Model-based Optimal Control of Variable Air Volume Terminal Box

Transcription

1 Purdue Unversty Purdue e-pubs Internatonal Hgh Performance Buldngs Conference School of Mechancal Engneerng 216 Model-based Optmal Control of Varable Ar Volume ermnal Box Fuxn Nu he unversty of alabama, Unted States of Amerca, Zheng O'Nell he unversty of alabama, Unted States of Amerca, Xaohu Zhou he unversty of alabama, Unted States of Amerca, Defeng Qan he unversty of alabama, Unted States of Amerca, Follow ths and addtonal works at: Nu, Fuxn; O'Nell, Zheng; Zhou, Xaohu; and Qan, Defeng, "Model-based Optmal Control of Varable Ar Volume ermnal Box" (216). Internatonal Hgh Performance Buldngs Conference. Paper hs document has been made avalable through Purdue e-pub a servce of the Purdue Unversty Lbrares. Please contact epubs@purdue.edu for addtonal nformaton. Complete proceedngs may be acqured n prnt and on CD-ROM drectly from the Ray W. Herrck Laboratores at Herrck/Events/orderlt.html

2 3191, Page 1 Model-based Optmal Control of a Buldng HVAC System Fuxn Nu 1 *, Zheng O Nell 1, Xaohu Zhou 2, Defeng Qan 1 1 he Unversty of Alabama, uscaloosa, AL, USA (Phone: , Emal: fnu@crmson.ua.edu) 2 Iowa Energy Center, Ankeny, IA, USA * Correspondng Author ABSRAC A model-based optmal control strategy s explored to mnmze a buldng Heatng, Ventlaton and Ar- Condtonng (HVAC) energy consumpton n the heatng mode. Energy performance models for ndvdual component, ncludng the Ar Handler Unt () heatng col, the supply fan and the Varable Ar Volume (VAV) termnal box reheat col, are bult through a data-drven method. hermal response of the room ar s establshed usng a non-lnear regresson based dentfcaton approach. he supply ar temperature and the room ar temperature are consdered as the constraned condton. A platform of AMPL (A Modelng Language for Mathematcal Programmng) s used to for mathematcal modelng and lnks to the optmzaton solvers. A case study usng the data collected from the Energy Resource Staton at the Iowa Energy Center was conducted usng the proposed strategy. he comparson between the baselne and the smulaton-based case wth the proposed modelbased optmal control ndcated that a 22.1% savngs potental of total energy consumpton could be acheved. 1. INRODUCION In the U.S., A Varable Ar Volume (VAV) system s one of most commonly used ar system for multple-zone commercal buldngs due to ts capablty to meet the varyng heatng and coolng loads of dfferent buldng thermal zones. One of the key components of a VAV system s the termnal VAV box. here s an ar damper and a reheat col n the box. How to effectvely and effcently control the HVAC system wth the VAV box plays a sgnfcant role to reduce energy consumpton and mantan acceptable ndoor envronment n buldngs. L et al. (215) mplemented an optmzaton-based model predctve control (MPC) algorthm for buldng HVAC systems and demonstrated ts benefts through buldng energy consumpton reductons as well as thermal comfort mprovements. A MPC smulaton framework was frst presented wth ts assocated performance benchmarked. he expermental results from the same buldng located at the Phladelpha Navy Yard were then presented. For the smulaton study, t was estmated that the MPC could reduce the total electrcal energy consumpton by around 17.5%. For the subsequently expermental demonstraton, the performance mprovement of the MPC algorthm was estmated relatve to baselne days wth smlar outdoor ar temperature patterns durng the coolng and shoulder season and t was concluded that the MPC strategy reduced the total electrcal energy consumpton by more than 2% whle mprovng thermal comfort n terms of zone ar temperature. Cho and Lu (28) developed and feldmplemented optmal termnal VAV box control algorthms. he thermal condtons and energy consumpton were compared between conventonal and mproved control algorthms usng the measured data. he results showed that optmal VAV box control algorthms can stably mantan the room ar temperature and reduce energy consumpton compared wth conventonal control algorthms. Lu et al. (25) presented the global optmzaton technologes for the HVAC systems. he objectve functon of a global optmzaton and constrants were developed based on physcal models of the major HVAC components. A modfed genetc algorthm was then used to solve the global optmzaton problem for mnmzng the overall HVAC system energy consumpton. Smulaton studes for a centralzed HVAC plant usng the proposed optmal method showed that the optmzaton method mproved the system performance sgnfcantly compared wth tradtonal control strateges. Yang and Wang (212) proposed an

3 3191, Page 2 optmal control strategy to control the HVAC system for mantanng buldng s ndoor envronment wth a hghenergy effcency. he control strategy utlzed a swarm ntellgence to determne the optmal amount of energy dspatched to ndvdual equpment n the HVAC system. A case study was conducted to smulate the real tme control process n a specfed buldng envronment. Compared to the Constant Ar Volume (CAV) system and the non-optmzed VAV system, the proposed optmal control strategy was capable of savng more energy n buldng operatons under the same envronmental condton. Kusak et al. (21) presented a data-drven approach to derve energy performance models. Data-mnng algorthms were employed to select sgnfcant parameters and estmate ndvdual HVAC component energy consumpton. o mnmze the total energy consumpton, a sngle-objectve optmzaton model was formulated and solved by the partcle swarm optmzaton algorthm. he partcle swarm optmzaton algorthm searches the near optmal solutons of the supply ar temperature and statc pressure setponts n an ar handlng unt (). he optmzaton results demonstrated a 7.66% savngs. Fong et al. (26) studed a smulaton based Evolutonary Programmng (EP) couplng approach, whch ncorporated the component-based smulaton and EP optmzaton. he HVAC system under the nvestgaton had an ar-sde system that contrbutes sgnfcantly to the overall energy consumpton. From the optmzaton result the proposed technque worked well n provdng the optmum combnaton of the chlled water supply temperature and supply ar temperature for a cost-effectve energy management throughout an entre year. Nassf et al. (24) optmzed the set ponts usng a two-objectve genetc algorthm for a supervsory control strategy. he optmzaton process was appled to an exstng HVAC system usng a detaled physcal VAV model. he energy demand from the smulaton case wth the optmzed control strategy s 19.5% less than that from the actual buldng wth the non-optmzed control strategy. he applcaton of the two-objectve optmzaton algorthm could help a better control n terms of mnmal daly energy use and maxmal daly thermal comfort n the buldng as compared to the one-objectve optmzaton approach. Modelng effort and requred computaton resource are bottlenecks for on-lne mplementatons of MPC at a large scale. Other optmzaton based control methods utlzed customzed physcs-based models that are complex and not scalable. he HVAC system operaton may get the smlar benefts by adaptng optmzaton based control from the nformaton captured n hstorcal operaton data. he goal of ths prelmnary study s focusng on how to utlze the short term hstorcal data to get the current tme optmal operaton pont. In ths paper, model-based optmal control for a buldng HVAC system s proposed to mnmze the total HVAC system energy consumpton wth constrants of occupants thermal comfort. he ndvdual component energy consumpton, ncludng an, a fan and VAV boxe was formulated. he fan energy consumpton model was derved through a data-drven approach based on a polynomal regresson algorthm. he optmal control approach was tested usng measurements from the Energy Resource Staton (ERS) Buldng at the Iowa Energy Center. We wll frst brefly ntroduce the ERS buldng, then the models for ndvdual HVAC component and zone thermal dynamc and optmzaton approach. Fnally, we wll talk about the savngs potentals that were demonstrated through the smulaton based study, lmtatons and future work. 2. BUILDING INRODUCION he data used for data-drven energy performance models was collected at the ERS Buldng of the Iowa Energy Center n Ankeny, Iowa. he Iowa Energy Center establshed the ERS Buldng for the purposes of examnng varous energy-effcency measures and demonstratng nnovatve HVAC concepts. he faclty s dvded nto a general area and two test areas (A and B). Each test area ncludes four thermal zones served by one. he basc descrpton of the ERS faclty s shown n Fgure 1. Mnmzng the total energy consumpton from the HVAC system B s the goal of ths case study. he HVAC system B s comprsed of a central and an overhead ducted ar dstrbuton that termnates wth four room-level VAV termnal boxes. Each test room s equpped wth a pressure-ndependent, sngle-duct VAV box. Each VAV box has both a hydronc and an electrc reheat col (Note: only hydronc reheat cols are used n ths study). VAV boxes wth reheat cols were tradtonally controlled usng the sngle maxmum control logc. he supply arflow rate setpont s reset from the zone maxmum arflow rate setpont when the space s at a full coolng stage proportonally down the zone mnmum arflow rate when no coolng s requred. hs mnmum arflow rate s mantaned as the space temperature falls through the dead band nto the heatng mode. he hot water valve then modulates to mantan the space at the heatng setpont untl t s fully open. he measured ponts ncluded outdoor ar temperature, return ar temperature, mxed ar temperature, supply ar temperature and volumetrc ar flow rate, ndvdual VAV box supply ar temperature and volumetrc ar flow rate, ndvdual room ar temperature, supply fan power consumpton, nlet and outlet water temperatures and mass flow rate of heatng col, and nlet and outlet water temperatures and mass flow

4 3191, Page 3 rates of VAV box reheat cols. he data wth one mnute samplng frequency from Oct 3 th 213 to Jan 3 th 214 was used n ths case study. he data are aggregated to 1 mnutes nterval for the tranng and testng of proposed data-drven models. Data sets used n ths case study were collected from regular operaton modes. No specal functon tests wth exctatons were performed. Fgure 1: he layout of energy resource staton n Iowa 3. MODELING AND OPIMIZAION he optmzaton objectve s to mnmze the total energy consumpton of the HVAC system ncludng, fan and VAV box n the heatng mode over the three months. Frst, data-drven energy performance model for the ndvdual energy consumpton component was formulated. he thermal comfort constrants for room ar temperatures and supply ar temperature were ncluded n the optmzaton problem formulaton. he optmzaton problem was solved usng a platform of AMPL (A Modelng Language for Mathematcal Programmng) (AMPL 216). Control varables nclude supply ar temperature, VAV box supply ar flow rates and supply ar temperatures. 3.1 Data-drven Energy Performance Model model he mxed ar temperature s formulated as follow. he return ar temperature s calculated usng the weghted average of ar temperature from all four rooms. r (1 r) (1) mx oat ra ra N m r 1 N m 1 ( ) (2) Where mx s the mxed ar temperature ( o C), r s the fresh ar rato, s the outdoor ar temperature ( o C), oat s the return ar temperature ( o C), ra N s the number of VAV box, N s 4 n ths case study. he thermal power consumpton from the heatng col s formulated as follow. he mass flow rate s the sum of the ndvdual VAV box supply ar flow rate.

5 Pan power (W) Where Q p mx 3191, Page 4 Q m c ( ) (3) m N m (4) 1 s the thermal power consumpton (W), m s supply ar mass flowrate (kg/s), c p s the ar specfc heat (J/(kg oc)), s the return ar temperature ( o C), mx s the number of VAV box, m s the supply ar mass flowrate at the th VAV box (kg/s). Fan model Fan electrcal power consumpton was bult based on the polynomal regresson method: P a m a m a m a (5) 3 2 fan Where Pfan s the fan power consumpton (W), a 1, a 2, a 3, a4 are the coeffcents of the fan power consumpton curve. able 1 presents the dentfed coeffcents of the proposed fan power curve. he comparsons between the regresson model predcton and the actual measurements are shown n Fgure 2. he R-square value of regresson model s.87, and the root mean square error (RMSE) s 149. able 1: Coeffcents of fan power curve Value a a a a Measured Predcted Fgure 2: Fan electrcal power consumpton comparson VAV box model Reheat energy consumpton by reheat cols of the VAV box at th VAV box was modeled by: Q m c ( ) (6) reheat p

6 Western room ar temperature ( o C) Where Qreheat s the reheat thermal power consumpton of the th VAV box (W), s the supply ar temperature at the th VAV box ( o C). 3191, Page 5 Room ar thermal response model A non-lnear regresson method based dentfcaton approach s appled to predct room ar temperature wth nput varables of outdoor ar temperature oat, VAV box supply ar temperature s, and VAV box supply ar flow rate m. For the nteror room, we are assumng that the outdoor ar temperature does not affect the nteror room ar temperature. herefore, the room ar temperature s manly related wth VAV box supply ar temperature and supply ar flow rate. he comparson of three dentfcaton method namely ARX model, State Space model (Nu et al. 215), and the proposed non-lnear regresson model, are shown n Fgure 3 usng western room ar temperature measurement data. For the non-lnear regresson method, ar temperature dentfcatons n four rooms were formulated usng Equatons (7) to (1). R-square and RMSE for these three data-drven methods are lsted n able 2. In ths case study, the non-lnear regresson method s selected as the room ar thermal response model due to the lowest RMSE. east m (7) r oat m (8) south r oat m (9) west r oat Where east r s the eastern room ar temperature ( o C), south r nteror r s, m (1) s the southern room ar temperature ( o C), west r s the western room ar temperature ( o C), nteror r s the nteror room ar temperature ( o C) Measured Non-lnear model State space model ARX model /3/213 11/3/213 12/3/213 1/3/214 Fgure 3: Western room ar temperature comparson able 2: R-square and RMSE for three models ncluded n Fgure 3 Non-lnear regresson method ARX model State Space model R-square RMSE

7 3191, Page Optmzaton formulaton In ths prelmnary case study, the optmzaton objectve functon s to off-lne mnmze the total energy consumpton of HVAC system ncludng, the fan and VAV boxes. he heatng n the heatng col and the VAV reheat col s provded by a central gas-fred boler. he coeffcent of the boler s assumed as.85. he control varables nclude the VAV box supply ar flowrate m (related to VAV box damper poston), VAV box supply ar temperature (related to VAV box damper poston and reheat valve poston) and supply ar temperature. It s expected that local and VAV box controllers wll take these optmzed setponts and decde the actuator actons accordngly. Objectve: Mnmze Q total Q Pfan N Qreheat (11) 1 he ndvdual room ar temperature and supply ar temperature are constraned n a fxed range. In addton, the heat transfer rates n the heatng col and reheat cols cannot exceed ther capactes. Subject to: () t (12) mn max r r r (13) mn max m c ( ) Q (14) p mx capa, m c ( ) Q (15) p capa, reheat r n each room wll be estmated usng Equatons (7) to (1). he mnmum room ar temperature 2 o C. he maxmum room ar temperature max r mn r was set as 22.2 o C. hese maxmum and mnmum ar temperatures were set as the exactly same wth those n real operatons at the ERS buldng. was set as 3.2 Modelng Platform and Optmzaton Solver For the proposed optmzaton-based control algorthm, AMPL was used to solve the optmzaton problem. AMPL s a hgh-level modelng language specfcally talored for optmzaton problem formulaton wth such features as automatc dfferentaton. AMPL nclude automatc dfferentaton tools and provdes a convenent nterface to stateof-the-art optmzaton solver ncludng Interor Pont OPmzer (IPOP) (Wachter and Begler 26). In ths case study, the resultng optmzaton problem s solved usng the IPOP solver. All the model equatons were defned n the AMPL platform frst. After readng all the constant parameters and nput varable the AMPL calls the IPOP solver to help to compute the optmal soluton. 4. RESULS AND DISCUSSIONS Data from Oct 3 th 213 to Jan 3 th 214 was used to analyze the proposed model-based optmal control strategy. Fgure 4 presents the room ar temperature behavors under the optmal control. he results ndcate that the room ar temperatures are more stable than the measurement data shown n Fgure 3 (western room as the example). Majorty room ar temperatures fall n the range of 2 o C to 22.5 o C. he temperature varaton n the southern room s the bggest due to the large dsturbance such as solar radaton. Fgure 5 and 6 show the optmzed supply ar temperature and supply ar flow rate (Note: the summaton of optmzed VAV box supply ar flow rates). he supply ar temperature was narrowed between 13 o C and 16.5 o C. But the supply ar flow rates were ncreased for most of days. Whenever the outdoor ar temperature was low, the model-based optmal supply ar flowrate was hgh.

8 VAV supply ar temperature ( o C) VAV supply ar temperature ( o C) supply ar temperature setpont ( o C) supply ar flowrate (kg/s) Room ar temperature ( o C) Outdoor ar temperature ( o C) 3191, Page Eastern room (Optmzaton) Southern room (Optmzaton) Western room (Optmzaton) Interor room (Optmzaton) Fgure 4: Room ar temperatures from the case wth optmal control and outdoor ar temperature Baselne (Measured) AMPL optmzaton Baselne Optmzaton /3/ /3/213 12/3/213 1/3/214 Fgure 5: Optmzed supply ar temperature and ar flowrate Fgure 6 and 7 compare the VAV box supply ar temperature and ar flowrate between the baselne and the case wth optmal control. he baselne VAV box supply ar temperature s n the range of 15 o C to 35 o C. he model-based optmal VAV box supply ar temperature was rased by 5 o C, whch was n the range of 2 o C to 4 o C. he VAV box supply ar flowrates are ncreased except for the nteror room when the outdoor ar temperature was low n January. Because the nteror room ar temperature s nfluenced less by the outdoor ar temperature. For the modelbased optmal control, the VAV supply ar flow rate wth the low outsde ar temperature condton s very hgh. he ar mass flow rate of the southern room can get up to.7 kg/s Eastern room (Baselne) Southern room (Baselne) Western room (Baselne) Interor room (OBaselne) Eastern room (Optmzaton) Southern room (Optmzaton) Western room (Optmzaton) Interor room (Optmzaton) Fgure 6: VAV box supply ar temperature

9 Fan power consumpton (W) otal power consumpton (W) thermal power consumpton (W) Boler thermal power consumpton (W) VAV supply ar flowrate (kg/s) VAV supply ar flowrate (kg/s) 3191, Page Eastern room (Baselne) Southern room (Baselne) Western room (Baselne) Interor room (OBaselne) Eastern room (Optmzaton) Southern room (Optmzaton) Western room (Optmzaton) Interor room (Optmzaton) Fgure 7: VAV box supply ar flowrate Fgure 8 shows the energy consumpton comparson between the baselne and the case wth the proposed optmal control ncludng the thermal power consumpton, the VAV box reheat thermal power consumpton, the fan power consumpton and the total power consumpton. he thermal power consumpton of the model-based optmal control s lower than that from the baselne. he VAV box reheat thermal power consumpton of the modelbased optmal control s slghtly lower than that of the baselne. However, the fan power consumpton of the modelbased optmal control s hgher than that of the baselne. Fnally, the total power consumpton of the model-based optmal control s lower than that of the baselne. Fgure 9 shows the quantfed energy comparsons of the case wth the proposed optmal control and the baselne. he total energy consumpton can be saved by 22.1%. he VAV box reheat energy consumpton s reduced by 28 kwh from 2,442 kwh to 2,234 kwh. he thermal energy consumpton s reduced by 962 kwh from 1792 kwh to 83 kwh. he fan energy consumpton s ncreased by 165 kwh from 293 kwh to 458 kwh. he results ndcate that the major energy consumpton of the HVAC system s consumed by VAV reheat col. By ncreasng the ar flow rate, the thermal power consumpton and the VAV reheat col energy consumpton wll be reduced. 22.1% of the energy savng can be acheved by applyng the modelbased optmal control Baselne Optmzaton 24 2 Baselne Optmzaton (a) Baselne Optmzaton Baselne Optmzaton (b) (c) (d) Fgure 8: (a) thermal power consumpton; (b) VAV box reheat thermal power consumpton; (c) Fan power consumpton; (d) HVAC system total power consumpton

10 Energy consumpton (kwh) 3191, Page % Energy savng Reheat Fan Baselne Optmzaton Fgure 9: Energy consumpton comparson 5. CONCLUSIONS AND FUURE WORK In ths paper, a model-based optmal control s ntroduced by optmze the total HVAC system energy consumpton. Data-drven energy performance models for ndvdual component ncludng the, the fan and the VAV box reheat col energy consumpton, are bult. he proposed optmal problem was solved usng IPOP based on the AMPL programmng platform. Measurements from the real buldng were used for creatons of data-drven models and as the baselne for the energy consumpton comparson. he results of the model-based optmal control applcaton n ths smulaton-based off-lne study n the heatng mode ndcated that: he model-based optmal control greatly saves the total energy consumpton. he room ar temperature by the model-based optmal control s more stable. he energy savng of model-based optmal control s realzed by ncreasng fan supply ar flow rate to reduce the energy consumpton and VAV box reheat col energy consumpton. Some future works are lsted as follows: he data-drven model s based on a fxed hstorcal data set. It s better to use a movng wndow to ncorporate HVAC operaton changes. Addtonal optmal control n the coolng mode wll be conducted to analyze the annual energy performance. Demonstraton and mplementaton of the proposed optmal control n the Buldng Energy Management System n a real buldng. NOMENCLAURE temperature ( o C) r rato ( ) N number ( ) Q power consumpton (W) m ar mass flow rate (kg/s) c ar specfc heat (J/(kg oc)) a coeffcent ( ) Subscrpt mx oat ra mx outdoor ar temperature return ar varable ar volume

11 3191, Page 1 s fan reheat r mn max east south west nteror supply ar handle unt fan reheat room mnmum maxmum eastern southern western nteror REFERENCES AMPL. (216). AMPL, a mathematcal programmng language. L, P., Vrabe, D., L, D., Bengea, S. C., Mjanovc, S., & O Nell, Z. D. (215). Smulaton and expermental demonstraton of model predctve control n a buldng HVAC system. Scence and echnology for the Bult Envronment, 21(6), Cho, Y. H., & Lu, M. (28, January). Optmal termnal box control algorthms for sngle duct ar handlng unts. In ASME 28 2nd Internatonal Conference on Energy Sustanablty collocated wth the Heat ransfer, Fluds Engneerng, and 3rd Energy Nanotechnology Conferences (pp ). Amercan Socety of Mechancal Engneers. Lu, L., Ca, W., Cha, Y. S., & Xe, L. (25). Global optmzaton for overall HVAC systems Part I problem formulaton and analyss. Energy converson and management, 46(7), Lu, L., Ca, W., Soh, Y. C., & Xe, L. (25). Global optmzaton for overall HVAC systems Part II problem soluton and smulatons. Energy Converson and Management, 46(7), Yang, R., & Wang, L. (212, May). Optmal control strategy for HVAC system n buldng energy management. In ransmsson and Dstrbuton Conference and Exposton (&D), 212 IEEE PES (pp. 1-8). IEEE. Kusak, A., L, M., & ang, F. (21). Modelng and optmzaton of HVAC energy consumpton. Appled Energy, 87(1), Fong, K. F., Hanby, V. I., & Chow,.. (26). HVAC system optmzaton for energy management by evolutonary programmng. Energy and Buldng 38(3), Nassf, N., Kajl, S., & Sabourn, R. (24, June). Evolutonary algorthms for mult-objectve optmzaton n HVAC system control strategy. In Fuzzy Informaton, 24. Processng NAFIPS'4. IEEE Annual Meetng of the (Vol. 1, pp ). IEEE. Wächter, A., & Begler, L.. (26). On the mplementaton of an nteror-pont flter lne-search algorthm for large-scale nonlnear programmng. Mathematcal programmng, 16(1), Nu, F., O Nell, Z., Zuo, W., & L, Y. (215). Assessment of dfferent data-drven algorthms for energy consumpton predctons. ACKNOWLEDGEMEN he authors would lke to thank the Iowa Energy Center for supportng ths work by provdng data.