, capable of correcing he main hermal model under abnormal operaing condiions Wide selecion of hermal overload curves; sandard for ypical applicaions, user defined for unusual applicaions and volage dependan for special applicaions, feaured long sars of ineria loads. A Moor Sar Lockou feaure inhibiing he sar of he machine in he case of non-availabiliy of sufficien hermal reserve o complee he acceleraion. The lockou ime is calculaed based on he available hermal capaciy, he imum learned value of Thermal Capaciy Used (TCU) during one of he las 5 successful sars and he rae of emperaure change for he moor a sandsill. A wide selecion of hermal overload curves; sandard for ypical applicaions, user-defined for unusual applicaions and volage-dependan for special applicaions, feauring long sars of ineria loads. Thermal model biasing in response o he curren unbalance ha causes an exensive heaing effec. The opion o selec separae cooling consans for he moor in he sopped and running saes. A curren unbalance elemen capable of issuing a warning abou a poenially dangerous level of unbalance and of ripping he moor off line on single phasing. A Sar Supervision Elemen prevening an excessive number of moor saring sequences. A mechanical Jam Deecor. An acceleraion limi imer. Phase Shor Circui and Ground Faul Proecion Funcions. Volage and Frequency elemens ensuring moor operaion wihin specified limis. Phase Reversal Deecion. Power Elemens o monior and respond o abnormal moor loading condiions. MPD failure deecion. Communicaion capabiliy o hos compuers o allow easy inegraion ino exising DCS and SCADA sysems. Cos jusifiable. Can be adaped (rerofied) o muli-vendor MCC s and moor sarers. ndusrially hardened by means of a conforming coaing, o work in mill environmen. Highly accurae predicions of mechanical and insulaion failure, as well as he broken roor bar condiion, wihou removing he moor from service and wihou he need for residen expers. The capabiliy of reading/capuring moor currens and volages during elecrical sysem fauls. The capabiliy of recording and soring in he device s nonvolaile memory, ime-samped evens relaed o abnormal moor siuaions. Addiional proecion funcions can be provided using expensive equipmen such as vibraion sensors and/or insrumens o display he curren specrum of he moor, o predic incipien failures. These are no covered in his documen. 3. Thermal Proecion Theory There are wo main ypes of hermal risks for an overheaed moor: saor insulaion may degrade and/or roor conducors may decrease heir capabiliy o resis bending (deformaion) forces or even mel. Deerioraion of saor insulaion presens he chemical process ha is governed by an Arrhenius equaion [6[, [7]. NEMA Moor nsulaion Class defines he imum allowable emperaure rise above he Fig 1. Aging Facor of Moor nsulaion. Moor Thermal Model Proecion Applicaions 43

4 ambien or hermal limi, if emperaure exceeds his limi i doesn cause immediae insulaion failure bu decreases he insulaion s expeced lifeime. A fairly accurae approximaion of Arrhenius equaion saes ha an operaing emperaure increase of 10 C in excess of he hermal limi cus he life of saor insulaion by half. The percen of life vs emperaure characerisics for differen classes of insulaion are shown a Figure 1. The hermal risk for a squirrel cage roor is ha he roor conducors may deform or mel. Since here is no insulaion, he roor conducors can be operaed a a much er emperaure han he saor conducors. is difficul and impracical o provide a numerical emperaure value defining he roor hermal limi. Moor designers address he imum allowable roor emperaure under sall, acceleraion or any oher fas ransien condiions by saing he sall ime hermal limis for a ho or cold moor. These values mus correspond o he sysem volage level during he sall even. For he majoriy of applicaions, he safe sall ime defines he roor hermal limi, bu in some special cases moor capabiliy during sall and acceleraion is dicaed by he saor hermal limi. A rule of humb o define a saor-limied moor says: When he volage raing of he moor is equal o or greaer han 10 imes he horsepower raing, he moor is saor limied. For example: 500 HP, 6900 V. [8] Seady-sae operaions such as running overloads are usually no an issue for he roor. Under running condiions he saor is subjec o exensive heaing. Thus a saor overload proecion elemen ensures an overall sufficien level of hermal proecion for a roor roaing a near synchronous speed. The seady sae and ransien hermal behavior of he saor and roor conducors of a moor depends on he deails of he moor hermal circui. The moor designer ypically uses a raher deailed hermal circui, including separae represenaions of saor iron, roor iron, saor conducors, roor conducors, inernal air, exernal air, moor shell and end shields. Deails of he hermal circui depend on he venilaion consrucion of he moor, including drip proof, oally enclosed fan cooled, and oally enclosed non-venilaed. For example, hea sorage in each circui elemen as well as convecive or conducive hea ransfer beween various pairs of circui elemens is included in he model. A ypical moor hermal circui used by a moor designer may have on he order of 0 nodes and 0 branches, resuling in a dynamic response characerized by several ime consans. Moor designers are ypically ineresed in a few sandard hermal scenarios including seady sae loading, cold, ho and successive saring. The designer checks he compued seadysae emperaure of he saor winding o make sure i is wihin he capabiliy of he seleced insulaion sysem, designers also define he ime limis o wihsand overloads. is also very imporan o deermine running and sopped moor cooling raes especially for oally enclosed non-venilaed moor designs and in some applicaions wih inermien use raings. The moor designer is also ineresed in allowable cold and ho salled imes. Salled hermal calculaions are usually performed assuming adiabaic condiions. The designer ofen concedes he fac ha he peak emperaure of he saor winding may emporarily exceed he seady sae capabiliy of he insulaion sysem, aking ino accoun he expeced applicaion of he moor and how many imes i is expeced o be salled cold or ho in a lifeime, in making a design compromise. Afer a design is complee, a summary of he hermal model becomes available. Basic informaion includes he seady sae hermal raing of he moor, ho and cold sall imes, and he cooling ime consans of he moor. For medium and large moor designs complee hermal damage curves of allowable ime versus curren are provided as a sandard. Once he moor has been designed, and he basic operaional parameers have been esablished for seady sae load and cold and ho sall imes, he responsibiliy shifs o hermal proecion for he moor. For majoriy of service condiions he operaing profile of he moor maches he assumpions made by he moor designer, so ha he main job of hermal proecion is o say ou of he way and le he moor run. However, if moor is abused by mechanical breakage or human error hen proecion seps in o assure here is no risk of hermal damage. The quesion is, wha model should be used o proec he moor when i is running? Wha is a reasonable compromise beween accuracy and complexiy? Wha physics should be included? Wha should be used as an esimae of operaion limi? As we menioned before he ideal mehod would be o have he direc accurae emperaure measuremen and use aging facor o esimae he consumed moor hermal capaciy. Bu emperaure sensors (RTD) have a delayed response o hermal ransiens such as sall and acceleraion and can serve as a basic crierion for a hermal model. How deailed should he model be? We should cerainly provide a model wih enough flexibiliy o proec moors ha have a dynamic hermal response represened by several ime-consans. A single ime-consan is no always adequae [6]. Physics shows ha here are a leas 4 disinc hermal ime-consans: for he saor conducors, and for he roor conducors. For example, when hea is generaed in he saor conducors, he firs effec is o raise he emperaure of he conducors. The saor winding in he saor slos are surrounded by a seel magneic core. Therefore, as he windings ge ho, hea begins o flow from he windings ino he seel core. The combinaion of he hermal capaciy of he winding and he hermal conduciviy/impedance beween he winding and he seel core esablishes a shor imeconsan. Hea ha coninues o flow from he winding ino he surrounding core is sored in he core, causing is emperaure o rise, bu more gradually han he iniial rae of rise of he windings, because of he greaer hermal capaciy of he core. Evenually, he emperaure of he core (and he moor frame, ec.) also rises, causing hea ransfer by convecion o he surrounding air. The combinaion of he hermal capaciy of he core and he frame and he hermal impedance beween hem and he cooling air esablishes a ime-consan ha is much 44 Moor Thermal Model Proecion Applicaions

5 longer han ha of he winding-core ineracion. So, he nex quesion is, wha is he bes way o go beyond a single ime-consan model? The mos reasonable way o model he hermal sae of he moor is o measure moor curren and o correlae i in real ime o moor hermal damage curves. The manufacurer s hermal damage curves represen he resuls of simulaions of a complee moor model, including a muli-node hermal model. The curves capure he muli-ime-consan parameers and hermal damage imes for running, sall and someimes acceleraion condiions of he moor. Typical curves are shown a Figure 3. Any poin on he moor hermal damage curve represens a hermal ime limi a a specific level of curren, or in oher words: The hermal limi defines how long a moor can wihsand he corresponding level of saor curren wihou exceeding he hermal boundary specified by he moor manufacurer. Deails of he hermal model implemenaion, based on overload curves are given in he nex secion. n his secion we answer wo imporan heoreical quesions concerning a hermal model based on moor hermal damage curves (overload curves): 1. Wha is he relaionship beween sandard overload curves and a single ime-consan hermal model?. Does an overload curve based hermal model behave correcly when i is used in applicaions in which he load is no consan? We urn o mahemaical analyses of he physics o answer heses wo quesions, saring wih an analysis of a single imeconsan model. The hermodynamic behavior of homogeneous body a res (moor) heaed by elecrical curren can be described by a single ime-consan hermal equaion: () () () dt C () R H T() d T moor emperaurerise above ambien moor curren C specifichea capaciyof hemoor H runninghea dissipaion facor R elecricalresisance is convenien o rewrie equaion (1) in erms of per uni emperaure rise and per uni curren: T T () T () () () / raed / T raed curren moor raed emperaure a hermallimi rip condiion per uni emperaurerise per uni curren n ha case, equaion (1) can be rewrien as: (1) () dt d C H () raed () T () H T R The imum emperaure is relaed o he raed curren such raed R ha 1. n ha case, equaion (3) can be rewrien as: H T () dt () T () (4) d Equaion (4) can be used o analyze he hermal response of a single ime-consan model o a seady overload. can be shown ha he soluion of equaion (4) for a seady overload, saring from a cold iniial condiion, is given by: T / () ( 1 e ) per uni moor curren (a consan) T () per uni moor emperaure rise Equaion (5) can be solved for he amoun of ime needed for he emperaure rise o reach he hermal limi of he moor, i.e. T()1: () () ln 1 ime esimaedbya simple hermal model for hemoor emperaure o reach hermallimi To develop a comparison beween a single ime consan hermal model and overload curves, we now urn our aenion o sandard overload curves, which are given by: ( ) ( ) 87.4 CM 1 rip ime, seconds CM curvemuliplier To compare sandard overload curves wih he behavior of a single ime consan model, i is useful o sar by recognizing ha he numeraor of he righ hand side of equaion (7) corresponds o a ime consan: CM CM CM ( ) Equaion (6) and equaion (8) are ploed in Figure. n order o make he curves align for large values of curren, i is necessary o saisfy he following consrain: C CM CM H (3) (5) (6) (7) (8) (9) Moor Thermal Model Proecion Applicaions n oher words, in order for an overload curve o mach a single ime-consan hermal model during a simple sep overload, he 45

6 We hen ake he firs wo erms in a Taylor s expansion of ln 1 x wih respec o x around he poin x 0: ln ( ) ln(1 x) ln(1) x x ( ) 1 x 1 (1) Fig. Single Consan Thermal Model vs Relay Overload Curve Comparison ime-consan implied by he curve muliplier of he overload curve mus be se equal o he ime-consan of he single imeconsan model. n Figure, he raio of he ime divided by he ime-consan is ploed agains per uni curren. can be seen ha alhough equaion (6) is no exacly he same as equaion (8), he approximaion is very close, paricularly for large values of curren. For lower values of curren, he sandard overload curves are a beer approximaion o ypical moor overload curves han a single ime-consan model. Tha is because here are a leas wo ime-consans in he hermal response of a moor. Over shor ime inervals, he hermal response of a moor is dominaed by hea ransfer from he saor and roor conducors o iron. Over longer ime inervals, he hermal response is dominaed by hea ransfer from he iron o cooling air. A single ime-consan model canno be accurae over he full range of operaion and ends o overproec a moor when i is operaed near is raed load. A sandard overload curve provides proecion ha is a closer mach o a moor s hermal limi. The close proximiy of he wo curves for large values of curren is no a coincidence because boh models are equivalen o an adiabaic model for large values of curren. This can be shown mahemaically by finding he asympoic behavior of he wo curves. Firs, equaion (8) is given approximaely by: ( ) CM 1 CM ( ) 1 (10) A similar approximaion can be shown o hold for equaion (6) by rewriing and aking a Taylor s expansion in erms of he reciprocal of he square of he curren. Firs, we rewrie o explicily show he dependence on he reciprocal of he square of he per uni curren: ( ) ln 1 1 ( ) ln ln( 1 1/ ) ( ) ln( 1 x) x 1/ 1 1/ (11) Equaion (8) describes how long i will ake a sandard overload curve o reach hermal limi for a consan overload. We now urn our aenion o how a sandard overload curve behaves during cycling loads. We sar wih he differenial equaion ha is used o implemen sandard overload curves: dt d () () (13) To gain insighs ino wha he response is o a cycling load, we will consider a simple cycling load in which he curren alernaes beween no load and an overload value: (14) Moor heaing is proporional o he square of he curren, so he effecive curren for heaing over he cycle is: (15) Equaion (15) can also be expressed in erms of a duy cycle raio: (16) f he curren and heaing are expressed in per uni and he low cycle curren is approximaely equal o zero, he seady sae boundary condiion for ripping he moor becomes: 1 D CM 1 low 0 curren during he low cycle curren during he cycle low H ime inerval for he low cycle effecive ime inerval for he cycle D + D duycycle raio ( 1 D) low + low (17) Equaion (17) defines he appropriae response o a duy cycle. can be shown ha a single ime-consan model provides approximaely his response. The nex quesion is wha is he response of a sandard overload curve o a duy cycle? Analysis of a sandard curve under load cycling condiions will show ha he response is correc, and will reveal how o properly se an overload curve model o mach he behavior specified by equaion (17). We mus consider values of curren below pickup, during which our moor hermal model is defined by he following differenial equaion: 46 Moor Thermal Model Proecion Applicaions

7 dt d (18) The facor ho 1 cold is included o mach he ho and cold sall imes specified by he moor manufacurer. By including he facor in he cooling compuaion, he ho overload curve is effecively shifed down by he correc amoun relaive o he cold overload curve o accoun for he difference in ime o rip of ho and cold moor condiions. For he load cycle under consideraion, he curren during he unloaded par of he cycle is approximaely equal o zero, so he differenial equaion given by (18) reduces o: dt () T () (19) d cool Taken ogeher, equaions (19) and (13) describe he behavior of our model during he assumed load cycle. The approximae emperaure rise during he overload porion of he load cycle esimaed by he overload curve is compued by muliplying equaion (13) by he overload ime: 1 ( ) T 1 (0) CM The approximae emperaure drop esimaed by he cooling model during he unloaded porion of he duy cycle is compued by muliplying equaion (19) by he appropriae ime, wih per uni emperaure equal o 1, because ha is wha i will be approximaely equal o during a limi cycle ha approaches ripping: 1 Tlow low (1) cool The overload deecion boundary is deermined by seing he ne emperaure change equal o zero. This implies ha he oal of he righ hand sides of equaions (0) and (1) aken ogeher is equal o zero: T () cool ho ho sall ime cold coldsall ime + T low 1 ( 1) 0 1 CM () Equaion () can be rearranged o show ha sandard overload curves respond correcly o cycling loads. Equaion () also reveals how o properly selec parameers for a load cycling applicaions: cool 1 D CM 1 ho 1 cool cold cooling ime consan () (3) Equaion (3) expresses he acual overload deecion boundary of an overload curve model in erms of is seings, he duy cycle, and he amoun of overload. Excep for he facor of τ τ cool, equaion (3) is exacly he same as he ideal overload CM deecion boundary, specified by equaion (17). Equaion (3) cool and equaion (17) will be idenical, provided ha T low τ τ cool CM is se Moor Thermal Model Proecion Applicaions equal o one resuling in he following consisency consrain: 87.4 CM cool (min) (4) 60 Equaion (4) represens a consisency consrain relaing he cooling ime-consan and he curve muliplier of a sandard overload curve. Figure 9 shows wha can happen if i is no saisfied. There are hree cases shown for a cycling load wih an approximae per uni heaing value of one. n he firs case, he cooling ime-consan is se oo long resuling in over-proecion and early moor ripping. n he second case, he cooling imeconsan is se according o equaion (4) o mach he implied ime-consan of he curve muliplier, and he proecion is correc. n he hird case, he cooling ime-consan is se oo shor, resuling in under-proecion and possible moor overheaing. 4. Thermal Model Algorihm The hermal model algorihm was developed in order o creae he hermal image of he moor and closely rack he hermal condiions for all saes of moor operaion. The following saes of moor operaion are recognized: Moor Sopped: Curren is below zero level hreshold and moor swiching device indicaes he open saus. Moor Saring: Sae is declared when previous sae was Sopped and curren greaer han % of he moor full load amps has been deeced. The moor curren mus increase o he level of overload pickup (service facor imes full load amps) wihin 1 second oherwise moor will ransfer ino he nex sae: Running Moor Running: Sae is declared when previous sae was Saring and moor curren drops below overload pickup level. Moor Overloaded: Sae is declared when previous sae was Running and moor curren raises above he overload pickup level. Fig 3. Moor Thermal Limi Curves 47

8 Thermal Capaciy Used (TCU) evaluaes he hermal condiion of he moor. TCU is expressed as percenage of he hermal limi used during moor operaion. Per EEE Sd (10) he moor hermal limi is presened in he form of a imecurren curve for 3 possible moor overload condiions: locked roor, acceleraion and running overload. Every poin on his curve represens he imum allowable save ime a a saor curren above normal load. TCU is incremenally updaed every 100 milliseconds and he inegraed value of TCU is sored in he hermal memory regiser of MPD according o he following equaion. T T 1 TME NTERVAL 100% TME TO TRP (5) The following example can be a good illusraion of TCU accumulaion during he cold moor sar; iniial TCU is equal o 0%. Moor saring paern (1) and relay overload curve () are shown a Figure 3. For simpliciy assume ha he ime inerval for TCU updae is 1 second. Every poin of moor curren on his plo corresponds o he number of seconds ha moor can wihsand before ripping on overload. The numerical values showing he progress of TCU accumulaion during 17 seconds of moor acceleraion are presened in able. We can observe ha by he end of a successful saring he hermal memory of he moor proecion device (MPD) accumulaes 46.7% of TCU. Thus HCR is 8 sec / 10 sec 0.8 and he level of sabilized TCU feauring he ho moor is equal o 0%, or in oher words he allowed moor hermal wihsand ime a overload condiions will effecively decrease by 0%. f he moor load is lower hen 100% he TCU level corresponding o he ho moor condiion is proporionally lower: 75% load 15% TCU, 50% load 10% TCU and so on. The unbalanced saor phase curren will cause addiional roor heaing due o he developed negaive sequence curren and flux roaing in he opposie direcion o roor roaion wih approximaely double he power sysem frequency. The skin effec in he roor bars a his frequency will cause a subsanial increase in roor resisance and hence increased heaing, which is no accouned for by he regular hermal model. n order o accoun for his addiional heaing facor he Equivalen Curren concep is inroduced. The idea is ha he curren inpu ino he hermal model is biased o reflec he addiional heaing caused by he negaive sequence componen of he load curren. EQ M (1 K ( 1) ) (6) where: EQ - equivalen moor heaing curren M - real moor curren 1 - posiive sequence componen of real moor curren - negaive sequence componen of real moor curren K - unbalance bias facor The Unbalance Bias K facor reflecs he degree of exra heaing caused by he negaive sequence componen of he load curren and can be defined as he raio of Posiive Sequence Roor Resisance o Negaive Sequence Roor Resisance. is pracical and quie accurae o use he esimae mehod o define he K facor. Equaions for ypical and conservaive esimaes are presened below. (7) Table. Thermal Capaciy Used (TCU) calculaion. Typically he moor manufacurer provides locked roor hermal limi curves or locked roor safe sall ime values for moor condiions: cold moor ambien emperaure) and ho moor ambien + raed rise emperaure). n order o disinguish beween he aforemenioned moor condiions he addiional moor parameer, Ho/Cold Sall Time Raio (HCR) is included in MPD algorihm. These parameers define he proporional increase of TCU of he moor running fully loaded a a seled emperaure compared o he moor resing a ambien emperaure. For example le us assume ha according o he moor daa shees he Cold Safe Sall Time is 10 seconds and he Ho Safe Sall Time is 8 seconds. where LRC is he moor locked roor curren. Of cause, in order o provide a complee hermal model of he moor in service, he cooling process mus be aken ino accoun. Cooling is characerized by Cooling Time-consans. These consans define he rae of cooling under sopped and running operaing condiions. When he moor is running a raed load, TCU accumulaed during he moor sar will decay exponenially and will sabilize a he level of TCU maching ho moor hermal condiions. f he moor load is lower, hen obviously he hermal balance poin is proporionally reduced. The sopped moor will also be subjeced o he exponenial decay of TCU sored in MPD hermal memory during moor operaion. Naural cooling of he roaing moor or forced cooling by means of he special fans insalled on he machine shaf cause a much er cooling rae of he running machine compared o he moor a sandsill, ypically he raio is :1. 48 Moor Thermal Model Proecion Applicaions

9 Thus separae Cooling Time-Consans are used in he Thermal Model Algorihm. The equaions o calculae TCU decay of he cooling moor are as follows: Where: TCU START (%) is he iniial value of TC accumulaed by he momen he cooling sars; (min) is duraion of cooling; is he Cooling Time Consan; TCU is he seady sae level of TC END (%) (8) 3. RTD bias imum This poin is se o he emperaure rise equal o he moor insulaion hermal limi. Typically for NEMA B class moors insulaion class is F wih emperaure rise above ambien of 115ºC. The TCU a imum emperaure poin is equal o 100%. Rae of change of TCU beween he adjacen poins is approximaed as linear. The seady sae hermal condiion for he moor a sand sill is he ambien emperaure, which is corresponding o TCU END (%) 0. (9) The seady sae hermal condiion for he running moor is calculaed as: TCU Where: END eq SF FLA HCR ( 1 ) 100% (30) n some unforeseen siuaions, when he moor cooling is blocked or ambien emperaure deviaes significanly from he indusry sandard value (40ºC), i becomes difficul o accuraely replicae he moor s hermal condiion based solely on he measured curren. Tha is why i is pracical o apply an independen algorihm, calculaing TCU by means of saor RTDs (resisance emperaure deecors) and correcing he hermal model upwards if needed. The RTD-TCU Curve is consruced based on he 3 key poins. See Figure 4 for deails. 1. RTD bias minimum Se o 40 C or anoher value of ambien emperaure, if he appropriae RTD is available. TCU is equal o 0%.. RTD bias mid poin The mid-poin emperaure is se according o he moor s ho running emperaure and is calculaed as follows: Raed Temperaure Rise + Ambien Temperaure For example: The emperaure rise for NEMA Class B moors wih 1.15 Service Facor, is 90ºC. Thus he emperaure value for his poin is 130ºC. The TCU quaniy for his poin is he value of a seady-sae running raed moor load, and can be found as: TCU CENTER ( 1 HCR) 100% (31) Fig 4. RTD Bias of Thermal Model 5. Thermal Model Behavior a Differen Operaional Condiions n order o illusrae how TCU varies during moor operaion le us review he following moor daa and operaional sequences. Le us assume ha he following moor informaion is available o us. Moor hermal limi curves are as presened a Figure 3. Moor Cold and Ho Locked Roor Times a 100% of he sysem volage are 34 and 6 seconds respecively. A 80% of he sysem volage Cold and Ho Locked Roor Times are 50 and 38 seconds respecively. Moor Acceleraion a 100% of he sysem volage is 17 seconds. Maximum locked roor curren is 6 imes ha of full-load amperes (FLA). The MPD overload curve ha we employ as a limi o calculae TCU, is shown in Figure 3. Please noe ha he locaion of his curve is beween he ho and cold hermal limi curves supplied by he moor manufacurer. The ime-curren relaion in his curve is per following equaion: T orip (sec) 1 EQ (3) Moor Thermal Model Proecion Applicaions 49

10 The Running and Sopped Moor Cooling Consans are respecively 0 and 40 minues. Moor Service Facor Curren Unbalance Facor: 6 Sequence 1: Combined operaion (Figure 5) Sae A. niially he moor is a ambien emperaure. TCU 0%. The moor is ready o sar. Secion AB. The moor is successfully sared a 100% volage. Acceleraion ime 17.1 seconds, TCU accumulaed during sar is 46.7% (deails are in Table ) Secion BC. The moor runs for 45 minues a a seady load of 80% wih 10% curren unbalance. TCU by he end of he period, exponenially decays o level of 19.5 %. TCU is calculaed per equaion 5. Secion CD. The Moor runs a 15% balanced overload for 15 minues. TCU incremens o he level of 67.7%. Secion DE. The Moor runs a 15% overload wih 10% curren unbalance unil he hermal capaciy reaches 100% and he relay rips he moor offline in 8.5 minues. is no well illusraed on he graph, bu he addiion of curren unbalance a he running overload sae decreases he rip ime by 1.5 minues or 15% (he calculaed balanced overload rip ime for he secion DE is 10 minues). Secion EF. The moor is a sandsill and cools down o ambien emperaure for 150 minues. TCU decays o approximaely 0 level. The rae of cooling is imes slower han of he running moor. Fig 6. Sall Trip. 100% Volage Fig 5. Thermal capaciy used during moor operaion. Sequence : Moor sall The moor can be seriously damaged if a roor sall occurs during he sar aemp. Sall can occur due o a mechanical breakage or a human misake. The salled moor draws curren equal o locked roor amps. Locked roor ime (LRT) values provided by he moor manufacurer specify he hermal limi for he moor a ambien and raed condiions. Typically LRT is specified for he moor sars performed a 80% and 100% of he sysem volages. Fig 7. Sall Trip. 80% Volage Figures 6 and 7 demonsrae how he hermal model provides an adequae proecion where he moor is aken offline before he hermal limi is reached. This siuaion has been evaluaed for ho and cold moor condiions a boh 100% and 80% of he sysem volages applied o he moor. Sequence 3: Running overload Three differen scenarios are considered: The moor is overloaded immediaely afer a cold sar. An overload is applied o he moor ha was sared, and, prior o overload, run unloaded for hours. An overload is applied o he moor ha was sared and, prior o overload, run a full load for hours. The overload ha was applied in all hree cases was 15% of moor full-load amps.the moor hermal limi ime values allow for applying a 15% overload o he cold and ho moor for 50 and 9 minues respecively (daa can be found in 50 Moor Thermal Model Proecion Applicaions

11 Figure 3). The firs case is characerized by severe hea generaion in he roor bars during he sarup. mmediaely following, he moor sarup, he overload heas up he saor windings prevening hea ransfer o he environmen. This siuaion presens a serious hermal impac and he moor is aken offline faser in comparison o he oher wo cases. Trip ime in his case is 16.3 minues. The second scenario presens an overload of he moor a ambien emperaure. niial TCU is 0%. According o he hermal model algorihm compuaions, he rip will be implemened 31 minues afer he overload is applied; which is lower han he cold moor limi (50 min). n a real applicaion, he emperaure of he unloaded running moor is ypically er han he ambien emperaure, because of he associaed moor losses. This fac explains why he significan margin beween he cold overload rip ime (31 min) and he cold hermal limi (50 min) is required. The hird scenario shows he ho overload (i.e. he moor is assumed o be a he raed emperaure). The iniial TCU in his case, he momen before he overload is applied, is 5%, so he ripping ime is proporionally lower, compared o he cold overload. Tripping ime in his case is 3 minues, which is lower han he ho hermal limi (9 minues). Sequence 4: Consecuive saring Per NEMA MG1 sandard (11) medium and large inducion moors are required o wihsand hermally: consecuive sars, coasing o res beween sars, wih he moor iniially a ambien emperaure (cold sars) One sar wih he moor iniially a raed load operaing emperaure (ho sar) proecion devices are capable o learn and sore, in he nonvolaile memory, TC value uilized by moor during successful sar and use his value in he sar inhibi algorihm. Sequence 5: Cyclic load According o consideraions discussed in a previous secion of his paper, he main crierion for a hermal model s adequae response o cyclic load is he maching of he implied heaing ime-consan o he explici running cooling ime-consan (see equaion 4). Le us review a balanced cyclic load (i.e. he effecive heaing) (equaion 16) of 1. Afer he cold sar, he moor varies he load every 30 seconds a beween 0% and 160% of he full-load curren. Per equaion 4, he running cooling consan is calculaed as follows cool 87.4 CM (min) 60 (33) n order o provide a more accurae hermal model response o cyclic load condiions, he cooling ime-consan should be adjused o he calculaed value. A he same ime his change (from 0 o 17.5 minues) would cause no significan impac o he oher moor operaing sequences. Figure 9 demonsraes he imporance of cooling consan value in he hermal model response o cyclic load condiions. Three cases are shown for a cycling load wih an approximae per uni effecive heaing value of one. n he firs case, he cooling ime-consan is se long, resuling in over-proecion and premaure hermal model riggering. n he second case, he cooling ime-consan is se o mach he implied ime-consan of he curve muliplier, and he hermal model adequaely responds. n he hird case, he cooling ime consan is se shor, resuling in under-proecion and possible moor overheaing. An illusraion of he hermal model response o consecuive saring is shown on Figure 8. As you can see, he hermal model provides he sar sequence required by NEMA. An imporan enhancemen o he hermal algorihm is he Sar nhibi funcion, which is employed o preven excessive moor saring in cases where here is no enough hermal capaciy available o perform a successful sar. Modern inelligen Fig 9. Thermal model response o cyclic load Sequence 6: Saring of ineria loads Fig 8. Ho and Cold Consecuive Sars The hermal model algorihm has an addiional enhancemen ha allows he coordinaion of proecion wih -ineria long sars, while acceleraion ime is greaer han he safe moor sall ime. The volage-dependan dynamic hermal limi curve is employed o accoun for varying hermal limis corresponding o he acceleraion curren levels a he differen erminal moor volages. Figure 10 shows an example of a 100% volage ineria sar Moor Thermal Model Proecion Applicaions 51

12 lasing 17 seconds (curve 1), and a locked roor ime limi of 8 seconds (curve 4). Acually curve 4 implies he line of he same ²T. n many shor moor sar applicaions i is reasonable o conservaively approximae ha he hermal limi remains he same during moor acceleraion. n he shor sar applicaions an error inroduced by his assumpion doesn preven he moor from successfully saring. The hermal limi curve is hus consruced from secions, 3 and 4. f he same approach is applied o he case shown on Figure 10, i will resul in he TCU reaching 100% in he middle of he acceleraion (Figure 11, curve 1). As we menioned in previous secions of his paper, as he hermal limi is a funcion of moor speed during acceleraion, he acceleraion hermal limi (curve 5) shows up differenly from he locked roor limi. Each poin on curve 5 corresponds o curren value which, in urn, corresponds o moor roaion speed during sarup. Based on his, we can indirecly find he reference beween moor speed and hermal limi, and consruc an updaed moor hermal limi curve which will include secions and 5 shown on Figure 10. The new curve helps achieve a successful moor sar (Figure 11, curve ) despie he fac ha locked roor safe ime is shorer han acceleraion period. The proecion mehod described above is relevan for an ideal siuaion wih a consan erminal volage of 100%. n realiy he sysem volage can deviae from 100% because of he volage drop during moor sarup. The locked roor curren (LRC) is almos direcly proporional o he volage applied o he moor erminals during acceleraion, his fac mus be aken ino consideraion when he acceleraion porion of he hermal limi is used in he hermal model algorihm. same applicaion reduced o 80% volage sar (Figure 10, curve 7). LRC a 80% is 4.8 imes of FLC. From he 100% volage case we know ha he locked roor condiion is referenced o he hermal limi of 88, and he allowed locked roor safe ime for an 80% volage sar yields 1.5 seconds, bu according o he acceleraion hermal limi curve (Figure 10, secion 5) he hermal limi ime corresponding o 4.8FLC is 40 seconds which is much er han he allowed value. This means ha if he Fig 11. Thermal Model Response o High neria Load Sars moor salls under he reduced volage condiions i becomes underproeced and appears o be in real danger of burning. To handle his siuaion he hermal model is equipped wih a mechanism capable of dynamically responding o volage variaions during moor sarup. Line 6 on Figure 10, shows he new posiion of he acceleraion curve 4, shifed in response o he volage reducion o 80%. The successful sar under hese operaional condiions is shown on Figure 11, curve 3. This echnique provides adequae hermal proecion in cases of -ineria load applicaion. n some cases where he hermal limi difference beween locked roor and acceleraion condiions is no clearly idenified, his elemen should be suppored wih a zero speed sensor. 6. Applicaion Descripion Fig 10. Volage Dependen Thermal Limi Curves For example, for a 100% volage sar (Figure 10, curve 1) he locked roor hermal limi is calculaed based on a LRC of 6 imes full load curren (FLC) and 8 seconds of he allowed locked roor safe ime, and ²T is equal o 88. Afer 14 seconds he moor acceleraes o approximaely 80% of he raed speed and he curren drops o he level of 4.8 imes ha of FLC. The allowed ime o wihsand 4.8 FLA for his sage of acceleraion is 40 seconds; ²T9. Now le us consider he This case sudy examines he nduced Draf (D) fan applicaion on he A. B. Brown Uni Selecive Ccaalyic Reducion (SCR) Projec, locaed in Evansville, ndiana. Uni is owned by Vecren Corporaion, and he role of Black & Veach (B&V) on his projec was o consruc an SCR faciliy in his plan. The SCR Projec Scope of Work included modifying boh D fans for caalys draf losses. The moors were powered from 13.8 kv swichgear. 5 Moor Thermal Model Proecion Applicaions

13 Moor raings and daa Moor Parameer Value Moor Horse Power 5500 HP Raed Volage 1300 V Phases 3 Moor Full Load 893 RPM Service Facor 1.15 Frequency 60 Hz Raed Full Load Curren 6 A Raed Locked Roor Curren 105 A nsulaion Class F Ambien Temperaure 43 C Temperaure SF C Temperaure SF C Table 3. Basic Moor Daa Table 3 presens he moor informaion peraining o he D fan moors. Moor saring and hermal characerisics The moor manufacurer provided he hermal limi curve under locked roor, acceleraion, and running overload condiions, as well as ime-curren curves during acceleraion a raed volage and a minimum specified saring volage. Some of he imporan moor characerisics (from he manufacurer s daa shee and curves) are summarized in Table 4. Descripion Moor Daa Table 4. Moor Saring and Thermal Limi Characerisics Proecion philosophy Volage Value Acceleraion Raed Volage in Seconds 100% 8.0 Acceleraion minimum Volage in Seconds 80% 53.0 Cold Locked Roor Safe Sall raed volage and 100% 6.0 ambien emperaure in seconds Cold Locked Roor Safe Sall min volage and 80% 47.0 ambien emperaure in seconds Ho Locked Roor Safe Sall raed volage a 100% 3.0 service facor load operaing emperaure in seconds Ho Locked Roor Safe Sall min volage a 80% 4.0 service facor load operaing emperaure in seconds Maximum Sars Per Hour N/A Maximum Cold Consecuive raed Volage 100% Maximum Cold Consecuive min Volage 80% Maximum Ho Consecuive raed Volage 100% 1 Maximum Ho Consecuive min Volage 80% 1 Running Cooling Time Consan in minues N/A 9 niial / Modified (during Sarup) Sopped Cooling Time Consans in minues N/A 16 / 1 The D fans on he A. B. Brown Projec are fed from a 13.8 kv auxiliary elecric sysem and are proeced by a mulifuncion moor proecion device (MPD). The fundamenal philosophies used in seing he MPD are as follows: The relay provides hermal proecion of he moor during abnormal saring or running condiions, prevening hermal damage o he moor (i.e., he MPD curve is placed below he moor hermal damage curves). The relay allows he moor o be sared successfully wihou nuisance rips, in accordance wih he number of sars and hermal/cooling characerisics recommended by he manufacurer The relay seings allow proper coordinaion wih he respecive ie and main circui breakers on he 13.8 KV bus o which he moors are conneced. Typically he B&V specificaions require he moor design o mee he following crierion: Moor safe sall ime a minimum saring volage shall no be less han moor acceleraion ime a minimum saring volage, plus seconds. The moor manufacurer could no mee his requiremen for his -ineria applicaion and indicaed ha a speed swich would be provided in lieu of his requiremen. The speed swich opion was no used because he MPD provided a range of seing opions for he overload feaure. The MPD was originally se using he cusom overload curve feaure o mach he moor characerisics, in addiion o all he above lised proecion crieria. Problems during sarup of D fans The problem ha he commissioning eam faced during sarup was ha he successive moor sar-ime delays deermined by he MPD hermal model were inconsisen wih wha was allowed by he moor manufacurer. The moor daa shee allowed he following operaional characerisics: Two successive cold sars or one ho sar. Following his sequence a new sar would be allowed afer any of he following: - A cooling period of 40 minues if he moor was running a service facor load and hen sopped. - A cooling period of 10 minues if he moor was running unloaded and hen sopped. - A cooling period of 0 minues if he moor was deenergized, coased o res, and lef idle. was observed ha he MPD was delaying resar by 40 o 43 minues afer every sar aemp, regardless of wheher i was a second cold resar or he firs ho resar. This performance was unaccepable o he clien who waned reliable cold saring as well as a resar ime consisen wih ha indicaed by he moor manufacurer. Some of he moor parameers recorded in he MPD during he sarup of one of he fans are as follows: Hoes RTD Values: 70 C. Learned Saring Curren: A. Average Moor Load: 60 percen of he raed curren. was also noiced ha he MPD hermal model was accumulaing almos all he available hermal capaciy even during he firs cold successful sar, hus prevening Moor Thermal Model Proecion Applicaions 53