Model Predictive Control and Fault Detection and Diagnostics of a Building Heating, Ventilation, and Air Conditioning System ABSTRACT 1.

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1 Model Predctve Control and Fault Detecton and Dagnostcs of a Buldng Heatng Ventlaton and Ar Condtonng System 3366 Page Sorn BENGEA * Pengfe LI Soumk SARKAR Sergey VICHIK 2 Veronca ADETOLA Keunmo KANG Teems LOVETT Francesco LEONARDI Anthony KELMAN 2 Unted Technologes Research Center Unted Technologes Corporaton East Hartford CT USA 2 Department of Mechancal Engneerng Unversty of Calforna Berkeley CA USA ABSTRACT The paper presents the development and applcaton of Model Predctve Control (MPC) and Fault Detecton and Dagnostcs (FDD) technologes to a large-scale HVAC system ther on-lne mplementaton and results from several demonstratons. The two technologes are executed at the supervsory level n a herarchcal control archtecture as extensons of a baselne Buldng Management System (BMS). The MPC algorthm generates optmal set ponts whch mnmze energy consumpton for the HVAC actuator loops whle meetng equpment operatonal constrants and occupant thermal-comfort constrants. The MPC algorthm s mplemented usng a new computatonal toolbox the Berkeley Lbrary for Optmzaton Modelng (BLOM) whch generates automatcally an effcent optmzaton formulaton drectly from a smulaton model. The FDD algorthm uses heterogeneous sensor data to detect and classfy n real-tme potental faults of the HVAC actuators. The performance and lmtatons of FDD and MPC algorthms are llustrated and dscussed based on measurement data recorded from multple tests.. INTRODUCTION The large potental economc mpact of advanced technologes underlyng modern Buldng Management Systems (BMS) have led to ncreased efforts focused on developng desgnng and mplementng model-based control and dagnostcs technologes for buldng HVAC systems wth the objectve to estmate ther cost effectveness. The potental economc mpact s apparent both from the hgh energy-consumpton levels of buldng HVAC systems estmated currently at 27% (EPA 28) and from lmtatons of exstng control technologes for HVAC systems. Model-based paradgms have been employed to ntegrate n a drect and systematc way sensor data from multple subsystems wth the objectve to generate optmal set-ponts whch lead to ncreased overall effcency. Ths paper descrbes a model-based optmal set-pont control algorthm MPC and a data-drven equpment fault dagnostcs mplemented at supervsory level as extensons of a baselne Buldng Management System (BMS). The focus s on ther development mplementaton and performance estmaton based on the results of tests conducted n two commercal buldngs. Integraton of the two technologes nto the same model-based framework addresses two major challenges n buldng control systems: cost of deployment (relatve to energy savngs) and optmzaton of the HVAC system effcency throughout ts lfe. Although prevous efforts (Adetola et al. 23; Bengea et al. 24) have demonstrated energy savngs separately for dagnostcs and optmal control algorthms at varous buldng scales the model-based technologes have not always led to cost-effectve solutons due to the cost of commssonng of nstrumentaton and algorthms. The effort descrbed heren mnmzes these costs n two ways. Frst by deployng the MPC and FDD algorthms on the same platform wthn the same framework usng the same sensor sutes for large-sze HVAC unts. Second by employng an automated tool for formulatng optmzaton problems assocated wth MPC algorthms. In addton the proposed ntegrated framework has the potental to maxmze the buldng system effcency throughout ts lfetme by enablng mplementaton of fault-tolerant technologes that ntegrate the two algorthms. Fault detecton and dagnostcs technologes have sgnfcant potental to reduce energy neffcences resultng from faults and degradaton of buldng equpment and materals; errors n operatng schedules and crtcal desgn/plannng flaws. A comprehensve lterature revew can be found n (Katpamula 25a and 25b) where the FDD methods are broadly categorzed nto two classes namely model-based and data-drven. Model-based technques prmarly nvolve ether physcs-based models such as APAR rules n (Schen 26) sophstcated Modelca models n (Wetter 29) EnergyPlus smulaton models n (Pedrn et al. 22)) or emprcal models such as extended Kalman Flter n (Yoshda 996). Although model-based technques perform well often

2 3366 Page 2 calbraton and valdaton of such models may become expensve. Data-drven technques have the advantage that requre a reduced calbraton and valdaton effort; they range from smple statstcal analyss (Seem 27) prncpal component analyss (Xao and Wang 29) to complex machne learnng models such as artfcal neural network (Petsman and Bakker 996). The algorthm mplemented for ths effort uses a probablstc graphcal-model based technque to model the hstorcal performance of varous HVAC subsystems n a data-drven manner. Specfc faults of HVAC actuators such as dampers and valves are flagged and dagnosed n real-tme upon detectons of any devatons from the modeled nomnal behavor. Based on expermental data t was estmated that the FDD algorthm correctly dagnosed the HVAC subsystem faults n 84% of the cases mssed the detecton of 6% of the events and generated false alarms n % of the cases when faults were seeded. Model Predctve Control technologes are appled optmal control algorthms that use dynamcal and steady-state models and predctons of plant dsturbances to mnmze a selected performance cost whle satsfyng operaton and equpment constrants (Morar and Lee 999; Mayne et al. 2; Borrell 23). In ths effort an MPC algorthm was mplemented at supervsory level to perodcally solve an optmzaton problem and generate optmal sequences of set ponts for Ar Handlng Unts (AHUs) and Varable Ar Volume unts (VAVs). A smlar herarchcal archtecture has been proposed n (Kelly 988). mulaton and expermental results have been reported prevously for smaller scale HVAC systems (Henze et al Clarke et al. 22 L et al. 22) and for radant HVAC systems (roky et al. 2). A smlar mplementaton of an MPC technology as the one descrbed here was reported n (Bengea et al. 24) for a medum-scale Mult-Zone Unt for a commercal buldng. The efforts presented heren buld on ths prevous mplementaton by employng the Berkeley Lbrary for Optmzaton Modelng (BLOM) (Kelman Vchk and Borrell 23) to automatcally formulate the MPC algorthm and mplementng t for a large-scale buldng. Ths new computatonal toolbox sgnfcantly reduces the development effort of translatng nonlnear smulaton-orented models nto effcent constraned optmzaton problem formulatons for MPC. The performance results estmated based on sensor measurements and meter data ndcate that MPC algorthm reduced energy consumpton by more than 2% whle mprovng thermal comfort. The paper s organzed as follows. Secton 2 descrbes the HVAC system confguraton and the models used for MPC desgn. The FDD algorthm desgn and calbraton are presented n the Secton 3. Secton 4 presents the MPC algorthm and the tool chan used to automate the optmzaton problem formulaton. Expermental results and performance estmates based on test data are descrbed n Secton BUILDING HVAC AND CONTROL-ORIENTED MODELS Ths secton descrbes the buldng HVAC system used for testng the control and dagnostcs algorthm ts confguraton and the served zones. It also detals some of the models used by the MPC algorthm. 2. Descrpton of Buldng HVAC System Ths secton descrbes the man HVAC subsystems ther local control loops and nstrumentaton. The HVAC system has a centralzed archtecture n whch a steam-to-hot-water heat exchanger plant serves multple AHUs n two dentcal large-sze buldngs located at the Navy Recrut Tranng Center Great Lakes IL. The HVAC systems consst of three AHUs servng 57 VAVs. Each of these AHUs serves 8 VAV unts located n 9 compartments each wth a capacty of several tens of occupants whch are occuped durng nght-tme. The temperature set pont s based on a crcadan varaton wth hgher set ponts (durng heatng season) durng nght-tme. Ths schedule s programmed n the BMS and s dentcal for all zones. The focus of ths effort n on AHUs and ther VAVs whch are nstrumented as detaled n Table. The local control algorthms for each of the subsystems of Table are descrbed below: The VAV dampers d and re-heat col valves are controlled based on two coordnated Proportonal- VAV VAV Integral (PI) algorthms and rules that are drven by the zone set pont trackng error. The local controllers seek to mantan the zone temperature wthn comfort bands T T ] that change at pre-scheduled ntervals and [ LB UB repeat every 24 hours. The dscharge ar temperature to each zone s controlled n open-loop (due to a lack of

3 dscharge ar temperature sensors for most of the unts). The volumetrc ar flow rates 3366 Page 3 V VAV are controlled by modulatng the VAV dampers d VAV to meet the scheduled set pont values. The AHU fan speeds are controlled n order to mantan the pressure set ponts scheduled n BAS. The by-pass face dampers and the heatng col valves are controlled based on loops that track a dscharge ar temperature set pont. The damper s controlled to mantan a mnmum Mxed Ar Temperature (MAT) set pont (durng the heatng season) whch s coordnated wth the freeze-protecton control rule. Common sensors (baselne nstallaton) Specal sensors nstrumente d for ths effort Common actuators Table. Instrumentaton of the HVAC systems AHU Instrumentaton VAV Instrumentaton Spaces Volumetrc ar flow rate Zone meterng staton temperatu Re-heat col valve poston re CO 2 sensor sensors Dscharge ar mxed ar and return ar temperature sensors; damper and valve poston sensors Fan VFD speed and power meter One AHU was nstrumented wth BTU meters for both heatng and coolng cols and volumetrc ar flow rate meterng staton The same AHU was nstrumented wth more accurate averagng mxed and dscharge temperature sensors Forecast of outdoor ar temperature (downloaded on-lne from NA) Dampers: face by-pass damper controllng the mxed ar flow porton through the heatng deck; outdoor ar and return ar Heatng and coolng col valves Three VAVs have been nstrumented wth BTU meters nlet ar temperature sensors re-heat col valve poston sensors and damper poston sensors 8 VAVs have been nstrumented wth dscharge ar temperature sensors Dampers Re-heat col valves Zone relatve humdty sensors 2.2 Control-Orented Models Ths secton descrbes the models used for the MPC algorthm desgn. In vew of the tme-scale separaton of the zone temperature dynamcs (wth a tme response n the order of tens of mnutes) and HVAC subsystems (wth a tme response at most a few mnutes) the only dynamcal model consdered n ths approach corresponds to the zone temperature dynamcs. The followng models are developed at steady-state: outdoor ar fracton model; mxed ar temperature model; AHU heatng col model; AHU total ar flow rate model; AHU supply fan model; VAV re-heat col model. All expressons consdered n ths model are polynomal n order to facltate dervatons of frst and second order dervatves requred for the optmzaton solver as explaned n Secton 4.2. The zone temperature for each zone s modeled usng a nonlnear Auto-Regressve wth External dsturbance (ARX) model whch was selected from a larger famly of models based on ther modelng errors: T ( k ) T ( k) T ( k ) T ( k 2) T 2 ( k) T 2 3 ( k ) m sa ( k) T sa S ( k) T S ( k) d where the notaton s defned n the Secton Nomenclature and the samplng tme s 5 mnutes. The parameters d are dentfed usng several measurement tests: a subset of the measurement sets 2 3 S 2 was generated from experments desgned wth selected nput profles; another subset was selected from hstorcal data. The controlled test nputs are AHU heat col valve poston v the VAV re-heat col valve postons v and the VAV supply ar flow rates VAV HC m sa S AHU HC () ; a set of data s llustrated n Fgure (left). Although these tests were appled to all three AHUs and ther correspondng VAVs a model was used to generate estmates of VAV dscharge ar temperatures Tsa S ( k) for the VAVs that were not nstrumented wth these addtonal sensors. The ablty of the models to predct zone temperature was subsequently evaluated usng new sets of data. Such a set of data s llustrated for one zone n Fgure (rght).

4 Counts Counts Temperature [F] Temperature [F] Temperature [F] Flow [kg/s] Command [%] Temperature [F] Command [%] Error [F] Command [%] zonetemp [F] 3366 Page 4 zone # AHU HCV : : 3: 6: 9: VAV RCHV /4 2/5 2/6 tme /4 2/5 2/6 samples data model error 2F lne -2F lne -2 2: : 3: 6: 9: 5 VAV DAT 6 Ar Flow 5 2/4 2/5 2/6 Tme : : 3: 6: 9: zone zone 5 zone 6 zone 3 zone 45 zone 46 zone 6 zone 75 zone : : 3: 6: 9: Fgure. (Left) Normalzed tme seres data of the nputs v v HC and 46 AHU HC sa S T 44 test for AHU 42 and correspondng zone temperatures measurements; (Rght) Model valdaton results usng new data /4 2/5 2/6 Tme /4 2/5 2/6 Tme VAV m Ar flow T for a system dentfcaton sets based on whch t s concluded that the zone temperature modelng error s smaller than 2 F Table 2. 6: HVAC steady-state 9: models and assumptons 36 2: : 3: HVAC Subsystems Assumptons Equatons 4 m-dot(dat-zone temp) Outdoor ar fracton 2 m-dot(dat-zone temp5) Steady-state models as functons of 2 f m-dot(dat-zone temp6) c2 d c d c and m-dot(dat-zone temp3) mxed-ar outdoor ar damper specfcally for m-dot(dat-zone temp45) m-dot(dat-zone temp46) temperature -2 m-dot(dat-zone temp6) heatng season TMA f T ( f) TRA m-dot(dat-zone temp75) m-dot(dat-zone temp76) -4 Thermal power of Steady-state models as functons of 2: : AHU heatng cols 3: 6: 9: mass ar flow rate nlet and dscharge PHC m SA cpa ( TDA AHU T ) MA TSF ar temperatures AHU supply mass ar Constant ar flow leakages n the m SA AHU c SA m SAVAV flow rate c SA Electrcal power of supply fans Thermal power of VAV re-heat cols supply ducts to zone VAVs Functon of suppled ar flow Steady-state models as functons of volumetrc ar flow rate nlet and dscharge ar temperatures P SF c 3 SF c SF m 3 SA AHU m SA AHU c 2 SF c SF m 2 SA AHU W HC n c VAV T SA VAV TSA AHU c3 VAV v c HC 2 VAV m SAVAV T Pct Error (%) Pct Error (%) Fgure 2. Hstograms of the valdaton errors for models of Table 2 (mxed-ar temperature; AHU heatng col thermal power; AHU supply ar flow rate; AHU supply fan power; VAV re-heat col thermal power) All HVAC subsystem control-orented models are determned at steady-state due to ther shorter tme response (one order of magntude) relatve to the zone temperature dynamcs. The HVAC subsystems ther models and man assumptons are ncluded n Table 2 (usng the notaton descrbed n the Nomenclature secton). All the steady-state models of Table 2 are calbrated and valdated wth multple sets of data. The hstograms of the valdaton errors between model predctons and measurements are llustrated n Fgure 2. Constrants related to the length of ths paper preclude ncluson of addtonal tme seres data and more detaled dscussons of the assumptons and restrctons of these models.

5 3. FAULT DETECTION AND DIAGNOSTICS ALGORITHMS 3366 Page 5 Ths secton descrbes the mplemented FDD system whch uses a data-drven methodology ntegrated wth doman knowledge to detect and dagnose faults. The FDD tool-chan ncludes a data-drven off-lne step of learnng the nomnal behavors and an on-lne step of detectng off-nomnal behavors. Data-drven methodologes have several advantages such as low-cost commssonng scalablty adaptablty to system varaton/evoluton and lmted requrement of doman knowledge. The selected data-drven method conssts of a graphcal-network-based approach whch allows encodng the background doman knowledge and physcs-based understandng of the system whle allowng dscovery of new relatonshps wthn data streams usng structure learnng algorthms. The FDD tool-chan used n ths project has the followng steps: () Data acquston. Data-drven methods requre suffcent data n order to relably model a complex system. Data suffcency nvolves two major aspects: spannng the operatng space and statstcally sgnfcant amount of data. Both hstorcal data and functonal tests have been used n order to generate enough data to model dscrete graphcal models for dfferent buldng subsystems. () Data pre-processng. The two major steps are: data qualty verfcaton and data abstracton for modelng. In the data qualty verfcaton step sensor observatons are checked for data ranges rate of changes and communcaton relablty. In order to prepare data for dscrete probablstc graphcal models contnuous sensor observatons were dscretzed usng varous technques ncludng equal-wdth equal frequency and Maxmally Bjectve Dscretzaton (Sarkar et al. 23). () Model learnng. The graphcal structure of the FDD model s learned n an exclusvely data-drven manner to dscover relatonshps between varables nherent n the data. The structure s then valdated aganst doman knowledge and physcs based understandng of the system. Usng a goodness-of-ft metrc that s based on accuracy of predcton of selected crtcal varables model parameters are adjusted to acheve a good ft. The graphcal network model for FDD s used to analyze new valdaton data to generate an anomaly score quantfyng the extent of departure from the nomnal performance of varable gven the measurement of other related varables. Based on the anomaly scores and a sutably chosen threshold faults can be detected n any varable of the FDD model. The flagged events were then verfed aganst ground truth. (v) On-lne detecton. Probablstc graphcal models are generated for each relevant buldng sub-system. The developed FDD algorthms and ther graphcal representatons are dscussed and llustrated n Table 3 and Fgure 3 respectvely. The graphcal network models were calbrated and valdated usng multple sets of data generated by overrdng the BAS commands. Fgure 4 contans the results of a valdaton test for the FDD algorthm assocated wth the d damper. In ths case a fault was seeded by overrdng the damper command to 85% open whle the BAS command was only 4%. Usng the sensor nformaton from several temperature sensors the FDD algorthm detected correctly the seeded faults. Table 3. FDD approach detals correspondng to AHU subsystems Subsystem Faults FDD graphcal model nodes VAV Damper d VAV : stuck; ar leakages; stcky Damper poston supply ar flow rate heatng col termnal valve poston and ar flow thermal power unt Valve VAV HC : stuck; leakages; stcky Damper d : stuck; ar leakages; stcky Damper poston estmated outdoor-ar flow fracton (based on temperature measurements) AHU Valve stcky AHU HC : stuck; water leakages; Fan: capacty and effcency changes Heatng col valve poston ar flow thermal power ar flow rate face by-pass damper poston dfference between nlet and outlet water temperatures Fan speed electrcal power supply statc pressure ar flow rate

6 3366 Page 6 Fgure 3. Graphcal FDD models for the followng actuators: outdoor ar damper (left); AHU heatng col (center); AHU fans (rght) A small delay n generatng the fault flag s observed and ths s mplemented n the algorthm to ensure that the fault perssts for some tme before t s flagged and therefore reduce potental false alarms. More expermental data sets are presented and dscussed n Secton 5. d 5 Commanded Estmated 2/2 2/3 f /2 2/3 Fault Flag.5 2/2 2/3 Fgure 4. Illustraton of valdaton test data for the FDD algorthm assocated wth outdoor ar damper Outdoor ar damper: BAS command whch was overrdden; estmated poston (top); outdoor ar fracton (mddle); fault flag (bottom) 4. MODEL PREDICTIVE CONTROL AUTOMATED FORMULATION AND IMPLEMENTATION Ths secton descrbes the MPC problem the herarchcal control archtecture n whch t s mplemented and the automated tool chan employed for ts formulaton. 4. Model Predctve Control Formulaton An MPC algorthm s mplemented to generate optmal set ponts for the buldng HVAC subsystems n real tme by searchng for the most energy-effcent control nput sequences subject to system constrants (thermal comfort component performance) and dsturbances (weather nternal loads) smlarly to the mplementaton n (Bengea et al. 24). The MPC algorthm s mplemented at the supervsory level n a herarchcal archtecture whose sgnal flow s llustrated n Fgure 5. The MPC formulaton ntegrates n the same framework the control-orented buldng-system performance and zonetemperature models descrbed n Table 2 and operatonal and thermal comfort constrants. The algorthm s formulated as a determnstc optmzaton problem as descrbed below where we use the same notaton as n Secton Nomenclature and all the models are descrbed n Secton 2.2.

7 3366 Page 7 Sensor Data (Descrbed n Table ) Heatng Plant Buldng AHUs and VAVs Zones Weather Forecast Supervsory Fault- Tolerant System Bayesan Network Models (Descrbed n Table 3) Predcton Models (Descrbed n Table 2) Sensor Data Fault Detecton and Dagnostcs Component Constrants Model Predctve Control Fault-Isolaton Logc Component Faults Optmzaton Algorthm Local Control (Illustrated n Fgure ) AHU Control Set Ponts VAV Control Fgure 5. Herarchcal archtecture of the fault-tolerant system The problem s formulated separately for each AHU and served VAVs and spaces. t f Objectve cost: Mn P P P Penalty T T T ) t VAV AHU HC AHU SF VAV HC ( UB LB (2) ref Optmzaton VAV ar flow rates m VAV SA and re-heat col valve postons v VAV HC AHU varables (2 ref control nputs): dscharge ar temperature T AHU DAT and damper postons d and d MA Subject to: Equalty constrants for AHU VAVs and zone temperatures from Table 2 ref max TAHU DAT TAHU DAT ( TMA m SA AHU ) (3) AHU nequalty max m constrants AHU SA m AHU SA (4) d v (5) VAV nequalty constrants d d mn max VAV SA VAV SA MA AHU HC m m (6) v (7) VAV HC The lower and upper bounds d mn are preset as operatonal constrants. The comfort constrants are formulated as soft constrants va functons Penalty T T T ) n (2). These functons penalze the excursons of the ( UB LB [ T S LB T UB zone temperature outsde of the comfort bands ] whch are scheduled for each zone and are tmedependent. The soft-constrant formulaton does not cause any nfeasblty ssues when some zone temperatures may leave the comfort band (e.g. due to dfferent actual loads than forecasted). The above optmzaton problem s solved at 5 mnute tme ntervals and conssts of: updatng the sensor measurements and weather forecast; estmatng temperature states; dagnosng component faults; generatng optmzed set-ponts for the entre four-hour predcton horzon; communcatng the new set pont values (only for the next samplng tme) to BMS. Ths repeated calculaton of set ponts ensures soluton robustness and optmalty by usng the most recent measurements and outdoor temperature forecasts. The optmzaton problem formulaton workflow the process by whch the above mathematcal problem s converted nto an optmzaton algorthm s llustrated n Fgure Automated Optmzaton Problem Formulaton The MPC algorthm formulated n Secton 4. was converted nto an optmzaton problem by usng The Berkeley Lbrary for Optmzaton Modelng (BLOM) (Kelman et al. 23). BLOM brdges the gap between smulatonorented tools (mulnk Modelca etc.) and optmzaton-orented tools (Kallrath 24 Soares et al. 23). BLOM s based on a new formulaton for representng lnear and nonlnear mathematcal functons that ams to address some of the lmtatons of smulaton-orented tools. Ths formulaton allows for drect computaton of closed form

8 3366 Page 8 gradents Jacobans and Hessans. The ntal model formulaton nterface s based on mulnk and BLOM provdes a set of Matlab functons whch convert a mulnk model nto an optmzaton problem usng a specfc representaton format. Ths problem representaton s then used n a compled nterface to an optmzaton solver such as IPOPT (Wächter et al. 26). BLOM conssts of three man parts. Frst there s the mulnk front end where a dynamc model s represented usng bult-n mulnk blocks and the BLOM lbrary blocks. Second a set of Matlab functons s used to convert a mulnk model nto the nternal mathematcal representaton descrbed n (Kelman et al. 23). Lastly ths problem representaton s used by an nterface to an optmzaton solver such as IPOPT. The BLOM front end for mulnk ncludes (n addton to the regular mulnk blocks) nequalty cost functon and desgnaton of varables as free optmzaton varables or set by a user. As shown n Fgure 6 frst a model s created n mulnk and valdated usng forward smulaton. Second the model s converted to an optmzaton problem and exported to a solver (IPOPT). Thrd a problem data s suppled and a soluton s obtaned. The thrd step s repeated wth a new state measurement every tme step. For effcent onlne soluton of a large nonlnear MPC optmzaton problem n real tme t s crtcal that the sparsty structure of both the spatal connectvty n the model and the temporal causalty over the MPC predcton horzon are captured and represented n the optmzaton formulaton. BLOM s desgned usng an effcent sparse nonlnear problem representaton n order to capture ths nformaton from the system model n a way that the optmzaton solver can fully utlze. BLOM EPMO model Forward smulaton Model valdaton Problem data Auto translaton Export opt. problem IPOPT optmal control Fgure 6. The man steps for convertng the MPC algorthm nto an optmzaton problem formulaton usng BLOM Table 4 presents typcal performance of the BLOM lbrary wth IPOPT solver for the MPC problem formulated n Secton 4.. We present the executon tme of problem soluton for varous problem szes. The table shows that even for very large problems wth more than varables and constrants the lbrary acheves good performance and IPOPT converges quckly to a Karush-Kuhn-Tucker pont of the constraned fnte-tme optmal control problem. Table 4. BLOM executon results Predcton horzon length (steps) Number of varables n solver Number of constrants Non-zeros n Jacoban and Hessan Number of solver teratons Total soluton tme [sec] Tme spent n BLOM callbacks 34% 3% 29%

9 5. EXPERIMENTAL RESULTS AND PERFORMANCE ESTIMATION 3366 Page 9 Ths secton presents the performance estmates generated based on multple test conducted from Nov. 22 to March 23 for three AHUs. The performance results are descrbed separately for the FDD and MPC algorthms. The secton starts wth a descrpton of the method employed to estmate the overall system performance then descrbes aggregated performance results contnue wth plots of expermental data for both FDD and MPC algorthms and concludes wth a dscusson of the lmtatons of ths performance analyss. 5. Performance Estmaton for the MPC and FDD Algorthms The man performance metrcs addressed n ths effort are: overall energy consumpton peak power comfort and percentage of faults dentfed correctly. The overall energy (power) consumpton was calculated usng both electrcal energy (power) consumpton (for fans) and thermal energy (power) consumpton for heatng heat exchangers. The overall energy (power) consumpton was estmated by convertng the thermal component to an electrcal component usng the estmated Coeffcent of Performance (COP) of the heatng plant. The comfort crtera was ntally ntended to be addressed as a hard constrant (as a band around zone thermostat set ponts) but t was observed that the baselne control algorthms dd not meet ths constrant for several tme ntervals every day. Therefore a more realstc crtera was used that estmates comfort volatons (durng the heatng season) as t f t max( T ( t) T ( t)) dt (8) LB whch represents the accumulated tme nterval over whch the comfort constrant s not met (durng the heatng season) weghted by the level of constrant volaton. We present frst the overall results generated based on the sensor and meter data recorded from the demonstratons conducted durng the heatng season The overall results are llustrated n Fgure 7 for each AHU relatve to the baselne BAS schedule performance; the performance targets are llustrated as horzontal red lnes. In the followng paragraphs we frst dscuss the results pertanng to the MPC algorthm (energy consumpton peak power reducton and dscomfort reducton) and then the performance of the FDD algorthm. B4 AHU B4 AHU2 B3 AHU Average MPC Performance Relatve to Baselne for Each AHU[%] Energy Consumpton ReductonPeak Power Reducton Dscomfort Reducton Fault Dagnostcs Fgure 7. Illustraton of the overall results generated durng the demonstratons for MPC and FDD algorthms for each of the AHUs for the followng objectves: energy consumpton reducton peak power reducton thermal dscomfort reducton and fault dagnostcs system robustness. For each AHU 2 3 the results n Fgure 7 pertanng to energy savngs peak power reducton and thermal dscomfort are generated by averagng ts performance over all demonstraton days usng the followng formula: PerfMetrc ( AHU ) N PerfMetrc ( AHU MPC j ) PerfMetrc ( AHU Baselne ) N AHU MPC MPC j AHU Baselne Baselne k k (9)

10 Temperature ( C) 3366 Page The performance metrcs n (9) calculates two averages: the frst s across all MPC algorthm demonstraton days MPC and the second s for all the baselne days Baselne (durng whch the HVAC system s controlled by the j baselne algorthm) that are selected to be compared aganst the performance results generated n demonstraton day. Ths selecton s dscussed n the followng. k MPC j In lack of suffcent large sets of test data a crtera has to be used for selectng specfc baselne days and MPC demonstraton days for conductng performance analyss. The crtera selected for ths analyss s based on ambent temperature; ths selecton was based on the assumpton that n lack of occupancy data as s the case wth many demonstraton stes the ambent condtons generate the largest dsturbances that have to be rejected by HVAC system. Such a selecton s llustrated n Fgure 8 (left) where the ambent-temperature tme seres data for one MPC day and the correspondng baselne days are plotted. 45 Outdoor Ar Temperature 4 Baselne 2 MPC 35 Baselne Baselne Samples (5 mn.) 3:45 AM 6:5 PM Fgure 8. Illustraton of ambent temperature durng an MPC demonstraton day (red) and selected baselne days wth smlar ambent temperature pattern (left). Temperature values correspondng the MPC and baselne controllers for the same days (rght). The same fgure also llustrates (rght plot) the zone temperatures generated wth the correspondng algorthms durng the same days as selected n the left plot. The performance of the MPC algorthm and the baselne algorthms durng these days s further detaled n Fgure 9 whch llustrates that the baselne algorthms dd not meet comfort constrants when the set pont values were changed (accordng to the crcadan schedule mplemented n BAS). In order to meet these constrant when the set pont value s ncreased (durng heatng season) the MPC algorthm s peak power value exceeded the baselne algorthm s peak power values. Comfort Volatons MPC MPC MPC worked harder to mantan the comfort (hgher peak demand) Peak Demand Fgure 9. Illustraton of temperature comfort volatons AHU heatng col power fan power and total VAV thermal power durng the same days as those llustrated n Fgure 8.

11 Anomaly Score Anomaly Score Arflow Arflow Mean CO2 (PPM) Degree Hours ( C hrs.) Total Energy (kwh) 3366 Page The bar graphs n Fgure and further llustrate a subset of the test data based on whch the performance metrcs of Fgure 7 where calculated (usng formula (9) and three baselne days wth closest ambent temperature values for each MPC day). Energy consumpton and peak power reducton levels are llustrated n Fgure where negatve values n the peak power bar graph mean that MPC algorthm used hgher power levels. The mean zone CO 2 levels and comfort volatons are llustrated n Fgure. Comparson of Total Energy Consumpton (B73 AHU: Mar. 23 Demo) Day Day 2 Day 3 Day 4 Day 5 MPC Avg. Baselne Peak Demand Reductons (%) (B73 AHU: Mar. 23 Demo) Day Day 2 Day 3 Day 4 Day 5 Fgure. Total energy consumpton and peak power reductons of MPC and baselne algorthms Comparsons of Mean CO2 (B73 AHU: Mar. 23 Demo). Day Day 2 Day 3 Day 4 Day 5 MPC Avg. Baselne Comparson of Comfort Volatons (Temperature) (B73 AHU: Mar. 23 Demo) Day Day 2 Day 3 Day 4 Day 5 MPC Avg. Baselne Fgure. Mean zone CO 2 levels and temperature comfort volaton levels for MPC and baselne algorthms The overall FDD algorthm performance was estmated usng sensor and meter data recorded durng multple test wndows. Based on ths data t was estmated that the FDD algorthm correctly dagnosed the HVAC subsystem faults n 84% of the cases (level llustrated n Fgure 7) mssed the detecton of 6% of the events and generated false alarms n % of the total events whch consst of equal number of seeded and non-seeded (real) faults. The seeded faults were mplemented by overrdng the commands communcated by the controllers (wth the BACNet message prorty set at a value that enables the overrde) wthout communcatng these overrdes to the FDD algorthm. An example of a correctly dagnosed damper fault s llustrated n Fgure 2 were the traned VAV FDD algorthms correctly dagnosed the damper-stuck faults. Upon ths fault dagnostcs ths partcular fault was confrmed by nvestgated the actual VAVs. B74.2EN.S.PERIM: B74.3EN.S.INTER: Damper Poston Damper Poston Score Value Score Threshold F 7/8 7/9 7/2 7/2 7/22 7/23 7/8 7/9 7/2 7/2 7/22 7/23 Zone Temperature 75 Zone Temperature Setpont /8 7/9 7/2 7/2 7/22 7/23 F 7 Zone Temperature Zone Temperature Setpont 7/8 7/9 7/2 7/2 7/22 7/23 Fgure 2. Comparsons between nomnal (healthy) and faulty VAV unts

12 3366 Page 2 The lack of suffcent nstrumentaton and the naccuracy of sensors for buldng HVAC systems present sgnfcant challenges that result occasonally n mss-detecton or false postve classfcatons. Partcularly for hgh capacty HVAC unts wth large ar duct dameters the naccuraces of ar temperature sensors at dfferent locaton can result n false postve FDD outcomes. Several data sets are llustrated n Fgure 3 where the followng nconsstences are observed: () when d closes T MA ncreases and gets closer to T RA as expected but there are also tme ntervals over whch T MA exceeds T RA T ; () T MA exceeds T HR when d s fully open; () MA T exceeds THR and RA whch have smlar values by about 5 F. In all these cases the FDD algorthm can trgger false alarms on some tme sub-ntervals. The lmted sensor set data cannot be used to dstngush between multple cases: mscalbrated sensors; leakages that depend nonlnearly on damper postons; non-mxed ar flows wth non-unform temperatures. In vew of these lmtatons the outdoor ar damper faults that are seeded correspond to large varatons n d n the nterval [3% 7%] openng; where the lower bound s mposed by fresh ar constrants and the upper bound was selected to avod case () dscussed above. Wth ths lmted range on the outdoor ar damper seeded-faults whch mnmze the rate of false alarms for ths damper the false alarms are mostly generated for cases when large changes n set pont values occur T HR T RA T MA : : : 2: 3: : 2: 5: 8: : 8: : 6 4 9: : : 2: 3: 6 4 9: 2: 5: 8: : 8: : d actual d control Fgure 3. Illustraton of the outdoor ar damper postons and mpacted temperatures for three scenaros descrbed above the fgure 5.2 Lmtatons of the Performance Estmaton Method There are several lmtatons n the calculaton of the performance estmates of the FDD and MPC algorthms. The lmtatons are revewed and dscussed below for each algorthm. For the FDD algorthm these lmtatons are consequences of the followng factors: Only sngle faults are consdered n ths effort and they are exclusvely assgned to actuator faults; except for these faults the HVAC unts were consdered otherwse healthy. As prevously mentoned t s not possble to dstngush between all possble faults that can occur wth a lmted sensor and meter data set. HVAC control systems have a large degree of fault-accommodaton wthout explctly estmatng any faults. An example s dscharge ar temperature control loop at AHU level whch controls the volume flow rate of the mxed arflow through the heatng col deck and the heatng valve poston. A large number of combnatons between the flow rate and the heatng valve postons can lead to the same temperature dfferences between the mxed ar and dscharged ar. Wthout ntermedate sensors for measurng the nlet temperature to the heat exchanger an FDD algorthm has lmted nformaton for detectng any faults assocated wth these two actuators when usng only data generated wth the local controllers. The FDD performance reported n Fgure 8 corresponds only to the unts that were nstrumented wth addtonal sensors (as descrbed n Table ).

13 3366 Page 3 The estmaton of the uncertanty magntude n the reported performance levels of the MPC algorthm s lmted by factors related to sensor nstrumentaton and test data sze: Although the performance levels are estmated usng measurement data from 26 days dstrbuted unevenly durng the entre heatng season 22-3 t s unclear whether the dstrbuton of the nternal loads and ambent condtons was representatve for all heatng seasons n the selected buldngs. The level of sensor nstrumentaton needed to generate these estmates s beyond the level of nstrumentaton n standard commercal buldngs such as those used as for demonstratons for ths effort. Therefore an extrapolaton of the results n Fgure 7 to other heatng seasons ambent condtons or usage patterns cannot be made drectly. We note however that large levels of energy savngs were also demonstrated for a smaller AHU n smlar ambent condtons and dfferent HVAC confguraton and usage patterns (Bengea et al. 24). The method used for MPC performance estmaton s based on the assumpton that the largest dsturbance s ambent temperature and therefore smlarty n the outdoor ar temperature patterns s the most mportant crtera when selectng multple sets of days for performng energy consumpton comparsons. When suffcently large sets of data avalable usng multple crtera would ncrease the accuracy of the performance estmates. Less than 3% of the models are valdated. Due to lmted sensor nstrumentaton for two of the AHUs ( B4 AHU2 and B3 AHU n Fgure 7) the AHU and VAV heat exchanger models could not be valdated. Therefore the VAV re-heat col energy consumpton for these AHUs were estmated usng the same models as those used for the AHU for whch addtonal sensors were nstrumented (as descrbed n Table ). The MPC algorthm does not use zone occupancy models and therefore does not control drectly the CO 2 levels n the zones. The MPC algorthm met the mnmum outdoor ar damper constrant (desgned for the baselne algorthm to meet the fresh ar requrements). However after the demonstratons t was observed that the MPC algorthm consstently ncreased ths level n all zones by about 35% on average (across all zones served by all three AHUs). The lmtatons n the sensor and meter data prevent detaled estmaton of specfc portons of the reported energy consumpton levels n Fgure 7 that are due to decreasng the outdoor ar damper poston (whle stll meetng the mnmum damper-poston constrant) meetng dfferent occupancy loads and ncreasng thermal comfort. 6. CONCLUSIONS The paper presents the desgn mplementaton and performance results of two model-based algorthms based on tests conducted n two large-sze commercal buldngs durng the heatng season The MPC algorthm uses sensor data to generate perodc updates of AHU and VAV unt set pont values that reduce energy consumpton whle mantanng all zones temperatures wthn a comfort band. The FDD algorthm uses sensor and meter data to solate on-lne faults assocated wth the AHU actuators. The ndvdual performance benefts of the two algorthms are estmated based on test results compared aganst hstorcal baselne data generated durng test perods wth smlar ambent condtons. Although the energy performance depends on uncertantes whch cannot be completed characterzed wth lmted data the results demonstrate the potental of the algorthms to reduce energy levels to levels that provde favorable cost benefts. NOMENCLATURE AND MATHEMATICAL NOTATIONS AHU BLOM BMS CFM CO 2 COP FDD FTC GPM HVAC IPOPT MPC Ar Handlng Unt Berkeley Lbrary for Optmzaton Modelng Buldng Management System Cubc Feet per Mnute Carbon Doxde Coeffcent of Performance Fault Detecton and Dagnoss Fault-Tolerant Control Gallon per Mnute Heatng Ventlaton and Ar Condtonng Interor Pont OPTmzer Model Predctve Control

14 NA Natonal Oceanc and Atmospherc Admnstraton VAV Varable Ar Volume VFD Varable Frequency Drve and T Mass flow rate and temperature of suppled ar to space S m sa S T S sa S 3366 Page 4 T MA T Temperatures of Outdoor Ar () Mxed Ar (MA) and Return Ar (RA) respectvely RA T T T LB Ar temperature n space and upper (set pont durng coolng season) and lower (set UB S S d d MA d RA d FBD T sa AHU THD pont durng heatng season) bounds of the temperature comfort band for space Damper postons for Outdoor Ar () Mxed Ar (MA) Return Ar (RA) and by-pass ar flow streams respectvely T Temperature of ar suppled by AHU (downstream of hot and cold decks; upstream of VAV CD unts); Temperature ar dscharged at the outlet of the hot and cold decks respectvely f Rato between mass flow rate of outdoor ar flow and mass flow rate of the mxed ar flow v AHU HC VAV HC P v Normalzed poston of the heatng col valve (the subscrpt makes t clear whether ths belongs to the AHU heatng col of VAV re-heat col Power (thermal or electrcal) REFERENCES Adetola V. Ahuja S. Baley T. Dong B. Khawaja T. Luo D. O Nel Z. Shashanka M. 23 Scalable Deployment of Advanced Buldng Energy Management Systems ESTCP-EW-5 Project Techncal Report. Atanu Talukdar & Amt Patra. Dynamc Model-Based Fault Tolerant Control of Varable Ar Volume Ar Condtonng System. HVAC&R Research Vol 6 (2) 2. Pgs Baotc M. F. Borrell A. Bemporad and M. Morar. Effcent on-lne computaton of constraned optmal control. SIAM Journal on Control and Optmzaton 5: September 28 Bengea S. Kelman A. Borrell F. Taylor R. and Narayanan S. 24 Implementaton of model predctve control for an HVAC system n md-sze commercal buldng Journal of HVAC & R Research Volume 2 Issue pp Borrell F. J. Pekar M. Baotc and G. Stewart. On The Computaton Of Lnear Model Predctve Control Laws. Automatca 46(6):35-4 June 2. Borrell F. Constraned Optmal Control of Lnear and Hybrd Systems Lecture Notes n Control and Informaton Scences vol. 29. Sprnger 23. Bourassa N. Automatc Dagnoss for Alng Rooftop Ar Condtoners PIER Techncal Bref July 25. Brand M.E. Pattern Dscovery va Entropy Mnmzaton. In Uncertanty 99: AISTATS Brand M.E. Structure Learnng n Condtonal Probablty Models va an Entropc Pror and Parameter Extncton n Neural Computaton Journal Vol. No. 5 pp July 999. Chang L. E. Russell R. Braatz Fault Detecton and Dagnoss n Industral Systems Sprnger Verlag London 2. Dudley J.H. Black D. Apte M. Pette M.A. and Berkeley P. 2. Comparson of Demand Response Performacnr wth an EnergyPlus Model n a Low Energy Campus Buldng. 2 ACEEE Summer Study on Energy Effcency n Buldngs. Pacfc Grove CA. August Envronmental Protecton Agency 28 Report on Envronment Fnal Report EPA/6/R-7/45F. Unted States Envronmental Protecton Agency. Fernandez N; Brambley MR and S. Katpamula. Self-Correctng HVAC Controls: Algorthm for sensors and Henze G. D. Kalz C. Felsmann and G. Knabe. 24. Impact of forecastng accuracy on predctve optmal control of actve and passve buldng thermal storage nventory. HVAC&R Research Vol. No. 2 pp dampers n ar handlng unts US DOE report 29 (Contract DE-AC5-76RL83) Henze G.P. Kalz D. E. Lu S. and Felsmann C. Expermental Analyss of Model-Based Predctve Optmal Control HVAC&R Research Vol. No pp Kallrath J. Modelng Languages n Mathematcal Optmzaton ser. Appled Optmzaton. Kluwer Academc Publshers 24. S

15 3366 Page 5 Kelly G Control system smulaton n North Amerca. Energy and Buldngs Vol. pp Kelman A. Vchk S. Borrell F. BLOM: The Berkeley Lbrary for Optmzaton Modelng and Nonlnear Predctve Control Internal report Department of Mechancal Engneerng Unversty of Calforna Berkeley 23. Webste: L P. Barc M. Narayanan S. and Yuan S. 22 A mulaton-based Study of Model Predctve Control n a Medum-zed Commercal Buldng 2 nd Internatonal Hgh Performance Buldngs Conference at Purdue July West Lafayette IN. Ljung L. System Identfcaton: Theory for the User Prentce Hall Ma Y. Borrell F. Hencey B. Coffey B. Bengea S. Packard A. Haves P. Model Predctve Control for the Operaton of Buldng Coolng Systems n Proceedngs of the Amercan Control Conference July 2 Baltmore MD. Mayne D. J. Rawlngs C. Rao and P. Scokaert. 2. Constraned model predctve control: stablty and optmalty Automatca Vol. 36 No. 6 pp Morar M. and J. Lee Model predctve control: past present and future Computers and Chemcal Engneerng Vol. 23 pp Pette M.A.S. Knney and P. Haves. Analyss of an Informaton Montorng and Dagnostc System to Improve Buldng Operatons Energy and Buldngs 33 (8) (2) Radhakrshann R. D. Nkovsk K. Peker and A. Dvakaran. Locally Weghted Regresson for Fault Detecton and Dagnoss of HVAC Equpment IEEE Intl. Conf. on Industral Electroncs 26. Roth K. W. Westphalen D. Feng M. Y. Llana P. and Quartararo L. (25). Energy mpact of commercal buldng controls and performance dagnostcs: market characterzaton energy mpact of buldng faults and energy savngs potental. Report prepared for U.S. Department of Energy. TIAX LCC Cambrdge MA. Sarkar S. A. Srvastav and M. Shashanka Maxmally Bjectve Dscretzaton for Data-drven Modelng of Complex Systems Proceedngs of Amercan Control Conference (Washngton D.C.) 23 roky J Oldewurtel F Cgler J Prvara S. 2 Expermental analyss of model predctve control for an energy effcent buldng heatng system. Appl Energy. Vol. 88 pp Soares R. d. P. and A. Secch European Symposum on Computer Aded Process Engneerng-3 36th European Symposum of the Workng Party on Computer Aded Process Engneerng ser. Computer Aded Chemcal Engneerng. Elsever 23 vol. 4. [Onlne]. Avalable: Wächter and L. T. Begler On the Implementaton of a Prmal-Dual Interor Pont Flter Lne Search Algorthm for Large-Scale Nonlnear Programmng Mathematcal Programmng 6() pp ACKNOWLEDGEMENT The authors are grateful for the fnancal support and gudance provded by the SERDP/ESTCP Offce under the leadershp of Drs. Jeff Marqusee and Jm Galvn for project EW2-42. We also thank Mr. Peter Behrens Energy Manager at Naval Staton Great Lakes for hs support n conductng the demonstratons. Vews opnons and/or fndngs contaned n ths report are those of the authors and should not be construed as an offcal Department of Defense poston or decson unless so desgnated by other offcal documentaton.