Dynamic Model-Based Fault Detection and Diagnosis Residual Considerations for Vapor Compression Systems

Transcription

1 Prceedngs f the 26 Amercan Cntrl Cnference Mnneapls, Mnnesta, USA, June 4-6, 26 FrA7. Dynamc Mdel-Based Fault Detectn and Dagnss Resdual Cnsderatns fr Vapr Cmpressn Systems Mchael C. Ker, Andrew G. Alleyne, Senr Member, IEEE Department f Mechancal and Industral Engneerng Unversty f Illns at Urbana-Champagn Abstract - Ths paper presents a frst lk at the dynamc mpact f faults n vapr cmpressn systems. Lw-rder cntrl-rented dynamc mdels f subcrtcal vapr cmpressn cycles are used t develp senstvty tls that enhance the resdual desgn prcedure f dynamc mdel-based fault detectn and dagnss algrthms. Als, expermental results are presented that cnfrm the senstve utputs usefulness n an FDD algrthm. The enhanced fault nfrmatn carred n the mre senstve sgnals f a vapr cmpressn system wll allw sft faults t be detected earler, preventng damage t crtcal system cmpnents. V I. INTRODUCTION APOR cmpressn cycles are cmmnly used fr heatng and clng applcatns n ndustral, resdental and cmmercal settngs. As a drect result f ther wdespread use, the energy effcency f these cycles has receved sgnfcant attentn frm the research cmmunty. Wth advancements n cmpressr and valve technlges, the nclusn f advanced cntrl strateges n these systems has been prpsed as a vable means f mprvng the effcency f these systems []. Advanced cntrl strateges als enable the systems t cncurrently attan multple bjectves [2]. Anther ptental means fr mprvng the energy effcency f these systems stems frm the nclusn f fault detectn and dagnss (FDD) algrthms nt ther cntrl framewrk. FDD algrthms can be used t reduce the cst f system mantenance as well as ensure that the system s peratng effcently [3]. In general, current FDD algrthms fr vapr cmpressn cycles fall nt tw categres, steady-state mdel-based algrthms and neural netwrk/fuy mdel appraches [4]. Dynamc mdel-based fault detectn and dagnss algrthms, althugh nt prevalent n vapr cmpressn systems, have sme mprtant characterstcs whch culd ad n effectve fault detectn and slatn n ar cndtnng and refrgeratn systems. In rder t mplement dynamc mdel-based FDD algrthms a smple Ths wrk was supprted n part by the spnsrng cmpanes f the Ar- Cndtnng and Refrgeratn Center at the Unversty f Illns at Urbana-Champagn. M. C. Ker s a graduate student at the Unversty f Illns at Urbana- Champagn, Urbana, IL 68 USA. (emal: mker2@uuc.edu) A. G. Alleyne s a Prfessr at Unversty f Illns at Urbana- Champagn, Urbana, IL 68 USA (phne: ; fax: ; emal: alleyne@uuc.edu). dynamc mdel f vapr cmpressn systems whch retans suffcent accuracy s requred []. In prevus wrk, lumped parameter mvng bundary mdels have been develped fr smple vapr cmpressn system cmpnents [,2,5,6]. Recent wrk has expanded these mdels t nclude mre cmplcated system cnfguratns, wth cmpnents such as recevers and accumulatrs ncluded n the system mdel []. Snce the mdelng framewrk s readly avalable, the ptental advantages f dynamc mdel-based FDD algrthms n these systems shuld be dentfed. The nfrmatn currently avalable n the lterature n the dynamc mpact f faults n vapr cmpressn systems s qute lmted. Ths paper presents a frst lk at basc dynamc changes whch result frm a fault n these systems, and explres the benefts f dynamc mdel-based fault detectn algrthms n vapr cmpressn systems. Exstng theretcal tls are shwn t be hghly effectve n dentfyng the system utputs that are mst senstve t specfc faults. Ths senstvty nfrmatn allws the FDD desgner t antcpate apprprate sensr lcatns t mst effectvely mplement ther algrthms. In addtn, expermental results are presented that cnfrm the predcted senstve utputs, and detal hw the senstve sgnals culd be used t structure the resduals t dstngush between smlar faults n the evapratr and the cndenser. The remander f ths paper s rganed as fllws. Sectn II prvdes a dscussn f the faults cmmn t vapr cmpressn systems. Sectn III prvdes a bref summary f the dynamc vapr cmpressn cycle mdelng framewrk. Sectn IV presents theretcal analyss methds fr determnng a resdual s senstvty t varus faults. Sectn V presents expermental results whch dentfy apprprate system utputs t nclude n resdual desgn. Fnally, Sectn VI cncludes by hghlghtng the benefts f mprved fault senstvty n a vapr cmpressn cycle and emphases the apprprate utputs t nclude n a resdual t detect an ar flw fault n a specfc heat exchanger. II. AIR CONDITIONING AND REFRIGERATION FAULTS A number f surveys have been cnducted n falures n refrgeratn and ar-cndtnng equpment. Perhaps the mst cmplete survey was perfrmed by Stuppe and Lau n 989 [7]. Ths survey summares 5,76 falures whch ccurred between 98 and 987 n varus ar cndtnng /6/$2. 26 IEEE 442

2 and refrgeratn systems. Of the falures analyed, 72% were the result f electrcal falures. The majrty f these electrcal falures ccurred n the mtr wndngs f the cmpressr. In 22, Cmstck and Braun [8] cnducted a survey f cmmn faults n chllers. They fund that 64% f repar csts fr chllers were the result f cmpressr and electrcal falures. In many cases, the electrcal falures that ccur n the cmpressr are the result f the cmpressr beng verwrked due t sft faults, lsted belw, frmng n the vapr cmpressn system. Sft faults frce the system t wrk ver a hgher pressure dfferental, placng addtnal stran n the cmpressr that can reduce the lfetme f the cmpressr wndngs and decrease system effcency. In the case f cmpressr falure, the system s rendered cmpletely nperatve, and the repar csts are ften sgnfcant. Fault detectn algrthms whch can detect these sft faults early n ther develpment wuld reduce the cst f system mantenance by reducng the number f cmpressr falures [8]. Typcal faults whch shuld be ncluded n any cmprehensve FDD algrthm fr vapr cmpressn cycles are [9]: cndenser and evapratr fulng reductns n mass flw f the external flud refrgerant leaks cmpnent falures (hard faults) In many cases cmpnent falures are smple t detect due t ther abrupt nature and the extreme changes n system behavr whch result frm the lss f a crtcal system cmpnent [8]. Therefre, the remander f the dscussn n the paper wll fcus n the detectn f sft faults whch are mre dffcult t detect, and are ften the cause f the mre catastrphc cmpnent falures. III. DYNAMIC MODELING FRAMEWORK A basc vapr cmpressn cycle s cmpsed f fur prmary cmpnents: evapratr, cmpressr, cndenser, and an expansn devce. Addtnally, a hgh-sde recever and/r lw sde-accumulatr s generally added t the system as a means f strng excess refrgerant and ensurng safe peratn durng a varety f cndtns. Begnnng at the cndenser nlet, the hgh-pressure tw-phase flud flws thrugh the cndenser rejectng heat. Frm the cndenser the refrgerant flws t the recever where any excess charge s stred. Lqud frm the recever then flws thrugh an expansn valve and transtns frm a lqud t a tw-phase mxture at a lwer pressure. The refrgerant enters the evapratr, where heat s absrbed as the flud evaprates. Vapr frm the evapratr s cmpressed t a hgher pressure and cntnues cyclng thrugh the system. The fur cntrllable nputs t ths system are assumed t be cmpressr speed, expansn valve penng, and mass flw rates f ar acrss the evapratr and cndenser. A bref summary f the mdel s ncluded here as necessary backgrund. The nterested reader s referred t [] fr a mre cmplete descrptn f the mdel and the asscated dervatn. In general, the dynamcs f the cmpressr and expansn valve are fund t be sgnfcantly faster than the dmnant heat exchanger dynamcs, and are thus mdeled wth statc sem-emprcal relatnshps. A. Evapratr Mdelng f heat exchangers s cmplcated by the presence f tw-phase flud flw and cmplex nternal and external gemetry. The mvng bundary apprach s based n the assumptn f -dmensnal flud flw wth effectve dameter, flw length, and surface areas. The apprach als assumes equal pressure thrughut the heat exchanger. The heat exchanger s dvded nt regns based n the flud phase, and the effectve parameters are lumped n each regn. The nterface between flud phase regns s allwed t be a dynamc varable. The dervatn prcedure fr the evapratr requres the ntegratn f the gvernng partal dfferental equatns (PDEs) alng the length f the heat exchanger t remve spatal dependence. The flud enterng the evapratr s assumed t be tw-phase, whle the flud extng the evapratr s superheated vapr. Thus the evapratr s mdeled wth tw regns as shwn n Fg.. m xn > h n n Tw-Phase L (t) T wall, (t) L Ttal P(t) Superheat L 2 (t) x = T wall,2 (t) Fgure - Evapratr flud regns and lumped parameters. m h (t) ut ut The ntegratn f the three cnservatn equatns fr each regn results n sx equatns that can be smplfed t the nnlnear descrptr frm Z ( x, u) x = f ( x, u), where the elements f Z ( x, u) and f ( x, u) are nntrval and presented n detal n []. The state varables are defned n terms f pressures, enthalpes, etc. and are the result f the dervatn prcedure. The states f the evapratr mdel ( x e ) are length f tw-phase flw L, evapratn pressure e P, utlet e enthalpy h, and the tw lumped wall temperatures T, ut ew and T. The nputs t each f the cmpnent mdels are e generally utputs f ther cmpnent mdels. The nputs t the evapratr mdel, u e, are the nlet and utlet refrgerant mass flw rates m and n m (utputs f the valve and ut cmpressr mdels), the nlet enthalpy h (utput f the n valve mdel), and the temperature and mass flw rate f ar, (nputs t the verall system). T and e, ar, n m ar [ L P h T T ] T xe e e e, ut ew e = () [ m m h T m ] T = (2) u e e, n e, ut e, n e, ar, n e, ar 443

3 B. Cndenser wth Recever The cndenser s assumed t have tw flud regns, whle a tme-varyng mean vd fractn captures the dynamcs asscated wth small devatns abut saturated lqud cndtns at the utlet. m h m ( 2hnt2 t) n n P(t) nt x nt2 (t) > Superheat L (t) T wall, (t) L Ttal x = Tw-Phase L 2 (t) T wall,2 (t) Fgure 2 - The flud regn and lumped parameters f the cndenser wth recever mdel. The gvernng partal dfferental equatns fr mass and energy are ntegrated alng the length f the heat exchanger and lumped parameters are assumed. These sx dfferental equatns tgether wth the recever gvernng equatns are cmbned t elmnate the ntermedate varables, resultng n a mdel wth sx states: L, P, c γ, m, rec T, and w T. The resultng mdel s gven n equatn (3) and s f the descrptr frm Z ( x, u) x = f ( x, u), where the elements f the Z matrx are nntrval and gven n [] g γ = m rec T m w 66 T α α L m ( ) h hg + A ( Tw Tr ) L α LTtal (3) P L 2 m ( h h ) + α A ( T T ) nt 2 2 L m m ( hnt 2 h f ) UArec ( Trec Tamb ) A ( Tr Tw ) + α A ( Ta Tw ) A ( T T ) + α A ( T T ) 2 C. Cmpressr and Expansn Valve The cmpressr s mdeled usng vlumetrc and sentrpc effcences. A smple frst rder dynamc s ncluded n the cmpressr mdel t accunt fr the thermal capactance f the cmpressr shell. The valve expansn prcess s assumed t be senthalpc. Bth mdels use emprcal maps t accunt fr varatns n the peratng cndtns. A detaled dscussn f these mdels s presented n []. D. Lnear System Mdel Fr the theretcal analyss presented n ths paper the nnlnear evapratr and cndenser wth recever mdels were lneared. Cnnectng the mdular cmpnents tgether, an verall system mdel s generated and can be represented by the standard state space frmat gven n equatn (4). x = Ax + Bu (4) y = Cx + Du Where x s a vectr cntanng the states frm bth the evapratr and cndenser mdel, and u s the vectr f external nputs t the system mdel. The verall system mdel and the peratng cndtns arund whch the system was lneared can be fund n []. r 2 Ttal a r 2 IV. THEORETICAL FDD ANALYSIS The deas f parameter senstvty are drectly applcable t dynamc mdel-based FDD []. Typcally t s knwn hw physcal parameters are affected by the prpagatn f a partcular fault n a vapr cmpressn system, therefre a mdel senstvty analyss that explres perturbatns n the parameters can be used t dentfy the utputs well suted t FDD resdual desgn. Trajectry senstvty functns are a cmmn methd fr dentfyng the dynamc mprtance f system parameters, as they prvde a vsual representatn f the change n a system s respnse due t a varatn n a partcular parameter []. Trajectry senstvty functns, y, can be thught f as a frst rder apprxmatn f the parameter nduced errr, whch s represented by equatn (5). n s the nmnal parameter vectr, and s the parameter whse senstvty s beng explred. Fr the fllwng analyss, t s assumed that s % f the nmnal parameter value. The value f % s smewhat arbtrary, but t was selected snce t represents a fault level that wuld be desrable t detect, as devatns n parameters larger than % may negatvely mpact the perfrmance f the vapr cmpressn system. y δy ( t, β ) = δβ β (5) = n The case f external fulng n the evapratr and cndenser can be used t examne the effect f parameter varatn n system respnse. The buld up f a thermally nsulatng materal n the external surface f a heat exchanger, such as frst n an evapratr r drt n a cndenser, wll ncrease the thermal resstance between the refrgerant and the external flud. As the layer f materal ncreases n thckness t wll mpede the flw f the external flud. The trajectry senstvty framewrk can be used t explre the senstvty f system utputs t changes n a physcal parameter that wll mpact the verall system n a manner smlar t the actual fault. In the case f external fulng, the prmary effect s a reductn n heat transfer t the external flud. Therefre, the senstvty f the vapr cmpressn system mdel t perturbatns n the external heat transfer ceffcents fr bth heat exchangers can be explred, and shuld prvde utput senstvty nfrmatn relevant t fulng. T mplement the trajectry senstvty framewrk, the lnear system mdel frm Sectn III.D can be lneared wth respect t a physcal parameter. T remve any scalng ssues that result frm unt dscrepances n the mdel, bth the nputs and utputs were scaled, as shwn n equatns (6) thrugh (9). The nputs were scaled by ther nmnal values t prvde an equal weghtng amng the varus system nputs. The utputs were scaled t prvde the mst useful nfrmatn frm an FDD standpnt. Ideally, the analyss shuld prvde the FDD desgner wth the system utputs that wll have the strngest sgnal t nse rat. Ths nfrmatn can be extracted by scalng the utputs f the trajectry senstvty analyss by the standard devatn n the measured sgnal. Fr example, n ur system the 444

4 evapratr pressure sensr has a standard devatn f Pe = kpa accrdng t manufacturer data. The value was verfed by runnng the system at a steady-state peratng cndtn and usng an unbased estmatr, resultng n a measured standard devatn f 2.65 kpa. The same verfcatn prcedure was used fr the cndenser pressure sensr, and a value f Pc = kpa was used n the scalng matrx. There was n manufacturer data n the uncertanty f the thermcuple measurements. Therefre, an unbased estmatr was used and a value f T =.2 C was fund t represent the uncertanty n the sensrs. The scalng wll mdfy analyss t prvde the number f standard devatns the faulty utput wll vary frm the nrmal system utput as the result f a % change n a partcular system nput. y W y = β y B x A A x B A + Wuu = β β C x W C W C + y β y (6) D D Wuu (7) W y β W u s the weghtng matrx gven n equatn (8), and W y s the matrx gven n equatn (9). u { u, T, m, ω, T m } W =. (8) dag v a a, e k ac,, a, c W = dag,,,, (9) y P e T T P c T Fg. 3 presents the smulated devatn n utput respnse t a % step n the valve nput cmmand f the evapratr external heat transfer ceffcent devates by % frm ts nmnal value. It s clear frm the fgure that partcular system utputs, specfcally the evapratr ar utlet temperature, are mre respnsve t the frmatn f fulng n the external surface f the evapratr. Fg. 4 presents the smulated devatn n utput respnse t a % step n the valve nput cmmand f the cndenser external heat transfer ceffcent s reduced by % frm ts nmnal value. In ths case the mst respnsve utput frm a sgnal t nse perspectve s the cndenser pressure. Fg. 3 and Fg. 4 ndcate the utputs that shuld be ncluded n a structured r drectnal resdual n an FDD algrthm. Fr example, f the FDD desgner nly wshed t detect these tw fault cndtns, the algrthm wuld requre nly the measurement f evapratr ar utlet temperature and cndenser pressure. Althugh cndenser pressure respnds t bth faults, the evapratr ar utlet temperature wll nly respnd t a fault n the evapratr heat transfer ceffcent. Hence, the ncrease n cndenser pressure culd be used t detect a fault, and the evapratr ar utlet temperature sgnal wuld ndcate the lcatn f the fault. The reader shuld als nte the dfference n scale between the tw smulated devatn respnses n Fg. 3 and Fg. 4. Clearly, the system utputs explred n ths study are mre senstve t changes n the evapratr external heat transfer ceffcent. Ths wuld mply that a frsted evapratr wuld be easer t detect than a fuled cndenser. Nrmaled Errr (Std. Devatns) T e,r T c,a T e,a Tme (s) Fgure 3 Change n system respnse t a valve step as the result f external evapratr fulng. Nrmaled Errr (Std. Devatns) Tme (s) Fgure 4 - Change n system respnse t a valve step as the result f external cndenser fulng. V. EXPERIMENTAL SENSITIVITY RESULTS T e,r T c,a T e,a In addtn t the theretcal analyss f system changes that result frm devatns n physcal system parameters, actual faults can be ntrduced n an expermental test stand t verfy the senstvty f the dentfed utputs. In general, prevus studes have ether used a reductn n the mass flw rate f the external flud r the ntrductn f a blckage nt the external flud flw path t assess the mpact f fulng n a vapr cmpressn system [3,4,9]. In ths study, the mpact f a reductn n ar mass flw rate ver each heat exchanger s explred separately. A. Expermental System The results presented n ths sectn were taken frm an expermental test stand at the Unversty f Illns at Urbana-Champagn. The test stand has the ptental t mmc the behavr f a varety f vapr cmpressn system cnfguratns. The expermental system has a semhermetc recprcatng cmpressr, a sngle cndenser, an array f expansn devces, tw evapratrs and an nternal heat exchanger. The system cntans suffcent bypasses and valves t allw the system t be cnfgured n a sngle r dual evapratr frmat wth the chce f a thermal expansn valve, rfce tube, autmatc expansn valve, r an electrnc expansn valve regulatng the mass flw f the system. The system has fve cntrllable nputs; cmpressr speed, valve penng, bth evapratr fan speeds, and the cndenser fan speed. The system s fully nstrumented wth 6 pressure gauges, 2 mass flw meters, and 24 thermcuples. A cmplete descrptn f the system can be fund n []. 445

5 Fr the expermental results presented n ths paper the system was placed n a sngle evapratr cnfguratn that bypassed the nternal heat exchanger. The electrnc expansn valve was used as the expansn devce. A blck dagram f the cnfguratn used fr the expermental results s presented n Fg. 5. A pcture f the system s presented n Fg. 6. Fgure 5 - Dagram f the expermental system cnfguratn. Fgure 6 - The expermental test stand lcated at the Unversty f Illns at Urbana-Champagn. B. Reductn n Evapratr Ar Mass Flw Rate Cnsder the mpact f a reductn n the ar mass flw rate ver the evapratr n a vapr cmpressn cycle. Ths type f fault culd be caused by a varety f physcal cndtns n the system, such as a blckage f the ar ntake (fulng/frstng), r n a mre severe case, a fault n the fan mtr. The dynamc and steady state mpact f ths fault wuld prpagate thrughut the system. Therefre, n settng up an FDD algrthm the desgner wuld need t knw whch system utputs are mst senstve t the fault. One f the key effects f a reductn n ar mass flw rate ver a heat exchanger s a decrease n the heat transfer ceffcent between the heat exchanger wall and the ar. The average ar temperature passng ver the evapratr cl als decreases, further hnderng the heat transfer frm the refrgerant t the ar. T explre the mpact f a reductn n evapratr ar mass flw rate, the system was set t run at a steady-state peratng cndtn. Wth all ther nputs held cnstant, the evapratr ar mass flw rate was decreased by %. The resultng devatn n utput respnse frm the steady-state set pnt s presented n Fg. 7. In ths case, the ar mass flw rate decrease ccurred at t = 2 secnds, and the utputs were scaled by ther sensrs standard devatn as n Sectn IV. Ths prvdes the FDD desgner wth the strngest sgnals t dentfy an ar mass flw fault n the evapratr. It s clear frm the fgure that the evapratr ar utlet temperature and the evapratr refrgerant utlet temperature respnd sgnfcantly t an ar mass flw fault. Nrmaled Errr (Std. Devatns) T e,r T c,a T e,a Tme (s) Fgure 7 - Output devatn frm a % decrease n evapratr ar mass flw rate. C. Reductn n Cndenser Ar Mass Flw Rate In a smlar manner t the evapratr ar mass flw fault, a % fault n the cndenser ar mass flw rate can be ntrduced. The level f fault was cntrlled by reducng the pwer suppled t the fan, whch was crrelated t a reductn n the mass flw f ar ver the heat exchanger. Thus, a specfc level f ar mass flw fault culd be gradually ntrduced nt the cndenser. Fg. 8 presents the utput devatn resultng frm a % decrease n cndenser ar mass flw rate. In general, a vapr cmpressn system s less respnsve t a cndenser ar mass flw fault, therefre the sgnals were lw pass fltered t enhance the vsual dentfcatn f sgnal senstvty. Frm a vsual nspectn f Fg. 8, the cndenser pressure appears t exhbt a cnsstent upward drft as a result frm the decrease n ar mass flw rate. The evapratr ar utlet temperature and refrgerant utlet temperature seem t respnd n a mre scllatry manner, thugh ths may be partally due t varatns n ambent cndtns. It shuld be nted that, as was predcted n Sectn IV, the se f the devatns as the result f a reductn n cndenser ar mass flw rate are smaller than thse frm an equvalent ar mass flw rate fault n the evapratr. Ths wuld agan mply that fulng faults n the evapratr wll be easer t detect than a fault f cmparable magntude n the cndenser. Nrmaled Errr (Std. Devatns) T e,r T c,a T e,a Tme (s) Fgure 8 - Output devatn frm a % decrease n cndenser ar mass flw rate. 446

6 D. FDD Implcatns External heat exchanger fulng wll mpact a vapr cmpressn system n tw dstnct ways. The buld up f a layer f thermally nsulatng materal n the surface f the heat exchanger wll ncrease the thermal resstance between the ar and the refrgerant. As the layer ncreases n se n a cnventnal tube and fn heat exchanger, the pressure drp acrss the heat exchanger wll ncrease frm the reductn n free flw area thrugh the fns. Ths wll decrease the ttal mass flw rate f ar passng ver the heat exchanger. The senstvty analyss suggested that the cndenser pressure and evapratr ar utlet temperature wuld be suffcent t detect the buld up f a thermally nsulatng materal n the external surface f the tw heat exchangers. Frm an expermental nvestgatn f the mpact f a reductn n ar mass flw rate, t was seen that these tw utputs d n fact respnd sgnfcantly t the ar flw fault. The senstvty analyss dd nt capture all f the sgnals that wuld respnd, as seen by cmparng the refrgerant utlet temperature respnse n Fg. 3 and Fg. 7. Ths s lkely due t the fact that the senstvty analyss ntrduces a change n a sngle physcal parameter t apprxmate the cmbned effects parametrc and nput effects that result frm an actual fault. Althugh the senstvty analyss may underestmate the effects f certan nput-utput varables, t s mprtant t nte that t was successful n dentfyng the fllwng characterstcs: Cndenser fulng s harder t detect than evapratr fulng. The evapratr ar utlet temperature and cndenser pressure can be used t detect and dstngush fulng faults n the evapratr and cndenser. The FDD desgner culd use the senstvty nfrmatn t create a structured r drectnal resdual [2]. Wth an apprprate resdual structure the algrthm wll be able t dstngush between dfferent types f faults wthn the vapr cmpressn system. VI. CONCLUSION Dynamc mdel-based FDD algrthms ffer sgnfcant benefts fr handlng the transent nature under whch many vapr cmpressn systems perate. The mdels allw bth steady-state and dynamc parameters t be used n the desgn f FDD resduals, makng the algrthm senstve t the sft faults whch are cmmn t these systems. Effectve FDD algrthms that prvde early detectn f sft faults n vapr cmpressn systems wll result n mprved system perfrmance and wll sgnfcantly reduce the number f catastrphc falures that ccur. These cmbned factrs make the nclusn f FDD algrthms n vapr cmpressn systems an ntegral part f mprvng the ar cmfrt, refrgeratn, and relablty prvded by these systems ver a wde range f applcatns. Future research wll use the tls presented n ths paper t develp and mplement a dynamc mdel-based FDD algrthm n a vapr cmpressn system. NOMENCLATURE Varable Explanatn Subscrpt Explanatn T Temperature f Lqud P Pressure g Vapr h Enthalpy Inner u Internal Energy Outer Cp Specfc Heat T Ttal ρ Densty ave Average Heat Transfer α Ceffcent cs Crss-Sectnal m Mass Flw Rate r Refrgerant A Area w Wall L Length e Evapratr V Vlume c Cndenser x Mdel States, Qualty v Valve u Mdel Inputs nt Interface Mdel Parameter n Nmnal REFERENCES [] B. P. Rasmussen, Dynamc Mdelng and Advanced Cntrl f Ar- Cndtnng and Refrgeratn Systems, Phd. dssertatn, Dept. Mech. Eng., Unversty f Illns at Urbana-Champagn, Urbana, IL, 25. [2] X. D. He, S. Lu, and H. Asada, Mdelng f Vapr Cmpressn Cycles fr Multvarable Feedback Cntrl f HVAC System, Jurnal f Dynamc Systems, Measurement and Cntrl, vl. 9, n. 2, pp. 83-9, 997. [3] J. E. Braun, Autmated Fault Detectn and Dagnstcs fr Vapr Cmpressn Clng Equpment, Jurnal f Slar Engneerng, vl. 25, pp , 23. [4] A. K. Halm-Ow, and K. O. Suen, Applcatns f fault detectn and dagnstc technques fr refrgeratn and ar cndtnng: a revew f basc prncples, Prceedngs f the Insttutn f Mechancal Engneers, Part E: Jurnal f Prcess Mechancal Engneerng, vl. 26, n. 3, pp. 2-32, 22. [5] B. T. Beck, and G. L. Wedeknd, Generalatn f the System Mean Vd Fractn Mdel fr Transent Tw Phase Evapratng Flws, Jurnal f Heat Transfer, vl. 3, n., pp. 8-85, 98. [6] E. W. Grald, and J. W. MacArthur, A Mvng Bundary Frmulatn fr Mdelng Tme-Dependent Tw-Phase Flws, Internatnal Jurnal f Heat and Flud Flw, vl. 3, n. 3, pp , 992. [7] D. E. Stuppe, and T. Y. S. Lau, Ar Cndtnng and Refrgeratn Equpment Falures, Natnal Engneer, vl. 93, n. 9, pp. 4-7, 989. [8] M. C. Cmstck, J. E. Braun, and E. A. Grll, A Survey f Cmmn Faults fr Chllers, ASHRAE Transactns, vl. 8, n., pp , 22. [9] I. B. D. McIntsh, W. A. Beckman, and J. W. Mtchell, Fault Detectn and Dagnss n Chllers- Part : Mdel Develpment and Applcatn, ASHRAE Transactns, vl. 6, pp , 2. [] M. C. Ker, B. P. Rasmussen, and A. G. Alleyne, Parametrc Senstvty Analyss and Mdel Tunng Appled t Vapr Cmpressn Systems, n Prc. f IMECE, Orland, FL, 25, paper n [] J. B. Cru Jr., Feedback Systems, McGraw-Hll, New Yrk, 972. [2] Gertler, J., Fault Detectn and Dagnss n Engneerng Systems, Marcel Dekker, Inc., New Yrk,